Court Opinion

ID: 3066248
Source: CourtListenerOpinion
Date Created: 2015-10-14 23:52:40.121783+00
Date Added: 2024-06-11T07:38:22.218544
License: Public Domain

United States Court of Appeals
      for the Federal Circuit
                ______________________

        CARNEGIE MELLON UNIVERSITY,
               Plaintiff-Appellee

                           v.

     MARVELL TECHNOLOGY GROUP, LTD.,
      MARVELL SEMICONDUCTOR, INC.,
             Defendants-Appellants
            ______________________

                      2014-1492
                ______________________

   Appeal from the United States District Court for the
Western District of Pennsylvania in No. 2:09-cv-00290-
NBF, Judge Nora Barry Fischer.
                ______________________

                Decided: August 4, 2015
                ______________________

     E. JOSHUA ROSENKRANZ, Orrick, Herrington & Sut-
cliffe LLP, New York, NY, argued for plaintiff-appellee.
Also represented by ERIC SHUMSKY, Washington, DC; BAS
DE BLANK, Menlo Park, CA; PATRICK JOSEPH MCELHINNY,
MARK G. KNEDEISEN, CHRISTOPHER MICHAEL VERDINI,
K&L Gates LLP, Pittsburgh, PA; THEODORE J. ANGELIS,
DOUGLAS B. GREENSWAG, DAVID T. MCDONALD, Seattle,
WA.

    KATHLEEN M. SULLIVAN, Quinn Emanuel Urquhart &
Sullivan, LLP, New York, NY, argued for defendants-
2     CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY
                                               GROUP, LTD

appellants. Also represented by EDWARD J. DEFRANCO,
JOSEPH MILOWIC, III, CLELAND B. WELTON, II; SUSAN
RACHEL ESTRICH, MICHAEL THOMAS ZELLER, Los Angeles,
CA; KEVIN P.B. JOHNSON, Redwood Shores, CA; DEREK
SHAFFER, Washington, DC; ROY WANG, Marvell Semicon-
ductor, Inc., Santa Clara, CA.

    ANN A. BYUN, Hewlett-Packard Company, Wayne, PA,
for amicus curiae Hewlett-Packard Company.

   ANTHONY PETERMAN, Dell Inc., Round Rock, TX, for
amicus curiae Dell Inc.

   MARTA Y. BECKWITH, Aruba Networks, Inc.,
Sunnyvale, CA, for amicus curiae Aruba Networks, Inc.

    DAN L. BAGATELL, Perkins Coie LLP, Phoenix, AZ, for
amici curiae Broadcom Corporation, Google Inc., Lime-
light Networks, Inc., Microsoft Corporation, SAS Institute
Inc., XILINX, Inc. Also represented by KENNETH J.
HALPERN, Palo Alto, CA.

    DONALD MANWELL FALK, Mayer Brown, LLP, Palo Al-
to, CA, for amici curiae Jeremy Bock, Michael A. Carrier,
Bernard Chao, Jorge L. Contreras, Robert A. Heverly,
Timothy R. Holbrook, Amy Landers, Mark A. Lemley,
Yvette Joy Liebesman, Brian J. Love, Tyler T. Ochoa,
Pamela Samuelson, Christopher B. Seaman, Lea Shaver,
Toshiko Takenaka. Also represented by BRIAN J. LOVE,
Santa, Clara, CA.

    DANIEL B. RAVICHER, Ravicher Law Firm, Coral Ga-
bles, FL, for amicus curiae Daniel B. Ravicher.

   J. ANTHONY DOWNS, Goodwin Procter LLP, Boston,
MA, for amici curiae Boston University, Rice University,
Texas A&M University, The University of Kansas, The
University of Pittsburgh, The University of Minnesota.
CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY        3
GROUP, LTD

Also represented by WILLIAM M. JAY, Washington, DC;
DAVID ZIMMER, San Francisco, CA.
                ______________________

  Before WALLACH, TARANTO, and CHEN, Circuit Judges.
TARANTO, Circuit Judge.
     Carnegie Mellon University (“CMU”) sued Marvell
Technology Group, Ltd. and Marvell Semiconductor, Inc.
(collectively “Marvell”) for infringing two patents related
to hard-disk drives. A jury found for CMU on infringe-
ment and validity, and it awarded roughly $1.17 billion as
a reasonable royalty for the infringing acts, using a rate of
50 cents for each of certain semiconductor chips sold by
Marvell for use in hard-disk drives. The district court
then used that rate to extend the award to the date of
judgment, awarded a 23-percent enhancement of the past-
damages award based on Marvell’s willfulness (found by
the jury and the district court), and entered a judgment of
roughly $1.54 billion for past infringement and a continu-
ing royalty at 50 cents per Marvell-sold chip.
     Marvell appeals. We affirm the judgment of in-
fringement and validity. As to the monetary relief: We
affirm the rejection of Marvell’s laches defense to pre-suit
damages. We reverse the grant of enhanced damages
under the governing willfulness standard, which does not
require that Marvell have had a reasonable defense in
mind when it committed its past infringement. We reject
Marvell’s challenge to the royalty (past and continuing)
with one exception.
    That exception involves an issue of extraterritoriali-
ty—whether the royalty, in covering all Marvell sales of
certain chips made and delivered abroad, improperly
reaches beyond United States borders. We conclude that
the royalty properly embraces those Marvell-sold chips
that, though made and delivered abroad, were imported
into the United States, and we affirm the judgment to the
4     CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY
                                               GROUP, LTD

extent of $278,406,045.50 in past royalties (50 cents for
each of the 556,812,091 chips the jury could properly find
were imported), plus an amount to be calculated on re-
mand that brings that figure forward to the time of judg-
ment, and the ongoing royalty order to the extent it
reaches imported Marvell-sold chips. But as to the Mar-
vell chips made and delivered abroad but never imported
into the United States, we conclude that a partial new
trial is needed to determine the location, or perhaps
locations, of the “sale” of those chips. To the extent, and
only to the extent, that the United States is such a loca-
tion of sale, chips not made in or imported into the United
States may be included in the past-royalty award and
ongoing-royalty order.
                      BACKGROUND
    CMU owns U.S. Patent No. 6,201,839, titled “Method
and Apparatus for Correlation-Sensitive Adaptive Se-
quence Detection,” and related No. 6,438,180, titled “Soft
and Hard Sequence Detection in ISI Memory Channels,”
both granted to Drs. Aleksandar Kavcic and José Moura.
The patents’ written descriptions are largely identical,
and both patents claim methods, devices, and systems for
improved accuracy in the detection of recorded data when
certain types of errors are likely due to the recording
medium and reading mechanism. The inventions are
particularly suited for the magnetic data-storage media of
hard-disk drives in computers.
    The record in the case teaches that a storage disk in a
typical hard-disk drive is coated with microscopic granu-
lar magnetic material segmented into vast numbers of
magnetic “bit regions” arrayed in concentric tracks. Each
region may be polarized so that its north pole may point
in either of two directions, and that choice of polarity
allows for recording of digital data. In particular, data
may be encoded in transitions, i.e., in how one magnetic
region’s orientation compares with (is the same as or
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY        5
GROUP, LTD

differs from) the orientation of the next magnetic region
in line as one moves in a particular direction. In a hard-
disk drive, a read-write head hovering above the disk,
moving along a track, can detect the orientations of
neighboring magnetic regions, thereby reading data, or
alter the regions’ orientations, thereby writing data.
    Although hard-disk drives constituted a mature and
well-known technology by the time of the ’839 and ’180
patents, the demand to store ever more data on each disk
gave rise to ever new challenges. One way to store more
data is to make the magnetic regions on the disk smaller
and smaller, thereby increasing the number of changes in
magnetic polarity within each track. But shrinking the
magnetic regions makes it difficult in practice for a read
head—which detects magnetic forces and translates them
into electrical signals, the so-called “measured signals”—
to accurately identify the actual polarities and transitions
on the disk. It becomes harder to distinguish region-to-
region boundaries at which polarity changes from those at
which it does not.
    Two such difficulties are central to this case. First, a
change in magnetic polarity at one region-to-region
boundary can affect the measured signal the read head
obtains from more than one magnetic region. How much
that spill-over effect occurs—how much “noise” there is in
the measured signal obtained by the read head—can
depend on what polarity changes there actually are, i.e.,
on the actual “signal” encoded on the disk. The patents
term this “signal-dependent noise.”        Second, nearby
(adjacent or almost adjacent) regions and boundaries tend
to have related amounts of measurement error. The
patents term this “correlated noise.” Those two noise
effects are sometimes together called “media noise.” For
technical reasons the parties have not treated as critical
to the issues on appeal—including properties of the mate-
rials composing the magnetic regions and properties of
the read heads—the noise problems become more signifi-
6     CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

cant when the size of the magnetic regions shrinks below
certain levels. See J.A. 2210 (signal distortion occurs
when magnetic region size nears media grain size).
    Although increasing miniaturization of disks’ magnet-
ic regions permits the storage of more data in the same
amount of space, the benefit can be lost if the data cannot
be read accurately because of noise problems. Working
together at CMU’s Data Storage Systems Center, Dr.
Kavcic, as a graduate student, and Dr. Moura, as a pro-
fessor renowned for expertise in signal processing, con-
ceived of ways of reducing the errors due to media noise
and reliably detecting the data recorded on a hard disk.
Their solution, embodied in the claims of the two patents
at issue, uses a form of maximum-likelihood detection to
estimate, given a measured signal (e.g., a sequence of
voltage levels produced by a read head’s response to
detected magnetic forces), the most likely sequence of
data symbols actually recorded (by polarization of mag-
netic regions) on the disk. In theory, for a measured
signal consisting of N “samples” taken from N recorded
symbols, the most likely recorded-symbol sequence could
be determined by comparing every possible N-length
sequence of symbols with the measured N-sample signal
to determine which sequence best matches the measured
signal, by some measure of similarity. But the number of
possible sequences to compare grows exponentially with
N. More efficient methods are desirable.
     One such method (on which the patents at issue here
build) takes its name from Andrew Viterbi, a founder of
Qualcomm Inc. The Viterbi method proceeds, in effect,
two symbols at a time. It starts with the set of possible
first symbols for the sequence and possible second sym-
bols and determines which pair makes the measured
signal sample most likely. For example, if symbols corre-
spond to single bits and the first symbol is 0, the Viterbi
method compares whether a measured sample (say of 0.2
Volts) is more likely if the next recorded bit is a 0 or a 1
CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY          7
GROUP, LTD

