Full opinion text
MEMORANDUM AND ORDER SARIS, District Judge. I. INTRODUCTION In this patent infringement case, plaintiff Bose Corporation accuses defendant JBL, Inc. and Infinity Systems Corp. (collectively, “JBL”) of infringing U.S. Patent No. 5,714,721, entitled “PORTING” (“the ’721 patent”), which relates to a port inside a loudspeaker enclosure used to radiate acoustic energy from inside the speaker to the awaiting listener outside the speaker. Bose seeks a finding that JBL willfully infringed the patent by incorporating the ’721 invention in several of its speaker models and continuing to sell those products even after JBL learned of the patent. Bose seeks damages in the form of lost profits, reasonable royalties, and a permanent injunction. Bose also seeks trebling of its damages and attorneys’ fees. JBL maintains that several of its products are non-infringing, and as to its admittedly infringing products, asserts that the ’721 patent is invalid on the grounds of obviousness and prior sale/offer for sale in the United States. After a jury-waived trial, I ORDER entry of judgment for the plaintiff, Bose. Bose is awarded damages of $5,676,718.32. I also ORDER that a permanent injunction enter, enjoining the defendants from further infringement of the ’721 patent. II. FINDINGS OF FACT AND CONCLUSIONS OF LAW A. Background 1. The Parties Both parties are in the business of making loudspeakers and audio equipment. Plaintiff Bose Corporation (“Bose”) was founded by Dr. Amar Bose about thirty-five years ago, and makes loudspeakers and audio equipment for the consumer and automotive market. Bose also makes headsets for pilots and passengers of commercial aircraft. The defendant, JBL, Inc. (“JBL”) was founded by James B. Lansing in the 1940’s, and is also in the business of designing and manufacturing loudspeakers. JBL entered the consumer loudspeaker business in the 1950’s, and has been in the business since that time. Defendant Infinity was founded by three aerospace engineers in the late 1960’s. Infinity set out to integrate aerospace engineering technology into the audio industry to improve performance of music systems. Infinity introduced the industry’s first satellite/subwoofer speaker system. Both JBL and Infinity are owned by Harmon, International. 2. Designing Loudspeakers: The Basics In modern loudspeaker systems, sounds are created by a “transducer.” A transducer converts electrical energy into acoustical energy by moving a suspended paper or metal diaphragm forward and backward in a linear manner. The movement of this diaphragm acts as an air pump, which creates sounds that are recognizable by the human ear. In an early loudspeaker design, called a “bass reflex” design, the transducer is mounted in a box that has a specially designed opening called a port, or vent. In a bass reflex speaker, most of the sound or acoustic energy radiates from the loudspeaker enclosure directly from the transducer itself. Specifically, the transducer radiates the bass sound into the listening environment throughout much of the lower frequency range (i.e., sounds that have a low pitch). The port opening is used to create a “Helmholtz resonance,” which is a sound that is created when air moves across the surface of any opening. By creating a Helmholtz resonance, the port serves to expand the range of bass sounds a speaker can produce at the lowest frequencies. After the bass reflex design, loudspeaker engineers developed the “coupled cavity” or “band pass” system, which is a fully enclosed box whose only opening is the port. In a band pass system, the transducer is housed completely within the enclosure and all sound radiates from ports. Here, the port assumes a more important role because it is the source of all sound. Ideally, the sound radiating from a speaker accurately represents the sound intended to be played. For example, if a stereo system sends a single pure tone to the speaker, then the speaker should respond with a single pure tone. However, in actuality, no speaker system is perfect, and various acoustic phenomena come into play. These include: nonlinearity; harmonic distortion; and port noise. A brief description of each of these concepts is important, because they highlight the challenges posed by loudspeaker design, the particular role of the port, and the function of the ’721 invention. Nonlinearity, or compression, is the term used to describe the nonlinear relationship between the input into the speaker, in terms of electrical power, and the output in terms of sound pressure level. Ideally, there would be a direct relationship between input (measured in volts) and output (measured in decibels) such that a graph depicting that relationship would form a straight line. In reality, however, the output does not measure up to what one would expect given the input. One of the functions of a port tube is to maximize the degree to which the input and output share a linear relationship. Two other “impurities” that affect the quality of the sound created by the speaker are harmonic distortion and port noise. Harmonic distortion consists of extraneous sounds at precise frequencies that are multiples of the base frequency. For example, in a loudspeaker playing a 50 hertz (Hz) tone, harmonic distortion occurs at 100 Hz, 150 Hz, 200 Hz, 250 Hz and so on. The effect of harmonic distortion is to change the sound by destroying the purity of the pitch. Harmonic distortion is a distinct source of unwanted extraneous sound, and can be measured separately. A good port will work to minimize the level of harmonic distortion. Port noise consists -of the extraneous sounds produced across the frequency spectrum. Port noise is a particular problem at high volume levels where large amounts of air must be moved back and forth within the port. The larger the volume of air moving through the port, the more erratic and “jumbled” the air flow becomes. This erratic behavior of the air as it moves through and exits the port tube is known as turbulence. Turbulence in the port creates port noise, which, at least in one form, makes a “chuffing” sound. Chuffing is similar to the buffeting sound created when a car window is rolled down on a highway. If it is present, port noise is the most notable thing a listener would hear. Thus, a good port design should also minimize port noise. 3. Port Noise Complaint In 1987, Bose introduced a three-piece loudspeaker design called the Acoustimass 5, consisting of a bass module and two small satellite speakers. The bass module produced the lower _ frequency, or bass, sounds while the satellite speakers produced the higher frequency sounds. The concept behind the Acoustimass system was to produce “virtually invisible” loudspeakers by building a'bass module that could be hidden anywhere in a room, and having small satellite speakers to reproduce the higher pitched notes. For the system to work properly, the listener must not be able to detect where the bass sound is coming from; the sound should be “non-localizable.” From the listener’s perspective, all bass sound should appear as if it is radiating from the small satellite speakers. The bass module of the Acoustimass 5, Series I was a band pass design, with the output transducers (or “woofers,” as they are known in the industry) buried within the enclosure itself. Essentially, all of the sound generated by the woofers radiated from the port in the side of the enclosure. The bass module of the Series I used