HSSWHTPAPERRevE

© 2001 - 2003 American Technology Corporation

All Rights Reserved •Part # 98-10006-1100 Rev. E

H Y P E R S O N I C ™ S O U N D

Theory, History, andthe Advancementof ParametricLoudspeakers

A TECHNOLOGYOVERVIEW

Authors: James J. Croft, Chief Technology OfficerJoseph O. Norris, Non-Linear Acoustics

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Theory, History and The Advancement of Parametric Loudspeakers Rev. E •

Contents

The Beginnings of HSS at American Technology Corp ....................................................... 3

Early Experiments ............................................................................................................. 3

ATC’s Discovery of Parametric History and Theory ............................................................ 4

Non-Linear Acoustics 101 ................................................................................................ 4

The History of Parametric Acoustic Arrays in Air ................................................................ 6

Prior Art Efforts ...................................................................................................................... 9

Parametric Problems Remaining to be Solved in 1997 ....................................................... 13

Some Significant Problems of Prior Art Systems ........................................................... 13

Types of Solutions Required ........................................................................................... 13

A Partial List of Key ATC Proprietary Solutions ................................................................ 14

Signal Processing ............................................................................................................. 14

A Further Novel and Advantageous Approach to SSB ........................................................ 20

Transducer Technology ........................................................................................................ 21

General Requirements .................................................................................................... 21

Advancements in Parametric Emitter Development ........................................................... 24

Piezoelectric Film Parametric Transducer ..................................................................... 25

Parametric Loudspeaker Facts and Limits........................................................................... 27

© 2001 - 2003 American Technology Corporation • All Rights Reserved • Part # 98-10006-1100 Rev. E

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The Beginnings of HSS atAmerican Technology Corp

Early ExperimentsWithout any knowledge of other efforts with

parametric loudspeakers, initial attempts at de-modulating sound directly in the air at AmericanTechnology Corporation were conducted byElwood (Woody) Norris in his Poway, Californiagarage during the spring of 1996. The experimentsused two Goldstar FG-2002C signal generatorsand two Murata MA40A ultrasonic piezoelectricbimorph transducers. Each transducer was drivenindependently by a generator in an attempt to heara non-linearly generated difference frequency.Since the emitters were most effective at around39kHz, one was driven at 39kHz and the other at39kHz + xkHz, where x is an audible frequency. Ifx =1, the difference frequency is 1kHz.

A few transducer configurations were tried, in-cluding pairing them side by side (facing the sameway), facing them at 90 degrees from each other,and facing them toward each other. The differencefrequency effect was noticeable, but very weak(barely audible). The difference frequency couldbe more easily heard if the second generator’s sig-nal was repeatedly swept through a fixed range offrequencies. A range of 40kHz to 49kHz wouldgive a sweeping 1kHz to 10kHz difference fre-quency. The best results were obtained by pointingthe transducers at one another, while placing atube between them in order to amplify the weakdifference frequency signals.

It was thought at the time that the effectcould be related to “beats” since the beat frequencyis always the difference frequency. Beats are a lin-ear phenomenon, though. When two primarytones are summed or combined, they alternatelyreinforce and annihilate each other (at the differ-ence frequency rate). The resulting signal (whichhas a frequency of [f1+f2]/2) will come and go at aslow rate. The ear can only detect beat frequenciesof a few Hz. Signals with a higher beat frequency

just sound like a continuous tone, with a slightwarble. Also, it is important to note that a beat fre-quency is not an audio signal itself. It is simply therate at which two higher frequencies go in and outof phase. This is an example of linear superposi-tion.

Woody was able to show early on that the HSSphenomenon was not related to beats. He used awideband microphone and a spectrum analyzer toshow that a sum frequency was also present. It was,of course inaudible, being in the 80kHz range. Theexact cause of the tone was a mystery at the time.Woody suspected that there was a “non-linearity”in the air. What it was, we didn’t know.

