Am. Tech. Ceramics Corp. v. Presidio Components, Inc.

Full title: AMERICAN TECHNICAL CERAMICS CORP. and AVX CORPORATION, Plaintiffs, v…

Court: UNITED STATES DISTRICT COURT EASTERN DISTRICT OF NEW YORK

Date published: Sep 23, 2020

490 F. Supp. 3d 593 (E.D.N.Y. 2020)

Opinion

14-CV-6544 (KAM) (GRB)

2020-09-23

AMERICAN TECHNICAL CERAMICS CORP. and AVX Corporation, Plaintiffs, v. PRESIDIO COMPONENTS, INC., Defendant.

Brad Michael Scheller, Timur E. Slonim, Peter Francis Snell, Vincent M. Ferraro, Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C., New York, NY, Harold Stewart Laidlaw, Flushing, NY, Heather Repicky, Ronald E. Cahill, Nutter McClennen & Fish LLP, Boston, MA, for Plaintiffs. Brett Schatz, Charles H. Brown, Gregory Ahrens, Wood, Herron & Evans, L.L.P., Cincinnati, OH, Jeremy D. Richardson, Freeborn & Peters LLP, New York, NY, for Defendant.

MATSUMOTO, United States District Judge

Brad Michael Scheller, Timur E. Slonim, Peter Francis Snell, Vincent M. Ferraro, Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C., New York, NY, Harold Stewart Laidlaw, Flushing, NY, Heather Repicky, Ronald E. Cahill, Nutter McClennen & Fish LLP, Boston, MA, for Plaintiffs.

Brett Schatz, Charles H. Brown, Gregory Ahrens, Wood, Herron & Evans, L.L.P., Cincinnati, OH, Jeremy D. Richardson, Freeborn & Peters LLP, New York, NY, for Defendant.

MEMORANDUM & ORDER

MATSUMOTO, United States District Judge: On June 21, 2019, a ten-day patent infringement trial ended with a unanimous verdict finding defendant, Presidio Components, Inc. ("Presidio" or "Defendant"), liable for patent infringement. The jury determined that Presidio infringed patents held by plaintiffs, American Technical Ceramics Corp. ("ATC") and AVX Corporation ("AVX," and together with ATC, "Plaintiffs"), by making or selling over 15 million Buried Broadband ("BB") capacitors, between November 6, 2008 and January 9, 2017. The jury awarded royalty damages to Plaintiffs totaling $738,981.75, but awarded no lost profits, and rejected each defense raised by Presidio, save one, not at issue here.¹ Neither party is entirely satisfied with the trial's outcome. Each now moves to challenge the verdict.

1 The jury returned an advisory verdict finding one claim term indefinite (ECF No. 220-9, Completed Verdict Form, Question No. 12), but the court subsequently determined that Presidio failed to prove indefiniteness at trial by clear and convincing evidence. (ECF No. 214.)

Plaintiffs are convinced the jury erred when calculating damages based on a reasonable royalty rate, resulting in a grossly inadequate award. Their theory defies simple explanation, but may be summarized as follows. During Plaintiffs’ summation, their counsel advocated for both a lost profits measure of damages, and a reasonable royalty. Although Plaintiffs preferred lost profits, which would have conferred a larger award, counsel was forced to acknowledge that a small subset of the infringing units, about one-fifth of the total, were ineligible for lost profits, either because Presidio did not sell them, or because Plaintiffs did not offer a competing product. For this smaller tranche of capacitors, Plaintiffs sought a reasonable royalty, the statutory floor for infringement damages. Plaintiffs’ counsel urged the jury to adopt a $0.25 royalty rate, and provided the jury with the specific damages amounts for each patent that would inevitably result should the jury apply the proposed royalty rate to the smaller subset of accused products.

Alas, the verdict reflected the very damages figures stated by Plaintiffs’ counsel, to the penny. Much to Plaintiffs’ chagrin, however, these damages figures, proposed to the jury exclusively for about one-fifth of the units, comprised the entirety of Plaintiffs’ damages award. The reasonable inference, Plaintiffs assert in post-trial submissions, is that the jury settled on a $0.25 royalty rate, but, in effect, omitted the bulk of infringing units from its calculations. If so, this error was a statutory violation, as patent law requires no less than a minimum royalty for each infringing unit. Plaintiffs insist the jury's manifest error must be rectified and, therefore, move for a new trial on the issue of damages, pursuant to Federal Rule of Civil Procedure 59(a), or, alternatively, an amended judgment under Rule 59(e). (ECF No. 220-1, Plaintiffs’ Memorandum of Law in Support of Plaintiffs’ Motion for a New Trial on Damages or an Amended Judgment ("Pls.’ Mot.").)²

2 Defendant served its opposition to Plaintiffs’ motion on January 7, 2020. (ECF No. 221, Presidio's Opposition to Plaintiffs’ Motion for a New Trial on Damages or an Amended Judgment ("Def.’s Opp.").) Plaintiffs replied on January 21, 2020. (ECF No. 222, Plaintiffs’ Reply in Support of Plaintiffs’ Motion for a New Trial on Damages or an Amended Judgment ("Pls.’ Reply").)

Presidio challenges the verdict in two respects: the jury's findings of infringement, and its rejection of Presidio's anticipation defense with respect to one of the patent claims. Thus, Presidio moves for judgment as a matter of law ("JMOL"), pursuant to Rule 50(b) of the Federal Rules, or alternatively, a new trial. (ECF No. 227-1, Defendant Presidio Components, Inc.’s Memorandum in Support of Motion for Judgment as a Matter of Law and a New Trial ("Def.’s Mot.").)³ Plaintiffs oppose the motion.

3 Plaintiffs served their opposition to Presidio's motion on January 7, 2020. (ECF No. 228, Plaintiffs’ Opposition to Presidio's Motion for Judgment as a Matter of Law and a New Trial ("Pls.’ Opp.").) Presidio replied on January 21, 2020. (ECF No. 229, Defendant Presidio Components, Inc.’s Reply in Support of Motion for Judgment as a Matter of Law and a New Trial ("Def.’s Reply").)

In addition, Plaintiffs are seeking supplemental damages for Presidio's continuing infringement after the time period considered at trial, pre- and post-judgment interest, and taxable costs.⁴ (ECF No. 226-1 (UNDER SEAL), Plaintiffs’ Memorandum in Support of Plaintiffs’ Motion for Supplemental Damages, Pre- and Post-Judgment Interest, and Costs ("Pls.’ Dmgs. Mot.").)⁵ As with Plaintiffs’ motion for a new trial, Presidio opposes the bulk of the damages and fees Plaintiffs now seek.

4 Plaintiffs have also moved for an award of reasonable attorneys’ fees. (See ECF No. 223-1, Plaintiffs’ Memorandum of Law in Support of Plaintiffs’ Motion for Reasonable Attorneys’ Fees.) That motion will be considered separately, and comprise the subject of a subsequent Memorandum and Order.

5 Presidio served its opposition to Plaintiffs’ damages motion on January 7, 2020. (ECF No. 231, Presidio's Opposition to Plaintiffs’ Motion for Supplemental Damages, Pre- and Post-Judgment Interests, and Costs ("Def.’s Dmgs. Opp.").) Plaintiffs replied on January 21, 2020. (ECF No. 232, Plaintiffs’ Reply in Support of Plaintiffs’ Motion for Supplemental Damages, Pre- and Post-Judgment Interest, and Costs ("Pls.’ Dmgs. Reply").)

For the reasons that follow, the court: (1) GRANTS Plaintiffs’ motion for a new trial with respect to royalty damages; (2) DENIES Plaintiffs’ motion for a new trial with respect to lost profits damages; (3) DENIES Plaintiffs’ motion for an amended judgment increasing royalty damages; (4) DENIES Presidio's motion for JMOL and a new trial in its entirety; and (5) GRANTS in part, and DENIES in part, Plaintiffs’ motion for supplemental damages, pre- and post-judgment interest, and taxable costs, as set forth in greater detail below.

BACKGROUND

I. The Parties and Patents-in-suit

Plaintiffs commenced this action on November 6, 2014 (ECF No. 1, Complaint ("Compl.")), accusing Presidio of infringing United States Patent No. 6,144,547 ("'547 Patent"), and United States Patent No. 6,337,791 (" '791 Patent," together with the '547 Patent, the "Patents-in-suit"). (See generally Compl.; see also ECF No. 1-3, Compl., Ex. 1 (annexing Patents-in-suit).)⁶ ATC is a wholly-owned subsidiary of the publicly traded AVX Corporation, and is based in Huntington Station, New York. AVX owns the '547 Patent, which it licensed to ATC in November 2014, and ATC owns the '791 Patent. (See ECF No. 79, Claim Construction Order ("Cl. Constr. Order") 2.) Presidio is a privately-owned company based in San Diego, California.

6 Plaintiffs also claimed infringement predicated on United States Patent No. 6,992,879 ("'879 Patent"), but withdrew that claim after the Patent Trial and Appeal Board voided the '879 Patent. (ECF No. 82, December 2016 Joint Status Letter, 1; ECF No. 116-2, Plaintiffs’ Memorandum of Law in Support of Motion for Summary Judgment, 2 n.1.)

The parties are manufacturers of electrical devices, such as capacitors. (Cl. Constr. Order 2) Capacitors are electronic components that store and release energy within a circuit, and are used in a variety of electrical systems, including consumer electronics. (Id. ) Capacitors typically consist of two parallel conductive, usually metal, plates separated by a non-conductive, insulating material known as a "dielectric." (Id. )

The Patents-in-suit describe "multilayer ceramic capacitors" ("MLCCs"), which are created through the combination of multiple capacitors by stacking several layers of conductive material and non-conductive, or dielectric, material. (Cl. Constr. Order 2-3.) All parties manufacture and sell MLCCs. (Id. 3.) Defendant manufactures products known as BB capacitors, which Plaintiffs contend practice and infringe the Patents-in-suit. Plaintiffs filed the Complaint seeking, inter alia , a judgment that Presidio infringed the Patents-in-suit, damages arising from the alleged infringement, an award of attorneys’ fees pursuant to 35 U.S.C. § 285, injunctive relief prohibiting Presidio from engaging in further infringement, an accounting, and an award of interest and costs. (Compl. 5-6.)

Four-and-a-half years after this case began, during which time the parties engaged in extensive discovery, inter partes review, two claim construction hearings pursuant to Markman v. Westview Instruments, Inc. , 517 U.S. 370, 116 S.Ct. 1384, 134 L.Ed.2d 577 (1996), and cross-motions for summary judgment, the case proceeded to trial. Over the span of two weeks, Plaintiffs presented evidence to a jury that Presidio infringed the Patents-in-suit, and sought damages commensurate with Plaintiffs’ economic injury. (See Minute Entries dated 6/10/2019 to 6/21/2019.)

II. The Trial

A. The '791 Patent

1. Infringement of Claim 2

Claim 2 of the '791 Patent ("Claim 2") requires "second dielectric layer length and the second dielectric layer width dimensions co-extensive with the first dielectric layer length and the first dielectric layer width dimensions respectively of the first dielectric layer ...." (ECF No. 227-2, '791 Patent, col. 4, ll. 40-45 (emphasis added).) At trial, the parties disputed whether Presidio's BB capacitors satisfied the "co-extensive" requirement, as well as other limitations in Claim 2.

Presidio's technical expert, Dr. Michael Randall, testified that Presidio's BB capacitors do not meet the "co-extensive" requirement, and therefore, do not infringe Claim 2. Dr. Randall relied, in part, on close-up images of allegedly infringing capacitor chips. The exemplar immediately below, upon which Defendant relied, magnified the bottom right and bottom left corners of a capacitor chip to illustrate that the first and second dielectric layers are not equal in length and, therefore, are not co-extensive:(ECF No. 227-3, Plaintiffs’ Ex. PDX-005.127; see also ECF No. 227-6, Trial Ex. CQ (close-up images of dielectric layers).) Dr. Randall, advancing his conclusion that the lengths of the dielectric layers in the accused devices are not co-extensive, emphasized the non-overlapping red and blue line markers extending from the widest extent of the first and second dielectric layers. (Tr. 1893:13-21.)⁷

7 The caption "Tr. _" refers to the transcript for the trial held in this action from June 10 through June 21, 2019. The transcript for each day's proceedings appears on the docket as follows: Day 1 – June 10, 2019 (ECF No. 209); Day 2 – June 11, 2019 (ECF No. 210); Day 3 – June 12, 2019 (ECF No. 211); Day 4 – June 13, 2019 (ECF No. 212); Day 5 – June 14, 2019 (ECF No. 213); Day 6 – June 17, 2019 (ECF No. 235); Day 7 – June 18, 2019 (ECF No. 219); Day 8 – June 19, 2019 (ECF No. 236); Day 9 – June 20, 2019 (ECF No. 204); Day 10 – June 21, 2019 (ECF No. 234). Citations to the trial record herein refer to the relevant page and line number of the collective transcript.

Furthering that point, Mr. Alan Devoe, Presidio's President and corporate designee, described the impact of Presidio's "corner rounding" process, and how it results in a first and second dielectric layer with different dimensions. (Tr. 1148-63.) Corner rounding, explained Mr. Devoe, is an "important" and time-consuming aspect of Presidio's capacitor manufacturing process, designed to minimize damage to the ceramic capacitors when they collide with one another. (Id. ) As Mr. Devoe elaborated at trial:

[T]he ceramic of the capacitor is very delicate.... [T]here are a lot of ceramics that are very strong in this world; maybe like what we use for our dishes, that kind of thing. But the ceramic for the capacitors has been optimized to give good electrical properties as the primary objective, and then it's just not the strongest ceramic in the world.

... [T]he problem with a sharp corner is that as we're processing the parts, the capacitors can hit each other in the bag, and then ... they can put little chips on the edges. And every capacitor that has

a chip out, if it's above a certain very small size, would be thrown away.

So ... the first reason to corner round is to try to reduce the chipping to prevent us -- to save the parts.

(Id. 1153:7-22; see also id. 1151-52.)

Plaintiffs made their infringement case through their technical expert, Dr. Craig Hillman. Dr. Hillman testified that a person of ordinary skill in the art ("POSITA") of capacitors would understand that the first and second dielectric layers are co-extensive when "at the interface where they meet they extend over the same area ...." (Tr. 650:10-12; accord id. 729:15-17 ("[W]hen we talk about co-extensive, they extend over the same area. The area that they share is that interface between each other."); see also id. 736:9-14 ("They [i.e. , the first and second dielectric layers] don't share the same space or same common area space at the top of the second dielectric layer. They don't share that same common space at the bottom of the first dielectric layer. There is only one place where they share that common space; and are therefore co-extensive. It's at this interface where this metal electrode is present.").)

To elucidate, Dr. Hillman navigated the jury through approximately 100 images of accused devices magnified by his laboratory, which displayed the BB capacitors’ dielectric layers extending over the same area. (Tr. 729:22-730:25; e.g. , ECF No. 228-4, Demonstratives of Plaintiffs’ Infringement Expert, 5.110-113.) Dr. Hillman also clarified that the word "same," in this context, allowed for certain "tolerances," i.e. acceptable increments of variation between the dimensions of the dielectric layers. (Tr. 670:21-671:11.) Dr. Hillman noted that Presidio's own product catalog, as well as its customers, and the capacitor industry at large, deemed capacitor layers the "same" without regard to minor variations, so long as the differences fell within acceptable tolerances. (Id. 671:10-11.) In one instance, Dr. Hillman directed the jury's attention to micrographs of Presidio's accused BB0502 capacitors, and affirmed that, when held to the standards set forth in Presidio's catalog, the first and second dielectric layers are of "the same length, and the same width." (Id. 671:11; ECF No. 228-6, Trial Ex. 167 (Micrographs of Presidio BB0502).)

Dr. Hillman also criticized Dr. Randall's methodology for testing co-extensiveness, and, ipso facto , Dr. Randall's assessment that the BB capacitors did not have co-extensive dielectric layers. Dr. Hillman identified three key errors in Dr. Randall's analysis:

First , according to Dr. Hillman, Dr. Randall failed to properly measure co-extensiveness. (Tr. 733:19-20.) Dr. Hillman reiterated that the "only place" where the dielectric layers actually share a common space, is at the interface where a metal electrode exists between them. (Id. 736:9-14; see id. 733:22 (defining co-extensive as "extending over the same area").) By simply measuring where each dielectric layer was widest or longest (id. 736:23-24), Dr. Hillman thought Dr. Randall had elided the relevant measurement, the point where the layers shared a common space or area with one another, "at the metal electrode" between them. (Id. 737:20-23.) In Dr. Hillman's view, this flawed approach infected each and every one of the images undergirding Dr. Randall's non-infringement conclusion. (Id. 740:2.)⁸ Second , Dr. Hillman testified that Dr. Randall predicated his opinion on improperly cross-sectioned images of the accused BB capacitors. (Tr. 733:20-21.) By this, Dr. Hillman meant that Dr. Randall relied on "artifact[s] or defect[s]" in Presidio's BB capacitors that were caused by "some aspect of Presidio's manufacturing process." (Id. 744:1-2.) Dr. Hillman expounded on this error using the image below, extracted from Dr. Randall's expert rebuttal report:

8 Dr. Hillman also rejected Presidio's contention that corner rounding has any impact on co-extensiveness. (Id. 741:6-8.) As Dr. Hillman noted, corner rounding is a universally shared practice by capacitor manufacturers and, by design, does not cut into the relevant electrode interface at which the dielectric layers’ dimensions are measured for co-extensiveness purposes. (Id. 741:12-22.)

(ECF No. 228-4, Trial Ex. 167, PDX-005.135.)

Directing the jury's attention to the yellow highlighting, Dr. Hillman explained:

This is a highly localized defect. You can see there is [an] extensive amount of cracking in the first dielectric layer .... No capacitor manufacturer wants cracks in their capacitors. That's going to cause failure at some point and a very unhappy customer.

So this yellow artifact highlighted in yellow that Dr. Randall is using as a justification on why they are not co-extensive, is likely some defect. Defect either caused by the manufacturing process at Presidio; or by the people who cross sectioned this capacitor.

(Tr. 744:21-745:6.) Dr. Hillman independently cross-sectioned the capacitors, and concluded that the yellow-highlighted artifact was not present in the other capacitors from the same lot. (Id. 745:11-15.)⁹ Dr. Hillman remarked that, had Dr. Randall presented a "deeper" cross-section of the capacitor, it would be clear that the supposedly incongruous length and width of the dielectric layers in Dr. Randall's images were the result of idiosyncratic defects, and so, did not "represent the dimensions of that capacitor whatsoever." (Id. 744:13-14.)

9 Dr. Hillman believed that the artifact highlighted in yellow was a "large amount of metal somehow ingressed into the dielectric layer." (Id. 745:9-10.)

The third error, according to Dr. Hillman, was Dr. Randall's "impossible standard" of measurement that neither Presidio, nor the capacitor industry, would have recognized. (Tr. 745:24-25.) Dr. Hillman testified that, assuming, arguendo , Dr. Randall measured the dielectric layers in the appropriate area (error one), and the selected images did not feature unrepresentative defects (error two), it was still only the excessive magnification of Dr. Randall's images that gave the impression of material length and width variations. (Id. 745:22-23, 746-47; see ECF No. 228-4, Trial Ex. 167, PDX-005.139.). In actuality, the variations that Dr. Randall identified, were but "1/20th what the industry would view as a difference" in the length or width of the dielectric layers, and well within Presidio's stated tolerances. (Tr. 747:21-748:12.)