straight, cylindrical ports. However, when the Series I system was played loudly, the bass module would emit port noise. The port noise contained higher frequency components, or chuffing, giving away the location of the bass module. This destroyed the “nonlocalizability” feature that was a goal of the system. The port noise problem became a focus of Bose engineers as they set out to design the Acoustimass 5, Series II bass enclosure to replace the predecessor Series I. Engineer Brian Gawronski began experimenting with a prototype bass box, first altering the cylindrical port tube by placing flared ends on the input and output side. After informal testing, Gawronski concluded that these ends would not provide a significantly better performance than the straight cylindrical port tube. Gawronski confirmed this belief by devising a test to measure quantitatively port noise. In the test, a computer generated a 50 Hz pure tone that was played by the bass module under test, and a microphone was placed about four or five inches away from the bass module. The computer applied the tone, and recorded the sound pressure produced by the 50 Hz tone being picked up by the microphone. The computer generated a graph with this data, showing the output of the bass module. Gawronski recorded these graphs in his notebook, which showed that the straight port with rounded flared ends exhibited some improvement over the straight cylindrical port. Gawronski did not consider that improvement to be sufficient, however, and continued to struggle with the port noise problem. In the spring of 1990, Gawronski shared his port noise complaint with his cubicle neighbor at Bose, engineer Gerald Caron. Inspired by a drawing of a jet aircraft engine on his wall, Caron suggested that Gawronski try shaping the input end of the port to resemble the intake of a jet engine. Not knowing what else to try, Gawronski took the suggestion. Gawronski recalled thinking that jet engines presumably had to work hard to get a smooth flow of large amounts of air into the engine at high speeds. He gave a copy of the jet engine drawing to his designer, who made “flares” for him in the model shop. Each flare later became an intake and output end of the port. After making the flares, the designer told Gawronski that the shape of the intake followed an ellipse. Gawronski then installed the elliptical flares into his prototype bass module and listened to them at the lab bench. He eventually experimented with two back-to-back flares to form an elliptical port. When Gawronski tested the prototype with the back-to-back elliptical flares, the port noise problem was gone. The elliptically flared port showed a 30 to 40 dB improvement over the straight cylindrical port, with 30 dB being about 32 times better and 40 dB being about 100 times better. With those results, Gawronski considered the port noise problem to be solved. The elliptical port design was incorporated in the Acous-timass 5, Series II. B. The ’721 Patent 1. The Disputed Claim On February 3, 1998, the U.S. Patent and Trade Office issued to Bose the ’721 patent, which discloses and claims a loudspeaker enclosure with an elliptical port. The only independent claim, Claim 1, reads as follows: A loudspeaker enclosure with at least one port for radiating acoustic energy to a region outside said enclosure and having an inside volume, said at least one port having an axis and characterized by predetermined acoustic mass intercoupling said inside volume and the region outside said enclosure having a smoothly flared output end within said inside volume, wherein said port defines a boundary between the acoustic mass therein and said inside volume, said boundary being defined by an ellipse having a major diameter. The only claim term in dispute in this case is the phrase “said boundary being defined by an ellipse having a major diameter.” The defendants concede that all the other limitations of claim 1 are met by the accused products. This Court has construed the phrase “ellipse having a major diameter” to mean the geometric definition of ellipse, a shape defined by the formula: where “a” and “b” are constants. See Bose Corp. v. JBL, Inc., 98 F.Supp.2d 80, 85-86 (D.Mass.2000). 2. Bose’s Use of the ’721 Patent Invention In addition to the Acoustimass 5, Series II, Bose incorporated the ’721 invention into subsequent Acoustimass and Lifestyle products. These include: the Acoustimass 5, Series III; Acoustimass 6; Acoustimass 7; Acoustimass 10; and Acoustimass 15 loudspeaker systems. Bose also incorporated the invention into its “Lifestyle” music systems and home theater products, including: the Lifestyle 5; Lifestyle 20; Lifestyle 25; Lifestyle 8; Lifestyle 12; Lifestyle 30; Lifestyle 40; and Lifestyle 50. In addition, Bose sells powered speakers that can be combined with a Lifestyle system to provide music to another room of a house, either in stereo or home theater sound. These speakers also contain the invention of the ’721 patent. 3. Meanwhile, over at JBL ... In 1994, JBL was selling two stereo products, the MUSIC 1 and MUSIC 2, which Bose claims competed with its Acoustimass 5, Series II system. The MUSIC 1 had four components: two bass modules, or subwoofers, and two satellite speakers. Each bass module included a cylindrical port with radiused ends. These systems had not been selling well in the marketplace. The engineers at JBL and Infinity were also struggling with the deficiencies of the straight cylindrical port tube. Sometime in the spring of 1995, JBL engineer Allan Devantier approached a mechanical engineer, Mona Lisa Alexander, and asked her to design a port tube that would minimize port noise and distortion. Ms. Alexander did not know initially the particular product for which she was designing the port tube; she later found out it was to be used for the redesign of the MUSIC 2 bass module. She understood that her goals in designing the port tube were to minimize noise, turbulence, and harmonic distortion in the port tube to improve its overall performance. Ms. Alexander, who has a degree in aeronautical engineering, drew upon her knowledge of fluid dynamics and mechanics as she set out to design her port tube. After finding nothing helpful in the audio engineering scholarship she consulted, she looked to a fluid mechanics textbook for guidance. Analogizing the port tube to a duct for transmitting fluid, Ms. Alexander concluded that both ends of the port tube should be flared and should have gradual transitions with an inlet that slowly converges and an outlet that slowly diverges. After adapting an illustration in her text that showed an inlet for a nozzle defined by a quarter of an ellipse, Ms. Alexander then realized that given her parameters, she would need to alter the figure used in the book. She decided upon an ellipse profile. Having settled upon the shape for the port tube, Ms. Alexander designed a computer model of the port tube. Next, actual prototypes were created and tested acoustically. Ms. Alexander did not participate in that testing. At some point during the testing, Ms. Alexander was asked if she’d like to see the prototype port tube installed in a bass module. She agreed, and went to a room where there were several bass modules. Ms. Alexander recalls seeing a Bose Acoustimass 5, Series II bass module in the room at that time, but had not seen one previously. It was Ms. Alexander’s belief that JBL had acquired a Bose module for comparative