(i.e., if the sequence begins 00 or 01). 1 It then iterates the
process with the next symbol. It ultimately produces a
sequence of most likely symbols, and by discarding un-
likely pairings as it goes along, it demands far fewer
computations, and far less data retention, than an all-
possible-sequences comparison approach. Those savings
can make a large practical difference.
     In the language of the patents, which is common to
the field, each potential pairing of one symbol to the next
(e.g., a first bit of 0 with a second bit of 0) is called a
“branch.” That usage reflects how the possible symbols at
any time of sampling can be displayed in matrix form,
with the columns representing times of sampling (t0, t1, t2,
etc.) and the items in each column the possible symbols at
that time; the matrix looks like a “trellis,” and the lines
connecting pairs of symbols in adjacent columns are
“branches.” The Viterbi method assigns to each branch a
“branch metric,” a value representing the likelihood of the
measured signal sample arising given the symbol pairing
of that branch. Importantly for present purposes, a user

    1   Each “symbol” need not be a single bit, i.e., a 0 or
1. It might instead, for example, be two bits (00, 01, 10, or
11), thereby creating more possibilities for each symbol
and more possible pairings of symbols. It is also possible
to use 0, 1, and -1 as choices—for example, to represent,
respectively, no change in polarity, a polarity change from
north-facing-back to north-facing-forward (considering the
direction of the read head’s scanning), and a polarity
change from north-facing-forward to north-facing-back.
We identify one simple choice in text for illustrative
purposes. The parties have not identified any way in
which the symbol choice affects the issues before us.
8       CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY
                                                 GROUP, LTD

of the method must choose one or more “branch metric
functions” to calculate and assign each branch metric. 2
    Applying a Viterbi “detector” (an implementation of
the Viterbi method) to hard-disk drives was not an inno-
vation of the CMU patents. Instead, the patents claim an
improvement over existing detectors by teaching use of
branch metric functions that are specifically adapted to
reduce the effects of the most likely errors caused by the
ever smaller magnetic regions used for storing data on
hard disks. Specifically, the patents teach that (1) differ-
ent functions may be used for different branches, depend-
ing in particular on the measured signal samples, and (2)
each branch metric function can take as its input a plural-
ity of adjacent signal samples, rather than a single sam-
ple. The former addresses signal-dependent noise, the
latter correlated noise.
    In 1997, Drs. Kavcic and Moura filed a provisional pa-
tent application. In May 1998 they published a paper in
the IEEE Transactions on Magnetics called Correlation-
Sensitive Adaptive Sequence Detection. The ’839 patent
issued in March 2001 from an application filed in April
1998, and the ’180 patent issued in August 2002 from a
continuation-in-part application filed in March 1999.
    Claim 4 of the ’839 patent is representative of the as-
serted claims:

    2   See Harris Corp. v. Ericsson Inc., 417 F.3d 1241,
1246 (Fed. Cir. 2005) (In “Maximum Likelihood Sequence
Estimation using the Viterbi Algorithm, . . . the receiving
device compares distorted sequences of received symbols
to hypothetical sequences of transmitted symbols to find
the sequence of symbols that was most likely transmitted.
The hypothetical sequences are distorted in accordance
with a model of the transmission medium.”).
CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY          9
GROUP, LTD

    4. A method of determining branch metric values
    for branches of a trellis for a Viterbi-like detector,
    comprising:
    selecting a branch metric function for each of the
    branches at a certain time index from a set of sig-
    nal-dependent branch metric functions; and
    applying each of said selected functions to a plu-
    rality of signal samples to determine the metric
    value corresponding to the branch for which the
    applied branch metric function was selected,
    wherein each sample corresponds to a different
    sampling time instant.
’839 patent, col. 14, lines 10–19; see also ’180 patent, col.
15, lines 39–51 (claims 1 and 2).
    Marvell, located in California, designs and sells semi-
conductor microchips, and it hires foreign companies to
manufacture them. It is a major seller in the market for
integrated circuits that control the read-write heads used
in hard-disk drives. No later than 2001, Marvell became
aware of the work that Drs. Kavcic and Moura had just
done to improve the accurate detection of data recorded on
hard disks. Based on that work, Marvell engineers, as
they were designing chips in the competition for the next
generation of read heads, built a simulator to use as a
“gold standard” for testing their chip designs, and they
paid tribute to their source in dubbing the simulator
“Kavcic Viterbi.” Marvell engineers later designed what
they considered a “sub-optimal” version of the Kavcic
Viterbi for use in a new generation of Marvell chips, and
they again acknowledged Dr. Kavcic’s work as a source,
internally naming their design the “KavcicPP” (“PP” for
“post-processor”). Still later, Marvell created a detector
that its engineers recognized “turn[ed] out to be the
original structure that Kavcic proposed in his paper.” J.A.
46,779. From 2003 to 2012, Marvell sold 2,338,380,542
chips built around those designs. J.A. 6.
10    CARNEGIE MELLON UNIVERSITY     v. MARVELL TECHNOLOGY
                                                 GROUP, LTD

     In 2009, CMU sued Marvell for patent infringement
based on Marvell’s development, use, and sale of those
chips. The parties went to trial on whether Marvell
infringed claim 4 of the ’839 patent and claim 2 of the ’180
patent under 35 U.S.C. § 271(a), § 271(b), or § 271(c). A
jury found that Marvell infringed both claims under all
three subsections. The jury also found that Marvell had
failed to establish by clear and convincing evidence that
either claim was anticipated or would have been obvious
in light of the prior art.
     Based on CMU’s evidence at trial, the jury awarded
CMU $1,169,140,271 as a reasonable royalty for Marvell’s
use of CMU’s inventions, corresponding to a 50-cents-per-
chip royalty on Marvell’s worldwide sales. The district
court added $79,550,288 to bring the award up to the date
of judgment to reflect Marvell’s continued sales of accused
chips. Under 35 U.S.C. § 284, the court enhanced the
damages by 23%, adding $287,198,828.60 to the award,
based on its own assessment of the lack of objective
reasonableness of Marvell’s defenses at trial and the
jury’s determinations that Marvell knew of CMU’s pa-
tents and knew or should have known that its actions
were likely to infringe (and, also, that it had no objectively
reasonable defenses). The district court separately denied
Marvell’s affirmative defense that CMU’s delay in bring-
ing suit should bar pre-suit damages under the equitable
doctrine of laches, concluding that the equities ultimately
favored CMU because of Marvell’s copying.
    Marvell appeals rulings on infringement, invalidity,
and damages, as well as willfulness and laches. We have
jurisdiction under 28 U.S.C. § 1295(a)(1).
                        DISCUSSION
   We review rulings on issues not unique to patent law
under the standards of the relevant regional circuit. Info-
Hold, Inc. v. Muzak LLC, 783 F.3d 1365, 1371 (Fed. Cir.
2015). Accordingly, here we review the denial of judg-
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY      11
GROUP, LTD

ment as a matter of law de novo and must affirm if “there
is sufficient evidence to support the verdict, drawing all
reasonable inferences in favor of the verdict winner.”
Blum v. Witco Chem. Corp., 829 F.2d 367, 372 (3d Cir.
1987). We review for abuse of discretion the denial of a
new-trial motion challenging the verdict as against the
weight of the evidence. Rinehimer v. Cemcolift, Inc., 292
F.3d 375, 383–84 (3d Cir. 2002). We review jury instruc-
tions de novo, asking “whether the charge, taken as a
whole and viewed in light of the evidence, fairly and
adequately submits the issue in the case to the jury.”
Abrams v. Lightolier Inc., 50 F.3d 1204, 1212 (3d Cir.
1995) (quotation marks and citation omitted). Other
standards of review are noted as needed below.
                             I
    The general contours of the parties’ dispute on liabil-
ity—on invalidity and infringement—are familiar ones.
CMU developed what it believed to be a new and im-
proved way of doing something useful—here, detecting
recorded data accurately. In the written-description
portions of its patents, it presented, among other things,
an optimal way to achieve its stated advance. Its claims,
however, were not limited to the optimal embodiment.
They claimed not only the optimal approach but also a
broader class of processes that exploit the inventors’ key
insight to solving the problems of the prior art—here,
dealing with the difficulty of detecting densely packed
data on hard disks by changing the way one calculates the
branch metric functions used for retrieving that data.
    Marvell does not dispute that CMU made an advance
over the prior art or that the claims have support in the
written description. Instead, Marvell asserts, on the one
hand, that it never implemented CMU’s claimed methods
because it developed a “suboptimal” solution different
from CMU’s primary embodiment in the patents. And it
asserts on the other hand that, if CMU’s claims are con-
12    CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY
                                               GROUP, LTD