Finally, Dr. Hillman noted that Presidio itself appeared to disagree with Dr. Randall's assessments. This alluded to Presidio's discovery admission, regarding two exemplar images of BB capacitors, that "the length and width dimensions of the layer of dielectric material directly above the internal electrode ... are coextensive, respectively, with the length and width dimensions of the layer of dielectric material directly below the internal electrode ...." (ECF No. 228-4, PDX-005.141, 142.) According to Dr. Hillman, Dr. Randall's approach yielded a conclusion contrary to Presidio's admission. (Tr. 749:1-7.)

2. Prior Art

Presidio also sought to invalidate the '791 Patent as anticipated by prior art. This defense, as relevant here, centered on the following limitation in Claim 2:

a first electrode layer mounted on the first dielectric surface of the first dielectric layer, with the first electrode layer having a first electrode layer length dimension and a first electrode layer width dimension each smaller than the respective first dielectric layer length dimension and the first dielectric layer width dimension[.]

(ECF No. 1-3, ECF pp. 2-7 ( '791 Patent).)¹⁰

10 The '791 patent was introduced as Plaintiffs’ Exhibit 2 at trial. (See Tr. 181:5.)

U.S. Patent No. 6,366,443 to Devoe et al. ("Devoe Reference" or "Devoe"), describes "a ceramic chip capacitor" that "exhibits increased capacitance from use of closely spaced interior conductive planes." (See ECF No. 227-12, Devoe Reference, col. 13, ll. 24-29.) Pertinently, the Devoe Reference states that "[t]he new capacitors are a new true monolithic structure, with the potentially delicate electrodes buried within the three-dimensional body of the capacitor ...." (Devoe Reference, col. 9, ll. 13-17 (emphasis added).) This language, among other things, led Dr. Randall to conclude that Devoe teaches each limitation of, and thereby anticipates, Claim 2. (Tr. 1732:6-9.) Specifically, he opined that Devoe's reference to "buried" electrodes encompasses the limitation in Claim 2 of a first electrode layer having length and width dimensions smaller than the respective length and width dimensions for the first dielectric layer. (Id. 1737-40.)

Dr. Randall advanced Presidio's anticipation argument by analyzing Devoe's drawings, including annotated Figure 2b, reproduced with designations below:(Devoe Reference, ECF p. 4 of 20 (coloration and designations added));¹¹ see also id. col. 12, ll. 45-49 ("FIG. 2 ... is a diagrammatic view of another possible ‘family tree’ of capacitors in accordance with the present invention generally characterized in that electrical connections are made on only one surface of the capacitor."). According to Dr. Randall, Figure 2b depicts a first electrode layer, mounted on the first dielectric layer first surface. (Tr. 1736:15-25.)

11 A version of this image appears in the rebuttal report of Plaintiffs’ expert, Dr. Stanley Shanfield. (See ECF No. 169-7.) Although the image itself was not introduced into evidence, it substantially reflects Dr. Shanfield's testimony and use of a similar demonstrative, the latter of which is not available on the public docket, and was not filed by either party in connection with these motions.

Dr. Randall then synthesized his visual analysis with a textual reading of the Devoe Reference. Defense counsel asked Dr. Randall to elaborate on Devoe's teaching that, "[b]y putting the capacitance forming elements into the interior of the ceramic capacitor, the present invention completely avoids the issue of surface anomalies." (Id. 1738:1-2; Devoe Reference, col. 9, ll. 43-46.) Dr. Randall offered the following interpretation:

[B]y putting the capacitive forming elements -- which are the internal electrodes -- elements into the interior of the surrounding body -- so they're inside, they're in the interior -- the present invention completely avoids the issue of surface anomalies.

So that's just saying that the internal structure of the capacitor is buried at side; it does not extend to the outside of the dielectric anywhere on the device.

(Tr. 1738:4-12.) In other words, "the internal metallizations [i.e. , electrodes] have to have less width and less length than the first dielectric's width and length." (Id. 1738:18-20.)

Dr. Randall further opined that Devoe's written description of "electrodes buried within the three-dimensional body of the capacitor," connotes electrodes "encapsulated" by the dielectric layers. (Id. 1740:14-18.) Put differently, Dr. Randall said, "the internal electrodes’ length and width must be less than the length and width of the dielectric layers." (Id. 1740:18-20.) Thus, based on Devoe's text and drawings, Dr. Randall expected a POSITA in capacitors would understand that the length and width of the first electrode is lesser than the length and width of the first dielectric layer length. (Id. 1737:21-24, 1738:21-1739:1.) In closing, Dr. Randall confirmed his view that the Devoe Reference discloses the relevant limitation of Claim 2. (Id. 1738:21-1739:5.)

Plaintiffs called upon Dr. Stanley Shanfield in rebuttal. At the outset, Dr. Shanfield emphasized that prior art does not anticipate a patent absent "clear and convincing evidence" that each and every element of the patent is expressly taught by the earlier reference. (Tr. 2116:25-2117:6; id. 2117:9-10 ("You can't assume the presence of anything. It's got to be explicit in the prior art.").) Applying the "clear and convincing" standard, Dr. Shanfield opined that the Devoe Reference does not explicitly teach the second element of Claim 2 (id. 2161:16-19), a "first electrode layer mounted on the dielectric [that] is smaller in length and width than the dielectric that it's mounted on." (Id. 2161:24-2162:3.)

Dr. Shanfield's rebuttal challenged two core premises underlying Dr. Randall's opinion. First , according to Dr. Shanfield, Dr. Randall's reliance on the drawings in the Devoe Reference, including Figure 2b, was misplaced. Although the Devoe Reference might show figures with "an electrode that is shorter in length than the dielectric layer," it is not clear what the electrode "looks like in the direction into or out of the screen," i.e. the width dimension. (Tr. 2162:11-18.)¹² According to Dr. Shanfield, Dr. Randall impermissibly assumed the first electrode was smaller than "the dielectric dimension in the other direction in to and out of the page," i.e. width, even though no such limitation is explicitly taught by the Devoe Reference. (Id. 2163:13-16.) Dr. Shanfield thus disagreed with Dr. Randall's characterization of the drawings as three-dimensional. "[T]he two dimensional drawing[s] of the capacitors," Dr. Shanfield stated, "don't tell you how long the electrodes are relative to the dielectric in the dimension in and out of the screen," even though the claim term in the '791 Patent "requires that the electrode be both less wide and less long" than the dielectric layer. (Id. 2187:1-6 (emphasis added).)¹³

12 Dr. Shanfield suggested Devoe may not have been concerned with maintaining a smaller length for the electrode because, "in many cases you would want to match the length of that electrode with the dielectric layer in that dimension to get maximum capacitance." (Id. 2162:18-22.)

13 Dr. Shanfield also noted that, where the Devoe Reference intends to regulate the capacitor's dimensions, it does so expressly. (See id. 2187:15-22 ("[T]he point I take from this is that when Devoe wants to talk about dimensions, he does, he brings it up, he's specific about it. So, if he wanted to specify that the width and length of electrodes in general was always smaller or it was smaller in some case than the dielectric, he would have said so and he didn't.") (discussing Devoe Reference, col. 10, ll. 56-65 ("[T]he associated interior metallization plane(s) is (are) larger than are the collective exterior metallization areas.")).)

Second , Dr. Shanfield disputed Dr. Randall's definition of "buried," as both unsupported and unduly narrow. (Tr. 2164, 2166-67.) Dr. Shanfield observed that Devoe does not define the term "buried." (Id. 2166:17-19 ("Q : Does the Devoe '443 patent provide any kind of definition, any definition for the term buried? A : Not at all.").) Nor would a POSITA, in Dr. Shanfield's view, necessarily understand buried to mean "completely covered or encapsulated[,]" rather than positioned in a capacitor with "layers above and below it." (Id. 2167:6-16.) As an example, Dr. Shanfield noted that "buried transmission lines" are generally partially exposed "to the outside world," in order to facilitate connections, despite being described as buried. (Id. 2167:9-13.)

In sum, Dr. Shanfield expressed the opinion that the Devoe Reference does not anticipate Claim 2 of the '791 Patent.

B. Damages

1. Plaintiffs’ Case

Plaintiffs’ damages expert, Dr. James Woods, testified that, between November 6, 2008, and January 9, 2017, Presidio made or sold 15,369,246 BB capacitors that infringed the '791 and/or '547 Patents. (Tr. 983:17, 987:6; ECF 220-4, Demonstratives of Plaintiffs’ Damages Expert, Dr. James Woods, PDX-008.20, 008.23.)¹⁴ Plaintiffs sought lost profits of $18,802,967 as compensation for Presidio's sales on 12,413,319 infringing units. (Tr. 983:15-986:1, 987:22-25; ECF 220-4, PDX-008.22.) Dr. Woods justified this figure by presenting his analyses and assumptions pursuant to the multi-factor test articulated in Panduit Corp. v. Stahlin Bros. Fibre Works, Inc. , 575 F.2d 1152 (6th Cir. 1978). (See generally Tr. 955-80.) Dr. Woods opined: (1) there was demand for the patented product; (2) Presidio did not have an alternative non-infringing substitute in the ultra broadband capacitor market; and (3) Plaintiffs had the capacity to manufacture and market sufficient capacitors to meet the needs of Presidio's customers. (Id. )

14 Dr. Woods explained that the relevant damages period for the '791 Patent began on November 6, 2008, six years before Plaintiffs filed the instant suit, in light of Presidio's knowledge of the patent, and ended approximately June or July of 2015, when Presidio removed the via components from the accused devices. (Tr. 957:11-19.) The damages period for the '547 Patent began November 6, 2014, the date the suit commenced, and ended January 9, 2017, the last date for which Plaintiffs had Presidio's sales data, as of the trial. (Id. 957:21-25.) Plaintiffs are seeking supplemental damages for infringing units made or sold since January 9, 2017. (See generally Pls.’ Dmgs. Mot.)

Plaintiffs’ lost profits damages calculation excluded 2,955,927 infringing units that were altogether ineligible for lost profits, either because Presidio did not sell them, or because Plaintiffs had no competitive alternative to those devices. (Tr. 986:3-17; ECF No. 220-4, PDX-008.23.) For this subset of accused products, Plaintiffs sought a reasonable royalty. (Tr. 988:8-16.) Dr. Woods explained that a reasonable royalty award was comprised of two elements: a royalty base, i.e. the number of infringing units, and a royalty rate. (Id. 989:15-19.) The minimum royalty award was the product of the royalty base and royalty rate. (Id. 989:19-21.)

Although barred by a pre-trial court order from proffering a specific royalty rate for both Patents-in-suit,¹⁵ Dr. Woods discussed the factors for the jury to consider under Georgia-Pacific v. U.S. Plywood Corp. , 318 F. Supp. 1116, 1120 (S.D.N.Y. 1970) (" Georgia-Pacific "), a 15-factor analysis of a hypothetical negotiation between the parties to reach an agreed royalty rate. (Tr. 990; see also ECF No. 220-4, PDX-008.27, -008.34, -008.35.) Dr. Woods’ testified as to the royalty rate, applying the Georgia-Pacific factors to each Patent-in-suit, as follows:

15 The court issued a pre-trial order granting Defendant's motion pursuant to Daubert v. Merrell Dow. Pharm., Inc. , 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993), and striking Dr. Woods’ royalty rate opinion. (See generally ECF No. 179, Memorandum and Order, dated May 30, 2019.) The court found the royalty rate articulated in Dr. Woods’ expert report inadmissible because he inappropriately "combined the plaintiffs and muddled their respective bargaining positions and interests" in the course of his Georgia-Pacific analysis, "rather than articulating and considering them separately." (Id. 73.) The court's Order left the door open to testimony based on "portions of Dr. Woods’ report and underlying opinion that can support a jury determination of a reasonable royalty without Dr. Woods’ ultimate conclusion." (Id. )

Factor No. 1: Established Royalty Rate.

The Patents-in-suit had not been licensed at the time of first infringement, so there was no established royalty rate. (Tr. 994:6-12.)

Factor No. 2: Comparable Patents Licensed by Infringer.

Presidio had not licensed comparable patents. (Id. 994:19-20.) Factor No. 3: Nature and Scope of the License.

The hypothetical license would be a non-exclusive license to sell the patented products. (Id. 994:22-995:13 ("[A]t the same time, ATC could continue making its own products, or it could license the patents to somebody else.").) As a result, this factor would exert downward pressure on the royalty rate. (Id. 995:10-13.)

Factor No. 4: Established Policy and Licensing Programs.

ATC's business was making ultra-broadband capacitors, not licensing them, which would make ATC reluctant to license the Patents-in-suit to Presidio. (Id. 995:24-996:8.) Whereas the third factor would decrease the royalty rate, this factor would militate in favor of a higher rate. (Id. 996:5-8.)

Factor No. 5: Commercial Relationship Between the Parties.

ATC would have known, at the time of a hypothetical negotiation, that it would be entering the ultra-broadband capacitor market and competing with Presidio. (Id. 997:10-13.) The parties would realize that Presidio's sales of the patented capacitors would cost ATC sales of its own. (Id. 997:17-23.) Dr. Woods opined that the prices for Presidio's capacitors generally ran $0.20 to $0.36 less than ATC's for the "most common-size capacitor." (Id. 1000:6-11.)

Factor No. 6: Derivative or Convoyed Sales.

Dr. Woods generally found no evidence that ATC or Presidio sold complementary products in tandem with sales of ultra-broadband capacitors, but noted that the benefit of providing a full range of capacitors to customers "places some of the pressure on the royalty rate." (Id. 1000:13-24.)

Factor No. 7: Duration of the Patent.

Here, according to Dr. Woods, the license agreement would be for the life of the Patents-in-suit, which would not have a bearing on the royalty fee. (Id. 1001:1-4.)

Factor No. 8: Profitability of the Product.

Dr. Woods testified that ATC would know, as of the hypothetical negotiation date, that Presidio would sell its capacitors for about $1.36 a capacitor, and earn incremental profits of approximately $0.90 cents per capacitor. (Id. 1001:6-14.)

Factor Nos. 9-11: Advantages Over Substitutes; Nature and Benefits of Patented Invention; Extent and Benefit From Infringer's Use of Patent.

Dr. Woods grouped Georgia-Pacific factors 9, 10, and 11 together because, in his opinion, they essentially turn on the same inquiry: "Can Presidio make an ultra-broadband capacitor without using the technology of the '547 Patent or the technology of the '791 Patent"? (Id. 1001:18-1002:1.) Based on the testimony at trial, including Dr. Hillman's and Mr. Devoe's, Dr. Woods concluded that Presidio could not manufacture an ultra-broadband capacitor without the technology of the Patents-in-suit. (Id. 1002:2-5.)

Factor No. 12: Customary Industry Royalties.

Due to a lack of public information concerning similar technology and pricing, Dr. Woods determined this factor had no impact on the royalty analysis. (Id. 1002:10-17.)

Factor No. 13: Portion of Profit Related to Invention.

The next factor turned on the portion of Presidio's profits on sales of the infringing capacitors attributable to the patented technology, as opposed to other components not in dispute. (Id. 1002:18-22.) Dr. Woods juxtaposed Presidio's BB capacitors, which typically sold for $1.36, at an incremental profit of $0.90, with non-ultra-broadband capacitors, which "can sell for as little as ten cents apiece." (Id. 1003:1-5.) Based on the comparison, Dr. Woods concluded that, "a substantial portion of the profit is related to the fact the [patented] technology allows products to participate in the ultra-broadband market." (Id. 1002:23-25.)

Factor No. 14: The Opinion of Qualified Experts.

Dr. Woods considered the opinions of Dr. Hillman in preparing his analysis. (Id. 1003:12-14.)

Factor No. 15: Reasonable Royalty.

Consistent with this court's pre-trial order, without stating a royalty figure, Dr. Woods envisioned that a hypothetical licensing negotiation between Presidio and AVX, which held the '547 Patent, would unfold as such:

[A]t the height of the negotiation the parties would understand that Presidio needs a licensed manufacturer to do BB capacitors.... [T]he parties would understand the demand for ultra-broadband capacitors would be expected to grow along with the demand for high-speed optical networks. In other words, at the time of the negotiation, they would understand sales are very small, but sales are going to be a lot bigger because the demand optical networking equipment is going to grow dramatically.

(Tr. 1004:7-16.) Furthermore, the parties would realize that, while AVX was not, and had no intention of becoming a participant in the ultra-broadband market, AVX and Presidio were still competitors in the general capacitor market. (Id. 1005:2-6.) The parties would further understand that Presidio would generate approximately $0.90 in incremental profit per unit, which would comprise the income stream to pay for the royalty. (Id. 1005:9-12.)

A hypothetical negotiation concerning the '791 Patent would follow a similar course, except ATC, the patentee, would know at the time that it was entering the ultra-broadband capacitor market, and thus direct competition with Presidio. (Tr. 1006:1-6.) ATC would also know that Presidio would market the ultra-broadband capacitor, and sell it, on average, for $0.20 to $0.36 less than ATC would charge for a similar capacitor. (Id. 1006:14-19.)

Notwithstanding the above analysis, Dr. Woods testified that lost profits represented the superior measure of damages in this case, at least with respect to the over 12 million infringing units eligible for such relief. (Id. 1010:5-18.)

2. Defendant's Case

Dr. Vincent Thomas provided expert testimony on damages for Presidio. Dr. Thomas first rebutted Dr. Woods’ lost profits analysis, particularly his assumptions concerning the relevant "but for" market. (Tr. 2042-43.) In Dr. Thomas’ opinion, there was little to suggest that customers were demanding capacitors with vias or L-shaped terminations, the inventive aspects of the Patents-in-suit. (Id. 2043:10-15.) Nor did Dr. Thomas detect any market for licensing the Patents-in-suit, aside from ATC's licensure of the '547 Patent from AVX. (Id. 2043:15-17.) In addition, it was Dr. Thomas’ understanding that the Patents-in-suit were not essential to the manufacture of ultra-broadband capacitors, and indeed, ATC itself did not use the Patents-in-suit for its products. (Id. 2044:13-15.)

Dr. Thomas further posited, based on information gleaned from Presidio, that its customers were not "concerned or complaining about products that don't have vias." (Tr. 2044:19-2045:1; accord id. 2046:5-8 ("Presidio has been selling products without vias for close to ten years and all of its ... capacitors currently do not have vias and I understand the market accepts those products just fine.").)¹⁶ If Presidio had not, as alleged, infringed the Patents-in-suit, Dr. Thomas believed Presidio "would have simply redesigned their products to not include vias or not include L-shaped termination with negligible material," rather than take them off the market. (Id. 2062:10-17.) Dr. Thomas testified that, absent the alleged infringement, Presidio would have made the same amount of sales and, by the same token, those sales would not have simply flowed to Plaintiffs. (Id. 2062:17-19.)

16 Dr. Thomas’ opinions in this regard were either based on, or echoed, the testimony of Presidio's other trial witnesses. (See, e.g. , id. 1144:18-25 (Alan Devoe: "[T]he BB 0402 without vias is one of our best performing products that we make. It's better than the other products that were slightly different sizes that had the vias in them.... It's a very successful product for us, the BB 0402 without vias."); id. 1823:19-22 (Dr. Randall: "[I]n the whole group in general, even though there is variation in the group, definitely the 0302 BBs without vias perform significantly better than the 0302 BBs with vias."); cf. id. 500:21-23 (Andrew Ritter, engineer employee for Plaintiffs, regarding '547 Patent : ("[It i]s my understanding that AVX does not inspect whether there's a certain amount of termination material on the top surface.").)

