  United States Court of Appeals
      for the Federal Circuit
              __________________________

    ENERGY TRANSPORTATION GROUP, INC.,
            Plaintiff-Cross Appellant,
                           v.
  WILLIAM DEMANT HOLDING A/S, WDH INC.,
 OTICON INC., OTICON A/S, BERNAFON AG, AND
               BERNAFON LLC,
             Defendants-Appellants,
                          AND

         WIDEX A/S AND WIDEX USA, INC.,
              Defendants-Appellants.
              __________________________

                2011-1487, -1488, -1489
              __________________________

    Appeals from the United States District Court for the
District of Delaware in Case No. 05-CV-0422, Chief Judge
Gregory M. Sleet.
               ___________________________

               Decided: October 12, 2012
              ___________________________

    BRIAN M. BUROKER, Gibson, Dunn & Crutcher, LLP,
of Washington, DC, argued for plaintiff-cross appellant.
Of counsel on the brief were MAYA M. ECKSTEIN, Hunton
& Williams LLP, of Richmond, Virginia; and YISUN SONG
and DANIEL G. VIVARELLI, JR., of Washington, DC; and
ENERGY TRANSPORT   v. WILLIAM DEMANT                      2


MARTY STEINBERG, Hunton & Williams, LLP, of Miami,
Florida.

    ROBERT GREENE STERNE, Sterne, Kessler, Goldstein,
& Fox, PLLC, of Washington, DC, argued for defendants-
appellants, William Demant Holding A/S, et al. With him
on the brief were JON E. WRIGHT, BRYON L. PICKARD and
JENNIFER S. BISK.

    WILLIAM H. MANDIR, Sughrue Mion, PLLC, of Wash-
ington, DC, argued for defendants-appellants, Widex A/S,
et al. With him on the brief were DAVID J. CUSHING, CARL
J. PELLEGRINI and JOHN B. SCHERLING. Of counsel were J.
WARREN LYTLE, JR. and BRIAN KENNETH SHELTON.
               __________________________

Before RADER, Chief Judge, and PLAGER and LINN, Circuit
                       Judges.
RADER, Chief Judge.
    The United States District Court for the District of
Delaware declined to order a new trial or relief from
judgment after a jury found that Defendants-Appellants
William Demant Holding A/S, WDH Inc., Oticon Inc.,
Oticon A/S, Bernafon AG, and Bernafon LLC (collectively
“Demant”) and Widex A/S and Widex USA, Inc. (collec-
tively “Widex”) infringed U.S. Patent No. 4,731,850 (“’850
Patent”). Energy Transportation Group, Inc. v. Sonic
Innovations, Inc., No. 05-422, 2011 U.S. Dist. LEXIS
60716 (D. Del. June 7, 2011). Demant and Widex (collec-
tively “Defendants”) appeal. Widex also appeals the
district court’s denial of its motion for JMOL of no willful
infringement. Plaintiff-Cross Appellant Energy Trans-
portation Group, Inc. (“ETG”) cross-appeals the district
court’s grant of JMOL of noninfringement of U.S. Patent
No. 4,879,749 (“’749 Patent”) on the basis that prosecution
3                     ENERGY TRANSPORT    v. WILLIAM DEMANT


history estoppel barred the jury’s finding of infringement
under the doctrine of equivalents. After a review of the
record, this court affirms.
                              I
    The ’749 Patent and the ’850 Patent, the “ETG Pat-
ents,” relate to technology for reducing acoustic feedback
in a programmable digital hearing aid. All hearing aids
have the same basic components: 1) a microphone that
picks up sound and converts it to an electrical signal, 2) a
speaker (also called a “receiver”) that converts the electric
signal back into sound waves, and 3) sound processing
circuitry, such as amplifiers and filters, located between
the microphone and speaker that adjusts the received
sound to compensate for any hearing impairment. The
path that sound travels from the microphone to the
speaker is called the “transmission channel” or “forward
path.” Some of the amplified sound from the hearing aid
speaker may also travel back to the microphone via an
“acoustic feedback path.” This unwanted sound then
“feeds back to the input” of the hearing aid and is ampli-
fied along with all other sound arriving at the input
microphone. The resulting vicious cycle of amplification
causes the unbearable whistling sound known as “feed-
back.”
    The ETG Patents share a common specification with a
priority date of June 1986. The specification describes a
method of reducing feedback by creating an electrical
feedback path and inserting a programmable filter in that
path to mimic the effects of acoustic feedback on the
phase and amplitude of a sound signal in the transmis-
sion channel. This electrical feedback signal then cancels
the acoustic feedback signal. ’850 Patent, col. 3, ll. 3–8.
Claim 14 is representative of the asserted method claims
of the ’850 Patent, and reads:
ENERGY TRANSPORT   v. WILLIAM DEMANT                       4


   14. A method of reducing acoustic feedback in a
   hearing aid comprising a microphone, a receiver
   fitted in an ear of a wearer of the aid, and a signal
   transmission channel interposed between said mi-
   crophone and transducer, comprising the steps of
   determining the effect on the amplitude and
   phase of a signal in said transmission chan-
   nel as a function of frequency of acoustic feedback
   between said receiver and microphone, and
   inserting between the input and output of said
   transmission channel a programmable filter
   programmed to equalize and reduce the effect of
   said acoustic feedback both in amplitude and
   phase on a signal in said transmission channel.
’850 Patent, col. 14, ll. 17–30 (emphases added). Asserted
claim 19 of the ’850 Patent is an independent device claim
that requires a filter programmed to effect substantial
reduction of acoustic feedback:
   19. A hearing aid comprising at least one input
   microphone, an output receiver, a signal trans-
   mission channel interposed between said micro-
   phone and said receiver, and a programmable
   delay line filter interposed in a feedback path
   between the input and output of said transmission
   channel, said programmable filter being pro-
   grammed to effect substantial reduction of
   acoustic feedback from said receiver to said mi-
   crophone.
’850 Patent, col. 14, ll. 60–68 (emphases added).
    A “programmable delay line filter” is prior art that
achieves customized amplification of different frequencies
of sound by different amounts. Such a filter separates
different sound frequencies and multiplies each by a
5                       ENERGY TRANSPORT     v. WILLIAM DEMANT