strued beyond the optimal embodiment, they must be held
invalid for claiming processes already known in the art.
    We conclude that the jury, properly instructed on the
applicable burdens of persuasion, could properly reject
both of Marvell’s arguments. The jury could find that the
claims at issue are not so broad as to encompass the prior
art at issue, but define a class of processes limited to
those not taught or made obvious by that prior art. Nor is
there any legal significance, standing alone, to Marvell’s
use of a “suboptimal” solution. The jury could find that
Marvell’s work differed from a particular embodiment of
CMU’s claims but came within the limitations set forth in
the language of the claims, which define the scope of the
protected invention. In other words, the jury could find
that the claims are located at the spot on the breadth
spectrum occupied by any valid, infringed claim: they are
broad enough to encompass the accused processes but not
so broad as to encompass the old or obvious.
                            A
    Marvell argues that there was overwhelming evidence
that the asserted claims were anticipated by U.S. Patent
No. 6,282,251, granted to Glen Worstell, or, in the alter-
native, that the claims would have been obvious in light of
the Worstell patent. In Marvell’s view, the evidence of
invalidity on those grounds was so strong that the jury
could not reasonably reject it, entitling Marvell to judg-
ment as a matter of law, and in any event the verdict
must be set aside as against the weight of the evidence,
requiring a new trial. Like the district court, we conclude
otherwise—for reasons that simultaneously dispose of
both of Marvell’s evidence-deficiency motions.
    “The burden of establishing invalidity of a patent or
any claim thereof shall rest on the party asserting such
invalidity,” 35 U.S.C. § 282, which the party must prove
by clear and convincing evidence, Microsoft Corp. v. i4i
Ltd. P’ship, 131 S. Ct. 2238, 2251–52 (2011). “Anticipa-
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY       13
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tion requires the presence in a single prior art disclosure
of all elements of a claimed invention arranged as in the
claim.” Connell v. Sears, Roebuck & Co., 722 F.2d 1542,
1548 (Fed. Cir. 1983). Marvell’s invalidity challenge fails,
because the jury could properly find that Marvell failed to
show by clear and convincing evidence that the Worstell
patent discloses, or makes obvious, “selecting a branch
metric function for each of the branches at a certain time
index from a set of signal-dependent branch metric func-
tions,” as required by claim 4 of the ’839 patent and, in
slightly different language, by claim 2 of the ’180 patent
(“selecting a branch metric function at a certain time
index . . . wherein the branch metric function is selected
from a set of signal-dependent branch metric functions”).
    The district court construed “signal-dependent branch
metric function” to mean “a branch metric function that
accounts for the signal-dependent structure of the media
noise.” Carnegie Mellon Univ. v. Marvell Tech. Grp., No.
09-cv-00290, 2010 WL 3937157, at *20 (W.D. Pa. Oct. 1,
2010) (quotation marks omitted). Under that construc-
tion, not contested here, Marvell contends that Worstell
discloses a set of branch metric functions that account for
the signal-dependent structure of the media noise. Antic-
ipation depends on that contention, and so does obvious-
ness, because Marvell makes no substantial argument for
obviousness independent of its contention about Worstell
on this point.
    Marvell points to a brief comment in Worstell that a
previously described branch metric function “can be
further modified to take into account transition noise,”
’251 patent, col. 10, lines 48–50, and argues that experts
for both sides agreed that “transition noise” is a type of
signal-dependent noise. The passage Marvell points to
explains that, rather than applying an identical branch
metric function to every branch, the function “can be
modified by multiplying the metrics which correspond to
transitions by a fraction which depends on the transition
14    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

noise standard deviation.” Id. col. 10, lines 54–56.
(“Transition” here refers to a change in magnetic polarity,
as might occur when a 0 is followed by a 1, or vice-versa.)
In Marvell’s view, the passage teaches two branch metric
functions—one for branches that do not correspond to a
transition and another, the same as the first but multi-
plied by a single fraction, for branches corresponding to a
transition. The two functions, Marvell says, form the
required “set” of signal-dependent branch metric func-
tions.
    The jury could reject Marvell’s position. Marvell’s ex-
pert himself noted that the branch metric function with-
out the fraction does not account for signal-dependent
noise and “it’s just that additional modification [i.e., the
additional fraction] [that] takes into account the signal
dependency.” J.A. 44,661–62. Moreover, the branch
metric function with the fraction is a single function: the
fraction that distinguishes it from the original, non-
signal-dependent Worstell function is a constant, not
varying from time to time, and any branch assigned that
function uses the same fraction-containing function. See
Carnegie Mellon Univ. v. Marvell Tech. Grp., No. 09-cv-
00290, 2011 WL 4527353, at *8 (W.D. Pa. Sept. 28, 2011);
Worstell ’251 patent, col. 9, Equation 20 and accompany-
ing text (filter tap weights Wi are constant); id. col. 10,
lines 48–66 (additional fraction is constant); J.A. 44,957–
58 (CMU expert); Oral Argument, No. 2014-1492, at 5:25
(Marvell agrees that additional fraction is constant). On
this record, it was not unreasonable for the jury to con-
clude that Worstell discloses at most one signal-
dependent branch metric function—the one with the
fraction—and not the claim-required “set.” There is no
dispute that “set” here requires more than one such
function, as the claims require selecting among a plurality
of such functions at a given time index.
    When Marvell argues here that “[b]oth functions must
be used to account for signal-dependent noise,” pointing to
CARNEGIE MELLON UNIVERSITY     v. MARVELL TECHNOLOGY          15
GROUP, LTD

the function without the fraction and the function with it,
Marvell Opening Br. 36, it confirms the basis for the
jury’s verdict. Marvell’s language confirms that the
unmodified and modified functions are each “functions.”
Only one, however, is signal-dependent. Marvell cannot
describe the choice between the two options as itself the
“function,” because that too would give Worstell only a
single “function,” not a “set.” Accordingly, Marvell’s
position is essentially that it is sufficient for the set collec-
tively to account for the signal-dependent nature of the
noise. But that is wrong under the clear claim language
as construed, which requires each of the functions them-
selves, the elements in the set, to account for that noise.
    Marvell never points to any evidence that Worstell
discloses multiple functions, each function possessing the
required property of accounting for signal-dependent
noise. The jury could find insufficient evidence that
Worstell teaches or suggests what the claim requires. We
therefore affirm the verdict of no proven invalidity.
                               B
    The jury found that Marvell both directly and indi-
rectly infringed the two (method) claims at issue by
developing, testing, and selling to its customers—notably,
some of the world’s leading makers of hard-disk drives—
products that practice the claimed methods. Marvell rests
its challenge to the jury’s finding solely on arguments
about whether its chips’ operation and one of its testing
activities meet the claim limitations. Marvell raises no
issue about other elements of infringement, such as the
knowledge element of indirect infringement. We reject
Marvell’s challenges, concluding that the jury had sub-
stantial evidence to support its verdict.
                               1
    The jury had sufficient evidence to find that use of the
products incorporating Marvell’s Media Noise Processor
16    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

(MNP) and Enhanced Media Noise Processor (EMNP)
designs infringes CMU’s patent claims—products we may
discuss together, Marvell not having identified differences
between them material to the outcome. CMU presented
substantial evidence that Marvell’s MNP and EMNP post-
processors carry out every step of the claimed methods.
See J.A. 41,815–28 (expert testimony); J.A. 34,941–59
(jury slides). CMU used Marvell’s internal documents to
show that Marvell’s devices first use a traditional Viterbi
detector (with traditional branch metric functions) to
identify the most likely symbol sequence and then use a
“post-processor” that recalculates branch metrics for a
subset of the branches corresponding to the most likely
errors. J.A. 34,941–59. Marvell’s devices calculate those
subsequent branch metrics using functions that change
over time, i.e., they select at certain times new parame-
ters that define a new branch metric function, and they
apply the different functions to multiple signal samples.
See J.A. 46,588. That essential characteristic is reflected
in the fact, noted above, that Marvell internally named its
post-processor the “KavcicPP” after one of CMU’s inven-
tors. For at least that subset of branch metric calcula-
tions, therefore, CMU presented evidence that Marvell’s
devices practiced the patents’ claims.
    Marvell argues that its method is carried out in a
post-processor and not a Viterbi detector, does not occur
“in a ‘trellis,’ ” and therefore is outside the claims. Mar-
vell Opening Br. 41–42. The parties stipulated that the
term “branch” means “a potential transition between two
states (nodes) immediately adjacent in time in a ‘trellis.’ ”
J.A. 3179. Marvell characterizes the calculations per-
formed by its MNP/EMNP post-processors as an evalua-
tion of error sequences, not branch metric calculations,
because they do not occur in a traditional Viterbi detector.
    The district court’s unappealed claim construction of
“Viterbi-like” defeats Marvell’s argument.       As noted
above, a “trellis” (a lattice whose nodes form a matrix) is
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY       17
GROUP, LTD

used as a graphical representation of the Viterbi detection
method. A trellis diagram shows all the possible branches
(symbol-to-symbol steps) for a given system. During
claim construction, Marvell argued to the district court
that the phrase “Viterbi-like” in the preamble to claim 4
of the ’839 patent limited the claim to detectors that
calculate a branch metric or perform “a step similar to
calculating branch metrics” for every branch of the Viterbi
trellis. Carnegie Mellon Univ., 2010 WL 3937157, at *22
(quotation marks and citation omitted). It argued that
“Viterbi-like” does not cover a post-processor that calcu-
lates a branch metric for only some, not all, branches,
citing the fact that during prosecution CMU distinguished
a prior-art reference that included a post-processor.
    The district court rejected Marvell’s arguments and
adopted CMU’s construction, which the parties and the
court understood to encompass a post-processor that
calculated some but not all branch metrics “in a trellis.”
Carnegie Mellon Univ., 2010 WL 3937157, at *22–25. The
district court properly concluded that CMU distinguished
the prior-art reference during prosecution not on the
ground that it used a post-processor but on the ground
that its post-processor did not apply branch metric func-
tions to a “plurality of time variant signal samples.” Id.;
see also J.A. 41,631–32 (Dr. Kavcic testifying to same at
trial). The court’s construction made clear, therefore, that
claim 4 of the ’839 patent is broad enough to cover a
method that calculates some but not all branch metrics in
accordance with the other claim limitations, regardless of
whether those calculations occur in a “Viterbi” detector.
And that is true a fortiori of claim 2 of the ’180 patent,
which does not even have the qualifier “Viterbi-like”
before the word “detector.”
    Given that construction, CMU’s evidence establishing
that Marvell’s post-processors carry out every step of the
claimed methods cannot be held insufficient on the
ground that the post-processors do not calculate metrics
18    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