Dr. Thomas also opined that a hypothetical license agreement allowing Presidio to sell the patented technology would have merited a reasonable royalty of only $0.01 for each of the '547 and '791 Patents. (Tr. 2036:18-2037:1; see also id. 2082:12-15 (discussing "very similar" factors dictating reasonable royalty analysis for '547 and '791 Patents ).)¹⁷ Dr. Thomas's Georgia-Pacific analysis was as follows:

17 The royalty was additive (i.e. , $0.02), if Presidio made or sold a product that incorporated technology from both Patents-in-suit. (Id. 2037:2-5.)

Factor Nos. 3 and 7

In a hypothetical negotiation, the parties would first want to know what is being licensed and for how long. (Id. 2073:13-18.) Presidio would understand that it was negotiating the terms of a non-exclusive, "bare patent license," whereby AVX or ATC provide mere usage rights for the patented technology, but nothing else in terms of development time, know-how, or manufacturing capabilities. (Id. 2073:22-2074:3; accord id. 2082:12-15.)

Factor Nos. 9, 10, and 14

When focusing on the inventive aspects of the Patents-in-suit, Dr. Thomas relied on Dr. Randall and others to guide his analysis. (Id. 2074:9-19.) Dr. Thomas noted that AVX's Accu-P capacitor embodied the '547 Patent, but he could not ascertain what incremental value the patented technology contributed to the Accu-P product. (Id. 2075:16-20.) It was also Dr. Thomas’ understanding that Accu-P products generally sold in the range of $0.09 to $0.14. (Id. 2075:21-24.) As for the '791 Patent, a hypothetical negotiation between Presidio and ATC would center on the use of vias. (Id. 2083:16-18.) Dr. Thomas also "didn't see significant value attributable to the use of vias." (Id. 2082:19-20.)

Factor Nos. 6, 8, 11, and 13

The composite of these factors essentially considers the profitability of the patented products, whether sales of patented products result in additional sales, and whether the infringer made use of the invention. (Id. 2076:3-10.) Factor 13 was the most critical factor, in Dr. Thomas’ view, because it concerned the profitability attributable to the patented technology. (Id. 2076:11-17.) According to Dr. Thomas, the principal flaw in Dr. Woods’ analysis was his assumption that Presidio could not sell ultra-broadband capacitors without using the patented technology. (Id. 2077:8-13.) Dr. Thomas believed that, in a hypothetical negotiation, and confronted by a high royalty demand from AVX or ATC, Presidio would have responded by removing, at low cost to Presidio, the inventive aspects of the Patents-in-suit: the L-shaped termination and negligible material at the top termination ( '547 Patent), or the vias ( '791 Patent). (Id. 2078:14-19; id. 2082:25-2083:3.) In that scenario, AVX and ATC's negotiating leverage would erode substantially, and Plaintiffs "wouldn't get anything." (Id. 2079:19-20.)

Factor Nos. 1, 2, and 12

Dr. Thomas agreed with Dr. Woods that these factors were irrelevant to a hypothetical licensing negotiation between Presidio and either ATC or AVX. (Tr. 2079:17-2080:2.)

Factor No. 5

Dr. Thomas acknowledged that there was "some competitive relationship" between Presidio and AVX, but ultimately concluded that any resultant upward pressure on the royalty would be mitigated because the competition was outside of the ultra-broadband capacitor market. (Id. 2080:9-16.) ATC and Presidio directly competed in the ultra-broadband capacitor market, but that competition post-dated the hypothetical negotiation date, and would likewise be mitigated by Presidio's access to a readily-available alternative to the patented technology. (Id. 2083:4-12.)

Factor No. 15

Based on the patented technology's de minimis benefit to Presidio, and the low cost of an alternative design, Dr. Thomas opined that Presidio would have agreed with AVX and ATC, respectively, to a $0.01 per unit royalty as a "very reasonable rate." (Id. 2081:9-14; accord id. 2083:23-2084:2.) Applying that rate would yield damages of $31,538 for the 3,153,827 units that infringed the '547 Patent, and $127,120 for the over 12.7 million units that infringed the '791 Patent, for total damages of $158,658. (Id. 2088:20-2089:3.)

3. Jury Verdict

On June 21, 2019, the parties made their closing arguments. Plaintiffs’ counsel, Peter Snell, Esq., urged the jury to award Plaintiffs lost profits damages of $12,226,594 and $6,576,373 for Presidio's infringement of the '791 and '547 Patents, respectively. (Tr. 2341:12-15.) Mr. Snell acknowledged that lost profits were not available for nearly 3 million infringing units that Presidio either did not sell, or were not sold by ATC or AVX. (Id. 2341:21-2342:3.) For these units, Mr. Snell explained, Plaintiffs were nonetheless statutorily entitled, at a minimum, to a reasonable royalty. (Id. 2342.) Mr. Snell advocated the jury adopt a royalty of $0.25. (Id. 2343:12.) He touted this figure as "split[ting] that difference" between $0.20 and $0.36, the price range by which Presidio's ultra-broadband capacitors undercut ATC's products. (Id. 2343:3-12.) Mr. Snell advised the jury that the arithmetic of Plaintiffs’ proposed royalty rate, applied to the nearly 3 million units ineligible for lost profits damages, worked out to $58,334.75 for the '547 Patent, and $680,647 for the '791 Patent. (Id. 2343:19-23 (emphasis added).)

Later that afternoon, the court gave the jury instructions following a charging conference with counsel. (Tr. 2415-70.) As pertinent here, the court charged:

If you find that ATC and AVX have established infringement, ATC and AVX are entitled to at least a reasonable royalty to compensate them for that infringement, in addition to lost profits. If you find that ATC and AVX have not proved their claims for lost profits, or have proved their claim for lost profits for only a portion of the infringing sales, then you must award ATC and AVX a reasonable royalty for all infringing sales for which they have not been awarded lost profits damages.

(Id. 2461:22-2462:5.) Instructions wrapped up at approximately 6:00 p.m., whereupon the jury retired to deliberate. (Id. 2471.) The jurors were provided with a verdict sheet and a written copy of the court's instructions, including the instruction above. (Id. 2470; ECF No. 191, Final Jury Instructions (Court Exhibit 2), Nos. 31, 40; ECF No. 191-1, Final Verdict Sheet (Court Exhibit 2A).)

At approximately 10:00 p.m. that evening, the jury reached a verdict. The jury found Presidio liable on all 19 infringement claims. (Tr. 2478-79; Completed Verdict Form, Question Nos. 1 and 2.) The jury also found that Presidio failed to prove by clear and convincing evidence that Claim 2 of the '791 Patent was invalid as anticipated by the Devoe Reference. (Tr. 2480; Completed Verdict Form, Question No. 6.) With respect to damages, the jury did not award Plaintiffs lost profits for the Patents-in-suit. (Tr. 2481; Completed Verdict Form, Question No. 13.) For Question 14 on the Verdict Form, regarding Plaintiffs’ entitlement to reasonably royalty damages, the jury entered $58,334.75 for the '547 Patent, and $680,647.00 for the '791 Patent. (Tr. 2481:14-18; Completed Verdict Form, Question No. 14.) After the court published the verdict in the courtroom, the jurors were polled, and then discharged. (Tr. 2481-82.) Plaintiffs did not object to the verdict before the jurors were excused from the courtroom.

DISCUSSION

I. Presidio's Motion for JMOL or a New Trial

Presidio seeks a judgment as a matter of law, notwithstanding the verdict, that Presidio's BB capacitors do not infringe Claim 2 of the '791 Patent, and moreover, that the Devoe Reference anticipates, and thus invalidates, the '791 Patent. (See generally Def.’s Mot. 1-2, 4-19.) Alternatively, Presidio asserts the court should retry the issues of infringement and anticipation. (Id. 20-21.) For the reasons below, the jury's infringement and invalidity findings stand because they were supported by legally sufficient evidence, and were not seriously erroneous. Presidio's motion must therefore be DENIED.

A. Standards Governing the Motion

When deciding issues in a patent case, a district court applies the law of the circuit in which it sits to non-patent issues, and the law of the Federal Circuit to issues of substantive patent law. Easyweb Innovations, LLC v. Twitter, Inc. , No. 11CV4550JFBSIL, 2016 WL 1253674, at *24 (E.D.N.Y. Mar. 30, 2016), aff'd , 689 F. App'x 969 (Fed. Cir. 2017) ; Duro-Last, Inc. v. Custom Seal, Inc. , 321 F.3d 1098, 1106 (Fed. Cir. 2003) (citations omitted). The Federal Circuit has generally applied regional circuit law to questions pertaining to Rule 50 motions. See, e.g. , Zodiac Pool Care, Inc. v. Hoffinger Indus., Inc. , 206 F.3d 1408, 1416 (Fed. Cir. 2000) (applying regional circuit law for JMOL motion at close of evidence). The Federal Circuit also applies regional circuit law when entertaining motions for a new trial under Federal Rule of Civil Procedure 59(a). See, e.g. , Lucent Techs., Inc. v. Gateway, Inc. , 580 F.3d 1301, 1309 (Fed. Cir. 2009).

1. Judgment as a Matter of Law

A court may grant judgment as a matter of law against a party if "a reasonable jury would not have a legally sufficient evidentiary basis to find for [that] party on that issue." Fed. R. Civ. P. 50(a). "A post-trial Rule 50(b) motion is properly made only if a Rule 50(a) motion has been made before submission of the case to the jury." Protostorm, LLC v. Antonelli, Terry, Stout & Krauss, LLP , No. 08-CV-931 PKC JO, 2015 WL 3605143, at *3 (E.D.N.Y. June 5, 2015), aff'd sub nom. Protostorm, LLC v. Antonelli , 673 F. App'x 107 (2d Cir. 2016) (citation omitted). Because a motion pursuant to Rule 50(b) "is in reality a renewal of a motion" pursuant to Rule 50(a), Lambert v. Genesee Hosp. , 10 F.3d 46, 53–54 (2d Cir. 1993) (citation omitted), the grounds on which a party may rely in a Rule 50(b) motion are "limited to those grounds that were specifically raised in the prior [ Rule 50(a) motion]." Galdieri–Ambrosini v. Nat'l Realty & Dev. Corp. , 136 F.3d 276, 289 (2d Cir. 1998) ); see Exxon Shipping Co. v. Baker , 554 U.S. 471, 485 n.5, 128 S.Ct. 2605, 171 L.Ed.2d 570 (2008).¹⁸ Three options abound when a district court rules on the renewed motion: "(1) allow judgment on the verdict, if the jury returned a verdict; (2) order a new trial; or (3) direct the entry of judgment as a matter of law." Aguilar v. Ham N Eggery Deli Inc. , No. 15CV2781KAMSMG, 2019 WL 4247228, at *2 (E.D.N.Y. Sept. 5, 2019) (citing Fed. R. Civ. P. 50(b) ).

18 Presidio properly moved for JMOL on the precise grounds at issue here, before the case was submitted to the jury. (See Tr. 1062; 1068:18-1069:4 (co-extensiveness); id. 2173:16-20 (anticipation).)

Courts evaluating a Rule 50 motion are required to consider the evidence in the light most favorable to the non-moving party, and to give that party "the benefit of all reasonable inferences that the jury might have drawn in [its] favor from the evidence." Aguilar , 2019 WL 4247228, at *2 (quoting ING Glob. v. United Parcel Serv. Oasis Supply Corp. , 757 F.3d 92, 97 (2d Cir. 2014) ). A jury verdict may be set aside pursuant to Rule 50, "only where there is such a complete absence of evidence supporting the verdict that the jury's findings could only have been the result of sheer surmise and conjecture, or there is such an overwhelming amount of evidence in favor of the movant that reasonable and fair minded [persons] could not arrive at a verdict against him." Bucalo v. Shelter Island Union Free Sch. Dist. , 691 F.3d 119, 127–28 (2d Cir. 2012) (internal quotation marks and citation omitted).

A court must also "give deference to all credibility determinations and reasonable inferences of the jury, and may not weigh the credibility of witnesses or otherwise consider the weight of the evidence." Id. (internal quotation marks and citation omitted). A motion for JMOL does not afford the losing party at trial a redo. Thus, a Rule 50 motion that effectively "asks the court to reweigh conflicting evidence, a function belonging to the jury," is ripe for denial. PPC Broadband, Inc. v. Corning Optical Commc'ns RF, LLC , 193 F. Supp. 3d 133, 141 (N.D.N.Y. Jun. 16, 2016).

2. Motion for a New Trial

The standard for granting a new trial pursuant to Federal Rule of Civil Procedure 59 is "somewhat less stern" than for entry of JMOL. AMW Materials Testing, Inc. v. Town of Babylon , 584 F.3d 436, 456 (2d Cir. 2009) (citing Nimely v. City of N.Y. , 414 F.3d 381, 392 (2d Cir. 2005) ). "A district court may grant a new trial pursuant to Rule 59 even when there is evidence to support the jury's verdict, so long as the court ‘determines that, in its independent judgment, the jury has reached a seriously erroneous result or its verdict is a miscarriage of justice.’ " Id. ; accord Mugavero v. Arms Acres, Inc. , 680 F. Supp. 2d 544, 558 (S.D.N.Y. 2010) (to grant a new trial, the court "must conclude that the jury has reached a seriously erroneous result or that the verdict is a miscarriage of justice, i.e. , it must view the jury's verdict as against the weight of the evidence.") (ellipses and brackets omitted) (citing Manley v. AmBase Corp. , 337 F.3d 237, 245 (2d Cir. 2003) ).

Although Rule 59(a) allows the court to revisit trial evidence, it is not a permission slip to "ignore the jury's role in resolving factual disputes and assessing witness credibility." Mugavero , 680 F. Supp. 2d at 558-59 (citation omitted); see Raedle v. Credit Agricole Indosuez , 670 F.3d 411, 418 (2d Cir. 2012) (holding that the jury's evaluation of witness credibility merits a "high degree of deference," and "jury verdicts should be disturbed with great infrequency"), cert. denied , 568 U.S. 1068, 133 S.Ct. 789, 184 L.Ed.2d 582 (2012). A trial judge "may not freely substitute his or her assessment of the credibility of witnesses for that of the jury simply because the judge disagrees with the jury." Raedle , 670 F.3d at 418 (citation omitted).

B. The Infringement Verdict is Supported by Legally Sufficient Evidence

1. Infringement Standard

Patent infringement generally consists of making, using, offering to sell, or selling any patented invention without authority. 35 U.S.C. § 271(a). Once the scope of the patent's claims are determined as a matter of law, "the properly construed claims are compared to the allegedly infringing device to determine, as a matter of fact, whether all of the limitations of at least one claim are present ... in the accused device." Mich & Mich. TGR, Inc. v. Brazabra, Corp. , 128 F. Supp. 3d 621, 631 (E.D.N.Y. 2015), aff'd sub nom. Mich & Mich TGR, Inc. v. Brazabra Corp. , 657 F. App'x 971 (Fed. Cir. 2016) (quoting Teleflex, Inc. v. Ficosa N. Am. Corp. , 299 F.3d 1313, 1323 (Fed. Cir. 2002) ).¹⁹ To prove infringement, the claimant bears the burden to show by a preponderance of the evidence that every element of one or more patent claims is present in the accused device. Uniloc USA, Inc. v. Microsoft Corp. , 632 F.3d 1292, 1301 (Fed. Cir. 2011) ; Siemens Med. Sols. USA, Inc. v. Saint-Gobain Ceramics & Plastics, Inc. , 637 F.3d 1269, 1279 (Fed. Cir. 2011) (citations omitted). The burden of proof remains with the plaintiff through all stages of the litigation. See Tech. Licensing Corp. v. Videotek, Inc. , 545 F.3d 1316, 1327 (Fed. Cir. 2008).

19 While Second Circuit precedent controls the application of Rules 50 and 59 to this case, Federal Circuit law is instructive regarding patent law issues. See Protostorm , 2015 WL 3605143, at *6.

2. Construction of "Co-extensive"

Presidio's challenge to the verdict centers on Claim 2's "co-extensive" element. In a nutshell, Presidio asserts the jury's infringement finding should be cast aside because Plaintiffs failed to prove that the first and second dielectric layers of Presidio's BB capacitors were exactly equal to one another in length and width. (Def.’s Mot. 1-2.) Inherent in Presidio's argument, is the assumption that "co-extensive" is defined as having equal dimensions.

Whether Presidio's BB capacitors featured a co-extensive first and second dielectric layers, as Claim 2 requires, was a hotly contested subject at trial. Plaintiffs’ expert, Dr. Hillman, testified that a POSITA would understand that the first and second dielectric layers are "co-extensive" when "at the interface where they meet they extend over the same area." (Tr. 650:10-12; id. 727:2-731:4.) The interface here, a metal electrode about 1/20th as thick as a human hair, is "[s]o thin that [the dielectric layers] are practically in contact with each other." (Id. 729:4-21.) Presidio argues that Dr. Hillman's testimony regarding co-extensiveness baselessly imported a "common space" limitation into the scope of the '791 Patent. (Def.’s Mot. 12 ("Nowhere in the '791 patent is there mention of "common space.").) Instead, Presidio insists that co-extensiveness must be determined by the "total, or actual, length and width" of the dielectric layers. (Id. )

As a threshold matter, neither party identified "co-extensive" as a term that the court was required to construe, either before or during trial. (See generally Cl. Constr. Order; ECF No. 136, Second Cl. Constr. Order.) Consequently, the court did not instruct the jury to apply a specific meaning for the term. (See Final Jury Instructions, No. 19 (instructing jury to accept court's definitions of "different level of polarity" and "a margin outward of the first electrode layer," but omitting instruction with respect to "co-extensive").) The Federal Circuit has "repeatedly explained, [that] ‘litigants waive their right to present new claim construction disputes if they are raised for the first time after trial.’ " Lazare Kaplan Int'l, Inc. v. Photoscribe Techs., Inc. , 628 F.3d 1359, 1376 (Fed. Cir. 2010) (quoting Broadcom Corp. v. Qualcomm Inc. , 543 F.3d 683, 694 (Fed. Cir. 2008) ); accord Alarm.com, Inc. v. SecureNet Techs., LLC , No. CV 15-807-RGA, 2019 WL 3996883, at *8 (D. Del. Aug. 23, 2019) ("Plaintiffs did not [object to the testimony or request that the court further modify or clarify the construction], and thus are attempting to present a new claim construction dispute for the first time after trial. Plaintiffs have waived that right.").