listening tests.' Ms. Alexander adamantly (and credibly) denies that she copied the Bose module in designing her port tube for JBL. Mr. De-vantier, however, admitted that JBL acquired Bose speakers to compare their acoustic features to JBL’s new systems. Moreover, in his monthly report updating the development of the MUSIC 10 series (the successor to the MUSIC 1), Devantier explicitly stated that the JBL prototype “will incorporate all the acoustic improvements we have been able to identify in a Bose subwoofer shaped box.” Devantier explained that he only meant to refer to the rectangular shape of the Bose sub-woofer box. I do not find this explanation credible. Devantier’s Product Brief of May 23, 1995 also links the JBL design directly to the Bose Acoustimass 5 (“AM5”) bass module, with an instruction to: “replace two small subwoofers with one subwoofer similar to the Bose AM5 subwoofer.” Certainly, Mr. Devantier was familiar with the design and engineering of the Bose AM5. The ultimate design of the MUSIC 10 was very similar to the Bose AM5; indeed, there was internal concern expressed to Devantier about those similarities. JBL also mimicked Bose’s marketing and trademark approaches in various ways. For example, JBL has used “Lifestyle,” a Bose registered trademark, to refer to its line of MUSIC 10 and MUSIC 20 products. Although Ms. Alexander independently conceived of an elliptical port, in other respects JBL did set out to copy the acoustic improvements, and market strategy for, the Bose subwoofer. JBL became aware of the ’721 patent almost immediately after its issuance in February of 1998; indeed, Bose filed this suit on the same day the patent issued. JBL did not obtain an independent written opinion of counsel on JBL’s legal posture in continuing to manufacture or sell speakers with elliptical ports. Instead, JBL relied on the advice of its counsel retained for its defense to the infringement suit. At that point, JBL was aware that several of its ports did contain an elliptical port tube, which the ’721 patent specifically called out. JBL considered retrofitting those products with non-elliptical ports, but did not do so. It is unclear whether or not JBL immediately stopped manufacturing all the products containing the elliptical port tube, but JBL did discontinue production of at least some of those products. But it is clear that JBL continued selling from its stock some of its products with elliptical ports. JBL then set out to design around the ’721 patent, aiming to make a port that was not a mathematical ellipse. Engineer Gregory Timbers, alerted to the existence of the patent by his superiors, began considering alternative shapes. Working with certain exponential equations, Timbers developed a smoothly flared port that he believed would not infringe the patent because it was not an ellipse. The result became known as the “exponential” port tube. Timbers alerted JBL Vice President Floyd Toole to this new port flare and showed him the math that defined it. Mr. Devantier also set out to design around the ’721 patent. He considered the properties of air flow, and the fact that the air in the tube would be accelerating quickly, then decelerating as it exited the tube. He developed three port shapes with smooth, continuous curves, and ran tests to measure their performance. He concluded that one port, which he called the Linear A, showed the most promise. He then gave his design engineers certain parameters so they could design the actual tube. C. Infringement 1. Literal Infringement An accused device may infringe in one of two ways: literally, or under the doctrine of equivalents. “Literal infringement requires that the accused device contain each limitation of the claim exactly; any deviation from the claim precludes a finding of literal infringement.” Litton Sys., Inc. v. Honeywell, Inc., 140 F.3d 1449, 1454 (Fed.Cir.1998). Determination of infringement, whether literal or under the doctrine of equivalents, is a question of fact. See Bai v. L & L Wings, Inc., 160 F.3d 1350, 1353, 48 USPQ2d 1674, 1676 (Fed.Cir.1998). In accordance with this Court’s construction of claim 1, Bose claims that JBL’s Linear A and exponential port tubes are, in fact, mathematical ellipses to one skilled in the art of loudspeaker design. Bose engineer Michael O’Connell, who has a masters degree in the field of human auditory perception and is pursuing a doctorate in electrical engineering at M.I.T., testified that by comparing laser scans of sample JBL port profiles, overlaid with a mathematical ellipse, certain of the JBL port boundaries coincide with a mathematical ellipse. As an example, O’Con-nell took a laser scan of JBL’s N24 port boundary (in other words, scanned an actual port), used a computerized graphics program to generate a mathematical ellipse, and overlaid the laser scan with the ellipse. (See Exh. Ill, attached). From a visual inspection, the two are indeed difficult to distinguish. O’Connell testified that, in the context of real world port consti'uction, the N24 port boundary would be considered to be defined by a mathematical ellipse. O’Connell offered the same opinion as to the other disputéd JBL models. JBL’s expert, Douglas Button, refuted O’Connell’s testimony that the laser scan with an ellipse overlaid demonstrated that JBL’s N24 boundary, for example, was defined by an ellipse. Button measured the differences between the laser scans of the JBL port tubes and the ellipses superimposed by O’Connell. Looking at each port tube, Button measured the differences in the cross-sectional radii between the two curves. The largest difference was exhibited by the SCS 125 port, which, at one point, deviated by 75 thousandths of an inch from the ellipse. The smallest difference was exhibited by the N24 port, which had a maximum difference of 10 thousandths of an inch. JBL also introduced evidence that the differences in radii of the actual ports as compared to the superimposed elliptical curves would result in a difference in the cross-sectional area of the portal between 4 and 12 percent. Bose tried to argue that such a disparity is meaningless in the “real world” of port design. There was also much baek-and-forth over whether the differences between the accused ports and a perfect ellipse would fall within “manufacturing tolerances.” After considering all the evidence, I find that the accused port tubes incorporating the Linear A and exponential curves do not literally infringe the ’721 patent. Despite extremely close visual similarities, literal infringement precludes any deviation from the claim as construed. 