for every branch of a trellis. Nor is the evidence made
insufficient by Marvell’s expert testimony that the Mar-
vell post-processor calculations do not produce branch
metrics because they calculate only the “difference” be-
tween two branch metrics of the Viterbi trellis branches.
J.A. 44,522–25. The parties’ stipulated construction of
“branch metric” requires simply a “numerical value of a
‘branch,’ ” J.A. 3179, and CMU presented evidence that
Marvell’s post-processors use and produce branch-specific
“numerical values.” J.A. 41,816–22, 44,017–20, 46,587–
88, 47,924, 54,266. For those reasons, the infringement
finding for the MNP and EMNP products must stand.
                             2
    The jury also had sufficient evidence to find that Mar-
vell infringed claims through its next-generation Non-
Linear Detector (NLD) chips. Marvell challenges that
finding on the ground that its NLD chips do not apply a
branch metric function to a “plurality of signal samples”
as required by the claims. We reject Marvell’s challenge.
    In Marvell’s NLD chips, the first stage of each branch
is a “noise whitening filter” that takes as input multiple
signal samples and produces a single combined output
that is then used to calculate the final branch metric.
J.A. 48,240–41, 48,249; see also J.A. 34,984. It is undis-
puted that the filter calculations may vary by branch and
with signal samples, and as Marvell’s own engineers
recognized, applying a “different noise whitening filter for
each branch” was “the original structure that Kavcic
proposed in his paper.” J.A. 46,779. For its NLD chips,
Marvell may have made some changes to eliminate some
redundancy in calculations, but it does not dispute that,
for at least some branches, its NLD chips take multiple
signal samples as their inputs, select parameters for the
function applied to those samples, and produce a branch
metric as a result. Marvell has not shown why that is not
enough under the claims as construed. And CMU’s expert
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY      19
GROUP, LTD

carefully showed element by element that the NLD chips
perform each of the claim-required steps. J.A. 41,847–57
(testimony), 34,976–87 (slides). The verdict of infringe-
ment for the NLD chips therefore must stand.
                             3
     Finally, the jury had sufficient evidence to find that
Marvell infringed when it used what Marvell called a
“simulator,” notably, when it used a computer to practice
the same methods it eventually implemented in its
MNP/EMNP and NLD chips. Marvell challenges that
finding on the grounds that “a simulation of a detector is
not itself a detector” and that, in any event, its simula-
tions did not apply branch metric functions to a plurality
of signal samples as the claims require. Marvell Opening
Br. 44. We reject Marvell’s challenge.
    Marvell mischaracterizes the claimed invention. As
used in the claims, the word “detector” does not refer to a
component for sensing the magnetic forces from the hard
disk, as Marvell suggests, a function performed by certain
electro-magnetic components in a “read head” in a hard-
disk drive—shown as a separate unit from the “detector”
in Figure 1 of the patents. The “detector” processes the
signal samples produced by the read head from its sens-
ing of the magnetic regions on a disk. The detector thus
indirectly detects the most likely orientations of the
magnetic regions (which encode data) given the signal
samples. The jury could find that Marvell was using just
such a “detector” in its “simulations” using a computer
more general than special-purpose chips.
     There was, additionally, ample evidence that Mar-
vell’s “simulations” operated on signal samples produced
from physical hard disks in hard-disk drives. CMU
showed that Marvell used its simulations to detect “data
that comes from a Toshiba hard drive.” J.A. 41,883 (also
noting similar evidence regarding Hitachi hard-disk
drives). Marvell notes in its brief here that its simula-
20       CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY
                                                  GROUP, LTD

tions process “data files (copies of actual wave forms).”
Marvell Opening Br. 44. The evidence, in short, was
sufficient to establish that Marvell’s simulations used
“detectors” on “signal samples.” At the same time, be-
cause it is undisputed that the simulations used branch
metric functions, the evidence also sufficed to establish
that the simulations applied branch metric functions to a
plurality of signal samples.
    Contrary to Marvell’s contention, Harris Corp. v. Er-
icsson Inc. does not show lack of infringement here. The
simple problem in Harris was that the claim required an
actual “communication system,” but Harris did not prove
that Ericsson’s actions, in “simulating” certain techniques
(also involving Viterbi detectors), involved any actual
communication system. A claim element was not proved
to be present. 417 F.3d at 1256. This case sharply differs
because no claim element was missing. Here, even the
“simulations” involved use of “signal samples.” The
meeting of all claim elements is the critical question, not
the use of the word “simulation,” which can mean differ-
ent things in different contexts. 3

     3  In a single clause, when introducing its Harris ar-
gument, Marvell states that if the claims reached its
simulations they would “cover an abstract idea not other-
wise subject to patenting.” Marvell Opening Br. 44. The
fleeting reference to “abstract idea” is not enough to raise
an issue of subject-matter ineligibility, and Marvell’s
actual argument following the reference rests on Harris,
which does not address that issue. Marvell neither cites
nor discusses either 35 U.S.C. § 101 or any case law under
it, much less any authority finding ineligibility of an
unconventional method, like CMU’s, for improving a
physical process by overcoming limitations in physical
devices—discerning more accurately what is on a physical
recording medium from what a read head has sensed. See
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY       21
GROUP, LTD

                             II
    Marvell’s remaining arguments challenge the mone-
tary remedies given for the infringement of CMU’s pa-
tents—the damages award and the continuing royalty.
We agree in part with Marvell’s challenges. We find error
in the enhancement of damages and error regarding
adherence to the territorial limits on the available reme-
dy. We reject Marvell’s other challenges.
                             A
    Marvell challenges the district court’s rejection of its
argument that the equitable defense of laches should bar
CMU’s recovery of damages for Marvell’s infringement
pre-dating CMU’s filing of this action. Although laches
requires proof of unreasonable, prejudicial delay in filing
suit, “[t]he application of the defense of laches is commit-
ted to the sound discretion of the district court.” A.C.
Aukerman Co. v. R.L. Chaides Constr. Co., 960 F.2d 1020,
1032 (Fed. Cir. 1992) (en banc). “A court must look at all
of the particular facts and circumstances of each case and
weigh the equities of the parties.” Id. Here, the district
court weighed the equities and concluded that Marvell
was not entitled to a laches defense to pre-suit damages.
We affirm.
    The district court conducted a thorough review follow-
ing the principles of our en banc decision in Aukerman. 4

Alice Corp. v. CLS Bank Int’l, 134 S. Ct. 2347, 2354 (2014)
(“[A]n invention is not rendered ineligible for patent
simply because it involves an abstract concept.
‘[A]pplication[s]’ of such concepts ‘to a new and useful
end,’ we have said, remain eligible for patent protection.”
(citations omitted; second and third alterations in origi-
nal)).
     4   CMU has preserved the contention that Auker-
man should be overruled, insofar as it allows a laches
22    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

It found that CMU’s delays in not filing suit until 2009,
after having notice of Marvell’s potential infringement as
early as 2003, “were unreasonable and inexcusable.”
Carnegie Mellon Univ. v. Marvell Tech. Grp., No. 09-cv-
00290, 2014 WL 183212, at *29 (W.D. Pa. Jan. 14, 2014).
The district court also determined that Marvell suffered
some evidentiary prejudice as a result of the delays, but
rejected Marvell’s contention that it had suffered econom-
ic prejudice, finding that Marvell, for its own economic
reasons, would have gone ahead with its infringement
regardless, accepting the risk of liability. Id. at *29–37.
Having found that Marvell satisfied the threshold re-
quirements to invoke laches under Aukerman, the district
court considered the entirety of the circumstances and
concluded that “the equities clearly favor CMU . . . rather
than Marvell, which copied CMU’s patents consciously
and deliberately for an entire decade.” Id. at *37.
     Marvell’s challenge to that conclusion rests entirely
on Serdarevic v. Advanced Medical Optics, Inc., 532 F.3d
1352 (Fed. Cir. 2008), where we said that “a plaintiff
relying on the unclean hands doctrine to defeat a defense
of laches must show not only that the defendant engaged
in misconduct, but moreover that the defendant’s miscon-
duct was responsible for the plaintiff’s delay in bringing
suit.” Id. at 1361. According to Marvell, the district court
could not weigh CMU’s delay in bringing suit against the
evidence of Marvell’s conscious copying without first

defense to pre-suit damages at all, in light of Petrella v.
Metro-Goldwyn-Mayer, Inc., 134 S. Ct. 1962 (2014), a
question currently under en banc consideration in SCA
Hygiene Products Aktiebolag v. First Quality Baby Prod-
ucts, LLC, No. 13-1564, 2014 WL 7460970, at *1 (Fed. Cir.
Dec. 30, 2014). Our affirmance of the denial of laches
does not depend on that broader legal contention.
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY      23
GROUP, LTD

concluding that the conscious copying caused CMU’s
delay. Marvell overreads Serdarevic.
     The plaintiff in Serdarevic made vague allegations of
misconduct, claiming “that the defendants’ ‘particularly
egregious conduct’ was the omission of Serdarevic as a co-
inventor.” Id. (citation omitted). We concluded that those
allegations did not rise to the level of particularly egre-
gious conduct that would defeat an otherwise-applicable
laches defense. We explained that, in previous disputes
about inventorship, courts had found a defendant’s mis-
conduct to be particularly egregious when it contributed
in some substantial way to the plaintiff’s delay. We
rejected the suggestion that any misconduct, including
“the very same conduct that forms the basis for [plain-
tiff’s] inventorship claims,” sufficed to weigh against
laches. Id. at 1361–62. “[I]n the context of an inventor-
ship action,” we explained, a plaintiff must go beyond
bare allegations of such conduct and show “that the
defendant’s misconduct was responsible for the plaintiff’s
delay in bringing suit.” Id. at 1361.
    The holding of Serdarevic, keyed to the inventorship
context, does not undermine the district court’s rejection
of laches in this case, based on its well-reasoned conclu-
sion that Marvell’s blatant and prolonged copying of
CMU’s inventions met the standard of particularly egre-
gious conduct. Serdarevic did not involve copying, let
alone egregious copying, and we did not hold that such
copying, to defeat laches, must have caused the unreason-
able delay. Nor does any other precedent cited by Marvell
restrict the relevance of copying.
    Indeed, the en banc court in Aukerman specifically in-
structed district courts to consider such copying, and it
did so without requiring that the relevant copying have
caused the delay: “Conscious copying may be such a factor
weighing against the defendant . . . .” 960 F.2d at 1033;
see also Gasser Chair Co. v. Infanti Chair Mfg. Corp., 60
24    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