Nor did Presidio object to Dr. Hillman's definition of co-extensive as an improper construction of that term, which, in any event, was fully previewed by Dr. Hillman in his expert report, served April 19, 2017. (See ECF No. 227-10, Expert Report of Dr. Craig Hillman, ¶ 79 ("Further, it is my opinion that for all accused BB capacitors, the length and width dimensions of the second dielectric layer, ... are co-extensive (extending over the same area ) with the length and width dimensions, respectively, of the first dielectric layer ....") (emphasis added).) Presidio thus "implicitly conceded that the term ["co-extensive"] is to be accorded its plain and ordinary meaning." Reckitt Benckiser Pharm. Inc. v. Watson Labs., Inc. , No. CV 13-1674-RGA, 2017 WL 3820943, at *2 (D. Del. Aug. 31, 2017) ("I am far from sympathetic to [defendant] given that they knew of Teva's construction well before my judgment."), aff'd sub nom. Indivior Inc. v. Dr. Reddy's Labs., S.A. , 930 F.3d 1325 (Fed. Cir. 2019). That is exactly how the court instructed the jury to proceed with respect to all undefined terms, including "co-extensive." (Final Jury Instructions, No. 19 ("For any words in the claim for which I have not provided you with a definition, you should apply their common meaning.").) Notably, Presidio did not object to the court's "common meaning" instruction at the charging conference. (See Tr. 1915.)

To the extent the jury considered Plaintiffs’ asserted "common space" limitation as part of the "co-extensive" term's common meaning, Presidio has waived any challenge to the verdict on that basis.

3. Evidence of Infringement

There was sufficient evidence to support the jury's determination that Presidio's BB capacitors infringed Claim 2 and, therefore, met the co-extensive limitation. Dr. Hillman amply supported his testimony with approximately 100 microscopic images of accused devices, demonstrating that the dielectric layers of the BB capacitors are co-extensive because they are equal in length where they share a common area. (Tr. 729:22:730:25; e.g. , PDX-5.110-5.113.) Dr. Randall's testimony to the contrary does not alter this result. It was the province of the jury to assess each expert's credibility, and having done so, it presumably attached greater weight to Dr. Hillman's testimony. "[F]aced with competing expert testimony on the question of whether" the dielectric layers were co-extensive, " ‘the jury was free to disbelieve [Presidio's expert] and credit [Plaintiffs’] expert.’ " Intellectual Ventures I LLC v. Motorola Mobility LLC , 870 F.3d 1320, 1327 (Fed. Cir. 2017) (quoting i4i Ltd. P'ship v. Microsoft Corp. , 598 F.3d 831, 850 (Fed. Cir. 2010) ); see also Edwards Lifesciences AG v. CoreValve, Inc. , 699 F.3d 1305, 1313 (Fed. Cir. 2012) (when "testimony at trial [is] in direct conflict, ... the court may not weigh the evidence, determine the credibility of witnesses, or substitute its version of the facts for the jury's version"); Zhiwen Chen v. Cty. of Suffolk , 927 F. Supp. 2d 58, 67 (E.D.N.Y. 2013) (holding that "it would be improper to grant a new trial under these circumstances as the issue of the force exercised by defendants was dependent on the assessment of the credibility of the witnesses") (citation omitted). The court cannot, and will not, disturb the jury's credibility determination.

Moreover, even if Defendant's preferred definition of co-extensive had been applied, both JMOL and a new trial would be unjustified because Plaintiffs convincingly demonstrated that the first and second dielectric layers have equal dimensions. Dr. Randall supported his non-infringement opinion, that the accused products’ dielectric layers are not equal in length and width, with a series of magnified images that appeared to show the bottom left and bottom right sections of the dielectric layers in a state of misalignment. (ECF No. 227-3, PDX-005.127; Tr. 1893; see also ECF No. 227-6, Trial Exhibit CQ.) Presidio also highlighted the impact of "corner rounding," its manufacturing process whereby the capacitors’ corners are sanded down and rounded, in order to protect the ceramic from cracking. (Tr. 1148-63.) According to Presidio, corner rounding shortens the second dielectric layer vis-à-vis the first dielectric layer, resulting in varied dimensions.

Plaintiffs proffered substantial evidence, however, showing that the dielectric layers were equal, even under Presidio's framework, and effectively discredited Dr. Randall's testimony. First, using a demonstrative, Dr. Hillman explained how Presidio employs a "dicing" process to manufacture the BB capacitors, which "naturally" results in dielectric layers of equal length and width. (Tr. 370:4-9 ("But let's remember how we talk about the manufacturing process. It's like a layer cake, you put down one on top of the other, and then they are cut. They are diced. Hundreds, if not thousands, of capacitors are all cut. And all the capacitors and all the layers have the same length and the same width."); ECF No. 228-4, PDX-005.110-5.113.)

Second, Dr. Hillman explained how Dr. Randall's contentions unraveled in the face of Presidio's own documents and admissions. Specifically, Presidio admitted in its responses to Plaintiffs’ Requests for Admission that two exemplar images of Presidio's BB capacitors, subsequently introduced at trial and relied on by Dr. Hillman, exhibited co-extensive dielectric layers. Similarly, the very images of corner rounded capacitors that Dr. Randall relied on undermined Presidio's theory that corner rounding somehow resulted in incongruent dielectric layers. As Dr. Hillman noted, the dielectric layers in these images fall within Presidio's stated "tolerances" for length and width variation, and are therefore co-extensive by Presidio's standards.

Third, Dr. Hillman discredited Dr. Randall's "impossible standard" of measurement. (Tr. 745:24-25.) The gist of Dr. Hillman's critique was that, with enough magnification, some difference in measurement will always be detectable. Dr. Randall relied on dimensional variations in Presidio's dielectric layers that are about 1/20th of what the industry would actually recognize as a "difference." (See id. 747:21-748:12.) Dr. Hillman reasonably inferred that Presidio itself would not, as a practical matter, endorse Dr. Randall's "impossible" standards. (Id. 745:24-25.)

Fourth, Dr. Hillman drew attention to Dr. Randall's reliance on improperly cross-sectioned capacitor images. Using a demonstrative, Dr. Hillman noted how one of Dr. Randall's images purported to display incongruent dielectric layers, but in reality, presented a two-dimensional cross section in which an artifact (e.g. , a piece of metal) intruded on one of the dielectric layers, giving the appearance of a disparity. Had the image been properly cross-sectioned, Dr. Hillman testified that the supposed disparity would have disappeared. (Tr. 744:3-14.) Dr. Hillman additionally noted that some capacitors in Dr. Randall's relied-on images were atypical of their lot, and contained artifacts that the bulk of capacitors did not.

In sum, the jury's determination that Presidio's BB capacitors conformed to the "co-extensive" limitation in Claim 2, was supported by sufficient evidence, and not seriously erroneous. Therefore, neither JMOL nor a new trial are merited with respect to the infringement verdict.

C. The Invalidity Verdict is Supported by Legally Sufficient Evidence

Presidio also advanced four distinct invalidity defenses at trial, only one on which is presently of concern.²⁰ Presidio contended that Claim 2 was invalid as anticipated by the Devoe Reference, which describes a "ceramic chip capacitor." The instant dispute centers on Devoe's use of the word "buried," in connection with its limitation that the internal electrodes are "buried within the three-dimensional body of the capacitor." (See Devoe Reference, col. 9, ll. 13-17.) According to Presidio, this language encompasses Claim 2's limitation that the length and width of first electrode layer be smaller than the length and width of the first dielectric layer, on which it is mounted. In other words, Presidio contends a "buried" first electrode is subsumed "in all three dimensions" by the first dielectric layer, including length and width, exactly as the '791 Patent requires. (Def.’s Mot. 18 (emphasis omitted).)

20 In addition to the anticipation defense at issue, Presidio sought to invalidate the '791 Patent as anticipated by U.S. Patent Nos. 6,034,864 and 5,757,611 (the "Gurkovich" and "Naito" references), and as obvious by a combination of the Naito and Devoe references. (See Final Verdict Sheet, Question Nos. 4, 5, 7.)

1. Anticipation Standard

A defendant in a patent infringement suit may attack the validity of the patent itself, regardless of whether it disputes the underlying infringement claim. 35 U.S.C. § 282(b). To do so, a defendant carries the heavy burden of proving the patent's invalidity by clear and convincing evidence, Microsoft Corp. v. i4i Ltd. P'ship , 564 U.S. 91, 111, 131 S.Ct. 2238, 180 L.Ed.2d 131 (2011), meaning evidence that instills in the court an "abiding conviction" that the patent's invalidity is highly probable. ActiveVideo Networks, Inc. v. Verizon Commc'ns, Inc. , 694 F.3d 1312, 1327 (Fed. Cir. 2012). "The burden to establish invalidity of a patent on a motion for JMOL is ‘doubly high’ because the movant must show that ‘no reasonable jury could have failed to conclude that [invalidity] had been established by clear and convincing evidence.’ " Adrea, LLC v. Barnes & Noble, Inc. , No. 13 CIV. 4137(JSR), 2016 WL 859685, at *4 (S.D.N.Y. Feb. 24, 2016) (citing Boehringer Ingelheim Vetmedica, Inc. v. Schering-Plough Corp. , 320 F.3d 1339, 1353 (Fed. Cir. 2003) ).

To prove anticipation, the defendant must prove by clear and convincing evidence "that a single prior art reference not only discloses all of the elements of the claim within the four corners of the document, but also discloses those elements arranged as in the claim." Cheese Sys., Inc. v. Tetra Pak Cheese & Powder Sys., Inc. , 725 F.3d 1341, 1351 (Fed. Cir. 2013) (internal quotation marks and alterations omitted). The reference may disclose the elements of the claim either "expressly or inherently." Trintec Indus., Inc. v. Top–U.S.A. Corp. , 295 F.3d 1292, 1295 (Fed. Cir. 2002). (See also Final Jury Instructions, No. 26 ("A claim is anticipated only if each and every element as set forth in the claim is found, either expressly or inherently described, in a single prior art reference.").) "Inherent anticipation requires that the missing descriptive material is ‘necessarily present,’ not merely probably or possibly present, in the prior art." Id. (citations omitted); see also Bettcher Indus., Inc. v. Bunzl USA, Inc. , 661 F.3d 629, 639 (Fed. Cir. 2011) (inherent anticipation "may not be established by probabilities or possibilities"). "The dispositive question regarding anticipation is whether one skilled in the art would reasonably understand or infer from the prior art reference's teaching that every claim limitation was disclosed in that single reference." Akamai Techs., Inc. v. Cable & Wireless Internet Servs., Inc. , 344 F.3d 1186, 1192 (Fed. Cir. 2003) (internal quotation marks and alterations omitted).

2. Evidence of Anticipation

Based on the trial record, the jury had before it sufficient evidence to reasonably find the Devoe Reference did not disclose all elements of Claim 2, specifically, an electrode layer smaller than the first dielectric layer in the length and width dimensions.²¹ The parties offered conflicting anticipation testimony by two experts, Dr. Randall for Presidio, and Dr. Shanfield for Plaintiffs. Dr. Randall testified that the term "buried," as used in the Devoe Reference, means "encapsulated," such that "the internal electrodes’ length and width must be less than the length and width of the dielectric layers." (Tr. 1740:9-20.) Although Devoe did not expressly define "buried" or "encapsulated," Dr. Randall predicated his opinion on Devoe's visual depictions, particularly Figure 2b, which Dr. Randall described as a three-dimensional rendering of an electrode positioned within the dielectric layer, and thus necessarily of smaller length and width than the dielectric layer. (Id. 1736-40.) In sum, Presidio's anticipation case required the jury to accept that "buried" meant "completely buried," and "encapsulated" meant "completely encapsulated," and that Figure 2b and other Devoe drawings depicted an electrode smaller in length and width than the dielectric layer on which it was mounted.

21 Presidio claims Plaintiffs conceded at trial that the Devoe Reference teaches each limitation of Claim 2, except the limitation at issue. (Def.’s Mot. 17.) Plaintiffs contest this point. (Pls.’ Opp. 14 ("Dr. Shanfield did not say that Devoe is only missing one element of claim 2.").) The dispute is of no moment, however, because the failure to expressly or implicitly disclose just one element of a prior art reference precludes anticipation.

Dr. Shanfield's rebuttal testimony credibly attacked Dr. Randall's core assumptions, providing sufficient basis for the jury to find Presidio fell short of its high burden of proof. Dr. Shanfield emphatically rejected Dr. Randall's assumption that the term "buried" connoted the complete encapsulation of the electrode by the dielectric layer. And indeed, nowhere in the Devoe Reference is the term "buried" defined. Dr. Shanfield also noted that a POSITA would understand that "buried" does not necessarily refer to complete encapsulation, as with "buried transmission lines," which are partially exposed. (Tr. 2166-67.)²² As for Devoe's drawings, Dr. Shanfield described Figure 2b and others visual renderings as "two-dimensional" depictions that "don't tell you how long the electrodes are relative to the dielectric in the dimension in and out of the screen ...." (Tr. 2187:2-4.) According to Dr. Shanfield, Dr. Randall assumed that Devoe's drawings disclosed the dimensions of the electrode into and out of the page.

22 Presidio suggests Dr. Shanfield inadvertently conceded Defendant's point by distinguishing the word "buried" from "encapsulated." The latter term, at least according to Presidio, means "a first dielectric layer is completely enclosed, such that the first electrode layer has a width [and length] that is smaller than the width [and length] of the first dielectric layer." (See Def.’s Mot. 19.) This "concession" supposedly proves anticipation because the Devoe Reference discloses a first internal electrode that is "ceramic-encapsulated." (Id. ) But Presidio mischaracterizes Dr. Shanfield's testimony. On direct examination, Plaintiffs’ counsel asked Dr. Shanfield whether a POSITA "would not have understood buried to mean completely covered or encapsulated?" (Tr. 2167:6-8.) Although Dr. Shanfield's answer, "[a]bsolutely not," resulted in an awkward double negative, his subsequent testimony clearly rejected the notion that Devoe disclosed completely encapsulated, or completely covered, internal electrodes. (Id. 2167-68.) In another instance, Presidio states that Dr. Shanfield's "only response" to Dr. Randall's testimony is "rank speculation" regarding how Devoe would have wanted the capacitor to be configured. (Def.’s Mot. 18-19.) This peculiar assertion blatantly ignores Dr. Shanfield's additional support for his opinion, as detailed in this Memorandum and Order.

At bottom, Presidio's challenge to the jury's anticipation verdict is meritless. Not only did the jury reasonably find that the Devoe Reference did not disclose all limitations of Claim 2, but, in the counterfactual scenario where the jury did find Claim 2 to be anticipated by Devoe, the court may very well have granted Plaintiffs relief under Rule 50 or 59. The Devoe Reference fails to explicitly define "buried" or "encapsulated," and while its two-dimensional drawings depict a first dielectric layer that is longer that the first electrode, there is no inherent basis to presume the dielectric is also wider. The dielectric layer may be wider than the electrode, but the electrode may also be equal in length. That Devoe leaves the door open to the possibility of a first dielectric layer that is longer and wider than the first electrode, is insufficient to anticipate Claim 2, explicitly or inherently. See MEHL/Biophile Int'l Corp. v. Milgraum , 192 F.3d 1362, 1365 (Fed. Cir. 1999) ("Inheren[t anticipation] may not be established by probabilities or possibilities. The mere fact that a certain thing may result from a given set of circumstances is not sufficient.") (citation omitted).

Likewise, Dr. Randall's assumption that Devoe's stated intention to "avoid[ ] the issue of surface anomalies" thereby implies complete encapsulation of the electrode (see Tr. 1738-40; see also Devoe Reference, col 9, ll. 43-46), ignored whether such anomalies could have also been avoided if the electrode and dielectric were of equal width. In fact, Dr. Shanfield believed Devoe may have desired equal dimensions in order to enhance capacitance. (Tr. 2162.) At a minimum, this conflicting testimony militates against setting the verdict aside, especially in light of Presidio's heavy burden to prove anticipation by clear and convincing evidence. See Corning Optical , 193 F. Supp. 3d at 141 (denying motion for JMOL or a new trial on infringement because "[e]ssentially, [defendant] asks the court to reweigh conflicting evidence, a function belonging to the jury, not the court on a Rule 50 motion"); cf. Mentor H/S, Inc. v. Med. Device All., Inc. , 244 F.3d 1365, 1376–77 (Fed. Cir. 2001) (reversing district court's grant of new trial on anticipation where court "substitute[d] its judgment" for the jury's, and asserted that prior art reference anticipated claim limitations, a conclusion not supported by the record given defendant's burden to establish anticipation by clear and convincing evidence).

In closing, there is no basis for the court to disturb the jury's verdict with respect to liability, or an anticipation defense thereto. The court now moves to the third, and most compelling challenge to the verdict, regarding the jury's damages award.

II. Plaintiffs’ Motion For a New Trial or an Amended Judgment

A. Standards Governing the Motion

The standard applicable to a motion for a new trial was discussed above, and will not be repeated herein. In addition to requesting a new trial, Plaintiffs seek an amended judgment increasing the jury's damages verdict by awarding a $0.25 royalty for all 15 million-plus infringing BB capacitors.

1. Motion to Amend Judgment

A district court may alter or amend a judgment, pursuant to Federal Rule of Civil Procedure 59(e), in order "to correct a clear error of law or prevent manifest injustice." Munafo v. Metro. Transp. Auth. , 381 F.3d 99, 105 (2d Cir. 2004) (citations and internal quotation marks omitted); Endo Pharm. Inc. v. Amneal Pharm., LLC , No. 12 CIV. 8060 (TPG), 2016 WL 1732751, at *1 (S.D.N.Y. Apr. 29, 2016) ("A district court may grant a ... Rule 59(e) motion to correct manifest errors of law or fact at trial[.]") (citation omitted). An alteration or amendment "is appropriate if the court in the original judgment has failed to give relief on a claim on which it has found that the party is entitled to relief." Continental Cas. Co. v. Howard , 775 F.2d 876, 883 (7th Cir. 1985), cert. denied , 475 U.S. 1122, 106 S.Ct. 1641, 90 L.Ed.2d 186 (1986).

A motion to alter or amend judgment is an "extraordinary remed[y] to be employed sparingly in the interests of finality and conservation of scarce judicial resources." Fireman's Fund Ins. Co. v. Great Am. Ins. Co. , 10 F. Supp. 3d 460, 475 (S.D.N.Y. 2014) (citations and quotations omitted). "The narrow aim of Rule 59(e) is to make clear that the district court possesses the power to rectify its own mistakes in the period immediately following the entry of judgment." Greene v. Town of Blooming Grove , 935 F.2d 507, 512 (2d Cir. 1991) (internal quotation marks and alterations omitted) (quoting White v. N.H. Dep't of Employment Sec. , 455 U.S. 445, 450, 102 S.Ct. 1162, 71 L.Ed.2d 325 (1982) ).

B. Waiver

As a threshold matter, the court must address whether Plaintiffs waived their right to challenge the verdict. Presidio contends, without further elaboration, that Plaintiffs waived all challenges to the jury's verdict, including the reasonable royalty award, by "fail[ing] to object[.]" (Def.’s Opp. 11.) Presumably, this refers to Plaintiffs’ failure to object to the verdict before the jury was discharged.

