MEMORANDUM AND ORDER
John W. Lungstrum, United States District Judge
This patent infringement case was tried to a jury in this Court from February 13, 2017, through March 3, 2017. By its verdict, the jury found the following: that Time Warner Cable1 infringed each of the [1138]*1138asserted claims of the five Sprint patents at issue;, that none of those claims is invalid; that Sprint proved reasonable, royalty damages in the amount of $139,800,000; and that Time Warner Cable’s infringement was willful. By Memorandum and Order of March 14, 2017, the Court issued findings of fact and conclusions of law, by which it rejected Time Warner Cable’s equitable defenses and denied Sprint’s claim' for enhanced damages. See Sprint Communications Co. L.P. v. Time Warner Cable, Inc., 2017 WL 978107 (D. Kan. Mar. 14, 2017) (Lungstrum, J.). Also on March 14, 2017, the Court entered judgment in Sprint’s favor in the amount of the jury verdict (plus postjudgment interest and costs).
This matter presently comes before the Court on Time Warner Cable’s posttrial motion for judgment as a matter of law pursuant to Fed. R. Civ. P. 50(b) (Doc. #485). For the reasons set forth below, the Court denies the motion.2
This matter a]so comes before the Court on Sprint’s motion for an’ amendment of the judgment, pursuant to Fed. R. Civ. P. 59, to add an award of prejudgment interest (Doc. #483). The Court grants the motion in part, and it awards Sprint prejudgment interest in the amount of $6,183,548.00. The ■ Court will issue ’ an amended judgment accordingly.
I. Time Warner Cable’s Motion for Judgment as a Matter of Law
A. Governing Standard
Judgment as a matter of law under Fed. R. Civ. P. 50(b) is improper “unless the proof is all one way or so overwhelmingly preponderant in favor of the movant' as to permit no other rational conclusion.” See Crumpacker v. Kansas, Dept. of Human Resources, 474 F.3d 747, 751 (10th Cir. 2007). In determining whether judgment as a matter of law is proper, a court may not weigh the evidence, consider the credibility of witnesses, or substitute its judgment for that of the jury. See Sims v. Great American Life Ins. Co., 469 F.3d 870, 891 (10th Cir. 2006). In essence, a court must affirm a-jury verdict if, viewing the record in the light most favorable to the nonmoving party, the record contains evidence upon which the jury could properly return a verdict for the nonmoving party; See Bartee v. Michelin North America, Inc., 374 F.3d 906, 914 (10th Cir. 2004). Conversely, the court must enter judgment as a matter of law in favor of the moving party if “there is no legally sufficient evidentiary basis for a reasonable jury to find for the issue against that party." See Sims, 469 F.3d at 891.
B. Damages
1. Time Warner Cable requests judgment as a matter of law on Sprint’s claim for damages. .Time Warner Cable renews the “Catch-22” argument that it made in motions- at the close of Sprint’s case and after the submission of all evidence. The argument proceeds as follows: Sprint presented evidence of a reasonable royalty only through its damages expert, Dr. Mohan Rao, Dr. Rao declined to apportion damages among the patents at issue, based on his assumption (from Sprint’s technical expert, Dr. Stephen Wicker) that the patents were “blocking patents,” meaning that any VoIP-PSTN connection would infringe at least one of Sprint’s patents. Thus, Sprint -was required to prove the assumption that the [1139]*1139patents were blocking patents. If there was no such evidence, then there was no basis for Dr. Rao’s royalty opinion, and Sprint’s damages claim must fail. If, on the other hand, Sprint’s patents were blocking patents, then Time Warner Cable must also have infringed prior to the accused Go-It-Alone system, which was launched in 2010. In that .case, in which Time Warner Cable infringed going back as far as 2003, 2010 would not be an appropriate date for the hypothetical license negotiation that informs the royalty determination. Dr. Rao considered only a 2010 hypothetical negotiation; thus, if the use of that date was improper, Dr. Rao would have no royalty opinion. Either way, argues Time Warner Cable, Dr. Rao’s royalty opinion lacks support.