In July of 1996, Woody Norris realized thatsending both frequencies through one transducerwould ensure that the airborne signals would alignand mix properly, and the effect would be maxi-mized because both signals (actually, a single com-posite signal) travel down a common axis. Herushed to his garage and tried it. He simply hookedboth signal generators to one emitter. The effectcould be clearly heard now. Soon, more transduc-ers were added to make clusters for more output.They were wired together so that the overall out-put was the sum of each individual emitter. Thetransducers were arranged in a hexagonal patternto maximize the number of emitters in a givenspace. Piezo bimorphs from both Murata andNicera were used, as were the lower outputPolaroid electrostatics. As previously stated, atATC it wasn’t known at the time that this had beendone before in other parts of the world. Still with-out the benefit of knowledge of the prior art, thefirst HSS patent filings were dated July 17, 1996.

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ATC’s Discovery of ParametricHistory and Theory

Non-Linear Acoustics 101A search was made at the San Diego State Uni-

versity library for references related to sum anddifference tones. The Journal of the AcousticalSociety of America had several papers mentioningsum and difference tones, but none found gavefurther theory or information. The phrase “Para-metric Array” was still unknown at ATC, sosearches were not performed under that name.

An acoustics text with a translated paper byHelmholtz was found. Titled, “On CombinationTones”, this paper provides a theory that is notcurrently accepted in the non-linear acousticsarena, but it is worth a brief look. In this paper,Helmholtz introduces his novel theory on howcombination tones (sum & difference) are gener-ated by a non-linear restoring force on a displacedmolecule. These were not subjective tones (a prod-uct of psychoacoustics, as were so-called “TartiniTones”), but ones that actually existed in the air.

He surmised that the ‘springs’ that keep airmolecules spaced apart exhibit a non-linear restor-ing force characteristic that manifests itself athigher displacement amplitudes.

Helmholtz’s theory and formulas predicted re-sults that initially seem to match what Helmholtzhad measured (and what we measured), so it wouldseem to be a valid theory.

However, the difference frequency amplitudeterm in his formula is interesting in that it predictsa rising level with a decreasing difference fre-quency which did not match our experimental re-sults. Other than two special cases we’ll return tolater, all HSS experiments to date had shown a fall-ing level for decreasing difference frequencies.Therefore, this theory needed to be set aside and anew one found.

Since two primary frequencies (in our case, ul-trasonic ones) are generating new frequencies inthe air, the shape of the primary wave must change

as it propagates. Fourier tells us that any wave canbe described with a series of sines and cosines. Ifone emitts two high-amplitude sine waves, as inthe Helmholtz example above, new frequencyterms appear, and the shape of the wavetrainchanges.

The accepted mechanism for this “propagationdistortion” is explained by A.L. Thuras, R.T.Jenkins, and H.T. O’Neil of Bell Labs in a 1934paper called Extraneous Frequencies Gener-ated in Air Carrying Intense Sound Waves, J.Acoust. Soc. Am. 6:173-180 (1935). The followingexplanation is taken from this paper, and from asimilar paper by L.J. Black, A Physical Analysis ofDistortion Produced by the Non-Linearity ofthe Medium, J. Acoust. Soc. Am. 12:266 (1940).

It turns out that if equal positive and negativeincrements of pressure are impressed on a mass ofair, the changes in the volume of the mass will notbe equal. The volume change for the positive pres-sure will be less than the volume change for theequal negative pressure. This can be seen in a plotof pressure vs. specific volume (1/r).

This is a qualitative picture of the relationshipbetween pressure and the inverse of density (theso-called specific volume).

This phenomena may be unfamiliar to those inthe relatively linear acoustics field of audio. Thewave equation which is customarily used in thesolution to acoustical problems is valid for smallsignal propagation only. The assumption involved

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in the derivation of the small signal wave equationis that the maximum displacement of the air par-ticles x be small compared to the wavelength l;x < l. In other words, the pressure fluctuations areso small that the specific volume appears to be alinear function of pressure. When this is not satis-fied, a plane wave or even a spherical wave propa-gated in the medium will not preserve its shape. Asa result, the magnitude of the fundamental de-creases and the magnitude of the distortion in-creases with propagation distance. A simpleexplanation of this phenomenon is given by L.J.Black. It goes as follows:

Each part of the wave travels with a velocity thatis the sum of the small signal velocity and the par-ticle velocity.