chosen weighting coefficient. Prior art hearing aids
permit selection of these coefficients to amplify incoming
sound to compensate for the particular wearer’s hearing
loss, as in a “forward path” filter. The ETG Patents use
such a programmable filter to reduce acoustic feedback.
     The ETG Patents describe a method of programming
coefficients for the acoustic feedback filter with the use of
a “host controller.” ’850 Patent, col. 6, ln. 55 – col. 7, ln. 3;
col. 9, ln. 12 – col. 10, ln. 44. The patient is fitted with a
hearing aid, which is connected to an external host con-
troller at the audiologist’s office. The host controller
calculates optimum coefficients for cancellation of acoustic
feedback. Then, according to the patents, those coeffi-
cients are programmed into the filter. The specification
explains that, using “adaptive strategies,” the filter can be
reprogrammed with different sets of coefficients and
compared to identify the most preferable frequency re-
sponse for the wearer. Id. at col. 6, ll. 67–68; col. 9, ln. 56
– col. 10, ln. 15. In the example described in the specifica-
tion, when the hearing aid is disconnected from the host
controller and worn outside the audiologist’s office, the
coefficients for the filter cannot be recalculated.
     The accused devices entered the market around 2001–
2002 with an adaptive filter technology for feedback
reduction. These devices repeatedly program the adap-
tive filter in the feedback path of the circuit with new
coefficients to cancel and eliminate feedback. The accused
devices accomplish this reprogramming feature with a
Least Mean Squares (“LMS”) optimization algorithm that
recalculates and updates the coefficients in the delay line
filter many times per second. The filters in the accused
devices – “LMS adaptive filters” – constantly adjust to
changes in feedback signal during normal hearing aid
operation.
ENERGY TRANSPORT   v. WILLIAM DEMANT                       6


                             II
    The asserted claims of the ’850 Patent each recite “a
programmable filter,” a “programmable delay line filter,”
or a filter that is “programmed” to reduce acoustic feed-
back. The district court construed “programmed” to mean
“provided with one or more values so as to produce a
response.” Energy, 2011 U.S. Dist. LEXIS 60716, at *27
n.9. Defendants assert the district court erred by not
limiting “programmed” to require that the values in the
claimed invention are “externally calculated” or are
“fixed” to impart cancellation of acoustic feedback.
    Claim construction is a question of law, which this
court reviews without deference. Cybor Corp. v. FAS
Techs., Inc., 138 F.3d 1448, 1456 (Fed. Cir. 1998) (en
banc). “[T]he words of a claim ‘are generally given their
ordinary and customary meaning’ . . . that the term would
have to a person of ordinary skill in the art in question at
the time of the invention.” Phillips v. AWH Corp., 415
F.3d 1303, 1312–13 (Fed. Cir. 2005) (en banc) (quoting
Vitronics Corp. v. Conceptronic, Inc., 90 F.3d 1576, 1582
(Fed. Cir. 1996)). “[T]he person of ordinary skill in the art
is deemed to read the claim term not only in the context of
the particular claim in which [it] appears, but in the
context of the entire patent, including the specification.”
Id. at 1313. While claim terms are understood in light of
the specification, a claim construction must not import
limitations from the specification into the claims. Id. at
1323.
    Nothing in the ’850 Patent claims indicates the plain
and ordinary meaning of “programmed” should be limited
to external or fixed programming. The claims do not
specify where the programming occurs, how frequently it
occurs, or what structure provides the programming.
Rather, the asserted claims recite “a filter . . . pro-
7                     ENERGY TRANSPORT   v. WILLIAM DEMANT


grammed to equalize and reduce the effect of . . . acoustic
feedback both in amplitude and phase,” or a “filter . . .
programmed to effect substantial reduction of acoustic
feedback.” ’850 Patent, col. 14, ll. 3–67. Indeed, Defen-
dants’ expert Dr. Morely admitted that at the time of the
invention, “one of ordinary skill in the art would have
known that any filter . . . could have been an adaptive
filter or a fixed filter.” J.A. 991. Thus, the language of
the claims supports the district court’s decision to refrain
from limiting the term “programmed” to require fixed or
external operation.
    Moreover, the specification gives no reason to con-
strue the claims to require that an external computer
calculate the values programmed into the filter. See
Innova/Pure Water, Inc. v. Safari Water Filtration Sys.,
381 F.3d 1111, 1117 (Fed. Cir. 2004) (“[E]ven where a
patent describes only a single embodiment, claims will not
be read restrictively unless the patentee has demon-
strated a clear intention to limit the claim scope using
words or expressions of manifest exclusion or restriction.”)
(internal quotations omitted). The embodiment described
in the specification, which utilized an external computer
connected to the hearing aid to calculate coefficients for
the programmable filter, reflects the size and complexity
of computers at the time of the patent application in 1986.
As Dr. Levitt, the lead inventor, explained, “the separa-
tion of components was really dictated by the technology
of the period. Conceptually, you could have them all
together.” J.A. 666. The ordinary meaning of “program-
mable,” as it would have been understood by one of skill
in the art at the time of the invention, does not limit
where the provided values originate. This court will not
import such an artificial temporally-dictated limitation on
the term “programmable.”
    The specification clearly contemplates that an adap-
ENERGY TRANSPORT   v. WILLIAM DEMANT                        8