F.3d 770, 775 (Fed. Cir. 1995) (“[T]he district court erred
in not considering that Infanti’s copying of Gasser’s chairs
could be egregious conduct.”). See also McIntire v. Pryor,
173 U.S. 38, 53–55 (1899) (discussing long history of
barring laches where defendant committed fraud, even if
fraud not responsible for plaintiff’s delay). That approach
is consistent with the equitable nature of the laches
determination, considering all relevant factors once the
threshold requirements are met.
    In this case, the district court went beyond the mere
conclusion of conscious copying. It considered the extent
and egregiousness of Marvell’s copying, the culpability on
the part of CMU in delaying suit, and the ramifications
for public policy of allowing a laches claim. It did not
abuse its discretion in concluding that the equities fa-
vored CMU and defeated Marvell’s defense.
                             B
    Marvell challenges the district court’s enhancement of
damages under 35 U.S.C. § 284, which says that “the
court may increase the damages up to three times the
amount found or assessed.” Where, as here, enhancement
is not asserted to rest on the infringer’s actual knowledge
that it was infringing, our precedent prescribes that a
district court may enhance damages only upon proof of
willfulness, which we have held to require “clear and
convincing evidence that the infringer acted despite an
objectively high likelihood that its actions constituted
infringement of a valid patent” and “this objectively-
defined risk . . . was either known or so obvious that it
should have been known.” In re Seagate Tech., LLC, 497
F.3d 1360, 1371 (Fed. Cir. 2007) (en banc); see also Safeco
Ins. Co. of Am. v. Burr, 551 U.S. 47, 57–58 (2007) (“stand-
ard civil usage” of “willful” reaches both knowing viola-
tions and those done in “reckless disregard”). We have
held that the second requirement is a factual matter
subject to review for substantial evidence. See SSL
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY       25
GROUP, LTD

Servs., LLC v. Citrix Sys., Inc., 769 F.3d 1073, 1090–91
(Fed. Cir. 2014). But we also have held that the first
requirement is not met when the infringer, whatever its
state of mind at the time of its infringement, presents in
the litigation a defense, including an invalidity defense,
that is objectively reasonable (though ultimately rejected),
and we have deemed that question a matter of law subject
to de novo review on appeal. See Halo Electronics, Inc. v.
Pulse Electronics, Inc., 769 F.3d 1371, 1381–83 (Fed. Cir.
2014). Following that approach, we reverse the willful-
ness determination and hence the enhancement.
                             1
    We begin with the findings and evidence regarding
what Marvell knew and should have known. The jury
found that Marvell knew of the patents before this action
began. J.A. 34,184–85. It also found that “Marvell actu-
ally knew or should have known that its actions would
infringe” the two claims at issue. J.A. 34,185–86. And
the district court itself made a “finding that Marvell acted
in a subjectively reckless manner with respect to the risk
of infringing the subject patents.” Carnegie Mellon Univ.
v. Marvell Tech. Grp., 986 F. Supp. 2d 574, 633 (W.D. Pa.
2013). We reject Marvell’s contention that those findings
cannot stand.
    Marvell concedes that its engineers “evaluated Dr.
Kavcic’s algorithm when designing the MNP” and does
not dispute that it knew Dr. Kavcic’s work was patented.
Marvell Opening Br. 71; see Carnegie Mellon, 986 F.
Supp. 2d at 632 (“Marvell’s engineers worked on multiple
projects bearing Kavcic’s name . . . .”). A January 2002
email from Marvell’s Greg Burd noted: “Kavcic’s detection
scheme is patented (assignee: Carnegie Mellon Universi-
ty, 2001).” J.A. 34,027. As indicated in Marvell’s repeat-
ed use of “Kavcic” in naming its work internally, the
evidence showed that “Marvell’s engineers duplicated the
technology described in Dr. Kavcic and Dr. Moura’s pa-
26    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

pers in their chips and simulators”; “shortly after begin-
ning work on the Kavcic model, Mr. Burd prepared a
preliminary write-up of the KavcicPP detector which
referenced the work of Dr. Kavcic and Dr. Moura,” a
write-up that “became the MNP circuit”; “Mr. Burd stated
that he was ‘generally following the papers,’ not the
patents, and that he ‘left it at that,’ ” but “the papers are
virtually identical to what is described in the patents”;
and “when Kavcic’s name was disassociated with the
project, there was no functional difference between the old
and new computer codes” and “the NLD used the original
structure proposed in Dr. Kavcic’s paper, and subsequent-
ly in the CMU Patents.” Carnegie Mellon, 986 F. Supp.
2d at 632–33.
    Marvell’s only responses to this robust evidence are
that it did not adopt the detailed algorithm laid out in the
CMU papers and the written description of the CMU
patents and that it obtained its own later patents for
what Mr. Burd described in the provisional application as
a “sub-optimal version of Kavcic’s detector,” J.A. 54,264.
Marvell Opening Br. 71–72. Neither response under-
mines the foregoing evidence. Indeed, the weakness of
Marvell’s responses tends to confirm the strength of the
evidence on what Marvell knew and should have known.
    That Marvell may not have ultimately copied the pa-
tents’ preferred embodiment does not show that it was, or
even thought it was, doing something outside CMU’s
claims—which the evidence from Marvell’s own docu-
ments and employees indicates it simply chose to ignore.
Similarly, as confirmed by the commonality of domi-
nant/subordinate patents, that Marvell sought and ob-
tained its own patents on particular detection techniques
does not mean that those techniques, much less the
specific accused Marvell actions, avoided the CMU patent
claims at issue. Many patents claim products or processes
that supplement or refine, and remain fully covered by,
inventions claimed in others’ earlier patents. See In re
CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY       27
GROUP, LTD

Kaplan, 789 F.2d 1574, 1577–78 (Fed. Cir. 1986); AbbVie
Inc. v. Mathilda & Terence Kennedy Inst. of Rheumatology
Trust, 764 F.3d 1366, 1379 (Fed. Cir. 2014). Thus, the
facts that Marvell sought and obtained patents gave it no
defense to patent infringement, see 35 U.S.C. § 282(b),
and did not establish a good-faith basis for believing that
it was not infringing.
                             2
    We agree with Marvell, however, that the enhance-
ment of damages must be reversed because the invalidity
defense it presented in this litigation was objectively
reasonable. Although we conclude that a jury could
properly reject Marvell’s invalidity defenses based on
Worstell, there was enough uncertainty about what
Worstell discloses and what CMU’s claims require that we
cannot say that the defenses were objectively unreasona-
ble. In this regard, it is significant, though hardly dispos-
itive, that the district court itself referred to Marvell’s
invalidity defense as a “close call” at the summary-
judgment stage. Carnegie Mellon Univ. v. Marvell Tech.
Grp., No. 09-cv-00290, 2011 WL 4527353, at *1 (W.D. Pa.
Sept. 28, 2011). We do not reprise the analysis of invalid-
ity set forth above. That analysis, we conclude, shows
simultaneously that the jury verdict rejecting the invalid-
ity defense must be upheld and that Marvell’s position on
invalidity was substantial enough that our enhancement
standard is not met.
    The district court, in concluding that the first Seagate
requirement is met, relied on several premises that are
contrary to governing law. The court reasoned that,
because invalidity “was a factual determination to be
made in this case[,] . . . the reasonableness of reliance on
such invalidity defense was also the prerogative of the
jury.” Carnegie Mellon, 986 F. Supp. 2d at 630–31 (foot-
note omitted). That view contradicts our standard of de
28    CARNEGIE MELLON UNIVERSITY     v. MARVELL TECHNOLOGY
                                                 GROUP, LTD

novo review of objective reasonableness as a legal matter
based on underlying facts.
     The court also relied on the proposition that it mat-
tered whether Marvell developed its invalidity defense
when undertaking its infringing activity. It said: “[I]n
order for Marvell to have a ‘reasonable defense’ to in-
fringement for the time period of 2001–2009, there needs
to be some proof that the basis for such invalidity defense
was known to the infringers or even the person having
ordinary skill in the art.” Id. at 630. The court stated
that “Marvell proffered no evidence that anyone at Mar-
vell knew of the Worstell Patent from 2001 until this
litigation began in 2009,” adding: “Even if the Court
concluded that Marvell has now put forth a reasonable
defense to infringement that has been developed during
litigation, such a determination would not be dispositive.”
Id. But our precedent is to the contrary. “The state of
mind of the accused infringer is not relevant to th[e]
objective inquiry” into the risk of liability to the defendant
necessary for a finding of recklessness. Seagate, 497 F.3d
at 1371. On that basis we have repeatedly assessed
objective reasonableness of a defense without requiring
that the infringer had the defense in mind before the
litigation. See Halo, 769 F.3d at 1381–83; Bard Peripher-
al Vascular, Inc. v. W.L. Gore & Assocs., Inc., 682 F.3d
1003, 1008 (Fed. Cir. 2012); iLOR, LLC v. Google, Inc.,
631 F.3d 1372, 1377 (Fed. Cir. 2011); DePuy Spine, Inc. v.
Medtronic Sofamor Danek, Inc., 567 F.3d 1314, 1336 (Fed.
Cir. 2009).
    The district court further seemed to confine its con-
sideration of Marvell’s defenses to those raised at trial,
excluding arguments presented earlier in the litigation,
such as at the summary-judgment stage.           Carnegie
Mellon, 986 F. Supp. 2d at 630–31 (“To the extent that
Marvell again believes the Court should deny a finding of
willfulness on the basis that the earlier defenses that
were not presented to the jury were reasonable, the Court
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY       29
GROUP, LTD

disagrees. If Marvell thought that any of those ‘other’
defenses were reasonable, it should have presented them
to the ultimate finder of fact, the jury.”). We see no basis
for that distinction. A defense may be objectively reason-
able and yet properly not be presented to the jury; exam-
ples include legal arguments such as claim-construction
arguments, but there may be other defenses that are
objectively reasonable yet not make the cut for consuming
the precious time and attention of the jury. Thus, we
have said that whether an infringer faced an objectively
high risk of liability should be “determined by the record
developed in the infringement proceeding,” Seagate, 497
F.3d at 1371, and that the record is not limited to evi-
dence presented to the jury.
    On the full record here, we conclude that Marvell had
an objectively reasonable defense to infringement. The
district court’s reasoning does not convince us otherwise.
We therefore reverse the enhancement of damages.
                             C
    Marvell presents several challenges to the jury’s roy-
alty determinations. It argues that the district court
abused its discretion in not excluding the testimony of
CMU’s damages expert, criticizing her qualifications and
her methodology. It argues that the evidence precluded a
royalty measured by 50 cents per unit and required a flat,
lump-sum fee not metered by the extent of benefit to
Marvell. And it argues that award improperly includes
“foreign chips in the royalty base.” Marvell Opening Br.
52. We reject all the challenges except the last: on that
issue we conclude that a partial new trial is needed, as to
those chips which never entered the United States, to
determine whether their “sale” can be said to have oc-
curred in the United States. With that exception, which
warrants a partial remand, we affirm (a) the judgment of
damages to the extent of $278,406,045.50, consisting of 50
cents per chip for the 556,812,091 chips that the jury
30     CARNEGIE MELLON UNIVERSITY     v. MARVELL TECHNOLOGY
                                                  GROUP, LTD