Waiver is a procedural issue, to be determined by Second Circuit law. See Cabinet Vision v. Cabnetware , 129 F.3d 595, 601 (Fed. Cir. 1997) ("Because waiver of a jury trial is a procedural matter not unique to patent law and is accomplished pursuant to local rules, we look to the law of the regional circuit."); see also Exmark Mfg. Co. Inc. v. Briggs & Stratton Power Prod. Grp., LLC , 879 F.3d 1332, 1347 (Fed. Cir. 2018) ("When reviewing damages in patent cases, we apply regional circuit law to procedural issues and Federal Circuit law to substantive and procedural issues pertaining to patent law.") (citation omitted). Generally, "a party waives its objection to any inconsistency in a jury verdict if it fails to object to the verdict prior to the excusing of the jury." Anderson Grp., LLC v. City of Saratoga Springs , 805 F.3d 34, 46 (2d Cir. 2015) (quoting Kosmynka v. Polaris Indus., Inc. , 462 F.3d 74, 83 (2d Cir. 2006) ); Barkley v. United Homes, LLC , 848 F. Supp. 2d 248, 254 (E.D.N.Y. 2012), aff'd sub nom. Barkley v. Olympia Mortg. Co. , 557 F. App'x 22 (2d Cir. 2014), as amended (Jan. 30, 2014) (challenge to verdict's purported award of duplicative damages was waived when defendants raised issue for first time in their post-trial motions). "The requirement of a timely exception is not merely a technicality," but rather, "function[s] ... to give the court and the opposing party the opportunity to correct an error in the conduct of the trial." Kosmynka , 462 F.3d at 83 (internal quotations and citations omitted); see also Bseirani v. Mahshie , 881 F. Supp. 778, 784 (N.D.N.Y. 1995), aff'd , Nos. 95–9109, 95–9145, 1997 WL 3632 (2d Cir. Jan. 3, 1997) ("[W]here counsel is or should be aware of the inconsistency in the verdict, and where resubmission to the jury would resolve the ambiguity," waiver is appropriate "to promote the efficiency of trials by allowing the original deliberating body to reconcile inconsistencies without resort to the presentation of evidence to a different body.") (internal quotations and citations omitted).

Here, the jury announced it had reached a verdict at approximately 10:00 p.m. on Friday, June 21, 2019. Immediately thereafter, the verdict was published, the jury was polled, and then discharged. Plaintiffs did not object to the jury's verdict or otherwise seek to preserve its post-trial rights before the jury exited the courtroom. Once the last juror departed, the court inquired about post-trial motions. The parties agreed to confer, and four days later, submitted a joint letter advising the court of their intention to file post-trial motions upon the entry of judgment. (ECF No. 193.)²³ The court entered judgment on November 14, 2019 (ECF No. 214), and Plaintiffs served this motion the following month.

23 The parties’ stipulated to filing a proposed judgment for entry by the court, pending the court's disposition of Presidio's motions on equitable waiver and indefiniteness. (Id. ) The parties further agreed to serve opening briefs for the instant motions no later than 28 days after the court's entry of judgment. (Id. )

It is indisputable that Plaintiffs first raised their challenge to the jury's reasonable royalty award well after the jury was discharged. Plaintiffs admittedly had a short window of time to object to the verdict before the jury exited, but Plaintiffs do not offer a compelling explanation why they could not, and did not, object before the jury was excused. Given the Second Circuit's strict application of the waiver rule, Plaintiffs’ waiver may not be excused on this ground. See, e.g. , Anderson Grp. , 805 F.3d at 47 (reversing decision not to find waiver, where district court reasoned that "complicated and unique" nature case made it reasonable for defendant "not to immediately voice objection," and rejecting proposition that "litigant's duty to object to a perceived error turns on the complexity of the issues at play."). Plaintiffs also imply that their objection to the verdict prior to the entry of judgment on November 14, 2019, may forestall waiver. (Pls.’ Mot. 6 (citing ECF No. 205-1, Plaintiffs’ Letter dated August 23, 2019, which described verdict as contrary to 35 U.S.C. § 284, and identified grounds for instant post-trial motion).) The court has identified no authority supporting Plaintiffs’ contention, whether in the Second Circuit, or elsewhere, and therefore respectfully rejects it. That does not end matters, however.

Waiver may be excused if a verdict constitutes "fundamental error." Perks v. Town of Huntington , 234 Fed. App'x 8, 11 (2d Cir. 2007). "Fundamental error" must be "so serious and flagrant that it goes to the very integrity of the trial." Jarvis v. Ford Motor Co. , 283 F.3d 33, 62 (2d Cir. 2002) (internal citations and quotation marks omitted). The Second Circuit's decision in Rodick v. City of Schenectady , 1 F.3d 1341 (2d Cir. 1993), is an instructive example of fundamental error sufficient to overcome waiver. In that case, the defendant challenged an inconsistent verdict after failing to timely object to an erroneous instruction and verdict form. Id. at 1347–49. The jury attributed to the vicariously liable defendant "a damage amount ten times greater than the liability assessed against each of the [directly responsible] individual defendants and 2.5 times greater than the damages assessed against the [individual defendants] collectively." Id. at 1349. Although the jury instructions "accurately described the law as far as they went," the verdict was ultimately inconsistent with applicable law. Id. at 1348. According to the Second Circuit, this injustice demanded a new trial despite defendant's untimely challenge to the verdict. Not only was the Rodick verdict inconsistent with the law of joint and several liability, but also "so contrary to basic concepts of respondeat superior that it would be a miscarriage of justice to let it stand." Id. ²⁴

24 The Rodick court did not expressly use the term "fundamental error" in its decision, but courts have recognized that the Second Circuit rooted its reasoning in "fundamental error" doctrine. See, e.g. , Shade v. Hous. Auth. of City of New Haven , 251 F.3d 307, 313 (2d Cir. 2001) ; Zellner v. Summerlin , 399 F. Supp. 2d 154, 160 (E.D.N.Y. 2005).

Plaintiffs contend the jury inadvertently awarded a reasonable royalty for only a small portion of the infringing BB capacitors, excluding the vast majority of units from its calculation. (Pls.’ Mot. 7-8.) The patent damages statute, 35 U.S.C. § 284, requires the court to award "no less than a reasonable royalty" for each infringing unit. If the jury did intend to award a $0.25 royalty for each infringing capacitor, a highly plausible assertion (as discussed below), yet through sheer mistake, excluded over 80% of infringing units from its calculation, then the verdict blatantly disregards the floor for patent damages established by Congress in section 284, and thereby deprives Plaintiffs of more than $3 million in rightful compensation. Such a "serious and flagrant" error strikes at the "very integrity of the trial," Marcic v. Reinauer Transp. Cos. , 397 F.3d 120, 124 (2d Cir. 2005), and therefore, merits consideration of Plaintiffs’ motion notwithstanding their untimely objection to the jury's verdict.²⁵ This outcome arguably cuts against "the purpose of waiver," which is "to promote the efficiency of trials," Bseirani , 881 F. Supp. at 784, but the court finds that the "fundamental error" exception subordinates interests of efficiency where, as discussed below, the verdict defies the clear-cut commands of Congress, codified in federal statute.

25 Presidio cites a litany of authorities to advance its contention that Plaintiffs’ waiver precludes a new trial. (Def.’s Opp. 11-12.) Generally, these cases feature no substantive or relevant discussion of the "fundamental error" exception. See, e.g. , Haskell v. Kaman Corp. , 743 F.2d 113, 123 (2d Cir. 1984) (no discussion of "fundamental error" exception); Lavoie v. Pacific Press & Shear Co., a Div. of Canron Corp. , 975 F.2d 48, 57 (2d Cir. 1992) (same); In re Vivendi Universal, S.A. Sec. Litig. , 765 F. Supp. 2d 512, 570-72 (S.D.N.Y. 2011), aff'd sub nom. In re Vivendi, S.A. Sec. Litig. , 838 F.3d 223 (2d Cir. 2016) (same). Presidio also relies on Barkley v. United Homes , 848 F. Supp. 2d 248 (E.D.N.Y. 2012), decided by the undersigned, but that case is distinguishable. There, defendants challenged a verdict's purported allowance for duplicative damages. The court found the challenge waived, in part, because defendants did not propose jury instructions or a verdict sheet that accounted for the risk of duplicative damages, and did not raise the issue at the charging conference. Id. at 255. The jury instructions here, by contrast, clearly instructed the jury to award Plaintiffs a minimum royalty for each unit found to have infringed, as required by 35 U.S.C. § 284. Finally, notwithstanding their waiver, the Barkley defendants did not sufficiently establish that the jury actually awarded duplicative damages. Id. at 257-261 (citation omitted). The instant circumstances, on the other hand, strongly suggest the jury failed to award a reasonably royalty for each infringing unit, as required by law.

C. The Damages Verdict Was Clearly Erroneous

Plaintiffs’ objection remains extant, and the court now turns to its merits. After reviewing the verdict, the trial record, and the applicable law, the court is left with the overriding conviction that, despite Plaintiffs’ waiver, the jury had a sufficient evidentiary basis to determine that Plaintiffs were entitled to a royalty rate of $0.25 for each infringing device, but erroneously awarded a lump sum that effectively excluded nearly 80% of the infringing units from its damages computation. The court will first explain why the trial record strongly suggests the jury intended to apply a royalty rate of $0.25, and then rule out alternative explanations for the damages award reflected on the completed verdict form.

1. Royalty Rate Evidence and Argument

As detailed above, Dr. Woods testified as Plaintiffs’ damages expert. Though a court order precluded Dr. Woods from proffering a specific royalty rate, he set forth his analysis of the factors governing the appropriate royalty rate under Georgia-Pacific , based on a hypothetical negotiation between the parties just prior to the infringement. See 318 F. Supp. at 1120. Regarding the '791 Patent, Dr. Woods noted that Presidio charged $0.20 to $0.36 less than ATC for the "most common-sized capacitor." (Tr. 1000:6-11.) Dr. Woods further noted that, at the time of hypothetical licensing negotiation for the '547 Patent, AVX and Presidio would understand that the latter stood to generate about $0.90 in incremental profit per unit, comprising the income stream for prospective royalty payments. (Id. 1005:9-12.) More generally, Dr. Woods told the jury that many of the same considerations guided his royalty rate analysis for both Patents-in-suit. (Id. 1006:14-19.)

In his summation, Plaintiffs’ counsel devoted the bulk of his damages argument to advocating for lost profits, with its potential for a vastly greater damages award. Plaintiffs’ counsel addressed the proper royalty award only as a secondary matter. Plaintiffs sought almost $19 million in lost profits for 12,413,319 infringing capacitors. (Tr. 2341:12-15.) Counsel acknowledged that an additional 2,955,927 BB capacitors were not included in Plaintiffs’ lost profits calculations, either because they were manufactured but not sold by Presidio, or because ATC and AVC themselves never sold a substitute for that product. (Id. 2342:4-9.) Counsel argued to the jury that Plaintiffs were still "entitled at a minimum to a reasonable royalty" for this smaller number of units. (Id. 2342:10-12.) Counsel recommended the jury apply a royalty of "25 cents per capacitor," which "split[s] the difference" between $0.20 and $0.36, the price difference between Presidio and ATC's products, according to Dr. Woods. (Id. 2343:3-12.) In terms of lump sums, Plaintiffs’ counsel urged the jury to award lost profits of $6,576,373 and $12,226,594, for the '547 and '791 Patents, respectively, which figures were based on lost profits evidence. (Id. 2343:14-18.) For the "approximately 3 million units for which the lost profit is not available," Plaintiffs’ counsel asked the jury to award $58,334.75 for the '547 Patent, and $680,647 for the '791 Patent. (Id. 2343:19-23.) Hours later, the jury found Presidio liable on all infringement counts. Although Plaintiffs were not awarded lost profits, the royalty award matched the exact amounts recommended by counsel: $58,334.75 for the '547 Patent, $680,647 for the '791 Patent. But, whereas Plaintiffs advocated for those awards solely with respect to the 2,955,927 units ineligible for lost profits, the completed verdict form gave no express indication that the award was limited to that smaller subset. Consequently, those amounts—$58,334.75 and $680,647—were entered as the total damages awarded to Plaintiffs for the '547 Patent and '791 Patents, respectively, and all 15 million-plus infringing units, collectively.

2. Likelihood of Error

By adopting the precise lump sum royalty that Plaintiffs’ counsel proposed for the smaller subset of approximately three million units, without awarding lost profits at all, the court finds that the jury most likely concurred with counsel's proposed royalty rate of $0.25, but inadvertently excluded over 12 million units—the vast majority of the more than 15 million infringing units—from its damages calculation. To accept the coincidence that the jury settled on a royalty rate below $0.25 for all infringing units, only to arrive at the precise damages total—down to the penny—advocated by Plaintiffs for 2,955,927 units, would ignore both logic and common sense. Yet, that is what Presidio advocates. Indeed, nowhere in Presidio's opposition is this coincidence acknowledged, much less confronted.

Instead, Presidio attempts to backfill a logical explanation for the jury's verdict. The principal assertion in defense of the damages award is that the jury merely, and randomly, selected an "intermediate" royalty rate, less than the $0.25 per unit sought by Plaintiffs, but more than the $.01 rate recommended by Presidio's expert, Dr. Thomas. (Def.’s Opp. 15.) According to Presidio, the jury's verdict equates to a reasonable royalty of $0.02 per unit for the '547 Patent, and 0.05 per unit for the '791 Patent. (Id. 11.) Presidio supposedly arrived at this calculation by dividing the jury's damages figure for each Patent-in-Suit ( '547 Patent: $58,334.75; '791 Patent: $680,647.00), by the corresponding number of infringing capacitors ( '547 Patent: 3,153,277 units; '791 Patent : 12,215,969 units). (Id. )

Presidio's math does not withstand an actual calculation, however. The jury's verdict only "equates" to $0.02 and $0.05 per unit if great liberties are taken when rounding the quotient. Presidio's division actually yields the following royalty rates:

• '547 Patent:

$58,334.75 (Total Award) divided by 3,153,277 (Infringing Units)

Royalty Rate = $0.0184997226 694641796454 926097517

• '791 Patent :

$608,647 (Total Award) divided by 12,215,969 (Infringing Units)

Royalty Rate = $0.055717806 749509596823 63306586649

(See Pl.’s Reply 2-3.)

Presidio's mathematical imprecision is telling. Hypothetical royalty rates of $0.02 and $0.05 might suggest the jury intentionally selected intermediate rates somewhere between $0.01 and $0.25, the rates proffered by the parties. The actual royalty rates, calculated above, can only be explained as random quotients. The only parts of the equation above susceptible to rational explanation are the dividend, i.e. the lump sum royalty award (proposed by Plaintiffs’ counsel), and the divisor, i.e. the number of infringing units. Notably, Presidio does not even round the resulting royalty rates consistently. Presidio rounds the rate for the '547 Patent up from approximately $0.1849 to $0.02, but inexplicably rounds the '791 rate down from approximately $0.0557 to $0.05, when it should presumably be rounded up to $0.06. Presidio's mathematical shenanigans appear to be a transparent attempt to explain away the verdict's inconsistency, and underscore Presidio's own wishful, but tortured rationale for the jury's decision-making process.

Presidio also argues that the record supported a low royalty, and intimates that Plaintiffs merely resent that the jury assigned more weight to Presidio's evidence than Plaintiffs’. (Def.’s Opp. 3, 15-20; id. 14 ("Plaintiffs’ request for a new trial is, in effect, a claim that the jury's reasonable royalty award was so low that the jury must have failed to award a reasonable royalty for all infringing units.").) At trial, Dr. Thomas testified that the Patents-in-suit's inventive aspects—vias for '791, and the L-shaped termination for '547 —had little to no value, and he hypothesized that Presidio simply would have removed these features from its ultra-broadband capacitors to circumvent any royalty demand. (Tr. 2062, 2076-79.) Dr. Thomas further opined that Presidio would have agreed to no more than a $0.01 royalty for each Patent-in-suit. (Id. 2081.) In Dr. Thomas's opinion, absent lost profits, total damages were limited to $31,538 for the '547 Patent, and $127,120 for the '791 Patent. (Id. 2088-89.)

Presidio fails to appreciate that the gravamen of Plaintiffs’ challenge is not the jury's selection of a specific, low royalty rate. The court finds that the verdict's infirmity lies not in its magnitude, but its lack of any apparent rationale. Neither Presidio's explanations, nor those surmised by the court, plausibly resolve the inexplicable coincidence at the heart of this verdict: the total royalty award mirrors the precise numbers stated by Plaintiffs’ counsel in closing arguments, but awards those sums in a manner that neither counsel, nor—in the court's view—anyone else, could have reasonably contemplated.

Further, although the trial record arguably supports a low royalty award, there is no evident support for applying different royalty rates for each Patent-in-suit. Dr. Thomas unequivocally stated that Presidio would have agreed with AVX and ATC to a royalty rate of $0.01 per unit sold for each Patent-in-suit. (Tr. 2081.) Likewise, Plaintiffs’ counsel implored the jury to award royalty damages based on a $0.25 royalty rate for both '547 and '791. (Id. 2343.) Although both parties identified distinct features of the '791 and '547 Patents, neither party compared the relative value of each patents’ inventive designs, and Presidio does not suggest otherwise. Cf. Warren v. Thompson , 224 F.R.D. 236, 240 n.7 (D.D.C. 2004), aff'd sub nom. Warren v. Leavitt , 264 F. App'x 9 (D.C. Cir. 2008) ("A trial court is not required to parse through transcripts in an effort to identify the grounds of a post-trial motion.") (quotation omitted). This bolsters the court's suspicion that the verdict is erroneous, because accepting its validity demands the inchoate assumption that the jury sua sponte adopted different royalty rates for each patent, despite no apparent evidentiary basis or advocacy for such distinction.

Presidio also comments that "Plaintiffs did not offer any evidence on what constitutes a reasonable royalty" during the trial. (Def.’s Opp. 14.) This is simply not true. Plaintiffs’ expert, Dr. Woods, gave lengthy testimony applying the Georgia-Pacific factors to the Patents-in-Suit. In pertinent part, Dr. Woods noted that Presidio's capacitors generally undercut ATC's prices by $0.20 to $0.36, and its BB capacitors typically sold for $1.36, at a $0.90 incremental profit—a revenue stream for prospective royalty payments—and that AVX and ATC would expect Presidio to compete with them in either the general capacitor or ultra-broadband market. (Tr. 1000, 1005.) Presidio ignores this testimony.

Instead, Presidio conflates this court's Daubert order, which barred Dr. Woods’ opinion concerning the precise royalty rates for the Patents-in-suit, with the wholesale preclusion of his testimony about a hypothetical royalty negotiation. (See Def.’s Opp. 14 (citing ECF No. 179, Daubert Order).) Presidio misconstrues the Daubert order. The court expressly declined to preclude Dr. Woods from testifying. ( Daubert Order 73 ("[T]here may be portions of Dr. Woods’ report and underlying opinion that can support a jury determination of a reasonable royalty without Dr. Woods’ ultimate conclusion."). And as Plaintiffs’ reply notes, Presidio neither objected to Dr. Woods’ opinions at trial, nor challenged the sufficiency of his opinions in post-trial submissions, including Presidio's opposition. (Pls.’ Reply 4.)

Finally, Presidio tries to leverage the well-established presumption that a jury follows the court's instructions, see Weeks v. Angelone , 528 U.S. 225, 234, 120 S.Ct. 727, 145 L.Ed.2d 727 (2000) (citing Richardson v. Marsh , 481 U.S. 200, 211, 107 S.Ct. 1702, 95 L.Ed.2d 176 (1987) ), to foreclose consideration of the jury's apparent error. (Def.’s Opp. 10-11.) The court instructed the jury to "award ATC and AVX a reasonable royalty for all infringing sales for which they have not been awarded lost profits damages." (See Final Jury Instructions, No. 40.) Presidio therefore urges the court to presume the jury heeded the court's instructions, and "awarded a reasonable royalty for all infringing units." (Def.’s Opp. 10 (citations omitted).) Leaving aside Presidio's tautological contention, the presumption on which it relies is overcome, where, as here, the jury arrives at a decision "for impermissible reasons, such as mistake, compromise, or lenity." United States v. Moran-Toala , 726 F.3d 334, 342 (2d Cir. 2013) (citations and internal quotation marks omitted). The reasonable inference drawn here is that the jury's damages award was the product of mistake, and the court cannot presume that the jury awarded a reasonable royalty for all infringing units as instructed.