tive filter would fit within the meaning of “programma-
ble.” The patent trumpets “the novel means employed for
effecting automatic adjustment of the programmable
filter to optimum parameter values as the speech level,
room reverberation and type of background noise change.”
’850 Patent, col. 11, ll. 51–57 (emphasis added). Although
this statement apparently refers to the programmable
filter located in the forward path rather than the feedback
path, there is no reason to construe the term “program-
mable” differently when used to describe a filter in the
feedback path. See Phillips, 415 F.3d at 1314 (noting
“claim terms are normally used consistently throughout
the patent”).
     The specification also describes “re-programming the
hearing aid to minimize acoustic feedback.” ’850 Patent,
col. 6, ll. 67–68. The patent teaches a specific “paired
comparison technique” that can be “repeated iteratively
until the optimum set of electroacoustic characteristics is
found” for feedback cancellation. Id. at col. 9, ln. 56 – col.
10, ln. 15. These disclosures teach adjustment of the
programmable filter in the feedback path in response to a
particular acoustic environment. In other words, the
specification does not envision a filter with permanently
“fixed” coefficients. In sum, the record in this case amply
supports the district court’s construction of “pro-
grammed,” which is consistent with the plain meaning of
the term and its usage in the specification. For these
reasons, this court affirms the trial court’s claim construc-
tion.
                             III
    This court reviews the grant or denial of a motion for
JMOL or for a new trial under the law of the regional
circuit. Revolution Eyewear, Inc. v. Aspex Eyewear, lnc.,
563 F.3d 1358, 1370 (Fed. Cir. 2009). The Third Circuit
9                     ENERGY TRANSPORT   v. WILLIAM DEMANT


conducts “a plenary review of the decisions of a district
court concerning judgment as a matter of law and deter-
mine[s] whether ‘viewing the evidence in the light most
favorable to the nonmovant . . . , there is insufficient
evidence from which a jury reasonably could’ reach the
conclusions that it did.” Rinehimer v. Cemcolift, lnc., 292
F.3d 375, 383 (3d Cir. 2002) (quoting Lightning Lube, Inc.
v. Witco Corp., 4 F.3d 1153, 1166 (3d Cir. 1993)). The
Third Circuit reviews a denial of a motion for new trial for
abuse of discretion. ld. at 383–84.
    This court affirms the district court’s denial of Defen-
dants’ motions for JMOL of invalidity and no infringe-
ment under the doctrine of equivalents for the ’850
Patent. This court evaluates written description, antici-
pation, infringement, and willfulness in turn.
A. Written Description
     Defendants argue that under the district court’s claim
construction, the claims lack adequate written description
because the specification only describes external calcula-
tion of coefficients that are fixed during normal operation
of the hearing aid. Compliance with the written descrip-
tion requirement is a question of fact, and this court
reviews the jury’s determination for substantial evidence.
Centocor Ortho Biotech, lnc. v. Abbott Labs., 636 F.3d
1341, 1347 (Fed. Cir. 2011). Having reviewed the record,
this court concludes that substantial evidence supports
the jury’s determination that the ’850 Patent is not inva-
lid for lack of written description.
    To satisfy the written description requirement, the
specification must “reasonably convey[ ] to those skilled in
the art that the inventor had possession of the claimed
subject matter as of the filing date.” Ariad Pharms., Inc.
v. Eli Lilly & Co., 598 F.3d 1336, 1351 (Fed. Cir. 2010) (en
banc). As discussed above, the specification supports the
ENERGY TRANSPORT   v. WILLIAM DEMANT                    10


district court’s claim construction, and provides adequate
written description to support the full scope of the claims
as construed. Inventor Dr. Levitt testified that the ’850
Patent explicitly indicates to one skilled in the art that
the hearing aid of the invention is “adaptive.” See, e.g.,
J.A. 666 (explaining statement in the ’850 Patent’s Ab-
stract that the hearing aid “adjust[s] automatically to the
optimum set of parameter values” conveys that invention
“was an adaptive hearing aid”). Defendants’ expert Dr.
Morley admitted that a person of ordinary skill in the art
would have understood that the programmable filter in
the ’850 Patent could be an adaptive filter. Dr. Dowling,
an expert hired by Defendants, stated in a Declaration
introduced as evidence at trial that it was his view that
“the ETG filter can be adaptive for feedback cancellation,”
and that “[no]body but a red faced liar could . . . say the
’850 [Patent] does not contemplate adaptive filtering.”
J.A. 1911 (first alteration in original).
     Thus, this record contained substantial evidence from
which the jury could conclude that the ’850 Patent con-
veys to one skilled in the art that the inventors were in
possession of a programmable hearing aid that could use
adaptive filtering for feedback cancellation at the time of
filing. This court therefore affirms the district court’s
denial of JMOL that the ’850 Patent is invalid for lack of
written description.
B. Anticipation
    The jury found Defendants did not prove by clear and
convincing evidence that any of the asserted claims of the
ETG Patents are invalid for anticipation or obviousness.
On appeal, Defendants assert Claim 19 of the ’850 Patent
is invalid for anticipation by U.S. Patent No. 4,783,818,
issued November 8, 1988, to Graupe et al. (“Graupe”).
Defendants did not argue at the district court that the
11                    ENERGY TRANSPORT    v. WILLIAM DEMANT


Graupe prior art anticipates Claims 13, 14, or 16 of the
’850 Patent, or that Graupe alone renders the claims
obvious. Thus, this court only addresses anticipation of
Claim 19. Anticipation is a question of fact; therefore this
court reviews the jury’s findings for substantial evidence.
Minn. Mining & Mfg. Co. v. Chemque, lnc., 303 F.3d 1294,
1301 (Fed. Cir. 2002).
    Because it was filed October 17, 1985, Graupe is prior
art to the ETG Patents under 35 U.S.C. § 102(e). Graupe
discloses a hearing aid that periodically enters an “identi-
fication mode” during which the amplifier is disconnected
and a test signal is supplied to the speaker and run
through an identification circuit to calculate new filter
coefficients to reduce feedback. On cross examination,
ETG’s expert, Mr. Matzen, agreed that “Graupe ’818 has
everything that is shown here in Claim 19.” J.A. 1100.
     This court interprets Mr. Matzen’s statement as an
admission that Graupe discloses every structural element
in Claim 19, but not as an admission of anticipation. On
cross and redirect, Mr. Matzen clarified that Graupe does
not consider the effect of acoustic feedback on a signal in
the transmission channel and therefore does not disclose
a filter that is “programmed to effect substantial reduc-
tion of acoustic feedback.” ’850 Patent, col. 14, ll. 66–67
(emphasis added). Therefore, Mr. Matzen, in fact, testi-
fied that Graupe does not disclose an important claimed
feature of the ’850 Patent.
    In response, Defendants argue that this court should
presume that Graupe achieved a “substantial reduction”
of acoustic feedback because it claimed to “cancel[ ] the
effects of . . . acoustic feedback.” Graupe, col. 10, ll. 52–
53. Indeed, an accused infringer enjoys a presumption
that allegedly anticipating material in a prior art patent
is enabled. Impax Labs., Inc. v. Aventis Pharms., Inc.,
ENERGY TRANSPORT   v. WILLIAM DEMANT                    12