2. Doctrine of Equivalents An accused device that does not infringe literally may still infringe under the doctrine of equivalents, if the patent holder shows that the accused device performs substantially the same function, in substantially the same way, to produce substantially the same result as the claimed invention. See Graver Tank & Mfg. Co. v. Linde Air Prods. Co., 339 U.S. 605, 608, 70 S.Ct. 854, 94 L.Ed. 1097 (1950); Johnston v. IVAC Corp., 885 F.2d 1574, 1581 (Fed.Cir.1989). Based on all the evidence, I make the following findings. Function. The function of the ’721 patent is to couple energy from within the speaker enclosure to the environment outside the speaker enclosure and to reduce or prevent audible noise associated with air flow through the port. The function is spelled out within the patent itself, which makes reference to “a port or tube for radiating acoustic energy to the region outside a loudspeaker enclosure smoothly flared at each end” and highlights the “tapered cross section of the flared port [that] helps reduce turbulent airflow that might cause audible noise when radiating at high velocity levels.” See Exh. 1, column 1, lines 8-10, 23-25; column 2, lines 22-25. JBL’s expert, Mr. Button, agreed with O’Connell that the JBL ports perform the same function as the elliptical port of the ’721 patent, though he points out that all ports perform several other functions as well. “Infringement under the doctrine of equivalents is not precluded merely because the accused device performs functions in addition to those performed by the claimed device.” Insta-Foam Prods., Inc. v. Universal Foam Sys., 906 F.2d 698, 702 (Fed.Cir.1990). The Court may look at the intrinsic evidence in the patent to discern the function of the claimed invention. See Hill-Rom Co., Inc. v. Kinetic Concepts, Inc., 209 F.3d 1337, 1341 (Fed.Cir.2000) (looking in an equivalents analysis to specification to discern “major objectives” of the cushions recited in the claims). Way. The way in which the ’721 port accomplishes the function is by virtue of the flaring at both ends of the port tube, the continuous curvature of the port, and the decreasing cross-sectional area of the port from either end of the port to its center. Despite undeniable evidence that the Linear A and exponential ports also have a continuous curvature, flaring at both ends, and a decreasing cross-sectional area throughout, JBL offered evidence to rebut Bose’s argument that the ports perform in substantially the same way. JBL offered the testimony of its engineers, including Button and Devantier, who conducted a series of tests and measurements of various port tubes, including those with boundaries defined by an ellipse, an exponential curve, and a Linear A curve. Mr. Button testified that the JBL ports have a gentler flare rate toward the center of the port, which causes “turbulent eddies,” or little tornadoes of port turbulence, to form further down the port than they would in a port defined by an ellipse. But Button had no empirical or analytical data to support his opinion that these “eddies” form in a substantially different way in JBL’s ports. Mr. Devantier testified that he, , in fact, purposely avoided measuring the “turbulent eddies” that create port noise because they would create randomness in his tests measuring harmonic distortion. Finally, even if one accepts that turbulent eddies may form at different places along a port tube of an ever-so-slightly different shape, this does not rise to the level of a substantial difference in the way the ports operate to reduce port noise to inaudible levels. So, this basis for distinction was unpersuasive. Based on all the testimony, and given the specific function of the ’721 patent, I find that the JBL ports operate in substantially the same way as a port boundary defined by an ellipse having a major diameter. Result. The result of the ’721 patent invention is the reduction of port noise to inaudible levels when the speaker is played at high volume levels. The patent itself states that “the particular curvature is preferably such as to enclose a volume of predetermined acoustic mass while producing inaudible noise at relatively high power levels.” See Exh. 1, col. 2, lines 22-25. Mr. O’Connell offered his opinion that, given the laser scans of the JBL port tubes, and the listening tests he conducted, the JBL ports function in substantially the same way to achieve substantially the same result as the ’721 patent invention. Specifically, the minimal visual differences, in conjunction with the continuous curvature, smooth flare, and continuous decrease in cross-section from the ends of the port to the center, with the result that no port noise is audible, led O’Connell to this conclusion. O’Connell did not perform empirical measurements on the JBL products accused of infringement. However, based on his background in human acoustic auditory perception and in loudspeakers, he performed listening evaluations. He used a reference listening room at Bose to evaluate the JBL SCS 125 with a track of Madonna’s “Erotica” (not, unfortunately, in evidence) and heard no audible port noise. This contrasted with his testing of JBL’s MUSIC 1 which did have audible port noise. In response, Mr. Button testified that the result of the curvatures in the JBL port tubes is different than that of the curvature in the ’721 patent. His opinion is based upon a paper he and Devantier presented to the Audio Engineering Society (“AES”). In that paper, Button and Devantier reported the results of their tests of several different port designs, including the ellipse, Linear A and exponential port curves. Significantly, no JBL engineer performed these tests on any of the ports at issue in this case. Moreover, the tests performed in the AES study did not specifically measure port noise, but compared the different ports’ performance in the areas of harmonic distortion and linearity. Although Devantier suggested that measurements of harmonic distortion could be correlated to port noise induced by turbulence, Devantier also acknowledged that harmonic distortion exists independently. JBL engineer Greg Timbers also testified that turbulence-driven port noise and harmonic distortion are two different concepts. Bose’s expert, Mr. O’Connell, further undercut the usefulness of the AES study. O’Connell testified that he knew of no way to predict whether a port will decrease port noise at high levels by measuring harmonic distortion. Although the AES results show some differences among the different port tube designs in harmonic distortion characteristics, the study is not helpful in assessing whether JBL’s ports reduce port noise in a different way, or with a different result, than the Bose ports. O’Connell showed graphically that the differences in result with respect to harmonic distortion did not correlate with any minor differences in result with respect to port noise. I conclude that the AES study, which did not test the ports at issue and which measured port functions other than reducing port noise, is of limited use here. Similarly, the descriptions of how “turbulent eddies” would form differently in a port of slightly different shape do not rebut the compelling evidence of nearly indistinguishable port profiles that both reduce port noise to an inaudible level. I find that any differences in the results achieved by the slightest tweak in the curvature are not substantial. Throughout this trial, JBL has urged me to see the emperor’s new clothes. The ports look the same to the naked eye; the laser scans and measurements demonstrate that any differences in the curvature are de minimus. The ports sound the same to the naked ear with respect to the elimination of chuffing; no tests demonstrated perceptible audible differences. In sum, I find that the JBL port tubes defined by the Linear A and exponential curve formulas perform the same function in substantially the same way, with substantially the same result, and therefore infringe the ’721 patent under the doctrine of equivalents. D. Invalidity A patent is presumed valid, and the burden of proving invalidity rests with the challenger. See 35 U.S.C. § 282. Invalidity must be proven by facts that are supported by clear and convincing evidence. See National Presto Indus. v. West Bend Co., 76 F.3d 1185, 1189 (Fed.Cir.1996). JBL contends that the ’721 patent is invalid, under two different theories. 