In a similar vein, Presidio concludes the jury must have disregarded "Plaintiffs’ counsel's improper suggestion during closing argument that $0.25 could serve as a reasonable royalty," because the court instructed the jury that "counsels’ opening and closing statements are to be disregarded." (Def.’s Opp. 10-11.) As an initial matter, Presidio appears to have misinterpreted the court's instruction. The jury was instructed that, "[w]hat the lawyers have said in their opening statements, in their closing arguments, in their objections, or in their questions is not evidence. " (Final Jury Instructions, No. 3 (emphasis added).) Needless to say, it would be nonsensical for counsel to spend countless hours preparing opening and closing remarks, and for the court to set significant time aside for such statements, only to require that jurors completely disregard counsel's summations. It was perfectly in keeping with the law, and the court's instructions, for Plaintiffs’ counsel to suggest to the jury that the evidence supported a royalty rate of $0.25. See United States v. Barbera , No. S1 02CR.1268 (RWS), 2004 WL 1229573, at *12 (S.D.N.Y. June 2, 2004) (noting counsel's "broad latitude" to suggest inferences to the jury during closing arguments). Further, Presidio does not intimate that counsel's closing remarks misrepresented the evidence. Cf. Porter v. United States , No. 08-CV-1497(CPS), 2008 WL 5451011, at *4–5 (E.D.N.Y. Dec. 31, 2008) ("The ‘prosecution and defense are entitled to broad latitude in the inferences they may suggest to the jury during closing arguments,’ provided they do not misstate the evidence.") (citing, inter alia, United States v. Smith , 778 F.2d 925, 929 (2d Cir. 1985) ).

Having established the jury's clear error with regard to damages, and dismissed Presidio's attempts to rationalize it, the court now turns to the appropriate remedy. D. A New Trial on Damages is Necessary

1. A New Trial is Appropriate

A new trial is appropriate under Federal Rule of Civil Procedure 59(a) because the court "is convinced that the verdict was manifestly erroneous." Manley , 337 F.3d at 246. The jury's lump sum damages award matches, to the penny, the exact figure suggested by Plaintiffs’ counsel, but only in relation to a partial subset of 2,955,927 infringing units. The jury did not award a royalty for all 15,369,246 infringing units, an error that flagrantly violates the clear mandate of the patent law, which requires that infringement claimants be awarded a reasonably royalty for all infringing units. See 35 U.S.C. § 284. The court has searched in vain for alternative explanations, and none rationally harmonizes the verdict with the record, or justifies the verdict's arbitrary and varying royalty rates. Cf. Gallick v. Balt. & O.R. Co. , 372 U.S. 108, 119, 83 S.Ct. 659, 9 L.Ed.2d 618 (1963) ("[I]t is the duty of the courts to attempt to harmonize the answers, if it is possible under a fair reading of them: ‘Where there is a view of the case that makes the jury's answers to special interrogatories consistent, they must be resolved that way.’ ") (quoting Atl. & Gulf Stevedores, Inc. v. Ellerman Lines, Ltd. , 369 U.S. 355, 364, 82 S.Ct. 780, 7 L.Ed.2d 798 (1962) ).

The court, therefore, orders a new trial on damages. The jury's liability and invalidity decisions, which are "conceptually distinct" from damages, shall remain undisturbed and those issues will not be retried. See Crockett v. Long Island R.R. , 65 F.3d 274, 279 (2d Cir. 1995) (directing retrial on damages only); see also Banks v. Travelers Cos. , 180 F.3d 358, 364 (2d Cir. 1999) (where "the error infecting the damages award [was] entirely separable from the underlying finding of liability, ... retrial of damages alone [was] appropriate"); Liriano v. Hobart Corp. , 170 F.3d 264, 272 (2d Cir. 1999) ("As a general matter, judges may order retrial on some but not all issues in a case, and they may do so even when the issues are related.").

2. The Lost Profits Verdict Will Not Be Disturbed

The new trial will be limited to the issue of determining a reasonable royalty. Although Plaintiffs seek to abrogate the jury's decision not to award lost profits, a new trial on that issue is unwarranted. Plaintiffs’ sole argument for retrying lost profits "is that the jury was operating under the ‘lost profits scenario’ that Dr. Woods testified about," i.e. awarding lost profits of $18,802,967 for 12,413,319 capacitors, and a royalty for the 2,955,927 remaining capacitors based on a $0.25 rate. (Pls.’ Mot. 1; see also Tr. 2343:13-23.) This contention is speculative, however. Unlike the jury's royalty award, which defies explanation, awarding Plaintiffs zero lost profits can be reconciled with the trial record.

"Lost profits damages are appropriate whenever there is a reasonable probability that, ‘but for’ the infringement, [the patentee] would have made the sales that were made by the infringer." Versata Software, Inc. v. SAP Am., Inc. , 717 F.3d 1255, 1263 (Fed. Cir. 2013) (internal quotation marks and citations omitted). A showing under the four-factor Panduit test is used to establish the required causation. Rite–Hite Corp. v. Kelley Co. , 56 F.3d 1538, 1545 (Fed. Cir. 1995). These factors include: "(1) demand for the patented product, (2) absence of acceptable noninfringing alternatives, (3) [capacity] to exploit the demand, and (4) the amount of profit [the patentee] would have made." Panduit , 575 F.2d at 1156. Causation of lost profits "is a classical jury question." Brooktree Corp. v. Advanced Micro Devices, Inc. , 977 F.2d 1555, 1578 (Fed. Cir. 1992).

Dr. Thomas found no evidence that Presidio's customers demanded capacitors with vias or L-shaped terminations, or that any market existed for licensing the Patents-in-suit. (Tr. 2042-43.) In his opinion, the Patents-in-suit were not critical to the manufacture or sale of ultra-broadband capacitors, a point he highlighted by noting ATC's non-use of the '791 and '547 Patents. (Id. 2044.) Because Presidio's customers were not concerned about vias or L-shaped terminations, Dr. Thomas deduced Presidio could have circumvented the Patents-in-suit without any sales migrating from Presidio to Plaintiffs. (Id. 2044-46, 2062.) Dr. Thomas supported his opinion with testimony from other trial witnesses, including one of Plaintiffs’ engineers, Andrew Ritter, as well as Presidio's President, Alan Devoe, and Plaintiffs’ expert, Dr. Randall. (Id. 1144 (Devoe), 1823 (Dr. Randall), 500 (Ritter).) Dr. Woods, Plaintiffs’ damages expert, testified that Presidio did not make or sell an alternative, non-infringing substitute in the ultra broadband capacitor market, and that Plaintiffs had the capacity to manufacture and market sufficient capacitors to meet the needs of Presidio's customers. (See id. 955-80.)

Although presented with conflicting lost profits testimony, the jury reasonably could have credited Dr. Thomas’ opinion and determined that Plaintiffs did not lose any sales as a result of Presidio's infringement. The lost profits verdict must therefore stand. To hold otherwise, would require the court to substitute the jury's credibility assessment with its own. The Second Circuit forbids this. See Metromedia Co. v. Fugazy , 983 F.2d 350, 363 (2d Cir. 1992), abrogated on other grounds as noted in Yung v. Lee , 432 F.3d 142, 147 (2d Cir. 2005) ("Where the resolution of the issues depended on assessment of the credibility of the witnesses, it is proper for the court to refrain from setting aside the verdict and granting a new trial."); see also Zhiwen Chen v. Cty. of Suffolk , 927 F. Supp. 2d 58, 67 (E.D.N.Y. 2013) (holding that "it would be improper to grant a new trial under these circumstances as the issue of the force exercised by defendants was dependent on the assessment of the credibility of the witnesses") (citation omitted). Plaintiffs’ motion for a new trial, to the extent it seeks to retry the jury's lost profits verdict, is therefore denied.

3. The Proposed Increase to Damages under Rule 59(e) is Unconstitutional

The court also denies Plaintiffs’ request for an amended judgment pursuant to Federal Rule of Civil Procedure 59(e). In lieu of a new trial, Plaintiffs alternatively ask the court to presume a $0.25 royalty rate, and apply that rate to all infringing units as a matter of law, in order to bring the damages award into compliance with 35 U.S.C. § 284. (Pls.’ Mot. 11-12.) Granting Plaintiffs relief in this manner would cause their damages award to surge from $738,981.75 to $3,842,311.50, a greater than 400% increase. (Id. 12.) Presidio argues that a unilateral enhancement of such magnitude would amount to an unconstitutional additur.²⁶ (Def.’s Opp. 27-29.) The court agrees. Under the Seventh Amendment, "no fact tried by a jury, shall be otherwise re-examined in any Court of the United States, than according to the rules of the common law." U.S. Const. amend. VII ("Re-examination Clause"). In Dimick v. Schiedt , the Supreme Court barred the use of additur in federal court as a violation of the Re-examination Clause. 293 U.S. 474, 482, 486, 55 S.Ct. 296, 79 L.Ed. 603 (1935). The Dimick court was concerned that unilateral increases of damages erode the "controlling distinction" between court and jury, namely, the power of the court "to determine the law and [the power of the jury] to determine the facts." Id. at 486, 55 S.Ct. 296. The prohibition against additur endures to present day. See, e.g. , Elyse , 367 F. App'x at 267 ; Lenair v. Gauthier , No. CIV.1:03CV299, 2007 WL 593567, at *1 (D. Vt. Feb. 21, 2007) ("Absent defendants’ consent, the court is not free to use additur because increasing a jury's award, handed down after it considered disputed evidence, ‘would violate the Seventh Amendment right to a jury trial.’ ") (quoting Gibeau v. Nellis , 18 F.3d 107, 111 (2d Cir. 1994) ); Peebles v. Circuit City Stores, Inc. , No. 01 Civ. 10195 (CSH), 2003 WL 21976402, at *13 (S.D.N.Y. Aug. 19, 2003) ("That alternative remedy [of additur] lies beyond the Court's power.").

26 Technically speaking, additur is "the process by which, if a trial court considers a verdict inadequate, it may condition the denial of plaintiff's motion for a new trial on defendant's consent to the entry of judgment in excess of the verdict." Elsevier Inc. v. Grossmann , No. 12 Civ. 5121 (KPF), 2018 WL 4908105, at *3 (S.D.N.Y. Oct. 9, 2018). "[I]t is a tool that judges use to fix damages—something that can generally be done only by the fact-finder—without actually having to hold a second trial." Liriano , 170 F.3d at 272. Although a court order unilaterally increasing the jury's damages award does not strictly conform to the definition of additur above, the distinction is immaterial. The Second Circuit proscribes both amended judgments increasing damages and additur, and refers to the two interchangeably. See, e.g. , Elyse v. Bridgeside Inc. , 367 F. App'x 266, 267 (2d Cir. 2010) (affirming denial of Rule 59(e) motion to increase damages award "on the ground that additur is constitutionally impermissible").

The Seventh Amendment does not bar all enhancements to damages awards, however, and the Second Circuit has recognized a limited exception to Dimick . In Liriano v. Hobart Corp. , defendant appealed a district court order that increased a jury's damages award to the plaintiff "to account for a hospital bill whose amount and nature were not in dispute." 170 F.3d at 272. The district court granted plaintiff's motion, and added $21,252.34 to the total jury award of $1,352,500. See id. at 278-79. In affirming, the Second Circuit held that, while additur is unconstitutional, "simply adjust[ing] the jury award to account for a discrete item that manifestly should have been part of the damage calculations and as to whose amount there was no dispute," was permissible. Id. at 273.

Plaintiffs here attempt to maneuver the instant motion through the narrow opening articulated in Liriano . (Pls.’ Reply 9.) But Liriano ’s reach does not extend so far, as recently illustrated by Elsevier Inc. v. Grossmann , a 2018 decision in the Southern District of New York. In Elsevier , book publishers sued under the Racketeer Influenced and Corrupt Organizations Act ("RICO") to recover damages for improper sales to defendant. No. 12 CIV. 5121 (KPF), 2018 WL 4908105, at *2 (S.D.N.Y. Oct. 9, 2018). At trial, plaintiffs introduced evidence regarding defendant's fraudulent practices, including a detailed spreadsheet substantiating $31,345 in damages. Id. Defendant testified on his own behalf, and claimed he was being falsely accused of fraud, but presented no other evidence to the jury. Id. The jury ultimately found defendant liable under 18 U.S.C. § 1962(c), but awarded only $11,108 in damages. Id. In a post-trial Rule 59(e) motion, plaintiffs argued that "a fair and reasonable jury, with the correct understanding of RICO liability," including the precept that an individual defendant is liable for all damages caused by the RICO enterprise, not just those caused by his personal involvement, would have awarded plaintiffs the full damages sought. Id. at *4. Plaintiffs further argued that Liriano permitted the requested increase. Judge Failla disagreed, and discussed why the exception to Dimick was inapt:

This is not a case where Plaintiffs are asking for a discrete adjustment to account for an undisputed amount. Instead, Plaintiffs are asking the Court to triple the amount of damages awarded by the jury. Furthermore, those damages were disputed by Defendant.... Because Plaintiffs are not asking for a discrete, undisputed adjustment to the awarded damages, Dimick remains applicable to this case.

Id. at *2.

Like Elsevier , this case lies well beyond the facts of Liriano . The parties heavily dispute the appropriate royalty and there is a genuine dispute concerning the royalty rate. See U.S. E.E.O.C. v. Massey Yardley Chrysler Plymouth, Inc. , 117 F.3d 1244, 1252 (11th Cir. 1997) ("Courts recognize an exception to Dimick where the jury has found the underlying liability and there is no genuine issue as to the correct amount of damages."). Although the court is convinced that the jury erred in awarding damages, to definitively conclude that the jurors agreed on a $0.25 royalty rate, in light of conflicting evidence, is a bridge too far. The sheer magnitude of the damages increase Plaintiffs seek also warrants extreme caution. Judge Failla felt compelled to abstain from increasing damages three-fold, by approximately $20,000. If Plaintiffs’ motion to amend under Rule 59(e) were granted, their damages award would balloon by a multiple of more than five, and in excess of $3 million. Such an increase would surpass all precedent, and ultimately, run afoul of the Constitution. Accordingly, Plaintiffs’ motion to amend the judgment under Rule 59(e) is denied.

III. Plaintiffs’ Motion for Supplemental Damages and Costs

Finally, the court turns to Plaintiffs’ motion for supplemental damages, prejudgment interest, post-judgment interest, and taxation of costs. (See generally Pls.’ Dmgs. Mot.) Given the pendency of a new trial, supplemental damages, prejudgment interest, and post-judgment interest cannot be fixed at a sum certain, at this time. Nevertheless, the court finds it prudent to decide on the parties’ legal disputes. Following a new trial, the parties can simply apply the court's legal conclusions in light of the new royalty rate and award, and stipulate to supplemental damages and interest.

A. Supplemental Damages

Pursuant to 35 U.S.C. § 284, "the court shall award the claimant damages adequate to compensate for the infringement, but in no event less than a reasonable royalty for the use made of the invention by the infringer," and "[w]hen the damages are not found by a jury, the court shall assess them." "The Federal Circuit has emphasized the mandatory nature of this directive and vacated damages awards that do not take into account all infringing activity." SIMO Holdings Inc. v. Hong Kong uCloudlink Network Tech. Ltd. , 396 F. Supp. 3d 323, 348 (S.D.N.Y. 2019) (procedural history omitted) (citing Finjan, Inc. v. Secure Computing Corp. , 626 F.3d 1197, 1213 (Fed. Cir. 2010) ). The parties agree that Plaintiffs are entitled to supplemental damages for the infringing BB capacitors made or sold after the time period considered at trial. (Pls.’ Dmgs. Mot. 1-4; Def.’s Dmgs. Opp. 5.) The parties also agree Presidio made or sold 3,401,142 additional capacitors that directly infringe the '547 Patent since January 9, 2017, the last date for which Presidio produced sales data before the close of discovery. (Pls.’ Dmgs. Mot. 2; Def.’s Dmgs. Opp. 2.)²⁷ Presently, there is no legally binding royalty rate to apply to the additional infringing units. Supplemental damages therefore cannot be calculated until the royalty rate for the '547 Patent is determined at the new trial. Accordingly, Plaintiffs’ motion for supplemental damages is denied, without prejudice to renew. Plaintiffs’ asserted royalty base will presumably comprise the capacitor units considered in the June 2019 trial, along with the infringing capacitors sold since January 9, 2017.²⁸ If there are additional infringing units made or sold after the time period covered in the new trial, Plaintiffs may once again seek supplemental damages for that subset.

27 Plaintiffs do not seek supplemental damages for the '791 Patent based on Presidio's representation that it has not made or sold any additional BB capacitors that infringe the '791 Patent. (Pls.’ Dmgs. Mot. 2 n.1; ECF No. 217, Stipulated Injunction, ¶ 2.)

28 As discussed below, the court awards prejudgment interest, pending judgment in the new trial. Prejudgment interest shall be applied to the royalty awarded in the new trial. See Comcast IP Holdings I LLC v. Sprint Commc'ns Co., L.P. , 850 F.3d 1302, 1315 (Fed. Cir. 2017) (affirming the "district court's assessment of prejudgment interest against [an infringer] based on the entire royalty award" where the jury awarded a lump-sum amount).

B. Prejudgment Interest

1. Undue Delay

Plaintiffs seek prejudgment interest on damages at the three-month Treasury Bill ("T-Bill") rate, compounded annually. (Pls.’ Dmgs. Mot. 5-6.) Upon a finding of infringement, "the [district] court shall award the claimant damages adequate to compensate for the infringement, ... together with interest and costs as fixed by the court." 35 U.S.C. § 284. "Prejudgment interest should ordinarily be awarded where necessary to afford the plaintiff full compensation for the infringement." Schwendimann v. Arkwright Advanced Coating, Inc. , 959 F.3d 1065, 1075–76 (Fed. Cir. 2020) (brackets omitted) (quoting Gen. Motors Corp. v. Devex Corp. , 461 U.S. 648, 655, 103 S.Ct. 2058, 76 L.Ed.2d 211 (1983) ). Prejudgment interest "serves to make the patent owner whole, for damages properly include the foregone use of money of which the patentee was wrongly deprived." Sensonics, Inc. v. Aerosonic Corp. , 81 F.3d 1566, 1574 (Fed. Cir. 1996). Thus, awarding "prejudgment interest is the rule, not the exception." Id.