468 F.3d 1366, 1382 (Fed. Cir. 2006). Even if “cancelling .
. . acoustic feedback” was enabled, however, the record
does not show that “cancellation” or “reduction” of feed-
back, as disclosed by Graupe, is the same as the “substan-
tial reduction” claimed in the ’850 Patent.            The
comparison of cancellation with substantial reduction was
a fact question for the jury, which made the implicit
finding that Graupe does not disclose “substantial reduc-
tion” of acoustic feedback.
    Indeed the record supports the jury’s finding. To be
specific, Mr. Matzen testified that Graupe would not
achieve substantial reduction of feedback because the
Graupe system calculates the wrong filter coefficients.
Graupe disconnects the amplifier during identification
mode. Therefore, the Graupe system does not have a
“transmission channel” when calculating the filter coeffi-
cients. This means Graupe cannot account for the effect
of acoustic feedback on a signal in the transmission
channel. Mr. Matzen testified that Graupe’s failure to
account for the effect of the signal through the transmis-
sion channel results in “so much error” that “it would not
be able to really effect substantial reduction of acoustic
feedback.” J.A. 1085.
    On appeal, Defendants argue that acoustic feedback
originates from the speaker, not the transmission chan-
nel. Both the ’850 Patent and Graupe calculate coeffi-
cients using a test signal that drives the speaker, so both
methods must result in the same amount of feedback
reduction. Defendants complain that Mr. Matzen did not
explain a reason why it mattered that a signal passed
through the amplifier and the rest of the transmission
channel before reaching the speaker.
    Again consulting the record, this court notes that De-
fendants did not present these arguments now before this
13                      ENERGY TRANSPORT    v. WILLIAM DEMANT


court on appeal to the jury during the trial. Mr. Matzen
testified that it is critical to consider a test signal that has
passed through the transmission channel in order to
obtain substantial feedback reduction.              Defendants’
expert, Dr. Soli, did not testify to the contrary. Dr. Soli
only explained Graupe’s method for calculating coeffi-
cients and transferring them to a programmable filter.
He then agreed, without elaboration, that the Graupe
process would “reduce the effect of acoustic feedback in
both amplitude and phase.” J.A. 1021. Defendants have
not pointed to any discussion by Dr. Soli of the impor-
tance (or lack thereof) of determining filter coefficients
based on a signal that passed through the entire trans-
mission channel.
    In sum, the jury assessed the credibility of both sides’
experts, and was entitled to credit Mr. Matzen’s testi-
mony that Graupe does not disclose substantial reduction
of feedback as required by Claim 19 of the ’850 Patent.
Accordingly, this court affirms the district court’s denial
of JMOL on anticipation.
C. Infringement
    The jury found no literal infringement of method
claims 13, 14, and 16 of the ’850 Patent, but found both
Widex and Demant infringed those claims under the
doctrine of equivalents. The district court denied Defen-
dants’ motions for JMOL of no infringement under the
doctrine of equivalents. This court affirms.
    “A device that does not literally infringe a claim may
nonetheless infringe under the doctrine of equivalents if
every element in the claim is literally or equivalently
present in the accused device.” Sage Prods., Inc. v. Devon
Indus., Inc., 126 F.3d 1420, 1423 (Fed. Cir. 1997). One
way that a patentee may prove that a particular claim
element is met under the doctrine of equivalents is by
ENERGY TRANSPORT   v. WILLIAM DEMANT                     14


showing that “the accused product performs substantially
the same function in substantially the same way with
substantially the same result” as claimed in the patent.
Crown Packaging Tech., Inc. v. Rexam Bev. Can Co., 559
F.3d 1308, 1312 (Fed. Cir. 2009); see Warner-Jenkinson
Co. v. Hilton Davis Chem. Co., 520 U.S. 17, 39–40 (1997).
     The jury’s verdict form required only a yes/no re-
sponse to the question whether each Defendant’s products
infringed each of the asserted claims literally or under the
doctrine of equivalents. For this reason, it is not possible
to determine which limitation or limitations of method
Claims 13, 14, and 16 the jury found were met only by
equivalents. This court finds the jury had substantial
evidence from which to conclude that Defendants’ prod-
ucts meet each of the disputed limitations (the “determin-
ing” step, the “inserting” step, and the “programmable
filter” / “filter therein programmed”), either literally or
under the doctrine of equivalents.
    ETG’s infringement expert, Mr. Brown, analyzed De-
fendants’ technical documents and demonstrated the
presence of each claim limitation or its equivalent in the
accused products. Dr. Gloster, ETG’s source code expert,
confirmed this testimony. Specifically, Mr. Brown pre-
sented sufficient linking testimony to demonstrate the
accused devices perform the step of “determining the
effect on the amplitude and phase of a signal in said
transmission channel,” as required by Claims 13, 14, and
16. Although the LMS adaptive filters in the accused
devices do not operate by measuring the amplitude or
phase of the acoustic feedback, the claims do not require
measurement. Mr. Brown testified that “the coefficients
of the [LMS adaptive] filter define phase and amplitude”
because the coefficients program the filter to respond to
the effect of feedback on phase and amplitude of a signal.
J.A. 763. Mr. Brown also opined that the LMS algorithm
15                      ENERGY TRANSPORT    v. WILLIAM DEMANT