The Court concludes, however, that there is no Catch-22 here as argued by Time Warner Cable- The issue is whether there was sufficient evidence to support Dr. Rao’s assumption of blocking patents. In its answer to a special verdict interrogatory, the jury' found that Sprint had proved that the appropriate date for the hypothetical negotiation was 2010. The jury had been instructed (in an instruction that Time Warner Cable has not challenged) that “[a] reasonable royalty is the amount of royalty payment that [the parties] would have agreed to in a hypothetical negotiation taking place at a time prior to when the infringing use first began.” As the Court has previously noted, if the prior infringement was by a different product, the date of the hypothetical negotiation date would be at the start of the present infringement and not at the start of the prior infringement. See Sprint Communications Co. L.P. v. Comcast Cable Communications LLC, 225 F.Supp.3d 1233, 1253-54, 2016 WL 7079522, at *14 (D. Kan. Dec. 5, 2016) (Lungstrum, J.) (hereafter Daubert Order) (citing Fujifilm Corp. v. Motorola Mobility LLC, 2015 WL 1265009, at *3 (N.D. Cal. Mar. 19, 2015)). Time Warner Cable has not challenged the jury’s finding that 2010 was the appropriate negotiation date. Moreover, that finding is supported by evidence that Time Warner Cable’s Go-It-Alone product was a distinct product launched in 2010 that used differed equipment or architecture. Thus, the fact that the jury found 2010 to be the appropriate date for the hypothetical negotiation does not mean that Time Warner Cable’s, pre-2010 activities did or did not infringe Sprint’s patents. Indeed, as the Court noted at trial, there is no competent evidence from which the jury could have made such a determination, as neither party’s expert offered such an opinion concerning . Time Warner Cable’s pre-2010 products. Accordingly, the jury’s finding and Dr. Rao’s use of a 2010 date does not mean that the patents could not be blocking patents, which in turn means that Sprint’s- positions are not irreconcilable and there is no Catch-22.
Addressing the relevant question, the Court- concludes that there was evidence presented at trial to support Dr. Rao’s assumption that Sprint’s patents were blocking patents. As noted above, Dr. Rao relied on Dr. Wicker for that assumption, and Dr. Wicker testified that there were no non-infringing alternatives for Time Warner Cable’s system in 2010. Time Warner Cable argues that Dr. Wicker did not testify that there were no non-infringing alternatives, but ¡that he addressed only particular alternatives proposed by Time Warner Cable’s experts .in discovery. At the conclusion of that testimony, however, Dr, Wicker testified that he did not find any acceptable non-infringing- alternatives “in general.” Viewed in the light most .favorable to Sprint, the non-moving party, this testimony provides evidence that there were no non-infringing alternatives. Time Warner Cable argues that Dr. Wicker failed to consider Time Warner Cable’s pre-2010 systems as alternatives, but Time [1140]*1140Warner Cable'was free to raise that issue in cross-examining Dr. Wicker or through its own expert, and it did neither. Thus, Dr. Wicker’s testimony that there were no non-infringing alternatives stood unrebut-ted. Moreover, under Time Warner Cable’s central argument, those pre-2010 activities also infringed and thus they would not have been non-infringing alternatives.
Time Warner Cable also argues that the lack of non-infringing alternatives does not mean that the patents were blocking patents as assumed by Dr. Rao. Time Warner Cable argues that the standard for non-infringing alternatives is narrower, in that such alternatives must be available and acceptable. In fact, the jury was instructed (in an instruction not challenged by Time Warner Cable) that it could consider evidence concerning the availability of a non-infringing alternative, which must be an acceptable product (with no mention of availability). A reasonable interpretation of blocking patents as used by Dr. Rao would be that any acceptable product would infringe Sprint’s patents. Thus, considered in the light most favorable to Sprint, the evidence was sufficient to allow the jury to find reasonably that Dr. Rao’s assumption had been proved and thus to accept Dr. Rao’s royalty opinion. The Court therefore denies Time Warner Cable’s motion for judgment on this basis.
2. Time Warner Cable also renews its argument — vdiich the Court has repeatedly rejected — that Dr. Rao’s royalty opinion-was improper and represented “junk science” because it was based on the verdict in the Vohage case, in which Sprint’s damages expert employed a 25-percent rule that the Federal Circuit has since ruled unreliable. As the Court has previously explained, Dr. Rao did not use the 25-percent rule in forming his royalty opinion in this case; in Vonage, the jury heard different damages opinions, and it did not find damages in accord with the opinion of Sprint’s damages expert; and the verdict represents a piece of information that the parties might have considered in a hypothetical license negotiation. See, e.g., Daubert Order, 225 F.Supp.3d at 1248-50, 2016 WL 7079522, at *9-10. Time Warner Cable has not provided authority that suggests that the verdict could not be used here. Nor has Time Warner Cable addressed the Court’s reasoning in consistently rejecting this argument. Therefore, the Court rejects this argument once again, and it denies the motion for judgment on this basis.
8. Finally, in a footnote, Time Warner Cable reasserts various failed arguments from its Daubert motion and its motions in limine. Time Warner Cable has not provided any basis for reconsideration of those earlier rulings, however (the footnote is devoid of argument), and therefore the Court summarily denies any such request for relief.