The maximum condensation in a wave is at thepoint of maximum pressure and this portion of thewave has the greatest phase velocity. The fact thatthe phase velocity is greater at the peak of the wavethan at the trough results in a wave whose shapechanges continuously as it is propagated.

Assuming the normal small signal velocity of c =344m/s and working through the equations with asound pressure level of 140dB (re. 20µ Pa) signal,gives a result of c ≈ 344.8m/s at the pressure peakof a wave.

This figure is only 0.24% higher than the smallsignal speed of sound. However, it says that thepeak will travel 80cm further than the ambient partof the wave in only one second. That’s a lot consid-ering the wavelength for a 40kHz signal is only8.6mm. In a 40kHz sinewave, the peak beginspropagating only 2.15mm behind the ambient(zero crossing), so for a 140dB signal it only takes0.0027s, or about 1 meter of propagation for thepeak to catch up to the zero crossing.

It should be noted that along with a travelingpressure wave, there are associated density andtemperature waves too. In other words, the densityand temperature at a point in space also varies withtime at the same frequency as the pressure wave.

The following chart shows the shape of a wavewhich has been distorted by the mechanism ex-

plained above. The blue line represents a puresinewave (a single-frequency signal); the red linerepresents the shape of the same wave after it haspropagated through the non-linear medium for atime.

The values used for the graph above are as follows:

SPL of the pure sinewave: 140dB (re. 20µ Pa)

Frequency: 40.0kHz

Propagation time: 0.0013 sec.

It can be seen that a high-amplitude sinewavetends to form into a sawtooth wave as it travels.The sawtooth wave contains odd and even har-monics. The 2nd harmonic is fully half the ampli-tude of the fundamental. This means that strongharmonics are created during the propagation of ahigh-intensity tone. Things get more interestingwhen there is more than one primary, or funda-mental, tone. In the two-tone case, f1 & f2, it canbe shown that the harmonics of each will appear, aswill the sum and difference frequencies, f1+f2 and|f1-f2|. This is the most simple case of a paramet-ric acoustic array.

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The History of Parametric AcousticArrays in Air

In late December of 1962, a Physics Professorfrom Brown University, Peter Westervelt, submit-ted a paper called Parametric Acoustic Array, J. Acoust. Soc. Am. 35 (4):535-537 (1963). Wes-tervelt considered primary waves interactingwithin a given volume and calculated the scatteredpressure field due to the non-linearities within asmall portion of this common volume in the me-dium. He goes on to describe the generation of adifference frequency tone along the collimatedbeam of a two-frequency signal. Many simplifyingassumptions were made, such as: no attenuation ofthe difference frequency, a perfectly collimatedprimary signal beam, the two primary signals at-tenuate at exactly the same rate, etc.

His was not as complete as the currently ac-cepted theory, but it was close. Some further re-finement was forthcoming, though.

In 1965, H.O. Berktay published the first paperthat gave an accurate and more complete theoreti-cal explanation of the parametric acoustic array:Possible Exploitation of Non-Linear Acousticsin Underwater Transmitting Applications, J.Sound Vib. 2 (4):435-461 (1965). His analysis wasmore general and more complete. He covers caseswhere the primary signals are expanding cylindri-cally or spherically, as well as the collimated planewave case we are interested in. He also didn’t limitthe analysis to the two-tone primary case. Rather,he uses the concept of the modulation “envelope”.This is very powerful because a parametric loud-speaker isn’t usually limited to making one tone ata time. The envelope analysis allows us to look atany primary signal spectrum. It turns out that thedemodulated signals (the ones we are ultimatelyinterested in) depend on this envelope function.