of the accused devices performs the same function (“de-
termine the effect on amplitude and phase of the signal
transmission”), in the same way (by “calculating the
coefficients”), with the same result of cancelling acoustic
feedback (i.e., “[the] output of that filter being the effect of
the acoustic feedback in the external channel”) as the
asserted claims. J.A. 736–37. The jury thus had substan-
tial evidence from which to conclude Defendants’ products
perform the equivalent of the “determining” step.
     This case is closely analogous to Hughes Aircraft Co.
v. United States, 140 F.3d 1470 (Fed. Cir. 1998), in which
this court found infringement under the doctrine of
equivalents where advances in computer technology
occurring after the patents issued allowed changes in the
nature and location of claimed calculations. Hughes
involved an apparatus to control the orientation of satel-
lites using commands from a ground control station. The
claims expressly required that the satellite provide the
ground station with data sufficient to calculate an “in-
stantaneous spin angle” (“ISA”) position. Id. at 1472. The
ground crew would then make the necessary calculations
and send a signal to the satellite to adjust its position.
Due to vast reduction in the size and vast improvement in
the capacity of computer components, the accused devices
were able to calculate the ISA position onboard the satel-
lite. The accused satellites transferred different informa-
tion to the ground station because the onboard computer
calculated ISA position. Despite this “missing limitation”
from the claims, the after arising technology still permit-
ted the ground crew to control the satellite. Id. at 1475.
The result was an insubstantial change in the way the
satellites performed the claimed function. Id.
    In this case as well, advances in computer technology
allowed the accused devices to relocate calculation and
programming of filter coefficients from an external host
ENERGY TRANSPORT   v. WILLIAM DEMANT                      16


controller into the hearing aid itself. The accused devices
“determin[e] the effect on the amplitude and phase” of
acoustic feedback using onboard calculations. ’850 Pat-
ent, col. 14, ll. 8–10. While the improvement in technol-
ogy allows Defendants’ products to constantly recalculate
filter coefficients using electronics located on the hearing
aid, the accused devices nonetheless perform the same
function in substantially the same way, with substantially
the same result claimed by the ’850 Patent, thus provid-
ing substantial evidence for the jury’s infringement ver-
dict.
    ETG also presented testimony to support a finding
that the accused devices perform the step of “inserting . . .
an electrical feedback path having a filter therein pro-
grammed” subsequent to the “determining step,” as
required by the district court’s claim construction. ’850
Patent, col. 14, ll. 8–16; Energy, 2011 U.S. Dist. LEXIS
60716, at *48. Mr. Brown testified that in electrical
terms, every time a new set of coefficients is supplied to
the filter, a new filter is “inserted.” Thus, the jury could
conclude that the “determining” and “inserting” steps
occur repeatedly, in order, when the accused devices are
in use.
    The district court did not make a contrary finding by
holding there was substantial evidence to support the
jury’s finding of no literal infringement of Claims 13, 14,
and 16. The district court noted the jury could have
concluded that the “determining” step is not literally met
because the equations used to calculate the coefficients for
the LMS filter do not directly address phase or amplitude.
See Energy, 2011 U.S. Dist. LEXIS 60716, at *46–47.
Alternatively, the record contained substantial evidence
from which the jury could have concluded that the “insert-
ing” step is performed only when the filter is built into the
hearing aid at the time of manufacture, and therefore the
17                    ENERGY TRANSPORT    v. WILLIAM DEMANT


accused devices do not literally perform the “inserting”
and “determining” steps in the order required by the
court’s claim construction. Id. at *48–49. The district
court did not find the “inserting” step is performed at the
time of manufacture; it found only that there was sub-
stantial evidence from which the jury could have reached
that conclusion.
    Defendants argue that their devices cannot be found
to infringe under the doctrine of equivalents because, if
the claims are “expanded” to cover the adaptive filters in
the accused devices, then the claims would also extend to
the prior art Graupe patent. See Wilson Sporting Goods
Co. v. David Geoffrey & Assoc., 904 F.2d 677, 684 (Fed.
Cir. 1990) (overruled in part on other grounds by Cardinal
Chem. Co. v. Morton Int’l, 508 U.S. 83 (1993)) (“[A] pat-
entee should not be able to obtain, under the doctrine of
equivalents, coverage which he could not lawfully have
obtained from the PTO by literal claims.”). An accused
infringer seeking to avoid infringement under the doc-
trine of equivalents on this basis bears the burden of
“presenting prior art which shows that the asserted range
of equivalence would encompass the prior art,” but the
patentee bears the ultimate burden of persuasion to show
that its claims do not cover the prior art. Streamfeeder,
LLC v. Sure-Feed Sys., Inc., 175 F.3d 974, 984 (Fed. Cir.
1999).
     Defendants have not presented prior art that bars
finding the accused devices infringe Claims 13, 14, and 16
under the doctrine of equivalents. Adaptive filters are
within the literal scope of the claims. This court has
rejected Defendants’ claim construction arguments seek-
ing to limit the scope of the term “programmable” to
filters with fixed or externally-calculated coefficients. The
jury found Claim 19 of the ’850 Patent literally infringed.
The jury therefore found the adaptive filters in the ac-
ENERGY TRANSPORT   v. WILLIAM DEMANT                     18