Nevertheless, Presidio opposes an award of prejudgment interest, citing "Plaintiffs’ undue delay in filing this lawsuit." (Def.’s Dmgs. Opp. 6.) Although pre-judgment interest should ordinarily be awarded, it may be limited or denied "where the patent owner has been responsible for undue delay in prosecuting the lawsuit." Enzo Biochem, Inc. v. Applera Corp. , No. 3:04CV929 JBA, 2014 WL 29126, at *3 (D. Conn. Jan. 3, 2014) (citing Gen. Motors Corp. , 461 U.S. at 657, 103 S.Ct. 2058 ). Plaintiffs allegedly had intricate knowledge of Presidio's BB capacitors, including the infringing features, as early as 2002, twelve years before filing suit. (Def.’s Dmgs. Opp. 6.) Presidio claims Plaintiffs’ needless delay in filing suit caused Defendant to waste hundreds of thousands of dollars on capital investments for the BB capacitors, and incur other economic harms. (Id. ; see also ECF No. 231-12, Declaration of Lambert Devoe, ¶¶ 6-9 (documenting $500,000 in expenditures related to BB capacitors between 2002 and 2014).) Had Plaintiffs filed this action more promptly, Presidio claims it would have redeployed "substantial investments into the BB capacitor product line ... to a non-infringing design." (Def.’s Dmgs. Opp. 7.)

Presidio's argument merely regurgitates claims previously rejected by this court, and repurposes them to evade prejudgment interest obligations. In October 2019, Presidio moved post-trial for a finding that Plaintiffs "waived their rights to sue for infringement under the '791 Patent because they had actual knowledge of Presidio's alleged infringement for more than a decade." (ECF No. 214, Memorandum and Order Denying Motion to Vacate, dated October 16, 2019 ("Oct. 16th Order"), 5.) Presidio asserted then, as now, that Plaintiffs "fail[ed] to enforce their rights for more than a decade after becoming aware of the alleged infringement." (Compare Oct. 16th Order 21-22, with Def.’s Dmgs. Opp. 6.) Presidio asserted then, as now, that Plaintiffs analyzed Presidio's BB capacitors as early as 2002, and determined the capacitors were covered by ATC's patents. (Compare Oct. 16th Order 22, with Def.’s Dmgs. Opp. 6.) Presidio principally relied then, as it does now, on communications from Plaintiffs’ engineers, including John Mruz, to show that Plaintiffs analyzed Presidio's BB capacitors as early as 2004. (Compare Oct. 16th Order 24, and ECF No. 206-2 (Ex. 13, Mruz Notes and Emails), with Def.’s Dmgs. Opp. 3-4, and ECF Nos. 231-4, 231-7 (Mruz Notes and Emails).)

The court rejected Presidio's contentions of undue delay in October 2019. (Oct. 16th Order 30 ("The court cannot find that even a preponderance of the evidence establishes Mruz's knowledge as early as 2002 or 2004 of both the '791 Patent and Presidio's alleged infringement.").) Presidio offers the court no discernable basis to deviate from its prior ruling. At bottom, "the withholding of prejudgment interest based on delay is the exception, not the rule[.]" Lummus Indus., Inc. v. D.M. & E. Corp. , 862 F.2d 267, 275 (Fed. Cir. 1988). Presidio's failure to establish that Plaintiffs unreasonably delayed suit to "bolster [their] litigation position or pad its bottom line," militates against an exception here. Kolcraft Enters., Inc. v. Chicco USA, Inc. , No. 09-CV-03339, 2019 WL 4242482, at *19 (N.D. Ill. Sept. 6, 2019) (citing Lummus , 862 F.2d at 275 ); see, e.g. , EcoServices, LLC v. Certified Aviation Servs., LLC , 340 F. Supp. 3d 1004, 1032 (C.D. Cal. 2018) (finding no undue delay where defendant put forth no evidence that plaintiff's delay was a litigation tactic or that defendant was prejudiced in any way); Green Mountain Glass LLC v. Saint-Gobain Containers, Inc. , 300 F. Supp. 3d 610, 627 (D. Del. 2018), aff'd sub nom. Green Mountain Glass, LLC v. Saint-Gobain Containers, Inc. , 773 F. App'x 619 (Fed. Cir. 2019) (awarding prejudgment interest where "Defendant has neither proven Plaintiffs unduly delayed in filing suit or that they have been prejudiced.").

2. Prejudgment Interest Rate

District courts are afforded "wide latitude in the selection of interest rates," and the Federal Circuit has authorized the use of state statutory rates, the prime rate, and pertinently, the U.S. T-Bill rate.²⁹ Schwendimann , 959 F.3d at 1076. The T-Bill rate "has been accepted and employed by many courts in patent cases as a reasonable method of placing a patent owner in a position equivalent to where it would have been had there been no infringement." ³⁰ Romag Fasteners, Inc. v. Fossil, Inc. , No. 3:10CV1827 (JBA), 2018 WL 3918185, at *10 (D. Conn. Aug. 16, 2018) (procedural history and citations omitted); see, e.g. , Laitram Corp. v. NEC Corp. , 115 F.3d 947, 955 (Fed. Cir. 1997) ; Datascope Corp. v. SMEC, Inc. , 879 F.2d 820, 829 (Fed. Cir. 1989), cert. denied , 493 U.S. 1024, 110 S.Ct. 729, 107 L.Ed.2d 747 (1990) ; Enzo Biochem , 2014 WL 29126, at *4 ; Accuscan, Inc. v. Xerox Corp. , 96 Civ. 2579, 2000 WL 280005, at *2 (S.D.N.Y. Mar. 14, 2000).

29 As a general matter, interest is awarded to "compensate [the lender] for the opportunity costs of the loan, the risk of inflation, and the ... risk of default." Till v. SCS Credit Corp. , 541 U.S. 465, 479, 124 S.Ct. 1951, 158 L.Ed.2d 787 (2004). The T-Bill rate is the "risk-free" interest rate charged on loans made to the United States government. See Applera Corp. v. MJ Research Inc. , No. 3:98cv1201 (JBA), 2005 WL 2084319, at *2 (D. Conn. Aug. 29, 2005). In contrast, the national prime rate "reflects the financial market's estimate of the amount a commercial bank should charge a creditworthy commercial borrower," Till , 541 U.S. at 479, 124 S.Ct. 1951, i.e. , a bank's largest and best customers with the lowest risk of default.

30 The T-Bill rate is a fundamentally conservative method of compensation, so much so that some courts consider it inadequate. E.g., SIMO Holdings Inc. , 396 F. Supp. 3d at 352 (setting prejudgment interest at prime rate, compounded quarterly, to "better approximate[ ] a corporate borrower's cost of funds," because the T-Bill rate would not adequately compensate plaintiff for the infringement); Stryker Corp. v. Intermedics Orthopedics, Inc. , 891 F. Supp. 751, 833 (E.D.N.Y. 1995) ("[I]n the Court's view the prime rate is more reflective of [the patentee's] cost of funds than the ... Treasury Rate.").

Courts may also award compound interest in order to ensure the patent owner is fully compensated. Accord Rite-Hite Corp. , 56 F.3d at 1555 (citation omitted); Mars, Inc. v. Coin Acceptors, Inc. , 513 F. Supp. 2d 128, 137 (D.N.J. 2007) ("Because a patentee's damages include the forgone use of money, compounded [interest] is needed to account for the time value of money.") (quoting AMP Inc. v. Lantrans, Inc. , 1991 WL 253796, at *7 (C.D. Cal. Nov. 7, 1991) ); see, e.g. , IPVX Patent Holdings, Inc. v. Taridium, LLC , No. 12-CV-5251 KAM SMG, 2014 WL 4437294, at *5 (E.D.N.Y. Aug. 6, 2014), report and recommendation adopted , No. 12-CV-5251 KAM SMG, 2014 WL 4437307 (E.D.N.Y. Sept. 9, 2014) ("[T]his Court's understanding is that interest is generally compounded annually, and I therefore conclude that annual compounding should be sufficient to compensate plaintiff."). "Whether to award simple or compound interest is within the discretion of the district court." Mars, Inc. , 513 F. Supp. 2d at 137 (citing Lam, Inc. v. Johns–Manville Corp. , 718 F.2d 1056, 1066 (Fed. Cir. 1983) ). The Federal Circuit, moreover, has rejected the notion that a prevailing patent litigant must affirmatively demonstrate entitlement to prejudgment interest above the T-Bill rate. Studiengesellschaft Kohle, m.b.H. v. Dart Indus., Inc. , 862 F.2d 1564, 1579–80 (Fed. Cir. 1988).

Presidio voices no specific objection to applying the three-month T-Bill rate, but opposes compounding interest, citing the lack of "evidence that [Plaintiffs] borrowed any money due to being deprived of the damages award." (Def.’s Dmgs. Opp. 9.) This objection fails. Compound interest may be awarded regardless of Plaintiffs’ borrowing needs or rates. See Rosco, Inc. v. Mirror Lite Co. , No. CV-96-5658CPS, 2009 WL 3587344, at *2 (E.D.N.Y. Oct. 26, 2009), aff'd , 394 F. App'x 714 (Fed. Cir. 2010) (compounding prejudgment interest quarterly even though prevailing party did not "submit[ ] any evidence of the rate at which it borrows money.").

For the reasons stated above, the court provisionally awards prejudgment interest to Plaintiffs at the three-month T-Bill rate, compounded annually. After the new trial concludes, the parties will confer and submit a stipulated judgment as to the precise amount of prejudgment interest, which shall be awarded "from the time that the royalty payments would have been received" for each Patent-in-suit, Gen. Motors Corp. , 461 U.S. at 655-56, 103 S.Ct. 2058, until the date of an amended final judgment on royalty damages.

C. Post-Judgment Interest

"The award of post-judgment interest is mandatory on awards in civil cases as of the date judgment is entered." Lewis v. Whelan , 99 F.3d 542, 545 (2d. Cir. 1996) ; 28 U.S.C. § 1961(a) (stating that post-judgment interest at the federal statutory rate "shall be allowed on any money judgment in a civil case recovered in a district court"). Post-judgment interest is calculated from the date of entry of judgment at a rate equal to the weekly average 1-year constant maturity Treasury yield, as published by the Board of Governors of the Federal Reserve System. 28 U.S.C. § 1961(a).

The parties agree that Plaintiffs are entitled to post-judgment interest. Accordingly, the court provisionally awards Plaintiffs post-judgment interest following the new trial, at the rate specified by § 1961, beginning from the date a new judgment awarding royalty damages is entered.

D. Taxation of Costs

Plaintiffs seek taxation of $298,337.54 in costs against Presidio. (Pls.’ Dmgs. Mot. 7; ECF No. 230-2, Bill of Costs.) The Bill of Costs breaks down into four broad categories: (1) docket and miscellaneous fees: $555.24; (2) trial and deposition transcripts: $49,847.20; (3) witness fees, travel expenses, and subsistence: $12,787.75; and (4) fees and costs for photocopies, printing, demonstratives, and technical assistance at trial: $235,147.35. (Pls.’ Dmgs. Mot. 7-8.) Presidio believes Plaintiffs have vastly overstated their costs and vigorously contest almost every expense. (See Def.’s Dmgs. Opp. 9-17.)

1. Legal Standard

Rule 54 of the Federal Rules of Civil Procedure provides that, "[u]nless a federal statute, these rules, or a court order provides otherwise, costs—other than attorney's fees—should be allowed to the prevailing party." Fed. R. Civ. P. 54(d)(1). "Construing this provision, the Supreme Court has held that the term ‘costs’ includes only the specific items enumerated in 28 U.S.C. § 1920." Whitfield v. Scully , 241 F.3d 264, 269 (2d Cir. 2001), abrogated on other grounds by Bruce v. Samuels , 577 U.S. 82, 136 S. Ct. 627, 193 L.Ed.2d 496 (2016). Pursuant to § 1920, the court, or the Clerk of Court, may tax as costs the following:

(1) Fees of the clerk and marshal; (2) Fees for printed or electronically recorded transcripts necessarily obtained for use in the case; (3) Fees and disbursements for printing and witnesses; (4) Fees for exemplification and the costs of making copies of any materials where the copies are necessarily obtained for use in the case; (5) Docket fees ...; [and] (6) Compensation of court appointed experts, compensation of interpreters, and salaries, fees, expenses, and costs of special interpretation services.

28 U.S.C. § 1920.

Local Civil Rule 54.1(c) enumerates ten items taxable as costs, clarifies which items are, and are not taxable without an order of the court, see Committee Note to Local Civ. R. 54.1, and controls insofar as it addresses a particular cost. See Balance Point Divorce Funding, LLC v. Scrantom , 305 F.R.D. 67, 70 (S.D.N.Y. 2015). The court is also aware that the Local Rules bar taxation of costs during the pendency of a new trial motion. Local Civ. R. 54.1(a). This Memorandum and Order contemporaneously resolves Plaintiffs’ motion for a new trial, however, and so the Local Rules do not inhibit taxation of costs.³¹ 2. Docket and Miscellaneous Fees

31 Local Rule 54.1(a) also provides that "[w]ithin thirty (30) days after the determination of any ... motion for a new trial, the party seeking [to] tax costs shall file a new notice of taxation of costs." Presidio's opposition does not refer to this provision, or the Local Rules’ prohibition against taxing costs during the pendency of a new trial motion. The court construes this silence as a waiver, and exercises its inherent authority to waive its Local Rules because strict adherence here would result in unnecessarily duplicative filings. See Somlyo v. J. Lu-Rob Enters., Inc. , 932 F.2d 1043, 1048 (2d Cir. 1991) ("The district court's inherent discretion to depart from the letter of the Local Rules extends to every Local Rule regardless of whether a particular Local Rule specifically grants the judge the power to deviate from the Rule.").

Plaintiffs seek $555.24 in docket and filing fees. (Pls.’ Dmgs. Mot. 8; ECF 230-10 (electronic docket excerpts reflecting filing fees for Complaint and pro hac vice application); ECF No. 230-11 (summons served on Presidio).) Under Local Civil Rule 54.1(c)(10), "[d]ocket fees, and the reasonable and actual fees of the Clerk and of a marshal, sheriff, and process server, are taxable ...." See also 28 U.S.C. § 1920(1) (the court may tax "[f]ees of the clerk and marshal").

Presidio only objects to a $25 pro hac vice filing fee. (Def.’s Dmgs. Opp. 9-10.) Plaintiffs respond by withdrawing this fee request. (Pls.’ Dmgs. Reply 4.) The court therefore awards Plaintiffs docket and filing fees limited to $530.24.

3. Trial and Deposition Transcripts

Plaintiffs seek $49,847.20 in costs for trial transcripts "necessarily obtained for use in the case," and deposition transcripts, video recordings, and exhibits "used at trial or for witnesses that testified at trial, or used by a party in a summary judgment motion." (Pls.’ Dmgs. Mot. 8-9.) Presidio asserts that three sub-categories of costs in this group are non-taxable: (1) deposition transcripts not used or received at trial; (2) videotapes of depositions; and (3) duplicative copies of exhibits to the depositions. (Def.’s Dmgs. Opp. 10-12.) Presidio does not object to the cost of trial transcripts.

Local Civil Rule 54.1(c)(2) provides that, unless the court orders otherwise:

the original transcript of a deposition, plus one copy, is taxable if the deposition was used or received in evidence at the trial, whether or not it was read in its entirety.... Costs for depositions taken solely for discovery are not taxable.

Notwithstanding Rule 54.1(c)(2) ’s "clear and unequivocal" wording, "cases have established the sensible rule that the costs of depositions not used at the trial may nevertheless be taxed for costs where they appear to have been reasonably necessary to the litigation at the time they were taken." Palm Bay Int'l, Inc. v. Marchesi Di Barolo S.P.A. , 285 F.R.D. 225, 235 (E.D.N.Y. 2012) (internal citations omitted) (collecting cases); accord Bauta v. Greyhound Lines, Inc. , No. 14-CV-3725 (RER), 2019 WL 8060181, at *4 (E.D.N.Y. June 17, 2019) ("Courts have not limited the meaning of the word ‘use’ to only include deposition transcripts that were admitted at trial.").

The "sensible" interpretation of Local Rule 54.1(c)(2) is the "general practice" in the Eastern District, see Bauta , 2019 WL 8060181, at *5, and defeats Presidio's objection to taxing deposition transcripts not used or received at trial. Every transcript Presidio contests relates to a witness who either testified at trial, or whose video testimony was played at trial, or whose testimony was cited in Plaintiffs’ summary judgment motion. (Def.’s Dmgs. Opp. 10-11; see ECF No. 230-13 (Deposition Invoices).) Courts in this District generally consider such costs taxable. See, e.g. , Bauta , 2019 WL 8060181, at *5 (awarding costs of deposition transcript, plus one copy, for witnesses who appeared at trial, regardless of whether transcript was entered into record). So too here. Presidio's objection to costs associated with video testimony likewise fails. "Video fees have been deemed taxable where there was an expectation among the parties that the video of the testimony might be presented at trial." In re Omeprazole Patent Litig. , No. 00 CIV. 4541 BSJ, 2012 WL 5427791, at *4 (S.D.N.Y. Nov. 7, 2012) (citations, internal quotation marks, and brackets omitted); but see Citigroup Glob. Markets, Inc. v. Abbar , 63 F. Supp. 3d 360, 362 (S.D.N.Y. 2014) (finding costs for videotaped depositions duplicative, given court's taxation of costs for original transcripts plus one copy, notwithstanding use of video at trial). Each video fee Presidio objects to, was either: (1) played at trial during Plaintiffs’ case-in-chief (see ECF No. 232-2 (excerpts of trial testimony: Richard Monsorno, Daniel Devoe, Mary Trinh, Lambert Devoe, Alan Devoe); (2) used, or was expected to be used at trial for impeachment purposes (see ECF No. 232-3 (excerpts of trial testimony: Dr. Michael Randall and Dr. Vincent Thomas); or (3) prepared at Presidio's request, and due to uncertainty regarding the witnesses’ availability for trial, as in the case of John Mruz and Victor Insetta, individuals who were not employed by the parties during this case. (See Pls.’ Dmgs. Reply 5.) The court finds that the video costs Plaintiffs seek are taxable.

Presidio's third objection raises a non-existent concern. Plaintiffs do not seek to tax costs for two copies of deposition exhibits, as Presidio asserts. (Pls.’ Dmgs. Reply 5 (citing Def.’s Dmgs. Opp. 12).) Presidio's confusion, reasonable though it may be, stems from separate line items in the deposition invoices for "EXHIBITS B&W" and "EXHIBITS COLOR." (See, e.g. , Deposition Invoices, ECF p. 12 of 36.) Plaintiffs represent that each line item corresponds to different exhibits, which is supported by the fact that each line item reflects different page counts. The court accepts Plaintiffs’ representation.

Accordingly, the court awards Plaintiffs the full $49,847.20 requested for the costs of deposition and trial transcripts, which amounts may increase due to the new trial.

4. Witnesses, Travel Expenses, and Subsistence

Plaintiffs also seek $12,787.75 in fees, travel expenses, and subsistence costs for John Mruz, Andrew Ritter, Evan Slavitt, Dr. Craig Hillman, Dr. James Woods, and Dr. Stanley Shanfield, witnesses for Plaintiffs who testified at trial and were deposed. Witness costs are taxable under 28 U.S.C. § 1920(3). Local Civil Rule 54.1(c)(3) permits taxation of witness fees and travel expenses authorized by 28 U.S.C. § 1821, so long as the witness testifies, as well as subsistence pursuant to § 1821, if the witnesses testifies and it is impractical for him or her to return to their residence day to day.

Pursuant to 28 U.S.C. § 1821(a)(1), "a witness in attendance at any court of the United States ... or before any person authorized to take his deposition pursuant to any rule or order of a court of the United States, shall be paid fees and allowances provided by this section." The witness's fees and allowances include: (1) $40 per day for each day's attendance; (2) actual travel expenses to and from the deposition or trial, assuming the witness utilized a reasonable means of transportation; and (3) a subsistence allowance at the applicable per diem rate. Id. § 1821(b), (c)(1).