C. Infringement
Time Warner Cable moves for judgment as a matter of law on Sprint’s claims for patent infringement. The jury found that Time Warner Cable infringed five Sprint patents. Time Warner Cable argues that Sprint failed in its proof with respect to nine particular claim limitations, which the Court addresses in turn.
1. Time Warner Cable asserts that Sprint failed to prove satisfaction of the “in response to” limitation found in four of the patents. In general, that limitation requires conversion or transfer of a voice communication “in response to” receiving a particular message. Time Warner Cable essentially argues that the conversion or transfer in its system is not “in response to” the receipt of the message because other steps are required after receipt for the conversion or transfer to occur. The Court rejects this argument.
In its claim construction order, the Court rejected Time Warner Cable’s pro[1141]*1141posed construction that would require the action taken “in response to” something be taken immediately; it noted that the term requires only some concept of causation, not immediacy; and it declined to construe the term. See Sprint Communications Co. L.P. v. Comcast Cable Communications LLC, 2014 WL 5089402, at *25 (D. Kan. Oct. 9, 2014) (Lungstrum, J.) (hereafter Markman Order). Thus, there is no additional limitation requiring that the conversion or transfer be “in response, to” the receipt of the message without any intervening steps or without any additional causes. Under the plain meaning of the term, the conversion or transfer could be “in response to” the receipt of the message even if other steps are also required for that conversion or transfer. Dr. Wicker provided specific testimony that this limitation as found in the four patents was satisfied by the accused system, and that testimony must be credited for purposes of this motion and provides a sufficient basis for the jury’s verdict.
2. Time Warner Cable asserts that Sprint failed to prove satisfaction of the “asynchronous communication” term in three patents. In the claim construction process, the Court was not asked to construe this term; and in declining to construe the term “asynchronous communication system,” the Court noted that the plain meaning of “asynchronous communication” was a communication in which the transmitting and receiving devices do not share a common clock. See Markman Order, 2014 WL 5089402, at *20. At trial, Sprint provided sufficient evidence that this term was satisfied in the accused system, as Dr. Wicker testified that the relevant communications were asynchronous because there was no strict timing relationship in Time Warner Cable’s managed IP network;3
Time Warner Cable • argues that the communications' were not asynchronous because they also passed through the DOCSIS network in Time Warner Cable’s system, which network used shared clocks. That argument goes to the weight of Dr. Wicker’s opinion only. Time Warner Cable did make that argument at trial, but the jury rejected it by its "verdict. The Court cannot conclude as a matter of law that this limitation was not satisfied, as Sprint did provide evidence to the contrary. Accordingly, the Court rejects this argument for judgment as a matter of law.
3. Time Warner Cable asserts that Sprint failed to prove satisfaction of the “processing ... to. select” limitation in three patents. In its claim construction order, the Court rejected Time Warner Cable’s proposed limitation that would have required the processing element actually to make the selection, and it instead construed this term to mean “processing ... to participate in the selecting.” See Markman Order, 2014 WL 5089402, at *14-15. Time Warner Cable now argues that other elements, not the processing element, actually make the selection of the network code or identifier in the accused system. Time Warner Cable has not explained, however, why the processing element does not participate in the selecting, in accordance with the Court’s construction. Sprint offered evidence, in the form of testimony by Dr. Wicker, that this limitation was satisfied in Time Warner Cable’s system. Thus, the Court rejects this argument for judgment as a matter. of law.4
[1142]*11424. Time Warner Gable asserts that Sprint failed to prove satisfaction of the “interworking unit” limitation found in three patents, which the Court construed to mean an “ATM interworking multiplexer.” See id. at *15-17. The jury found that the relevant claims were not literally infringed but. were infringed under the doctrine of equivalents. The Court instructed the jury with respect to equivalence as follows:
You may find that an element or step is equivalent to a requirement of a claim that is not met literally if a person having ordinary skill in the field of technology of the patent would have considered the differences between them to be “insubstantial” or would have found that the structure or action: (1) performs substantially the same function and (2) works in substantially the same way (3) to achieve substantially the same result as the requirement of the claim".
•The known" interchangeability of substitutes for an element of a patent claim also is a factor that bears upon whether an accused structure or action is substantially the same as the claimed structure or action. In order for the structure or action to be considered interchangeable, the structure of action must have been known at the time of the "alleged infringement to á person having ordinary skill in the field of technology of the patent.