cused devices literally meet the claimed limitation of a
“programmable filter.” ’850 Patent, col. 14, ln. 65. There
was no reason to resort to the doctrine of equivalents for
this limitation. When the jury found the claims not
invalid, it rejected Defendants’ expert’s testimony that if
the claims cover adaptive filters then they are anticipated
by Graupe.
    Moreover, Defendants admit that Graupe does not
meet the “determining the effect . . . of a signal in said
transmission channel” limitation of Claims 13, 14, and 16.
’850 Patent, col. 14, ll. 8-23; Demant Opening Br. at 52
(“Graupe does not determine the effect of the signal
through the transmission channel”). In effect, Defendants
thus admit that Graupe does not anticipate Claims 13, 14,
or 16 regardless of whether the accused devices meet
other limitations of those claims only under the doctrine of
equivalents. Moreover, on appeal, Defendants do not
present any combination of references that would render
Claim 13, 14 or 16 obvious in view of Graupe. In sum, the
record shows that Defendants have not shown that the
asserted range of equivalents would read on the prior art.
D. Willfulness
    Widex appeals the district court’s denial of JMOL of
no willful infringement. The district court denied ETG’s
motions for enhanced damages and for attorney’s fees,
however, and ETG has not appealed that decision. See
Energy, 2011 U.S. Dist. LEXIS 60716, at *52-59. Because
no consequences flow from the district court’s decision
regarding willful infringement, this court does not reach
the issue.
                            IV
    Defendants also seek a new trial on damages. This
court rejects Defendants’ challenges to the admission of
19                     ENERGY TRANSPORT    v. WILLIAM DEMANT


the report from the German Federal Cartel Office (“Cartel
Report”), the use of the 25 percent rule of thumb by ETG’s
damages expert, the amount of the damages award, and
the award of pre-judgment interest.
A. The Cartel Report
    This court applies regional circuit law to evidentiary
issues. The Third Circuit requires a party challenging the
district court’s evidentiary ruling to demonstrate that the
district court acted irrationally and arbitrarily. In re
Paoli R.R. Yard PCB Litig., 113 F.3d 444, 453 (3d Cir.
1997).
    Defendants argue that the trial court should have ex-
cluded the Cartel Report under Federal Rule of Evidence
403 because it was unduly prejudicial. The district court
admitted the Cartel Report into evidence and permitted
ETG’s damages expert to discuss the report in response to
Defendants’ presentation of royalty rates from certain
license agreements offered by the Hearing Instrument
Manufacturers Patent Partnership (“HIMPP”). HIMPP is
an industry group that pools patents needed for develop-
ment of programmable and digital hearing aids. HIMPP
licenses all of its patents for a flat 3% royalty on the price
of each hearing aid covered by one or more of the ap-
proximately 250 patents in the HIMPP patent pool.
Defendants’ damages expert used the HIMPP rates as
part of the basis for his opinion that a reasonable royalty
for access to the ETG patents would be in the range of
0.25 to 0.5%. ETG responded that the HIMPP royalty
rates are low, industry-friendly rates and not probative of
market rates for the ETG patents. As support, ETG cited
the Cartel Report’s findings that the hearing aid market
is highly concentrated and the industry enjoys “exceed-
ingly high profit margins” due to a lack of competition.
ENERGY TRANSPORT   v. WILLIAM DEMANT                    20


    The district court instructed that ETG would not be
permitted use the Cartel Report to “engage in hyperbolic
statements or . . . inflammatory language” characterizing
the Defendants’ activities as collusive. J.A. 1295. This
instruction helped limit the potential for undue prejudice
at trial. Indeed, Defendants did not object during trial to
the manner in which ETG used the Cartel Report.
    After the trial in this case, on April 20, 2010, a Ger-
man appellate court overturned the Cartel Report’s
ultimate conclusion that an “oligopoly” existed and stated
that “no restrictions on competition ensue from [HIMPP]”
and similar industry consortia. J.A. 2164. The German
court, however, “based its decision on the extensive inves-
tigations conducted by the Federal Cartel Office into
prevailing market conditions,” and those underlying facts
were not disturbed by the appellate court. J.A. 2160; see
Energy, 2011 U.S. Dist. LEXIS 60716, at *67. ETG relied
on the facts presented in the Cartel Report regarding the
hearing aid market and industry structure—not the legal
conclusion that the market was an oligopoly—to make its
case that the HIMPP licenses did not represent arms-
length transactions and that HIMPP royalties did not
represent prevailing market rates. ETG also relied on the
high profit margins on hearing aids evidenced in the
Cartel Report to argue for damages at a higher royalty
rate than that suggested by Defendants. These facts were
clearly relevant to the determination of a reasonable
royalty rate for the ETG patents. Defendants have not
shown that the district court acted irrationally or arbi-
trarily in finding that the probative value of the Cartel
Report outweighed any potential prejudice.
B. The 25 Percent Rule
   A party challenging a jury's verdict on damages “must
show that the award is, in view of all the evidence, either
21                     ENERGY TRANSPORT    v. WILLIAM DEMANT


so outrageously high or so outrageously low as to be
unsupportable as an estimation of a reasonable royalty.”
Rite-Hite Corp. v. Kelley Co., 56 F.3d 1538, 1554 (Fed. Cir.
1995) (en banc) (quoting Lindemann Maschinenfabrik
GmbH v. Am. Hoist & Derrick Co., 895 F. 2d 1403, 1406
(Fed. Cir. 1990)). In general, this court upholds a jury's
damages award “unless ‘grossly excessive or monstrous,’
clearly not supported by the evidence, or based only on
speculation or guesswork.” Oiness v. Walgreen Co., 88
F.3d 1025, 1031 (Fed. Cir. 1996) (quoting Brooktree Corp.
v. Adv. Micro Devices, Inc., 977 F.2d 1555, 1580 (Fed. Cir.
1992)).
    Defendants seek a new trial on damages because
ETG’s expert, Mr. Musika, used the 25 percent rule of
thumb in his analysis of a reasonable royalty rate. This
court has held that “the 25 percent rule of thumb is a
fundamentally flawed tool for determining a baseline
royalty rate in a hypothetical negotiation. Evidence
relying on the 25 percent rule of thumb is thus inadmissi-
ble under Daubert and the Federal Rules of Evidence,
because it fails to tie a reasonable royalty base to the facts
of the case at issue.” Uniloc USA, Inc. v. Microsoft Corp.,
632 F.3d 1292, 1315 (Fed. Cir. 2011). This court does not
depart from the counsel and holding of Uniloc.
    In this case, however, Mr. Musika’s references to the
25 percent “rule” (which is no longer a “rule”) did not
irretrievably damage the reasonableness of his method
and result in arriving at recommended royalty rates. For
instance, Mr. Musika relied more prominently on other
factors, such as separately determining that the infring-
ing products garner a 9.2% premium on operating profits
over non-infringing devices. Mr. Musika included this
figure as the top end of a range of possible royalties the
parties would have considered in a hypothetical negotia-
tion. Mr. Musika then considered other admissible fac-
ENERGY TRANSPORT   v. WILLIAM DEMANT                     22