1. Prior Sale/Offer for Sale, 35 U.S.C. § 102(b) First, JBL claims that the invention of the ’721 patent was “in public use or on sale in this country, more than one year prior to the date of the application for patent ...” 35 U.S.C. § 102(b). Here, then, only prior art that existed more than one year prior to the effective filing date of the ’721 patent application, December 3, 1990, serves as the basis for a section 102(b) invalidity argument. To succeed on this theory, JBL must demonstrate, by clear and convincing evidence, that there was a definite sale or offer to sell more than one year before the application for the subject patent, and that the subject, matter of the sale or offer to sell fully anticipated the ’721 patent invention or would have rendered the ’721 patent invention obvious by its addition to the prior art. See STX, LLC v. Brine, Inc., 211 F.3d 588, 590 (Fed.Cir.2000); Tec Air, Inc. v. Denso Mfg. Mich., Inc., 192 F.3d 1353, 1358 (Fed.Cir.1999) (citations omitted); see also Scaltech, Inc. v. Retec/Tetra, L.L.C., 178 F.3d 1378, 1383 (Fed.Cir.1999) (“[T]he first determination in the § 102(b) analysis must be whether the subject of the barring activity met each of the limitations of the claim, and thus was an embodiment of the claimed invention.”). “The ultimate determination that a product was placed on-sale under § 102(b) is a question of law based on underlying facts.” Ferag AG v. Quipp, Inc., 45 F.3d 1562, 1566 (Fed.Cir.1995). JBL does not come close to meeting its burden with respect to a § 102(b) challenge to patent validity. JBL contends that activities associated with a loudspeaker called the “Glastonbury II” created prior art that anticipates claim 1 of the ’721 patent under § 102(b). To make its case, JBL relied on the testimony of a colorful audiophile named James Maxwell Townshend, owner of Townshend Audio in London, and his investor/customer, David Davies. According to Townshend, sometime in the early 1980’s, he developed the first version of the Glastonbury II, a bass reflex loudspeaker that had a port that was a doubly flared pipe. Townshend testified that the flares in this original version were plastic, were joined by a cylindrical sleeve, and when connected were in the shape of an ellipse. Sometime in the beginning of 1987, Mr. Townshend changed the design of his speaker and started manufacturing the second version of the Glastonbury II. Townshend switched from plastic flares to aluminum spinnings for his port, which were also joined by a cylindrical plastic pipe. Townshend testified that the aluminum flares on each end of the cylindrical pipe were supposed to be elliptical in shape, although he acknowledged that the port may have had a tapered or flattened section as a result of the manufacturing process. He claimed that this second version of the Glastonbury II was sold in Great Britain and other parts of Europe in 1987. But this second version was just too large, and in response to customer complaints, Townshend switched to a third version of the Glastonbury II to reduce the weight of the speaker. He testified that the third version had an aluminum enclosure with reduced depth; this change necessitated a change to a longer port. That longer port was not elliptically shaped; it had a straight cylindrical section in the middle. Townshend testified that his company shipped one pair of Glastonbury II speakers to the United States, to a Mr. David Davies, a Mend of Townshend’s who had invested money in Townshend’s business. Townshend testified that he sent the third version of the speakers to Davies in late 1987, or in the early part of 1988. Town-shend’s memory as to the timing of the shipment was, to say the least, shaky; he changed the date while on the witness stand, and acknowledged that he had repeatedly changed the date over the course of pre-trial depositions. Most importantly, he could not be sure which port was installed in the speakers he sent to Davies. He admitted that any speaker shipped after April of 1988 should have contained a long (non-elliptical) port. Townshend has no documents or other evidence to corroborate his testimony regarding the shipment to Davies, and most of his records relating to the several versions of the Glastonbury II were lost in a flood in Malta. Mr. Davies testified that he received the Glastonbury II speakers from Townshend sometime in the middle of 1988. Davies has no records documenting his receipt of the speakers. At some time during 1990, Townshend sent Davies replacement ports for the speakers. These replacement ports were yet another design, called a tractrix. Davies testified that he personally replaced the original ports when he received the tractrix ports, but could not say exactly what the original ports looked like. All he could recall is that the replacement ports were shorter than the ones he pulled out. Davies discarded the original ports. The testimony on the Glastonbury II was rife with uncertainty and inconsistencies. I find that there is no credible evidence that Mr. Townshend shipped Mr. Davies’ speakers containing an elliptical port tube during the relevant time period. Moreover, even if one assumed that , the speakers shipped to Davies contained the “short form” Glastonbury II, JBL did not prove by clear and convincing evidence that even the “short form” Glastonbury II qualifies as prior art under § 102(b). Because of the connecting piece in the center, which was at least originally designed to adjust the two ends, it is unclear whether the short form port was an ellipse having a major diameter. On that point, Bose introduced evidence that the “short form” Glastonbury II model recovered from Mr. Townshend’s friend’s storage unit has a slightly flattened center section. (Exh. 607). This deviation would prevent the short form Glastonbury II from satisfying each element of claim 1 of the ’721 invention. See Scaltech, 178 F.3d at 1383. JBL also offered evidence of a “public use” and/or “offer to sell” of Davies’ set of Glastonbury II speakers. According to Davies and Townshend, sometime at the end of 1998, they transported Davies’ Glastonbury II’s to the home of a Mr. Rick Roberts, the proprietor of a Hi-Fi store, and demonstrated them. But since neither Townshend nor Davies was sure of the structure of the port in Davies’ speakers at that time, it was not clearly established which version of the Glastonbury II Townshend was trying to sell to Roberts. This demonstration does not bolster JBL’s anticipation claim. In short, I find the entire Glastonbury II line of testimony and evidence to be unreliable. I accordingly reject JBL’s § 102(b) challenge. 