could find were imported for use in the United States, (b)
the judgment bringing the royalty award forward in the
supplemental damages, though the amount must for the
time being be adjusted by the district judge on remand to
chips imported, using a reliable estimate of chips import-
ed (based on the method of estimating imports presented
to the jury or another reliable method), and (c) the order
of an ongoing royalty of 50 cents per chip, also to be
limited on remand, pending a new trial on the remanded
issue, to a reliable estimate of chips imported.
                              1
    Marvell challenges the admission of the testimony of
CMU’s damages expert, Ms. Lawton, because in its view
she lacks relevant expertise and disregarded evidence
that Marvell believes favored its much lower damages
estimate. Ms. Lawton filed voluminous, thorough, clearly
structured, comprehensively documented expert reports.
The district court conducted an extended live preview of
her testimony and determined that she was qualified and
her methodology was sound. We review the admission of
her testimony for an abuse of discretion. General Elec.
Co. v. Joiner, 522 U.S. 136, 138 (1997). We find no abuse.
    Rule 702 of the Federal Rules of Evidence sets stand-
ards for an expert witness’s qualification and the sub-
stance of the expert’s testimony. As relevant here, the
witness must be “qualified as an expert by knowledge,
skill, experience, training, or education.” The testimony
must be “based on sufficient facts or data” and be “the
product of reliable principles and methods” that the
expert “reliably applie[s] . . . to the facts of the case.” The
latter requirements are rooted in Daubert v. Merrell Dow
Pharmaceuticals, Inc., 509 U.S. 579, 592–93 (1993) (re-
quiring that “the expert’s opinion will have a reliable
basis in the knowledge and experience of his disci-
pline . . . properly . . . applied to the facts in issue”).
CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY       31
GROUP, LTD

    Ms. Lawton does not have a Ph.D. or a traditional ac-
ademic appointment, but those credentials are not re-
quired by Rule 702’s qualification standard. Indeed, even
“education” and “training” impose no such requirement,
and the Rule provides for “knowledge,” “skill,” and “expe-
rience” as other bases for qualification. The Third Circuit
allows “a broad range of knowledge, skills, and training to
qualify an expert” as such. Pineda v. Ford Motor Co., 520
F.3d 237, 244 (3d Cir. 2008) (quotation marks and citation
omitted). That approach is consistent with the post-
Daubert emphasis on the substance of expert testimony
and with the facts that experience can be gained in many
venues and that knowledge can be demonstrated by
mastery displayed in an expert’s analysis and responses
to questioning about it.
     The district court acted well within its discretion in
rejecting Marvell’s attacks on Ms. Lawton’s qualifications
and general methodology. The court considered Ms.
Lawton’s “range of knowledge, skills, and training” and,
like the many other courts before which she has appeared,
deemed her qualified to testify as an expert on reasona-
ble-royalty damages. See Carnegie Mellon Univ. v. Mar-
vell Tech. Grp., No. 09-cv-00290, 2012 WL 6562221, at *14
(W.D. Pa. Dec. 15, 2012). The court also examined the
basis for Ms. Lawton’s testimony by reviewing her lengthy
expert report, two updated expert reports, and a supple-
mental report and by holding an extended Daubert hear-
ing at which CMU’s counsel “essentially conducted his
direct examination of [Ms.] Lawton.” Id. at *1. For areas
outside her expertise, such as details unique to the semi-
conductor industry, the district court properly concluded
that Ms. Lawton could, indeed must, rely upon CMU’s
other experts having such industry-specific experience.
Id. at *14; see Apple Inc. v. Motorola, Inc., 757 F.3d 1286,
1321 (Fed. Cir. 2014) (“Experts routinely rely upon other
experts hired by the party they represent for expertise
outside their field.”), partly overruled in respect not rele-
32    CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY
                                               GROUP, LTD

vant here by Williamson v. Citrix Online, LLC, No. 2013-
1130, 2015 WL 3687459, at *6 (Fed. Cir. June 16, 2015)
(en banc in part). And, as noted more fully below, Ms.
Lawton in fact took reasoned account of the evidence that
Marvell says that she “disregarded.” Marvell Opening Br.
47. In these circumstances, the district court did not err,
as to either qualifications or substantive methodology, in
admitting Ms. Lawton’s testimony.
                            2
    Marvell’s challenge to the jury’s award of a 50-cent-
per-chip royalty is similarly unfounded—whether this
challenge is viewed as going to evidentiary sufficiency,
weight, or admissibility. Marvell challenges both the
choice of a per-unit license instead of a flat fee and the
rate of the per-unit license. We see no reversible error in
either respect.
    35 U.S.C. § 284 guarantees to a patent holder “in no
event less than a reasonable royalty for the use made of
the invention by the infringer.” One approach to calculat-
ing a reasonable royalty that measures the value of the
use of the patented technology posits a “hypothetical
negotiation” between a “willing licensor” and a “willing
licensee” “to ascertain the royalty upon which the parties
would have agreed had they successfully negotiated an
agreement just before infringement began.”         Lucent
Techs., Inc. v. Gateway, Inc., 580 F.3d 1301, 1324–25
(Fed. Cir. 2009). That approach, like any reconstruction
of the hypothetical world in which the infringer did not
actually infringe but negotiated in advance for authority
to practice the patents, does not require “mathematical
exactness,” but a “reasonable approximation” under the
circumstances. See Dowagiac Mfg. Co. v. Minn. Moline
Plow Co., 235 U.S. 641, 647 (1915).
    A key inquiry in the analysis is what it would have
been worth to the defendant, as it saw things at the time,
to obtain the authority to use the patented technology,
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY       33
GROUP, LTD

considering the benefits it would expect to receive from
using the technology and the alternatives it might have
pursued. See AstraZeneca AB v. Apotex Corp., 782 F.3d
1324, 1334–35 (Fed. Cir. 2015). Thus, a “basic premise of
the hypothetical negotiation” is “the opportunity for
making substantial profits if the two sides [are] willing to
join forces” by arriving at a license of the technology.
Gaylord v. United States, 777 F.3d 1363, 1368 (Fed. Cir.
2015) (discussing reasonable royalty damages in a copy-
right suit). At the same time, “[t]he economic relationship
between the patented method and non-infringing alterna-
tive methods, of necessity, would limit the hypothetical
negotiation.” Riles v. Shell Expl. & Prod. Co., 298 F.3d
1302, 1312 (Fed. Cir. 2002); see Aqua Shield v. Inter Pool
Cover Team, 774 F.3d 766, 771 & n.1 (Fed. Cir. 2014).
    In the determination of what the negotiation over op-
portunities and alternatives would have looked like, “the
nature of the invention, its utility and advantages, and
the extent of the use involved” are important considera-
tions. Dowagiac, 235 U.S. at 648. Past licensing practic-
es of the parties and licenses for similar technology in the
industry may be useful evidence. But such evidentiary
use must take careful account of any “economically rele-
vant differences between the circumstances of those
licenses and the circumstances of the matter in litigation.”
Gaylord, 777 F.3d at 1368; see Ericsson, Inc. v. D-Link
Sys., Inc., 773 F.3d 1201, 1227–28 (Fed. Cir. 2014); Vir-
netX, Inc. v. Cisco Sys., Inc., 767 F.3d 1308, 1330–31 (Fed.
Cir. 2014); Finjan, Inc. v. Secure Computing Corp., 626
F.3d 1197, 1211–12 (Fed. Cir. 2010).
    This court has noted the common (not universal) eco-
nomic justifications for using per-unit royalties for meas-
uring the value of use of a technology: doing so ties
compensation paid to revealed marketplace success,
minimizing under- and over-payment risks from lump-
sum payments agreed to in advance. Lucent, 580 F.3d at
1325–26; see Gaylord, 777 F.3d at 1369. In common-sense
34    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

terms, a per-unit royalty here allowed Marvell’s payments
to vary with the sales its infringing activity produced,
which are a good way of valuing what it was worth to
Marvell to engage in that activity. Marvell nevertheless
contends that the evidence of the parties’ past practices
compels a finding that the parties would have agreed to a
flat fee, not a per-unit royalty. But because CMU pre-
sented sufficient evidence pointing to “economically
relevant differences” between those past practices and the
circumstances of the negotiation here, neither CMU’s
expert nor the jury was required to agree with Marvell.
    Although Marvell points to three lump-sum license
agreements that CMU granted to others for permission to
practice these patents, CMU explained to the jury that
the licensees in each of those instances had longstanding,
collaborative research partnerships with CMU and had
invested substantial sums over the years in CMU’s hard-
disk-drive focused research. Significantly, those licenses
were granted before CMU ever developed the patentable
technology; the licensees gave CMU money with no guar-
antee that any usable technology would result, sharing
the costs of uncertain research in the hope of a future
potential benefit. CMU likewise offered sound economic
reasons to distinguish the other licensing example Mar-
vell relies on—an offer to Intel to grant it, in return for a
lump-sum payment, a license to a portfolio of patents that
included one of the patents at issue here. Unlike Marvell,
Intel was a longstanding partner of CMU’s, contributing
substantial funds over the years to CMU’s research
efforts. And Intel was not in the read-channel business;
CMU sought to license its patents to Intel to get its
“stamp of approval” as a boost to its other licensing ef-
forts. J.A. 41,299–300. In short, there was sufficient
evidence to find that a royalty—by which the total dollar
(but not per-unit) amount of Marvell’s payment would
increase with the volume of sales it made based on its use
of the technology—was an economically reasonable pay-
CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY       35
GROUP, LTD