Time Warner Cable argues that Sprint did not present sufficient evidence that the accused media gateway was equivalent to an ATM interworking multiplexer. The Court disagrees'. First, Dr. Wicker testified that the gateway satisfied "the function-way-result test referenced in the instruction. The Court does not" agree with Time Warner Cable that that-testimony was impermissibly conclusory,- as Dr. Wicker explained why he believed the two devices’ functions and results were identical and the ways were not’ substantially different. Dr. Wicker also testified that there was'known’interchangeability because different card's could be swapped into "the gateway. Time Warner Cable cites its own contrary evidence concerning the cards, but that dispute was properly ad-, dressed to the jury, which found equivalence here. The Court concludes that Sprint’s evidence ori this issue was sufficient, and it therefore denies this basis for judgment as a matter of law.
5. Time Warner Cable asserts that' Sprint failed to prove satisfaction of the “identifier” term in two patents. Tipie Warner Cable argues that the identifiers here must be VPI/VCl connections and that Sprint has not shown that the accused system had ATM identifiers. The Court rejects this argument, as the Court did not construe this term to add such a limitation. Time Warner Cable repeats its argument that because ATM "technology is required by the claims (by virtue of the “interwork-ing unit” construction), other elements must be ATM as well. In its claim construction order, the Court explained why it refused to construe “identifier” (which term is generally absent from the patents’ specification) to add such a limitation. See id. at *18. The Court again rejected this argument at the summary judgment stage, as follows:
Thus, under the Court’s constructions, the scope of the claims match the patents’ specifications, as a term is limited [1143]*1143to ATM technology only if the specification has done so. The specification does not make clear that the inventions are limited to ATM technology, other than by limiting the inventions to .the use of an ATM interworking multiplexer.
See Sprint Communications Co. L.P. v. Comcast Cable Communications LLC, 2016 WL 7052065, at *4 (D. Kan. Dec. 5, 2016) (Lungstrum, J.) (hereafter Summary Judgment Order). Thus, the fact that Sprint did not prove satisfaction of an additional limitation contrary to the Court’s claim constructions does not provide a basis for judgment for Time Warner Cable.
6. Time Warner Cable asserts that Sprint failed to prove satisfaction of the “narrowband system” limitation in two patents. Time Warner. Cable argués that the pertinent signaling passes through a Syniverse device, which is not a narrow-band system. Dr. Wicker specifically addressed and rejected this argument at trial, however, as did the jury in finding for Sprint. Dr. Wicker’s testimony is sufficient to support the jury’s verdict with respect to this issue.
7. Time Warner Cable asserts that Sprint failed to prove satisfaction of the “egress” limitation in two patents. The relevant claims refer to the user communication’s egress “from the packet communication system.” With respect to this limitation, Time Warner Cable 'argues that Sprint has failed to show that the communication egresses to another network. Time Warner Cable cites the patents’ specification for that requirement of egress to another network. The patént claims contain no such requirement, however, and it is too late for Time Warner Cable propose a new construction based on the specification. Time Warner Cable failed to propose such a construction at the claim construction stage or at trial, and thus Sprint was not required to show satisfaction of any additional limitation. The Court therefore rejects this basis for judgment ■ argued by Time Warner Cable.
8. Time Warner Cable asserts that Sprint failed to prove satisfaction’ of the ’064 Patent’s step of “converting the asynchronous communication into a user communication.” Time Warner Cable argues that Sprint has failed to show a conversion from something that wás hot a user communication to something that was. Dr. Wicker testified, however, that in the accused system IP packets (the asynchronous communications) are converted into TDM (a form for the PSTN)' (the user communication). That testimony is sufficient to meet the plain language‘of the claim, and the Court therefore rejects this argument for judgment.
9. Time Warner Cable asserts that Sprint failed to prove satisfaction of the limitation in the two patents requiring transfer to the packet communication system (PCS). Time Warner Cable argues that because the transferring element is contained within the PCS, there can be no transfer to the PCS. Time Warner Cable made the same argument at the claim construction stage. In its ruling at that time, the Court, in construing the terms “transmitting”, “receiving”, and “transferring”, declined to impose a limitation that would prohibit one of the two elements involved in the transfer from being part of the other. See Markman Order, 2014 WL 5089402, at *27-28. In so ruling, the Court noted that the relevant specification did not support such a limitation, as the specification indicated that the processing system (the transferring element) could be integrated into the packet-based network (the receiving element). See id. at *28. Time Warner Cable has not addressed that language from the specification in arguing again that the transferring element cannot be part of the receiving element. [1144]*1144Moreover, the Court further stated in its claim construction ruling that it could not impose the limitation urged by Time Warner Cable without a specific argument based on the particular transferring and receiving elements. See id. Although Com-cast made such a specific argument in another case with respect to a different patent at thq summary judgment stage, Time Warner Cable did not do so with respect to these two patents in this case prior to or at trial. Accordingly, the Court confirms its prior ruling that, under them plain language, these patent claims do not include the additional limitation urged by Time Warner Cable, and the Court therefore rejects this argument for judgment as a matter of law.