2. Obviousness JBL’s second challenge to the validity of the ’721 patent is that its subject matter was obvious, as defined by 35 U.S.C. § 103(a): A patent may not be obtained though the invention is not identically disclosed or described as set forth in section 102 of this title, if the differences between the subject matter sought to be patented and the prior art are such that the subject matter as a whole would have been obvious at the time the invention was made to a person having ordinary skill in the art to which said subject matter pertains. Obviousness under § 103 is a legal conclusion based on underlying factual inquiries, including: a) the scope and content of the prior art; b) the level of ordinary skill in the art; c) the differences between the claimed invention and the prior art; and d) objective evidence of nonobviousness. See Graham v. John Deere Co., 383 U.S. 1, 15, 86 S.Ct. 684, 15 L.Ed.2d 545 (1966). When making an obviousness analysis based on prior art teachings, reviewing courts must not fall prey to a “hindsight syndrome,” reasoning backward from the teaching of the patent itself. See In re Kotzab, 217 F.3d 1365, 1369 (Fed.Cir. 2000). According to the Federal Circuit, “the best defense against the subtle but powerful attraction of a hindsight-based obviousness analysis is rigorous application of the requirement for a showing of the teaching or motivation to combine prior art references.” In re Gartside, 203 F.3d 1305, 1319 (Fed.Cir.2000); see also B.F. Goodrich Co. v. Aircraft Braking Sys. Corp., 72 F.3d 1577, 1582 (Fed.Cir.1996). In other words, something in the prior art, considered as a whole, must “suggest the desirability, and thus the obviousness, of making the combination” of different elements to create the invention. Fromson v. Advance Offset Plate, Inc., 755 F.2d 1549, 1556 (Fed.Cir.1985) (citing Lindemann Maschinenfabrik GMBH v. American Hoist & Derrick, 730 F.2d 1452, 221 U.S.P.Q. 481, 488 (Fed.Cir.1984)). a. The Prior Art; Comparison to the ’721 Patent The term “prior art” for purposes of obviousness refers to the types of art enumerated in 35 U.S.C. § 102. See OddzOn Prods. v. Just Toys, Inc., 122 F.3d 1396, 1403 (Fed.Cir.1997). Holding that prior art for purposes of section 103 includes art of subsections 102(a), (b), (e), (f), and (g), the OddzOn court explained that these subsections “relate to knowledge manifested by acts that are essentially public.” Id. at 1402. Subsections (a) and (b) relate to public knowledge or use, or prior patents and printed publications. See id. JBL offered evidence of several pieces of prior art relating to loudspeaker porting and fluid flow design which it claims render the ’721 patent invalid for obviousness. These include: the Laupman patent; the Furukawa patent; the KEF 104/2 loudspeaker; the International Organization for Standardization’s International Standard 5167 (“ISO 5167”) relating to fluid flow; the Akimichi patent; and the Town-shend Glastonbury II speakers and brochures. I will address each of these references briefly. Both the Laupman and Furukawa references were considered by the PTO Examiner during prosecution of the ’721 patent. This makes their utility in an obviousness analysis even more challenging for JBL. See Hewlett-Packard Co. v. Bausch & Lomb Inc., 909 F.2d 1464, 1467 (Fed.Cir.1990) (noting that the burden of showing patent invalidity “is especially difficult when the prior art was before the PTO examiner during prosecution of the application.”) Laupman/Furukawa. Neither Laup-man nor Furukawa discloses a port with a boundary defined by an ellipse. The La-upman patent discloses a loudspeaker enclosure with a port tube having smoothly flared input and output ends; however, the port contains a straight center section and straight sidewalls. In addition, one embodiment depicted in the Laupman reference suggests removing the curved bottom portion of the port and replacing it with a flat plane, which would result in a port with three flat sides. This teaches away from using an elliptical port boundary. The Furukawa reference discloses a port with a flat, cylindrical center section. While the input and output ends of Furu-kawa are smoothly flared, the Furukawa port is not smoothly flared throughout, nor does it have a continuous decrease in cross-section. Bose was forced to revise its patent claim to avoid a prior art rejection based on Furukawa. See Bose Corp. v. JBL, Inc., 98 F.Supp.2d at 90. KEF 104/2. The KEF 104/2 loudspeaker is the product of a British audio company that sold speakers in the United States in the late 1980’s and early 1990’s. It contains a port with a circular shape. One of the designers of the KEF 104/2, Laurie Fincham, testified at trial that his design was aimed at reducing turbulence, and that he chose a curved port to achieve that goal. But a laser scan and mechanical drawing of the KEF 104/2 demonstrates it contains a straight tangent on its boundary that constitutes approximately 20-25% of the total length of the port. (Exh. 584; 584A). JBL argues that the straight tangent section is not part of the boundary between the acoustic mass and the inside volume because the straight tangent section is within the loud speaker wall. Nonetheless, looking at the KEF 104/2, I am not persuaded that it would have been obvious to one of ordinary skill in the art to stretch the circular section to create an ellipse. ISO 5167. Formally, the ISO reference is International Standard 5167, entitled “Measurement of fluid flow by means of orifice plates, nozzles, and venturi tubes inserted in circular cross-section conduits running full.” (Exh. 585) JBL claims that the ISO article, which is not about a port tube but rather about fluid flow, rendered the ’721 invention obvious. The ISO reference was before the PTO Examiner; the sketch of the curved duct and a citation to the ISO reference were contained in the textbook on fluid mechanics submitted to the PTO Office during prosecution. (See Exh. 1, “OTHER PUBLICATIONS” section on title page). The ISO reference does not disclose a port, or a loudspeaker enclosure, but discloses an inlet nozzle for measuring fluid flow. Moreover, the ISO reference dealt with uni-directional fluid flow, from left to right, as opposed to the bi-directional fluid flow in a port tube. The ISO reference also indicates that the “throat” of the nozzle, leading to the outlet end, should be cylindrical. The PTO examiner found the ’721 invention patentable, even with the benefit of the ISO reference accompanying the Furukawa and Laupman prior art. Akimichi. The Akimichi reference, Japanese Patent 58,121,895, discloses a bass reflex loudspeaker having a “small space 9,” which is used in one of the disclosed embodiments to couple the inside volume of the loudspeaker to the outside. What defendants call the Akimichi “port” is built into the wall of the loud speaker. The “small space 9” is in a “Venturi shape,” which Mr. Button described as elliptical. The “small space 9” looks, at least in one embodiment, to be somewhat elliptical. (See Exh. 588, p. 3, Figure IS). As Mr. O’Connell described the Akimichi “small space 9” structure, Akimiehi’s design actually serves to dissipate acoustic energy that would otherwise be available to create sound in a room. Mr. O’Connell thus used the term “lossy” to describe the “small space 9,” meaning that there is a loss of energy output. According to O’Connell, the “small space 9” actually causes turbulence which in turn creates (rather than reduces) port noise. He believes that the port is actually “space 8.” Mr. Button disputed Mr. O’Connell’s interpretation of the “small space 9,” insisting that the patent nowhere indicates that the “small space 9” is lossy. Button insisted 'that the patent describes the function of the “small space 9” as “the essence of creating a Helmholtz resonance.” In other words, Button testified that the “small space 9” performs the functions of the port as defined in the ’721 patent. While the testimony describing the Aki-michi structure was conflicting (not to mention somewhat baffling) on this point, the patent describes the “air resistance due to the Venturi effect” created by the “small space 9.” (Exh. 583 