Presidio's sole objection relates to witness costs for depositions that were not used or received at trial. Presidio relies on the apparent limiting language of the Local Rules, which state that, "[f]ees, mileage, and subsistence for the witness at the deposition are taxable at the same rates as for attendance at trial if the deposition taken was used or received in evidence at the trial." Local Civ. R. 54.1(c)(2). As stated above, this court applies the "sensible rule" to costs associated with depositions. The court thus finds taxable and awards those witness fees, travel expenses, and subsistence incurred in connection with depositions, where the witness deposed subsequently testified at trial. Upon review of Plaintiffs’ attached expense records (see ECF No. 230-14, Witnesses’ Travel Expenses; ECF No. 230-15, Applicable Per Diem Rates), the court finds all requested costs are taxable and reasonable, with one exception. Plaintiffs seek $983.16 for Dr. Shanfield's fees and expenses incurred in connection with his testimony at the Markman Hearing on August 31, 2016. (Pls.’ Dmgs. Mot. 13.) Plaintiffs have not identified any authority that permits recovery of such costs where the testimony involved was not related to a trial or deposition. As a result, this cost will not be taxed. Plaintiffs are therefore awarded $11,804.59 in witness attendance fees, travel expenses, and subsistence.

5. Photocopies, Printing, Demonstratives, and Technical Assistance

Finally, Plaintiffs seek $235,147.35, encompassing the costs of printing trial exhibits, preparing demonstratives for trial, creating a trial exhibit database for use at trial, generating deposition video clips for use at trial, computer technician assistance at trial, and copying documents for production in the litigation. (Pls.’ Dmgs. Mot. 14.) The court addresses each of the foregoing, and Presidio's objections, in turn.

i. Trial Exhibits and Witness Binders

Plaintiffs expended $4,243.96 printing four sets of trial exhibits, and $8,027.39 printing four sets of witness binders. Under Local Civil Rule 54.1(c)(5), "[a] copy of an exhibit is taxable if the original was not available and the copy was used or received in evidence." Moreover, "[t]he cost of copies used for the convenience of counsel or the Court are not taxable." Id. ³² Plaintiffs cite the undersigned's Chambers Practices, which require counsel to provide the court with two sets of trial exhibits, as justification for their duplication of the trial exhibits. (Pls.’ Dmgs. Reply 6 (citing Chambers Practices of Hon. Kiyo A. Matsumoto, Section V.A.11(a)(4).) Plaintiffs provided the court with two courtesy copies of trial exhibits, as required and ordered. The third and fourth sets of exhibits were used by Plaintiffs and Presidio, respectively. (Id. 6-7.) Clearly then, three of the four trial exhibit binders were prepared exclusively for the convenience of the court and defense counsel. On reply, Plaintiffs cite two docket orders by other courts that apparently taxed the type of costs Plaintiffs seek here. Because neither order sets forth its reasoning, this court cannot discern the legal bases underlying taxation in those instances. Ultimately, the plain language of the Local Rules dictates that three of the four trial binders exhibits are non-taxable.

32 The court finds the presence of this limiting language, not present in Local Rules 54.1(c)(2) and (3), bars application of the "sensible rule" for exemplification of trial exhibits and witness binders.

Likewise, Plaintiffs make no showing that the binders of witness exhibits were used or received in evidence, existed for any purpose other than the convenience of the court, witnesses, and counsel, or comprised non-duplicative exhibits not already included in the trial exhibit binder. The attached invoices and accompanying declaration of Plaintiffs’ counsel, fail to elaborate on these points. (See generally ECF No. 230-17, Witness Exhibits Invoice; ECF No. 230-3, Declaration of Peter F. Snell, Esq.) Moreover, Plaintiffs cite no language in the Local Rules that would permit taxation of such costs.

Accordingly, the court awards Plaintiffs $1,060.99 for the one taxable set of trial exhibits. The court will not tax any costs associated with Plaintiffs’ preparation of witness binders.

ii. Demonstratives

Plaintiffs seek $146,190 for the preparation and design of demonstratives at trial. (Pls.’ Dmgs. Mot. 15.) Taxable costs include "[f]ees for exemplification and copies of papers necessarily obtained for use in the case." 28 U.S.C. § 1920(4). Local Civil Rule 54.1(c)(6) provides that "[c]osts of maps, charts, and models, including computer generated models, are not taxable except by order of court." The Local Rules thus confer discretion on the court to award costs for preparing demonstratives. See Altvater Gessler-J.A. Baczewski Int'l (USA) Inc. v. Sobieski Destylarnia S.A. , No. 06 CIV. 6510 HB, 2011 WL 2893087, at *7 (S.D.N.Y. July 14, 2011).

Section 1920(4) is understood as "authoriz[ing] a court to tax the cost of preparing demonstrative aids, including charts, blow-ups, and computer graphics." DiBella v. Hopkins , 407 F. Supp. 2d 537, 539 (S.D.N.Y. 2005) ; see also In re Air Crash Disaster at John F. Kennedy Int'l Airport , 687 F.2d 626, 631 (2d Cir. 1982) (holding that § 1920(4) entitles a prevailing party to recover "reasonable expense of preparing maps, charts, graphs, photographs, motion pictures, photostats and kindred materials," as well as cost of producing demonstration models and exhibits) (citations and internal quotation marks omitted). In DiBella v. Hopkins , then-District Judge Chin, explained why awarding reasonable costs for demonstratives is a prudent exercise of the court's discretion under Local Rule 54.1 :

[B]low-ups, digital presentations of scanned documents, and other computer graphics serve the same function as exhibits and other papers used at trial, and there is no logical reason to differentiate between the former and the latter in terms of their taxability as costs. Digitized copies of documents shown on a television monitor or screen are the functional equivalent of photocopies of documents in jury binders.

[T]he use of technology to improve the presentation of information to the jury and/or to the bench should be supported. Computers, computer graphics, digitized documents, and other technological advancements have become important tools of the modern-day trial lawyer. As long as the cost is reasonable and the devices aid in the efficient and effective presentation of evidence, a prevailing party should be allowed to recover their expense. Here, both sides used computer technology and demonstrative graphics at trial, and the use of these items helped to facilitate the presentation of evidence.

407 F. Supp. 2d at 540 (internal quotation marks and citations omitted).

Not all courts in this Circuit agree. Recently, some cases have held or suggested that the lack of explicit textual reference to demonstratives or visual aids in 28 U.S.C. § 1920(4) renders such costs non-taxable. See, e.g. , Endo Pharms. Inc. v. Amneal Pharms., LLC , 331 F.R.D. 575, 580 (S.D.N.Y. 2019) (explaining why 28 U.S.C. § 1920 may not cover costs in developing trial graphics and demonstratives, but ultimately denying costs on grounds plaintiff failed to substantiate expenses with specific exhibits or tasks); Broadspring, Inc. v. Congoo, LLC , No. 13-CV-1866(RJS), 2016 WL 817449, at *6 (S.D.N.Y. Feb. 24, 2016) ("[T]he costs of DOAR's assistance with trial graphics and demonstrative services at trial ... which amount to over $136,000 — do not fall within the textual confines of 28 U.S.C. § 1920 and, accordingly, are not taxable."). Respectfully, the court disagrees with this restrictive approach.

Although the Second Circuit has not recently had occasion to clarify the meaning of "exemplification" under section 1920(4), demonstratives and visual aids are fairly encompassed by a reasonable reading of the statute. See Cefalu v. Vill. of Elk Grove , 211 F.3d 416, 427 (7th Cir. 2000) ("More commonly, [exemplification] signifies the act of illustration by example, a connotation broad enough to include a wide variety of exhibits and demonstrative aids.") (internal citation omitted); see also Warner Chilcott Labs. Ireland Ltd. v. Impax Labs., Inc. , No. CIV.A. 08-6304 WJM, 2013 WL 1876441, at *14 (D.N.J. Apr. 18, 2013) ("[T]he Clerk is not inclined to adopt a definition as restrictive as that in Black's Law Dictionary, thereby virtually eliminating the costs of all demonstrative evidence."). Patent litigation, in particular, demonstrates the illogic of defining "exemplification" on unduly narrow terms, thereby removing demonstratives from the ambit of taxable costs. Visual aids are indispensible to a lay juror's comprehension of the advanced, often technical subjects that arise in patent cases. Barring the prevailing party from recovering the costs of demonstratives would put counsel between a rock and hard place, and might cause reluctance amongst patent litigators to fully leverage available visual resources, thus compromising the presentation of the case. The court does not believe this outcome comports with the underlying intent of § 1920(4) or Federal Rule of Civil Procedure 54. Cf. United States v. Davis , No. 96-CR-912 (ERK), 2020 WL 2522079, at *1 (E.D.N.Y. May 18, 2020) ("Unquestionably the courts, in interpreting a statute, have some ‘scope for adopting a restricted rather than a literal or usual meaning of its words where acceptance of that meaning would lead to absurd results ... or would thwart the obvious purpose of the statute.’ ") (quoting Comm'r v. Brown , 380 U.S. 563, 571, 85 S.Ct. 1162, 14 L.Ed.2d 75 (1965) ).

In this case, Plaintiffs’ demonstratives and other models at trial effectively presented highly complex and technical evidence to the court and jury. Plaintiffs’ visual aids were indispensible to the jury's comprehension of the facts. As Plaintiffs note, demonstratives were used to display the accused products, "which are smaller than a grain of salt," and thus incapable of being shown to the jury without models and technology-assisted magnification. (Pls.’ Dmgs. Reply 8.) Plaintiffs also used demonstratives to show that Presidio's BB capacitors had "co-extensive" dielectric layers and "substantially L-shaped terminations," as required by the '791 and '547 Patents, respectively. (Id. ) Because Plaintiffs’ demonstratives and other visual aids were essential to facilitating the court and jury's comprehension, they are, broadly speaking, taxable.

Even so, at this juncture, the court will not award costs without additional information about billings for the demonstratives. In support of this motion, Plaintiffs attached invoices from CaseSight, Inc. ("CaseSight"), the vendor that prepared Plaintiffs’ demonstratives. (See ECF No. 230-18, CaseSight Invoices.) CaseSight's invoices provide generic billing descriptions that fail to specify whether the billed-for work product was necessary or used at trial. Descriptions like "Storyboard infringement demonstratives," "Infringement presentation," and "3D modeling of accused capacitors," while facially legitimate, shed little light on which demonstratives they relate to, and ultimately, why the hours spent on that project were reasonable and necessary.

To be clear, Plaintiffs need not account for each and every minute of CaseSight's time. But the court requires more visibility into CaseSight's contributions to justify the costs sought. This may be accomplished by a supplemental affidavit, preferably by a CaseSight professional with personal knowledge, itemizing the specific demonstratives CaseSight prepared, whether they were introduced at trial and for what purpose, and matching the line items in the invoices to specific demonstratives. Courts have demanded as much where the costs sought were comparable to, and even far below, the amounts requested here. See, e.g. , Endo , 331 F.R.D. at 581–82 (denying costs where plaintiffs "made no effort to link specific claimed costs [of $273,742.50] to specific trial exhibits or preparatory tasks, nor has it offered any other basis for determining what portion of its total claimed costs derive from unimaginative work like transcribing an audio file or enlarging a photograph."); Akiro LLC v. House of Cheatham Inc. , No. 12 CIV. 5775 JSR, 2013 WL 5548845, at *2 (S.D.N.Y. Sept. 27, 2013) (declining to award $1,412.07 for trial demonstratives where majority of demonstratives were not used at trial, and "even though the costs associated with unused demonstratives may still be awarded in some circumstances, defendants provide[d] no itemized list of all the demonstratives they purchased, and why they were all necessary."). The court thus denies, without prejudice, taxation of costs for the preparation and design of Plaintiffs’ demonstratives. Plaintiffs may move to tax these costs again, upon a more detailed showing. Following the new trial, if Plaintiffs seek further demonstrative-related costs incurred in connection with the damages trial, Plaintiffs will be required to demonstrate that such expenses are not duplicative of the costs sought here.

iii. Exhibit Database, Video Clips, and Technical Assistance

Plaintiffs also seek costs for CaseSight services unrelated to the preparation of demonstratives, namely, the creation of a trial exhibit database, digitizing of audio and visual recordings, and set-up and break-down of technology used during trial. (Pls.’ Dmgs. Mot. 15.) Costs for these services total $72,500. (Id. ; see also CaseSight invoices.)

These costs are taxable if they promoted "the efficient and effective presentation of evidence," DiBella , 407 F. Supp. 2d at 540, and therefore constituted "[f]ees for exemplification" under 28 U.S.C. § 1920(4) ; see Farberware Licensing Co. LLC v. Meyer Mktg. Co. , No. 09 CIV. 2570 (HB), 2009 WL 5173787, at *8 (S.D.N.Y. Dec. 30, 2009), aff'd , 428 F. App'x 97 (2d Cir. 2011) ("Here, the documentary exhibits were voluminous and the various visual aids that were presented at trial were helpful to the jury and the Court in focusing attention on the salient documents and concepts. Accordingly, Meyer is entitled to recover its reasonable costs for equipment and technological graphics."). On the other hand, the costs are not recoverable if they merely facilitated copying of exhibits for the convenience of counsel or the court. See Local Civil Rule 54.1(c)(5).

As with Plaintiffs’ demonstrative costs, the court requires more information. If Plaintiffs wish to recover the above-described costs, they must supply a supplemental affidavit detailing how CaseSight's digitization services, creation of an exhibit database, and technical assistance facilitated the trial, and link those services to specific invoice line items. The court is unsure what purpose the exhibit database served, other than as a readily-accessible repository of documents for counsel's convenience. Therefore, the affidavit should also clarify how the exhibit database aided the presentation of evidence at trial, in a way that the binder of trial exhibits, already taxed, did not. Plaintiffs’ motion to tax costs in this respect is therefore denied without prejudice.

iv. TIFF Conversion

Finally, Plaintiffs seek $4,186 in costs for converting native files to Tagged Image File Formats, or TIFFs,³³ in response to Presidio's discovery requests. (Pls.’ Dmgs. Mot. 16; ECF No. 230-19, Mintz Litigation Technology Support Invoices.) Courts consider sums spent converting native files to TIFFs as "costs of making copies of any materials" under section 1920(4). Balance Point , 305 F.R.D. at 73 ("By converting a native image into a different format, such as TIFF, one has simply duplicated the image and provided a new, modified copy."); accord Broadspring , 2016 WL 817449, at *7 ("Plaintiff may thus also tax the cost of electronic discovery that was made in response to Defendants’ request to convert files to TIFF before production."); see Race Tires Am., Inc. v. Hoosier Racing Tire Corp. , 674 F.3d 158, 166 (3d Cir. 2012) ("The most recent amendment to the statute, however, permitting an award to the prevailing party of the cost of making copies of ‘materials,’ plainly signifies that [ section] 1920(4) ’s allowance for copying costs is not limited to paper copying."). The court therefore awards in full Plaintiffs’ file conversion costs in response to Presidio's document requests.

33 TIFF is "[a] widely used and supported graphic file format[ ] for storing bit-mapped images, with many different compression formats and resolutions." Balance Point , 305 F.R.D. at 74 (quoting The Sedona Conference Glossary: E–Discovery & Digital Information Management 15 (4th ed. Apr. 2014)).

CONCLUSION

For the foregoing reasons, the court orders as follows:

(1) Defendant's Motion for Judgment as a Matter of Law or, alternatively, a New Trial, is DENIED in its entirety.

(2) Plaintiffs’ Motion for a New Trial or, alternatively, an Amended Judgment, is GRANTED in part, and DENIED in part. The court orders a new trial with respect to damages. The sole issue at trial will concern the appropriate royalty rate for both Patents-in-suit under the framework set forth in Georgia-Pacific v. U.S. Plywood Corp. , 318 F. Supp. 1116 (S.D.N.Y. 1970). The royalty rate(s) determined by the jury, or the undersigned in the event of a bench trial, will be applied to all infringing devices, pursuant to 35 U.S.C. § 284.

To further aid the fact-finder, the court hereby authorizes Plaintiffs to submit a revised expert report on damages to analyze hypothetical licensing negotiations between Presidio, on the one hand, and each of ATC and AVX, on the other. Defendant's damages expert may respond. The experts shall opine on the appropriate royalty rate for both Patents-in-suit. The parties are ordered to confer and file a joint letter within seven days of the entry of this Memorandum and Order, proposing a schedule for Plaintiffs’ revised expert report, Presidio's rebuttal, and Plaintiffs’ reply. Any motion practice relating to the revised expert report shall be presided over by the Magistrate Judge.

Plaintiffs’ motion is DENIED to the extent it seeks a new trial on the issue of lost profits, or an increase to the jury's damages award by amended judgment pursuant to Federal Rule of Civil Procedure 59(e).

(3) Plaintiffs’ Motion for Supplemental Damages, Pre- and Post-Judgment Interest, and Taxation of Costs, is GRANTED in part, and DENIED in part. Supplemental damages are denied, without prejudice, because there is no legally-binding royalty rate to apply to the additional infringing units. The additional infringing units will be incorporated into Plaintiffs’ royalty base in the new trial, potentially mooting the need for supplemental damages. If, following the new trial, Plaintiffs seek damages for any additional infringing units, the court will entertain Plaintiffs’ motion at that time.

Prejudgment interest is provisionally awarded at the three-month Treasury Bill rate, compounded annually. After the new trial concludes, the parties will confer and submit a stipulated judgment as to the precise amount of prejudgment interest, which shall be awarded from the time that the royalty payments would have been received for each Patent-in-suit, until the date of an amended final judgment on royalty damages.

Post-judgment interest is provisionally awarded at a rate equal to the weekly average one-year constant maturity Treasury yield, as published by the Board of Governors of the Federal Reserve System. 28 U.S.C. § 1961(a). The prejudgment and post-judgment interest rates shall be applied to Plaintiffs’ damages award following entry of judgment in the new trial.

The court taxes costs and awards Plaintiffs as follows:

• Docket and Miscellaneous Fees: $530.24 , comprised of the filing fee for the Complaint and the cost of serving Presidio with process.

• Trial and Deposition Transcripts: $49,847.20 for deposition and trial transcripts.

• Witnesses, Travel Expenses, and Subsistence: $11,804.59 in witness attendance fees, travel expenses, and subsistence costs.

• Photocopies, Printing, Demonstratives, and Technical Assistance: (i) $1060.99 for one set of trial exhibits; (ii) $0 for the preparation and design of Plaintiffs’ demonstratives, with leave to seek these costs again upon further substantiation; (iii) $0 for costs associated with creation of an exhibit database, video clips, and technical assistance, with leave to seek these costs again upon further substantiation; (iv) $4,186 in costs for converting native files to Tagged Image File Formats, or TIFFs. With respect to items (ii) and (iii), Plaintiffs must submit additional proof of such costs to the court no later than Monday, September 28, 2020.

Finally, the parties’ joint letter to the court regarding Plaintiffs’ revised expert report, due Wednesday, September 30, 2020, shall also set forth the parties’ plans to proceed with this case through the new trial. The letter should include proposed dates for the new trial, and state the parties’ interest in participating in good faith, settlement discussions, including a settlement conference before the Magistrate Judge.

SO ORDERED.