ment mechanism within the confines of the hypothetical
negotiation here.
    There also was ample evidence that 50 cents was an
appropriate amount for the per-chip license. CMU offered
evidence that, at the time of the hypothetical negotiation,
Marvell had no alternative to CMU’s technology, a conclu-
sion Marvell has not disputed here. E.g., J.A. 42,127
(CMU’s industry expert testifying that it was “life or
death” for Marvell to use CMU’s technology). There is
evidence too, after the fact but still relevant, that CMU’s
technology is so significant that it is used industry-wide.
J.A. 42,121, 42,127. At the time of the hypothetical
negotiation, Marvell faced strong market pressure to
improve the performance of its chips, and testimony and
internal documents showed (in sometimes-dramatic
language) that its previous attempt to produce a new
design was failing because the resulting chips produced
excessive heat. Finally, the evidence supported a finding
that, if Marvell could use CMU’s technology, it could pay
CMU 50 cents per chip and still meet its reasonable profit
goal—indeed, it would end up keeping upwards of three
quarters of the per-chip profit. J.A. 43,325–27.
    On the evidence presented at trial, the jury could
properly find that a royalty of 50 cents per chip reasona-
bly valued Marvell’s use of CMU’s technology and would
have been a good deal in the hypothetical negotiation.
Accordingly, subject only to the legal constraint based on
territorial limits, discussed next, the jury’s royalty deter-
mination must stand.
                             3
    What remains is Marvell’s invocation of the general
bar on extraterritorial application of our patent laws to
challenge the inclusion in the (past and ongoing) royalty
base of all of the chips resulting from Marvell’s “infring-
ing” use of the patented methods that Marvell sold,
worldwide. Specifically, Marvell contends that the dis-
36    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

trict court “erred in denying JMOL (and new trial or
remittitur) striking the portion of the damages award
that rested on sales of foreign chips that were manufac-
tured, sold, and used abroad without ever entering the
United States.” Marvell Opening Br. 52. That conten-
tion, notably, is limited, and appropriately so: Marvell
makes no meaningful extraterritoriality argument
against—and we see no problem with—applying the
royalty rate to chips that do enter the United States. But
there is a potential problem with including the chips
made and delivered abroad, and never imported into the
United States, unless those chips can fairly be said to
have been sold here. That question requires a remand.
    a. We begin with the governing law. The Supreme
Court has confirmed that the patent laws, like other laws,
are to be understood against a background presumption
against extraterritorial reach. Microsoft Corp. v. AT&T
Corp., 550 U.S. 437, 454 (2007); Deepsouth Packing Co. v.
Laitram Corp., 406 U.S. 518, 531 (1972) (superseded by
statute, see Microsoft, 55 U.S. at 442–45); Halo, 769 F.3d
at 1378–81; see Kiobel v. Royal Dutch Petro. Co., 133 S.
Ct. 1659, 1669 (2013) (similar principle applied to Alien
Tort Statute); Morrison v. Nat’l Australia Bank Ltd., 561
U.S. 247, 255 (2010) (Securities Exchange Act). The
background principle applies not just to identifying the
conduct that will be deemed infringing but also to as-
sessing the damages that are to be imposed for domestic
liability-creating conduct. Power Integrations, Inc. v.
Fairchild Semiconductor Int’l, Inc., 711 F.3d 1348, 1371–
72 (Fed. Cir. 2013) (applying principle in lost-profits case,
precluding damages for certain lost foreign sales); see also
WesternGeco LLC v. ION Geophysical Corp., No. 2013-
1527, 2015 WL 4032980, at *7–10 (Fed. Cir. July 2, 2015)
(rejecting lost-profits damages as improperly based on
foreign use in case under 35 U.S.C. § 271(f)(2)).
   Domestic actions often have extraterritorial effects,
and foreign actions domestic connections. Two sovereigns
CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY        37
GROUP, LTD

often might be able to apply their laws to closely related
aspects of what amount to an integrated economic activi-
ty—such as making something one place and selling it
elsewhere, or selling something one place to be put to
essentially its only use elsewhere. What constitutes a
territorial connection that brings an action within the
reach of a United States statute must ultimately be
determined by examining the “ ‘focus’ of congressional
concern” in the particular statute. Morrison, 561 U.S. at
266–67.
     For the present context, we think that § 271(a) pro-
vides the basis for drawing the needed line. It states a
clear definition of what conduct Congress intended to
reach—making or using or selling in the United States or
importing into the United States, even if one or more of
those activities also occur abroad. 5 Where a physical
product is being employed to measure damages for the
infringing use of patented methods, we conclude, territo-
riality is satisfied when and only when any one of those
domestic actions for that unit (e.g., sale) is proved to be
present, even if others of the listed activities for that unit
(e.g., making, using) take place abroad. Significantly,
once one extends the extraterritoriality principle to con-
fining how damages are calculated, it makes no sense to

    5   35 U.S.C. § 271(a) provides: “Except as otherwise
provided in this title, whoever without authority makes,
uses, offers to sell, or sells any patented invention, within
the United States or imports into the United States any
patented invention during the term of the patent therefor,
infringes the patent.” We need not separately discuss
“offers to sell,” which, we have held, requires a United
States location for the sale that is offered, not for the
offer. See Transocean Offshore Deepwater Drilling, Inc. v.
Maersk Contractors USA, Inc., 617 F.3d 1296, 1309 (Fed.
Cir. 2010).
38    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

insist that the action respecting the product being used
for measurement itself be an infringing action. Thus,
here the claim is a method claim, but the damages-
measuring product practices the method in its normal
intended use, cf. Quanta Computer, Inc. v. LG Electronics,
Inc., 553 U.S. 617 (2008) (applying exhaustion to sale of
unit that sufficiently embodies a method claim); and the
hypothetical negotiation would have employed the num-
ber of units sold to measure the value of the method’s
domestic use (before production and after), as discussed
above. In these circumstances, the inquiry is whether any
of the § 271(a)-listed activities with respect to that prod-
uct occur domestically.
    This approach accords with precedent. In Goulds’
Manufacturing Co. v. Cowing, 105 U.S. 253 (1881), the
Supreme Court approved an award, based on an account-
ing of the defendant’s profits, reaching units made in the
United States though some were to be used only abroad.
Id. at 256. In Railroad Dynamics, Inc. v. A. Stucki Co.,
727 F.2d 1506 (Fed. Cir. 1984), this court held that a
royalty award could reach units made in the United
States—valued at their sale price—regardless of whether
they were sold abroad. Id. at 1519. On the other hand, in
Power Integrations, we rejected a claim to lost-profits
damages based on the defendant’s “entirely extraterrito-
rial production, use, or sale of an invention patented in
the United States,” pointing to § 271(a). 711 F.3d at
1371–72; see also WesternGeco, 2015 WL 4032908, at *7–
10 (rejecting foreign use as basis for lost-profits damages).
    There are significant conceptual differences between
different measures of monetary compensation for in-
fringement—including between what agreement the
parties would have reached to value a defendant’s use of
the patentee’s technology (reasonable royalty) and what
amount of otherwise-made profits, based on sales at
certain prices, the patentee lost as a result of the defend-
ant’s use of the patentee’s technology (lost profits). See
CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY        39
GROUP, LTD

AstraZeneca, 782 F.3d at 1334–35; Warsaw Orthopedic,
Inc. v. NuVasive, Inc., 778 F.3d 1365, 1377 (Fed. Cir.
2015). But in the respect that is crucial here, we think
that there is a related constraint. In the lost-profits
context, this court indicated in Power Integrations that,
where the direct measure of damages was foreign activity
(i.e., making, using, selling outside § 271(a)), it was not
enough, given the required strength of the presumption
against extraterritoriality, that the damages-measuring
foreign activity have been factually caused, in the ordi-
nary sense, by domestic activity constituting infringement
under § 271(a). 711 F.3d at 1371–72. We think that the
presumption against extraterritoriality, to be given its
due, requires something similar in the present royalty
setting. Although all of Marvell’s sales are strongly
enough tied to its domestic infringement as a causation
matter to have been part of the hypothetical-negotiation
agreement, that conclusion is not enough to use the sales
as a direct measure of the royalty except as to sales that
are domestic (where there is no domestic making or using
and no importing). As a practical matter, given the ease
of finding cross-border causal connections, anything less
would make too little of the presumption against extrater-
ritoriality that must inform our application of the patent
laws to damages. See Morrison, 130 S. Ct. at 2884 (“[I]t
is . . . a quite valid assertion . . . that that presumption
here (as often) is not self-evidently dispositive, but its
application requires further analysis. For it is a rare case
of prohibited extraterritorial application that lacks all
contact with the territory of the United States. But the
presumption against extraterritorial application would be
a craven watchdog indeed if it retreated to its kennel
whenever some domestic activity is involved in the case.”).
    b. Marvell implicitly recognizes the significance of the
line for this case when it effectively limits its challenge to
inclusion in the royalty base of chips that were “manufac-
tured, sold, and used abroad without ever entering the
40    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