at 2, ¶ 9). Moreover, the patent offers several examples of shapes which could form these “small spaces,” only one of which resembles an ellipse. The patent further explains that the key to obtaining this “Ven-turi effect” is to have a small space that “includes an arbitrary place with reduced diameter.” (Id at ¶ 13). Mr. Button acknowledged that, as described in the patent, the narrowest part of a “small space 9” can be at any arbitrary place. The AMmichi patent caused chuffing in my head because the translation and diagrams were so difficult to decipher. I found support for the hypotheses of both Button and O’Connell in the language of the patent. But based on the testimony and the descriptions contained in the patent itself, the defendant has not provided clear and convincing evidence that the AM-michi reference discloses an elliptical port tube. Most significantly, it does not teach toward the ellipse shape for the purpose of reducing turbulence and port noise within a loudspeaker. To the extent the “small space 9” actually creates turbulence and dissipates acoustic energy, it teaches away from the invention of the ’721 patent. To the extent its function was to create a Helmholtz resonance, it does not teach toward the use of an ellipse to reduce turbulence or eliminate port noise. Glastonbury II. Pushing on, we come to JBL’s final prior art reference offered in support of its obviousness claim: an old friend, the Glastonbury II. Given the dead-on-arrival line of inquiry regarding whether, when, and how Mr. Townshend sold or demonstrated his “short form” Glastonbury II port (which at least approximates the ellipse shape) in the United States, I find that the “short form” Glastonbury II is not prior art to be considered under an obviousness analysis because it is not prior art under § 102. See OddzOn Prods., 122 F.3d at 1402 (reasoning that prior art to be used in a § 103 analysis must qualify under one of the subsections of § 102). As for the longer, more cylindrical Glastonbury II port, it adds little to an obviousness analysis, even if included in the category of prior art (assuming, though it was not proven by clear and convincing evidence, that the speakers shipped to Mr. Davies contained the long form Glastonbury II). This is because the long form Glastonbury II is so similar to Furukawa’s cylindrical design. I consider the incarnations of Glastonbury II relevant only to the-extent that they are probative on the issue of level of skill in the art of loudspeaker design at the time of the invention. See Orthopedic Equip. Co., Inc. v. United States, 702 F.2d 1005, 1012 (Fed.Cir.1983) (stating that evidence offered in support of § 102 defenses, though insufficient for that purpose, may still be probative on level of skill in the art). JBL also offers, as prior art, brochures of the Glastonbury II. Under § 102(b), a printed publication qualifies as prior art, regardless of its origin. Townshend produced a brochure of the Glastonbury II, and claims he distributed that brochure in the United States. However, it is unclear which port was contained in the speaker advertised in that brochure. The photograph in the brochure is that of the original speaker cabinet which Townshend claims housed the short form port, but the brochure specifications reflect that the depth of the speaker is 18 inches; this would indicate that the brochure described the speaker with the long form of the port. The brochure itself does not indicate the shape of the port, but says simply: “the forward facing port is aerodynamically flared both inside 'and out to eliminate ‘chuffing.’ ” (Exh. 576). Suffice it to say that, given the discrepancies about which port was depicted in the brochure, it, too, is of limited usefulness in an obviousness analysis. In sum, I find that none of the prior art references discloses an elliptical port for use within a loudspeaker. Taken as a whole, the prior art does not contain a motivation or suggestion to make modifications, or to adapt various elements of different references, in order to create the invention of the ’721 patent. b. Level of Ordinary Skill in the AH Factors which are considered in determining the level of ordinary skill in a given art include: “the various prior art approaches employed, the types of problems encountered in the art, the rapidity with which innovations are made, the sophistication of the technology involved, and the educational background of those actively working in the field.” Orthopedic Equip., 702 F.2d at 1011. I have already reviewed the prior art, and as to the remaining considerations, the parties do not meaningfully dispute the level of ordinary skill in the art of loudspeaker enclosure design during the relevant time period. Their dispute lies in the ultimate question of whether a person of ordinary skill would have found the ’721 invention obvious. In terms of educational background and technical sophistication, I find that one of ordinary skill in the art during the relevant time period would be a person with a bachelor of science degree in either electrical engineering, physics, mechanical engineering, or possibly acoustics. That person would be familiar with aerodynamics, fluid flow mechanics, and acoustics, and would have worked as a loudspeaker designer for two to three years, having kept up with current literature and trade magazines to keep abreast of new developments. As stated earlier, the short Glastonbury II is relevant to prove the level of ordinary skill in the art, even if it is not prior art for purposes of section 103. Specifically, I consider the following litany of facts. At some point in the 1980’s, Mr. Townshend developed a double-flared port constructed of two half-pieces joined with a sleeve. Townshend was able to tune the port by moving the two halves. Although he described the Glastonbury II port tube as adjustable to magazine reviewers, Mr. Townshend testified that, in practice, he did not move the two halves apart from one another, and that the resulting profile of the port was “very close” to a mathematical ellipse. Townshend acknowledged that there may have been a slightly flattened portion due to the manufacturing process. Mr. Townshend said that he determined that an ellipse should be the shape of the port tube based on his personal experience with sailing a Hobie Cat and as an engineer. Evidence of a contemporaneous independent development is relevant to obviousness as a secondary consideration. See Monarch Knitting Machinery Corp. v. Sulzer Morat GmbH, 139 F.3d 877, 883-84 (Fed.Cir.1998). Townshend then changed the design of his speaker in response to customer complaints that it was too large; by reducing the size of the speaker, he had to lengthen the pipe connecting the two flared ends of his port. Townshend claims he sold the Glastonbury II with the “long port” from late 1987 to 1989. This “long port” has a straight cylindrical center section reminiscent of the Furukawa prior art. Notably, Townshend changed the port design yet again, moving further away from an ellipse shape to a “tractrix” shape, with a long cylindrical section. c. Objective Evidence of Nonobviousness Bose appropriately offered objective evidence of nonobviousness. Evidence such as “commercial success, copying, long felt need, is relevant, and when present must be considered.” Glaverbel Societe Anonyme v. Northlake Marketing & Supply, Inc., 45 F.3d 1550, 1555 (Fed.Cir.1995) (citing Stratoflex, Inc. v. Aeroquip