D. Invalidity — Written Description Requirement
At trial, Time Warner Cable asserted that each patent claim at issue was invalid for failure to satisfy the written description requirement of 35 U.S.C. § 112. With respect to each claim, the jury found that Time Warner Cable had, failed to meet its burden to show such invalidity by clear and convincing evidence. Time Warner Cable now argues that its is entitled to judgment as a matter of law on this invalidity defense.
1. Time Warner Cable argues that the so-called Call Control Patents (the ’561 Patent and the ’052 Patent) are invalid because the relevant specification discloses an ATM switch that did not exist at the time of the patent applications. During trial, the Court- excluded testimony from one witness relating to the existence of such a switch, but Time Warner Cable’s technical expert, Dr. Paul Min, was subsequently permitted to testify that such a switch did not exist and that the inventor therefore did not possess his invention as required.
The Court rejects this argument. Time Warner Cable has not cited any authority indicating that a patent is invalid if something disclosed in the specification did not exist. Rather, the authority on which Time Warner Cable relies indicates that the specification must show possession of the invention claimed in the patent. See, e.g., Novozymes A/S v. DuPont Nutrition Biosciences APS, 723 F.3d 1336, 1344 (Fed. Cir. 2013). As the Court pointed out in its ruling excluding testimony from one fact witness, the patent claims here do not require the use of an ATM switch. Thus, the fact that no such switch existed is not dispositive.
Time Warner Cable argues in its reply that the claims do require a packet communication system and that the only disclosed embodiment of such a system in the specification uses an ATM switch. Again, however, Time Warner Cable has not supported that argument with relevant authority. At trial, the Court instructed the jury on the relevant law as follows:
A patent must contain a written description of the system or method claimed in the patent. In order to satisfy the written description requirement, the patent specification must describe each and every limitation of a patent claim, although the exact words found in the claim need not be used.
The written description requirement is satisfied if a person of ordinary skill in the field, reading the patent application as originally filed, would recognize that the patent application described the invention as finally claimed in the patent.
The written description requirement may be satisfied by any combination of the words, structures, figures, diagrams, formulas, etc., contained in the patent application. The full scope of a claim or any particular requirement in a claim need not be expressly disclosed in the [1145]*1145original patent application if a person having ordinary skill in the field of technology of the patent at the time of filing would have understood that the full scope or missing requirement is in the written description in the patent application. The specification need not describe in detail all possible examples to satisfy the written description requirement.
Time Warner Cable has not argued that the Court erred in giving this instruction. Thus, the jury was properly instructed that the full scope of the claim need not be expressly disclosed in the specification, so long as a person skilled in the art would have understood the scope of the claim. Nor must the specification describe all possible examples. Therefore, the fact that the embodiments do not include a system without an ATM switch is not dispositive and does not require judgment as a matter of law in Time Warner Cable’s favor.5-
2. Time Warner Cable next argues that the Call Control Patents should be deemed invalid as a matter of law because, although the patent claims are broad enough to cover an IP network without fixed end-to-end paths or separate signaling networks, the specification does not describe such an IP network. The Court rejects this argument as well. Time Warner Cable bore the burden to prove this defense by clear and convincing evidence, and the jury was entitled to reject this defense. Sprint cross-examined Dr. Min at some length, and the jury was entitled not to credit his expert testimony. Moreover, Dr. Wicker addressed and refuted these specific opinions by Dr. Min, and such evidence is sufficient to support the jury’s decision to reject this defense.
Time Warner Cable is essentially arguing that the specification had to disclose and describe all possibilities covered by the patent claims, but it has not cited any authority suggesting that the written description requirement must be applied in that way. Rather, under the law as explained to the jury, the specification must describe the invention claimed by the inventor, and the issue is whether one skilled in the art would recognize that the invention as claimed has been described. At trial, the parties offered contrary expert opinions, as Dr. Wicker testified that one skilled in the art would recognize from the specification that the claimed invention was not limited to the use of a fixed end-to-end path or the use of a separate signaling network. A reasonable jury could have credited that testimony over Dr. Min’s opinions. Therefore, the.Court denies the motion for judgment as a matter of law -on the issue of the written description requirement as applied to the Call Control Patents.
3. Time Warner Cable also argues as a matter 'of law that the so-called Broadband Patents (the ’064 Patent, the ’084 Patent, and' the ’429 Patent) are invalid for failure to satisfy the written description requirement. Time Warner Cable notes that under the Court’s claim constructions, the elements of “identifier”, “routing”, and “asynchronous communication” are not limited to ATM, and it argues that the specification discloses only ATM examples for those elements. The Court rejects this argument. Again, as the jury was instructed, the specification need not describe every possible covered example, as long as one skilled in the art would recognize from the specification that the invention is not so limited. Sprint did present evidence on this issue that supports the jury’s decision to reject this defense, as Dr. Wicker testified that one skilled in [1146]*1146the art would understand that those elements are not limited to ATM.