tors to show that the royalty was reasonable in light of
the unique relationship of the parties, the nature of the
invention, and the nature of the industry. See Georgia-
Pacific Corp. v. U.S. Plywood Corp., 318 F. Supp. 1116
(S.D.N.Y. 1970). Once again, this court does not endorse
Georgia-Pacific as setting forth a test for royalty calcula-
tions, but only as a list of admissible factors informing a
reliable economic analysis.
    Mr. Musika further performed an entirely separate
analysis of a reasonable royalty using the method set
forth in TWM Mfg. Co. v. Dura Corp., 789 F.2d 895 (Fed.
Cir. 1986). This analysis compared the average expected
profit margin on the infringing products, as set forth in
Defendants’ expert reports, to the industry average ex-
pected profit margin. Mr. Musika testified this analysis
showed the infringing products garnered a 6.4% increase
in expected profit margin based on the technology in the
ETG Patents. Mr. Musika’s suggested reasonable royalty
rates were thus tied to the benefit accorded by the patents
at issue. Thus, this case is not like Uniloc, where the
plaintiff’s expert did not offer acceptable alternative
methods to support his damages calculation. Cf. Uniloc,
632 F.3d at 1318. ETG’s expert provided an entirely
separate damages analysis that supported the jury’s
verdict.
    The jury did not adopt either expert’s damages analy-
sis wholesale, but awarded lump sum damages that
equate to effective royalty rates in the range of 4–5%.
Thus, this court perceives that the record supports the
jury’s award with substantial evidence based on Mr.
Musika’s TWR analysis and discussion of the premium on
operating profits enjoyed by the accused products. Defen-
dants have not shown the award is outrageous or grossly
excessive. The district court did not err in denying a new
trial.
23                    ENERGY TRANSPORT   v. WILLIAM DEMANT


C. The Damages Amount
    Defendants seek remittitur or a new trial because the
jury’s damages award was presumably calculated on a
royalty base that includes sales under the ’749 Patent.
The district court granted JMOL that the ’749 Patent is
not infringed under the doctrine of equivalents. As dis-
cussed below, this court affirms that ruling. The ’749
Patent expired in November 2006—about four months
later than the ’850 Patent, which expired in June 2006.
Both parties’ experts agreed at trial that if the ’749 Pat-
ent was found not infringed, the sales base should not
include sales that occurred after the ’850 Patent expired.
For example, the jury was presented with a sales base for
Demant through November 2006 of $417 million, com-
pared to only $357 million through expiration of the ’850
Patent in June 2006. Because the jury found both patents
infringed, it presumably used the larger sales base in
calculating its damages figures. Defendants suggest that
this court can grant relief by simply determining the
effective royalty rate granted by the jury and multiplying
it by the undisputed lower sales base for products sold
before the ’850 Patent expired.
     Defendants waived this argument by not asking the
district court to reduce the damages award in the event it
granted their motion for JMOL of noninfringement of the
’749 Patent. Defendants presented an alternate sales
base to the jury in the event it found only the ’850 Patent
infringed, and could have made the same argument to the
district court in their post-trial motions for JMOL and
remittitur. Defendants also did not file a motion for
reconsideration with the district court after their motion
for JMOL of noninfringement of the ’749 Patent was
granted. This court will not consider arguments raised
for the first time on appeal.
ENERGY TRANSPORT   v. WILLIAM DEMANT                     24


    Even if Defendants had not waived this argument,
this court cannot “correct” a damages figure by extrapo-
lating a royalty rate from the jury’s lump sum damages
award and multiplying that royalty rate by a revised sales
base. “Except in those cases in which it is apparent as a
matter of law that certain identifiable sums included in
the verdict should not have been there, the court may not
arbitrarily reduce the amount of damages, for to do so
would deprive the parties of their constitutional right to a
jury.” 11 Charles Alan Wright, Arthur R. Miller & Mary
Kay Kane, Federal Practice & Procedure § 2815 (2d ed.
Supp. 2012). An “identifiable sum” typically must be
separately listed on the jury verdict form. Garrett v.
Faust, 183 F.2d 625 (3d Cir. 1950) (verdict form sepa-
rately listed damages resulting from misrepresentation,
and district court appropriately deducted that amount
from final award because there was insufficient evidence
of misrepresentation); Cornell University v. Hewlett-
Packard Co., 609 F. Supp. 2d 279 (N.D.N.Y. 2009) (Rader,
J. by designation) (reducing damages by multiplying
“jury’s uncontroverted royalty rate of 0.8 percent” by
legally correct royalty base).
    Here, the verdict form only required the jury to award
a lump sum damages figure for each Defendant. The jury
was not asked to allocate the damages awarded over the
two patents at issue and was not required to specify a
reasonable royalty rate. There is thus no clearly identifi-
able sum in the verdict that is allocable to the non-
infringed ’749 Patent. While Defendants could have
sought remittitur from the district court, this court cannot
simply adjust the jury’s damages award under the cir-
cumstances of this case.
   This court also considered Defendants’ other argu-
ments regarding the amount of the damages award. In
sum, Defendants have not shown that the jury’s award is
25                    ENERGY TRANSPORT    v. WILLIAM DEMANT