United States.” Marvell Opening Br. 52; id. at 55 (“total
sales are an impermissible measure of damages because
they correlate with the number of chips used worldwide,
and thus do not estimate use of the patented method in
the United States”); id. at 58 (making a similar argu-
ment against the jury instruction). In any event, we see
no extraterritoriality bar to including within the royalty
base those chips which were imported into the United
States for use in the United States. Section 271(a) makes
clear that Congress meant to reach such “import[ation]”
and “use[]” as domestic conduct. And we have been
presented no basis on which to deem legally insufficient,
or of deficient weight for new-trial purposes, the evidence
CMU submitted to the jury, based on industry data
sources, of how many of Marvell’s hard-drive chips were
imported into the United States.
    We therefore deny JMOL as to the royalty based on
those chips. We also deny a new trial as to royalties
based on those chips. Marvell’s claim of error in the jury
instructions affects only royalties based on chips whose
inclusion depends entirely on the location of sale. We
therefore affirm the judgment insofar as the royalty rests
on imported chips. The amount is certain (stated above)
up to the close of the damages period before the jury. On
the other hand, a recalculation by the district judge is
needed to confine the supplemental damages to such chips
(pending a retrial on the remaining-chip issue), and a
similar narrowing is needed for the collection of ongoing
royalties (pending retrial).
    c. As to the remaining chips, avoiding extraterritori-
ality in relying on those chips in the royalty base depends
here on whether they were sold in the United States,
there being no other applicable basis in § 271(a) to justify
CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY       41
GROUP, LTD

including those chips. 6 As to those chips, we draw two
conclusions. First, Marvell is not entitled to JMOL on the
evidence and legal arguments presented to us. Second, a
new trial is needed to determine whether the sales are
properly said to have been in the United States.
    The standards for determining where a sale may be
said to occur do not pinpoint a single, universally applica-
ble fact that determines the answer, and it is not even
settled whether a sale can have more than one location.
See Halo, 769 F.3d at 1378–79 (collecting cases; relying in
part on N. Am. Philips Corp. v. Am. Vending Sales, Inc.,
35 F.3d 1576, 1579 (Fed. Cir. 1994)). Places of seeming
relevance include a place of inking the legal commitment
to buy and sell and a place of delivery, see id.; Transocean,
617 F.3d at 1311; cf. Norfolk & W. Ry. Co. v. Sims, 191
U.S. 441, 447 (1903), and perhaps also a place where
other “substantial activities of the sales transactions”
occurred, Halo, 769 F.3d 1379 & n.1 (focusing on where
“substantial activities of the sales transactions” occurred,
but declining to decide whether the location of contract
formation on the facts of that case would have established
a sales location). At this point, we do not settle on a legal
definition or even to say whether any sale has a unique
location. The governing legal standards have not been
the subject of meaningful briefing here. Identifying those
standards, along with relevant factual development, is
better undertaken in the remand we order, in part be-
cause further factual development may narrow the legal
issues actually requiring decision. At present, we do not
have a full understanding of, among other things, what a
“design win” meant legally and practically, how such a
“design win” in the United States in this case compares

    6   For the ongoing royalty, the question is a present-
and future-tense question. For simplicity, we refer just to
the past in our discussion.
42    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

with the activities that occurred in the United States in
Halo (which were insufficient), and where specific chip
orders were negotiated and made final. Until fuller
exploration of factual and legal issues occurs on remand,
it is premature to rule on whether sales occurred in the
United States for the chips at issue.
     We do hold that, on the arguments presented to us,
Marvell is not entitled to JMOL that the sales did not
occur in the United States. The district court explained
that Marvell had the opportunity to present evidence at
trial that the sales took place only abroad and simply
failed to do so. Carnegie Mellon, 986 F. Supp. 2d at 644.
The court concluded that the record made at trial, includ-
ing but not limited to a joint stipulation about the sales
process, permitted the “jury to find that the sales occurred
in the United States.” Id. at 645, 646. We cannot con-
clude otherwise on the record here and on the limited
effort Marvell has made to develop legal arguments about
sale-location standards.
    Chip designers like Marvell sell customized chips with
designs specifically tailored for incorporating into custom-
ers’ products. J.A. 42,123–24 (Marvell VP of sales:
“[E]very chip that Marvell designs for a customer is
specifically aimed for that particular customer. It’s not,
cannot be sold to the, you know, in the general market.”).
Because of the customized nature of the chips, designers
and potential customers put themselves through a
lengthy “sales cycle,” involving extensive joint work over
several years, before any sale is made and chips enter
mass production. Only at the end of that sales cycle, if
the chip designer is successful, does it secure a “design
win,” but that win generally results in a customer’s exclu-
sive use of that designer’s customized chip for a certain
period, amounting to tens or hundreds of millions of chips
over several years. J.A. 43,654–55 (parties’ joint stipula-
tion on the sales cycle); see J.A. 44,426 (executive at
Western Digital testifying that when he “recommend[ed]
CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY         43
GROUP, LTD

that Marvell be selected as the read chip channel suppli-
er,” Marvell would become “the exclusive read chip chan-
nel supplier”). One executive from a now-defunct chip
maker called the industry a “winner takes all business.”
J.A. 42,121.
    Marvell’s facilities are in northern California, and
CMU’s industry expert, Dr. Bajorek, showed that “with
the exception of the chip making . . . all the activities
related to designing, simulating, testing, evaluating,
qualifying the chips by Marvell as well as by its customers
occur[ ] in the United States.” J.A. 42,159; see also J.A.
35,075–77 (charts showing relevant activity and where it
occurred); J.A. 43,650–55 (parties’ joint stipulation). He
also used Marvell’s records to show that Marvell, from
California, provided potential customers with samples
and simulations incorporating its designs. E.g., J.A.
42,147–48; J.A. 53,570, 53,572, 53,612, 53,613. Marvell
itself stipulated that “[d]uring [its] sales cycle, [its] engi-
neers assist [its] customers in implementing [its] solu-
tions into their product.” J.A. 43,654. And there was
some evidence suggesting that specific contractual com-
mitments for specific volumes of chips were made in the
United States. Carnegie Mellon, 986 F. Supp. 2d at 645
(referencing testimony that sales were “signed off on” in
California); J.A. 42,162 (similar testimony by CMU’s
industry expert). Marvell points us to no evidence to the
contrary.
    On this record, we cannot say that a jury could not
find the chips to have been sold in the United States
(perhaps not only in the United States). The parties’ chip
stipulation, cited above, suggests a substantial level of
sales activity by Marvell within the United States, even
for chips manufactured, delivered, and used entirely
abroad. That evidence is strengthened by the record
details regarding Marvell’s contracting process, and
Marvell has not pointed us to significant evidence that
would block an inference that sales commitments oc-
44    CARNEGIE MELLON UNIVERSITY    v. MARVELL TECHNOLOGY
                                                GROUP, LTD

curred in the United States. On this record, and the
current set of legal arguments about “sale” standards,
Marvell is not entitled to JMOL that the royalty base
must exclude chips not imported into the United States.
    On the other hand, we do not think that CMU is enti-
tled to affirmance with respect to those chips. In the
portion of the jury instructions at issue here, the district
court first confirmed a limit on infringement liability:
“Marvell cannot be found to have directly or indirectly
infringed in connection with chips that are never used in
the United States.” J.A. 45,456. It then added: “To the
extent, however, that Marvell achieved sales resulting
from Marvell’s alleged infringing use during the sales
cycle, you may consider them in determining the value of
the infringing use.” J.A. 45,456. Marvell challenges that
instruction on the ground that it “includ[ed] sales of chips
manufactured and sold abroad without entering the
United States.” Marvell Opening Br. 58.
    Marvell is wrong to the extent it argues that the ob-
jected-to sentence is incorrect. The jury properly was told
that it “may consider” any sales that resulted from the
infringing use in order to value that use: for the reasons
stated above, consideration of such sales was a sound part
of determining the reasonable royalty for the infringing
use. But Marvell is right in identifying something miss-
ing from the instructions, namely, an instruction that
required the jury to find a domestic location of sale as to
those chips not made or used in, or imported into, the
United States. For those chips, but not for those which
did enter the United States, the instructions did not
“properly apprise[] the jury of the issues and the applica-
ble law.” Dressler v. Busch Entertainment Corp., 143 F.3d
778, 780 (3d Cir. 1998) (quotation marks and citation
omitted).
   If Marvell had properly objected to the omission of
such an instruction, we would apply the usual instruction-
CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY       45
GROUP, LTD

review standards to find the omission erroneous, and we
would find the error harmful as to those chips not made or
used in, or imported into, the United States. See Forrest
v. Beloit Corp., 424 F.3d 344, 349 (3d Cir. 2005) (“An error
will be deemed harmless only if it is ‘highly probable’ that
the error did not affect the outcome of the case.”). Marvell
makes no meaningful argument about the jury instruc-
tions except for the non-imported chips. And CMU makes
no meaningful argument—at most it makes a passing
assertion—that the record effectively compelled a finding
as to the domestic location of all of the chip sales.
    As the district court pointed out, however, Marvell did
not properly object to the omission of an instruction
focusing on the place of sale for those chips which were
not made or used in, or imported into, the United States.
Carnegie Mellon, 986 F. Supp. 2d at 644–45. Marvell does
not show otherwise on appeal. And it has pointed to no
place in the record supporting its assertion that, before
the time arrived for presenting proposals, objections, and
arguments regarding jury instructions, the district court
had declared that the location of sales was legally imma-
terial. Accordingly, we consider Marvell’s objection here
only under the standard of “plain error.” See Franklin
Prescriptions, Inc. v. New York Times Co., 424 F.3d 336,
339–40 (3d Cir. 2005) (“Where a party fails to object
properly, we may review for ‘plain error in the instruc-
tions affecting substantial rights.’      Fed. R. Civ. P.
51(d)(2).”).
    We think that the plain-error standard is met in the
circumstances of this case. “Plain error review is discre-
tionary—it should be exercised sparingly and should only
be invoked with extreme caution in the civil context.” Id.
at 341 (internal quotation marks omitted). We are to
determine if the error was “fundamental” and caused
“prejudice resulting in a miscarriage of justice,” consider-
ing “the obviousness of the error, the significance of the
interest involved, and the reputation of judicial proceed-
46     CARNEGIE MELLON UNIVERSITY   v. MARVELL TECHNOLOGY
                                                GROUP, LTD

ings if the error stands uncorrected.” Id. at 340–41 (in-
ternal quotation marks omitted). Here, we conclude, the
standard is met because of the fundamental importance of
the extraterritoriality principle; the degree of obviousness
of the error in light of Power Integrations, decided after
the trial in this case; and the centrality of a sale-location
determination to satisfying the extraterritoriality princi-
ple for the bulk of the chips used for the royalty determi-
nation. That is enough for a “miscarriage of justice”
under a rule whose function is to produce only a new trial,
not a judgment as a matter of law for the objecting party.
    We accordingly must vacate the portion of the damag-
es award, original and supplemented, and the portion of
the ongoing-royalty order, which apply the royalty rate to
chips not made or used in, or imported into, the United
States. A new trial is required to determine whether
those chips were sold in the United States.
                       CONCLUSION
    For the foregoing reasons, we affirm the judgment
finding patent infringement by Marvell and rejecting
Marvell’s invalidity defenses. We affirm the denial of
Marvell’s laches defense. We reverse the enhancement of
damages. We affirm the royalty awards, past and ongo-
ing, in part, and we vacate in part and remand as de-
scribed in this opinion.
     No costs.
 AFFIRMED IN PART, REVERSED IN PART, AND
     VACATED AND REMANDED IN PART