Time Warner Cable argues that Sprint has improperly relied on the Broadband Patent specification’s incorporation of the Call Control Patent specification. The cases cited by Time Warner Cable, however, db not prohibit such incorporation of one specification by another. Rather, the requirement is that the incorporating document identify clearly the particular material incorporated. See Hollmer v. Harari, 681 F.3d 1351, 1357 (Fed. Cir. 2012). With respect to the written description requirement, the question of' incorporation is viewed from the position of one skilled in the art. See id: As conceded by Time Warner Cable, the Broadband specification explicitly incorporates the Call Control specification.- Moreover, both Dr. Min and Dr. Wicker testified to such' incorporation. Thus, there is no basis to preclude consideration of the Call Control specification.in determining the validity of the Broadband Patents.
Time Warner Cable notes that the Court sustained an objection at trial to testimony by Dr. Wicker concerning his, reliance on the incorporation of the Call Control specification. In that instance, the. Court excluded one piece of testimony because that particular opinion had not been disclosed in Dr. Wicker’s expert reports. The Court did not strike any other testimony, however, in which Dr. Wicker had offered opinions without objection, Indeed, prior to the one objection made by Time Warner Cable, Dr. Wicker had testified without objection about how, in light of the incorporation, both specifications could be considered in determining the Broadband Patents’ satisfaction of the written description requirement. Dr. Min also conceded on cross-examination, without objection by Time Warner Cable, that both specifications applied to the Broadband Patents. Thus, despite the Court’s sustaining one objection, there was still sufficient evidence admitted at trial, including Dr. Wicker’s testimony that both specifications generally were not limited to ATM, to support the jury’s rejection of this argument by Time Warner Cable.
Finally, even if Dr. Wicker had been prohibited from relying on the Call Control specification, the result would not change, as Dr. Wicker specifically testified that the Broadband specification was not limited to ATM for these three particular elements!
. Accordingly, Time Warner Cable is not entitled to judgment as a matter of law simply because the Broadband specification shows ATM versions of these elements. As the Court has ruled repeatedly, because the specification limits the invention to ATM only with respect to the inter-working unit, other elements are not construed as limited to ATM. Thus, the jury’s implicit finding that the specification does not limit those elements to ATM is consistent and reasonable, Ultimately, Time Warner Cable’s defense presented a question of fact concerning how one skilled in the art would have understood the specification. Dr, Min’s opinions on that question were challenged in-cross-examination and in - Dr. Wicker’s contrary testimony, and the jury was entitled to reject Dr. Min’s testimony and find that.Time Warner Cable had not-- sustained its heightened burden of proof. The Court therefore denies the motion for judgment as a matter of law on this defense as applied to the Broadband Patents.
E. Invalidity — Anticipation or Obviousness
At trial, Time Warner Óable asserted that each patent claim at issue was invalid as obvious in light of two pieces of prior art, and it further asserted that most of the patent claims were invalid as anticipated in -light of one of those pieces of [1147]*1147prior art. The jury found in favor of Sprint on each of those assertions. In rather cursory fashion (in less than one page in its initial brief), Time Warner Cable now seeks judgment as a matter of law on those invalidity defenses, arguing that no reasonable jury could have found in favor qf Sprint. The Court rejects that argument. Time Warner Cable concedes that it had the burden at trial to prove these invalidity defenses by clear and convincing evidence. Time Warner Cable points to its own evidence on these issues, but that evidence was not unrebutted, as Dr. Wicker testified at some length that the disclosures in the asserted prior art were insufficient.6 In light of that evidence, the Court concludes that the jury could reasonably have found that Time Warner Cable failed to sustain its heightened burden of proof on these issues.
F. Willfulness
Finally, Time Warner Cable moves for judgment as a matter of law with respect to the issue of willfulness, which the jury found in' Sprint’s favor. Time Warner Cable has not explained why the Court should address this issue, however, which has become moot in light of the - Court’s denial of Sprint’s claim for enhanced damages. See Presidio Components, Inc. v. American Tech. Ceramics Corp., 2016 WL 4377096, at *10 (S.D. Cal. Aug. 17, 2016) (noting that the defendant’s posttrial motion for judgment as a matter of law on the issue of willfulness was essentially moot in light of the court’s decision not to award enhanced damages), appeal filed (Fed. Cir. Aug. 17, 2016).