“outrageously high” or unsupported by the evidence. Rite-
Hite Corp., 56 F.3d at 1554.
D. Pre-Judgment Interest
     Widex challenges the district court’s decision to award
pre-judgment interest despite ETG’s alleged delays in
filing suit. The award of pre-judgment interest is “the
rule, not the exception.” Sanofi-Aventis v. Apotex, Inc.,
659 F.3d 1171, 1177 (Fed. Cir. 2011). This court reviews
the trial court’s decision to award pre-judgment interest
for abuse of discretion. General Motors Corp. v. Devex
Corp., 461 U.S. 648, 657 (1983). Widex has not cited any
cases of this court reversing a district court’s decision not
to award pre-judgment interest. The district court did not
abuse its discretion in this case by following the standard
rule of awarding pre-judgment interest.
                             V
    ETG cross-appeals the district court’s grant of JMOL
of noninfringement of the ’749 Patent under the doctrine
of equivalents. The district court found prosecution
history estoppel bars assertion of equivalents in this case.
Energy, 2011 U.S. Dist. LEXIS 60716, at *41–44.
Whether prosecution history estoppel applies is a legal
question which this court reviews without deference.
Glaxo Wellcome, Inc. v. Impax Labs., Inc., 356 F.3d 1348,
1351 (Fed. Cir. 2004). This court affirms the judgment of
noninfringement of the ’749 Patent.
    ETG asserted Claims 1 and 2 of the ’749 Patent.
Claim 1 is representative and reads:
     1. A host controller for producing data from a
     computer for a programmable hearing aid to can-
     cel acoustic feedback comprising
ENERGY TRANSPORT   v. WILLIAM DEMANT                    26


       means for receiving signals from the hearing
   aid and measuring phase and amplitude,
       means for receiving signals from the hearing
   aid indicative of the summation of acoustic feed-
   back and acoustic feedback cancellation signals,
   and
       means controlled by the computer for adjust-
   ing the phase and amplitude necessary to elimi-
   nate acoustic feedback and produce a null
   summation.
    Claim 1 derives from application claim 33, which was
entered during prosecution after a similar claim was
rejected in view of prior art. See Office Action dated Oct.
17, 1989 in U.S. App. No. 07/155,374. The rejected claim
recited “means for receiving signals indicative of the
frequency gain and feedback characteristics.” Prelimi-
nary Amendment dated Feb. 12, 1988 in U.S. App. No.
07/155,374, Claim 24. This limitation was replaced in
the new claims by “means for receiving signals from the
hearing aid and measuring phase and amplitude.”
Similar language relating to the “null summation” tech-
nique for cancellation of acoustic feedback was also added.
The applicant explained the new claims as follows:
   The claims as amended relate to a host controller
   for producing the data necessary to cancel acous-
   tic feedback in a hearing aid. The cancellation of
   acoustic feedback is achieved by generating test
   signals which are transmitted to the hearing aid
   and by summing the acoustic feedback signal with
   an adjusted phase shift and amplitude signal to
   produce an acoustic feedback cancellation signal.
Amendment dated March 23, 1989 in U.S. App. No.
07/155,374, at 3. Thus, it appears the applicant nar-
27                    ENERGY TRANSPORT   v. WILLIAM DEMANT


rowed the claimed method of cancelling feedback from one
requiring only modifying frequency gain and unspecified
“feedback characteristics” to one specifically requiring
measurement of phase and amplitude.
    ETG argues its reason for entering the new claims
was to cover a different concept—“null summation”—as
opposed to receiving signals “indicative of frequency gain
and feedback characteristics” as recited in the rejected
claims. However, the “summation” concept was presented
in application claims 25–31.       See, e.g., Preliminary
Amendment dated Feb. 12, 1988 in U.S. App. No.
07/155,374, Claim 25 (requiring means for generating a
“feedback cancellation voltage” for “summation” with a
“feedback voltage” to “cancel feedback”). The examiner
had rejected the summation claims for failure to comply
with the written description requirement. See Office
Action dated Oct. 17, 1989 in U.S. App. No. 07/155,374,
at 2. Application claim 33 addressed the examiner’s § 112
rejection by clarifying how and where summation occurs.
    ETG has not overcome the presumption that the nar-
rowing amendment was made to secure the patent. Festo
Corp. v. Shoketsu Kinzoku Kogyo Kabushiki Co., 535 U.S.
722, 739 (2002). The prosecution history in this case
shows that the claim limitation at issue was added in
response to a rejection of closely related claims, and
provides no other explanation for the limitation. Honey-
well Int’l v. Hamilton Sundstrand Corp., 523 F.3d 1304,
1315–16 (Fed. Cir. 2008) (“If the prosecution history
reveals no reason for the narrowing amendment, the
presumption is not rebutted. . . . Silence does not over-
come the presumption.”) (internal citation omitted). This
court requires a strong showing – not present on this
record – to satisfy the “very narrow” exception to prosecu-
tion history estoppel for amendments only tangentially
ENERGY TRANSPORT   v. WILLIAM DEMANT                   28


related to the equivalent in question. Cross Med. Prods.
v. Medtronic, Inc., 480 F.3d 1335, 1342 (Fed. Cir. 2007).
    ETG’s argument that it did not relinquish equivalents
that involve “determining”—rather than “measuring”—
phase and amplitude, also fails. Prosecution history
estoppel bars application of the doctrine of equivalents
even where the applicant surrendered more claim scope
than was necessary to overcome a rejection. See Norian
Corp. v. Stryker Corp., 432 F.3d 1356, 1361–62 (Fed. Cir.
2005) (holding patentees are restricted by prosecution
history estoppel to “the scope of what they ultimately
claim”). Moreover, the difference between the phrase
“determining the effect of phase and amplitude” and
“measuring phase and amplitude” was clearly foreseeable.
ETG used the “determining” language in the ’850 Patent.
See ’850 Patent, col. 14, ll.8–10. The district court cor-
rectly applied prosecution history estoppel to bar asser-
tion of infringement under the doctrine of equivalents by
the accused devices, which do not “measure” phase and
amplitude.
                           VI
   For the forgoing reasons, this court affirms the judg-
ment of the district court.
                      AFFIRMED
                          COSTS
Costs to ETG.