Corp., 713 F.2d 1530, 1538-39 (Fed.Cir.1983)). Commercial Success. Bose did experience great commercial success with its products incorporating the invention of the ’721 patent. Bose’s sales of Acousti-mass and Lifestyle products increased significantly — over one third' — in the year after the patented invention was introduced in 1991. I will address the commercial success issues in more detail in my findings on damages, but I find that this factor does weigh in favor of nonobviousness. Copying. The documents prepared by Mr. Devantier certainly suggest that JBL was looking to its competitor Bose throughout the design and engineering of its loudspeakers. JBL admittedly had on site a Bose Acoustimass 5 bass module which it was using for “benchmarking” purposes. However, I found the testimony of JBL engineer Ms. Alexander to be very-credible. I find that, as to the elliptical port tube design, JBL engineers were working independently to develop a solution to the port noise problem. While I do not find that JBL copied the port tube itself, its adulation of the Acoustimass 5 bass module is the best evidence of the extent of its commercial success. Long Felt but Unmet Need. The dilemma of port noise in loudspeakers was a long-felt problem within the industry. Especially since the advent of the bass reflex and band pass enclosures, the port plays a much more dominant role. Mr. Fincham of KEF testified that in the 1984-85 time frame, KEF was concerned with port noise due to turbulence as it designed its 104/2 loudspeaker enclosure. Moreover, the Fu-rukawa patent, filed in 1989, is directed to the problem of port noise, and suggests a cylindrical port tube, lined with felt, as a solution. (Exh. 258). Mr. O’Connell from Bose, and Mr. Devantier and Mr. Button from JBL, agreed that the impetus to eliminate port noise, as well as other undesirable acoustic phenomena, was industry-wide. d. Hypothetical Claim Analysis Defendant urges the Court to use a methodology known as the “hypothetical claim analysis” to aid in determining whether the prior art prevents application of the doctrine of equivalents to a particular claim. See Marquip, Inc. v. Fosber America, Inc., 198 F.3d 1363, 1367 (Fed.Cir.1999). The Federal Circuit explained the two part inquiry with the following illustration: As a helpful illustration of the operation of this limitation on the doctrine of equivalents, this court visualized a hypothetical patent claim, sufficient in scope to cover literally the accused device. See id. [Wilson Sporting Goods Co. v. David Geoffrey & Associates, 904 F.2d 677 (Fed.Cir.1990)]; Key Mfg. Group, Inc. v. Microdot, Inc., 925 F.2d 1444, 1449, 17 U.S.P.Q.2d 1806, 1810 (Fed.Cir.1991) (“While not obligatory in every doctrine of equivalents determination, the hypothetical claim rationale ... helps define the limits imposed by prior art on the range of equivalents.”). Then this court examined whether the PTO would have allowed that hypothetical claim over the prior art at the time of invention. See Wilson Sporting Goods, 904 F.2d at 684. If the claim would have been allowed, then prior art is not a bar to infringement by equivalents. If the claim would not have been allowed, prior art bars a finding of infringement. Id. In particular, defendant points to KEF 104/2, Akimichi, and the Glastonbury II short elliptical port and claims that any hypothetical claim that would cover its Linear A and exponential curves would not have been patentable over this prior art. In examining the prior art, I conclude that the PTO would have allowed a hypothetical claim, for example, to a “substantially elliptical” port that is flared throughout and has a continuously decreasing cross-section. Such a claim encompasses the Linear A and the exponential curves, but does not sweep in the prior art. For the reasons stated above, there is no evidence that JBL’s curves, as used in the ports, were obvious in light of the three cited prior art references. e. Conclusion Although no one reference describes the claimed invention, JBL argues that the prior art taken as a whole contained a suggestion to combine the references. “If the invention is different from what is disclosed in one reference, but the differences are such that combination with another reference would lead to what is claimed, the obviousness question then requires inquiry into whether there is reason, suggestion, or motivation to make that combination.” Pro-Mold and Tool Co. v. Great Lakes Plastics, Inc., 75 F.3d 1568, 1573 (Fed.Cir.1996). Such a suggestion may come: (1) “expressly from the references themselves;” (2) “from knowledge of those skilled in the art that certain references, or disclosures in the references, are known to be of special interest or importance in the particular field;” or (3) “from the nature of a problem to be solved, leading inventors to look to references relating to possible solutions to that problem.” Id. (citations omitted). JBL is correct that the Court should consider the prior art as a whole, rather than simply piecemeal. Considered as a whole, however, I conclude that the prior art does not suggest the combination of various elements to form an elliptical port tube. The prior art references do not suggest that an ellipse would solve the problem of air turbulence at high volumes that causes port noise. Based on all the evidence, including the level of ordinary skill in the art, the prior art, and the objective factors, I find that the invention of the ’721 patent would not have been obvious to one of ordinary skill in the art at the time the invention was made. The most compelling evidence of obviousness, is the short Glastonbury II port, which was designed to be elliptical (though it likely had a flat section because of the manufacturing process) because it suggests a contemporaneous invention. But Mr. Townshend changed his port design repeatedly, moving in the direction from short to long, and then finally to a traetrix shape with a cylindrical section. This elongation demonstrates that the ellipse design was not an obvious means to reduce port noise. Finally, the objective considerations (most significantly commercial success) weigh in favor of nonobviousness. E. Willfulness Bose claims that JBL willfully infringed the ’721 patent. “Whether infringement is willful is a question of fact, and must be established by clear and convincing evidence.” See Comark Communications, Inc. v. Harris Corp., 156 F.3d 1182, 1190 (Fed.Cir.1998). A court looks to the totality of the circumstances, and the inquiry is whether the infringer acted in disregard of the patent, and “had no reasonable basis for believing it had a right to do the acts.” American Med. Sys., Inc. v. Medical Eng’g Corp., 6 F.3d 1523, 1530 (Fed.Cir.1993) (quoting Stickle v. Heublein, Inc., 716 F.2d 1550, 1565 (Fed.Cir.1983)). Courts are also required to consider any ameliorating or mitigating circumstances. See id. Generally, “a potential infringer with actual notice of another’s patent has an affirmative duty of care that usually requires the potential infringer to obtain competent legal advice before engaging in any activity that could infringe another’s patent rights.” Comark, 156 F.3d at 1190; see also Electro Med. Sys., S.A. v. Cooper Life Sciences, Inc., 34 F.3d 1048, 1056 (Fed.Cir.1994); Minnesota Mining & Mfg. Co. v. Johnson & Johnson Orthopaedics, Inc., 976 F.2d 1559, 1579 (Fed.Cir.1992). However, the fact that an infringer obtained an opinion of coun