Moreover, sufficient evidence of willful infringement was presented at trial. With respect to willfulness, the Court instructed the jury in relevant part as follows:
. In order to prove willful infringement, Sprint must prove, by a preponderance of the evidence, that Time Warner Cable knew or believed, or it was so obvious that it should have known, that there was a high likelihood that it was infringing a valid patent. In making that determination, you should consider all facts relating to Time Warner Cable’s knowl- ■ edge at the time it performed acts of infringement.
With respect to this question of willfulness, you are instructed that; under ' the law, Time Warner Cable had no duty to obtain any opinions of counsel.7
As discussed above, sufficient' evidence supports the jury’s findings of infringement and validity. The jury also heard evidence that Time Warner Cable was aware of Sprint’s patents. For instance, as noted by the Court in its posttrial findings and conclusions, Sprint presented credible evidence that . the .parties discussed Sprint’s patents, that Time Warner Cable monitored Sprint’s. infringement suit against Vonage, and that Time Warner Cable subsequently investigated Sprint’s patents. See Sprint v. Time Warner Cable, 2017 WL 978107, at *4-7. Thus, the jury reasonably could have found that Time [1148]*1148Warner Cable should have known of a high likelihood that it was infringing a valid patent. See i4i Ltd. Partnership v. Microsoft Corp., 598 F.3d 831, 860 (Fed. Cir. 2010) (evidence that the defendant knew about the patent and the plaintiffs product that practiced the patent supported the jury’s finding on this Seagate prong), aff'd on other grounds, 564 U.S. 91, 131 S.Ct. 2238, 180 L.Ed.2d 131 (2011). Accordingly, the Court denies the motion for judgment as a matter of law on the issue of willfulness.
II. Sprint’s Motion for Prejudgment Interest
Sprint moves to amend the judgment pursuant to Fed. R. Civ. P. 59(e) to add an award of prejudgment interest. 35 U.S.C. § 284 provides that a court should award damages for patent infringement “together with interest and costs as fixed by the court.” See id. The Supreme Court has set forth'the relevant standard:
The standard governing the award of prejudgment interest under § 284 should be consistent with Congress’ overriding purpose of affording patent owners complete compensation. In light of that purpose, we conclude that prejudgment interest should ordinarily be awarded. In the typical case an award of prejudgment interest is necessary to ensure that the patent owner is placed in as good a position as he would have been in had the infringer entered into a -reasonable royalty agreement. An award of interest from- the time that the royalty payments would have been received merely serves to make the patent owner whole, since his damages consist not only of the value of the royalty payments but also the foregone use of the money-between the time of infringement and the date of the judgment.
See General Motors Corp. v. Devex Corp., 461 U.S. 648, 655-56, 103 S.Ct. 2058, 76 L.Ed.2d 211 (1983) (footnote omitted). As Time Warner Cable notes, the Supreme Court further stated in General Motors that an award of prejudgment interest is not' required whenever infringement is found; that the court has some discretion in awarding interest; and that it may be appropriate to limit or deny interest, as when the patent owner has unduly delayed in prosecuting the lawsuit. See id at 656-57, 103 S.Ct. 2058. Thus, “prejudgment interest should be awarded under § 284 absent some justification for withholding such an award.” See id. at 657, 103 S.Ct. 2058.
Time Warner Cable makes two arguments for a denial of interest in this case. First, Time Warner Cable cites the Court’s statement, in its ruling denying enhanced damages, that the jury’s award adequately compensates Sprint for the infringement. See Time Warner Cable, 2017 WL 978107, at *14. The Court denied enhanced damages, however, because it concluded that this case was not egregious; see id, and its purpose was to state that the. jury’s verdict represented adequate compensation purely for the royalty it should have received in 2010. The Court did not, by that statement, address whether Sprint also lost the use of that money after that date. In fact, as in the typical case, a 2017 award would not fully compensate Sprint unless it received compensation for that time value. Second, Time Warner Cable argues that the Court should consider that Sprint did not initiate this suit until 14 months after the infringement began when Time Warner Cable’s Go-It-Alone system was launched on October 1, 2010. As it did in its posttrial findings, however, the Court finds that Sprint did not delay unreasonably in initiating this suit. See id. at *8-10; see also General Motors, 461 U.S. at 657 n.11, 103 S.Ct. 2058 (determination whether the plaintiff unduly delayed prosecution of the suit is committed to the discretion of the [1149]*1149district court). Accordingly, the Court, in its discretion, rules that there is no basis for departing from the usual rule here and that an award of prejudgment interest is therefore appropriate in this case.
Sprint requests prejudgment interest from October 1, 2010, when the accused system was launched. Without citation to any authority, Time Warner Cable suggests that interest should run only from the filing of this action. In General Motors, however, the Supreme Court specifically referred to an award of interest from the time of infringement to the date of judgment, and it noted that the purpose of such interest is to place the patent owner in the position it would have been in under a reasonable royalty agreement. See General Motors, 461 U.S. at 655-56, 103 S.Ct. 2058. As the Court instructed the jury in this case, damages are set by reference to a hypothetical license negotiation occurring just prior to the date of infringement. Thus, the Court will award prejudgment interest running from October 1, 2010, as requested by Sprint.
“Because there is no federal statutory interest rate on prejudgment interest, the rate imposed [is] left to the trial court’s discretion.” See Kleier Advertising, Inc. v. Premier Pontiac, Inc., 921 F.2d 1036, 1042 n.4 (10th Cir. 1990).8 Sprint proposes that the Court award interest at a prime interest rate ranging from 3.25 to 3.59 percent oyer the interest period. Sprint argues that such a rate is appropriate because it borrowed heavily during the interest period and could have avoided some of that borrowing if it had received money under a licensing agreement. In the alternative, Sprint seeks an award at the applicable postjudgment interest rate of 1.06 percent. Time Warner Cable argues that the postjudgment rate should be used.
The Court applies- its discretion here, but it takes; its cue from statements by the Tenth Circuit in Kleier. That court stated that the fate'was left to the trial court’s discretion,'but it nevertheless noted that the Seventh Circuit had in one case suggested use of the prime rate,- while the Ninth Circuit had in another case suggested using the 52-week Treasury bill rate. See id. In its case, however, the Seventh Circuit chose the prime rate over the post-judgment Treasury rate to account for the risk of default. See Gorenstein Enters., Inc. v. Quality Care-USA, Inc., 874 F.2d 431, 436-37 (7th Cir. 1989) (cited in Kleier ). In the other case cited in Kleier, the Ninth Circuit, in ordering that the Treasury rate be applied (unless the district court concluded that the equities demanded a different rate), noted the award’s purpose in not allowing the defendant to keep the income, earned on the money it effectively withheld from the plaintiff. See Frank Music Corp. v. Metro-Goldwyn-Mayer Inc., 886 F.2d 1545, 1552 (9th Cir. 1989) (cited in Kleier). There does not appear to be any risk of default by Time Warner Cable in this case; thus, the rate selected by the Ninth Circuit seems more appropriate here.
Moreover, as this; Court noted in-a recent case, courts in this district “have consistently applied the federal postjudgment interest rate set by 28 U.S.C. § 1961 in awarding prejudgment interest on federal claims.” See Marten Tranport, Ltd. v. PlattForm Advertising, Inc., 2016 WL 4000927, at *19 (D. Kan. July 26, 2016) (Lungstrum, J.) (citing cases), appeal filed (10th Cir. Aug. 23, 2016). Sprint notes that the Court applied the postjudgment rate in Marten because the plaintiff had not provided any reason for not applying that rate [1150]*1150there, see id., and it argues that there is such a reason here, namely Sprint’s borrowing during the .interest period. The Court is unwilling to,wade into and assess Sprint’s financial condition during that.period, however. The Court ■ concludes that application of an earning rate and not a borrowing rate is more appropriate here. Thus, the Court will apply the post-judgment rate also in awarding prejudgment interest in this case.
The parties agree that a rate of 1.06 percent (the rate used in the original judgment entered in this case) is the appropriate postjudgment interest rate. Applying that rate, Sprint (by way of an affidavit by its damages expert, Dr. Rao) calculates prejudgment interest in the ’ amount of $6,188,548.00 on damages from October 1, 2010, to the date of the original judgment, March 14, 2017. Time Warner Cable does not take issue'with that calculation. Thus, the Court in its discretion awards Sprint prejudgment interest in that amount, and it will issue an amended judgment' nunc pro twne in the total amount of $145,983,548.00.
Sprint ' also' argues that any post-judgment interest should be calculated on the total judgment that includes the -award of prejudgment interest. Time Warner Cable has not opposed this request, and the Court agrees that it is appropriate to determine postjudgment interest in that fashion, as will be made apparent in the amended judgment.9
IT IS THEREFORE ORDERED BY THE COURT THAT defendants’ posttrial motion' for judgment as a matter of law pursuant to Fed. R. Civ., P. 50(b) or for a new trial (Doc. #485) is hereby denied.
IT IS FURTHER ORDERED BY THE COURT THAT plaintiffs motion for an amendment of the judgment, .pursuant to Fed. R. Civ. P. 59, to add an award of prejudgment interest (Doc.- # 483) is hereby’ granted in part. The Court awards prejudgment interest to plaintiff in the amount of $6,183,548.00, and the Court will issue an amended judgment accordingly.
IT IS SO ORDERED.