To illustrate the concept of an envelope, it’s use-ful to look at some examples. An unmodulated40kHz carrier signal looks like this in the timedomain (what you would see on an oscilloscope):

The black line running across the peaks of thewave is the envelope. Notice there is also a blackline running across the troughs. This can also beused as the envelope boundary. As a rule, the lowerenvelope is a mirror image of the upper one. Belowis the same 40kHz carrier, now being amplitudemodulated by a 2kHz tone.

The envelope function in this case isE(t)=1+cos(2*π*2kHz*t), or -[1+cos(2*π*2kHz*t)].With an amplitude modulated carrier, the enve-lope is simply proportional to the modulation sig-nal, plus an offset constant. Also notice that thelower envelope is a mirror image of the upper one.

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Berktay assumes the primary wave has the form

P1(t) = P1E(t)sin(ωct)

where ωc is the carrier frequency and E(t) is thearbitrary envelope function. For a point along thetransducer radiation axis, the secondary (or de-modulated) signal is

P12A ∂β

p2(t) = _________ ___ E 2(τ) where 16πρ0c0

4zα ∂t2

zτ = t – ___ is the lag time, and c0

+ 1γ β = ___ 2

A is the cross-sectional area of the primarybeam, z is the distance along the beam, andα is theattenuation factor of the primary signal. Theamount of demodulation decreases with distance,but the demodulated signal at a given distancesums in phase with what has already been created.Therefore, a virtual end fired-array is realized.Near the emitter, the demodulated signal levelactually increases with distance. It should be notedhere that the effective array length is 1/α, where ais the amplitude absorption coefficient.

To summarize the Berktay solution: the de-modulated signal in a parametric array is propor-tional to the second time-derivative of theenvelope squared: ∂2

p2(t)α ___ E 2(t) ∂t2

This is called “Berktay’s Far-Field Solution”because he assumes we are far enough away fromthe source to ignore the presence of any ultrasound(or primary frequencies). The solution is valid forthe near-field, but the ultrasonic primaries co-ex-ist with the demodulated signals. This is the funda-mental expression for the output of parametricacoustic arrays.

If we ignore the linear frequency response forthe moment and use the Berktay solution to derivethe non-linear result of inputting a single 2kHz

tone into a double sideband amplitude modulatorwe get an output that shows that two pure tonesresult from this envelope, and they both have thesame amplitude. The 2nd harmonic, 4kHz, has thesame amplitude as the 2kHz fundamental. This isequivalent to 100% THD. It is clear that raw AM(amplitude modulation with a carrier) does notgive the desired results. The envelope must eitherchange its frequency content or its offset.

First, lets maintain the 2kHz envelope, but in-crease its offset. This gives a time-domain signalthat looks like this:

To get this signal, the carrier amplitude in thefigure shown above, was simply increased by a fac-tor of five. This results in a decreased modulationpercent. The earlier case was 100% modulated,where this one is only at 20%.

Now the desired 2kHz fundamental frequencydominates. It is 10.5 times greater in amplitudethan the 2nd harmonic. This is ≈ 19% THD. Thedistortion has been reduced by a factor of five, butthe carrier level had to be increased by the samefactor. The audio level has also increased by a fac-tor of 5.25. Had the modulation % been main-tained while the power was increased by a factor offive, the audio level would have increased by a fac-tor of 25. By reducing the modulation index we aregiving up conversion efficiency for a cleaner signal.While the THD is reduced, it still isn’t very goodand our efficiency is poor with this method. Moreon this quandary later. This is just a preliminarylook at Berktay’s solution.

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Some years went by and Westervelt made a pre-sentation on non-linear acoustics applications. Heclaimed that the array would not work in the air.We’ll let Dr. Blackstock (University of Texas) pickup the story from here:

“The exchange occurred in 1971, at a meetingsponsored by the Navy in Washington, DC. Myrecollection is that the meeting closed with infor-mal presentations by one or more participants.One of these was Peter Westervelt. He observedthat no one up to now had reported a successfulparametric-array-in-air experiment; moreover,there had been rumors of a failed classified experi-ment on the subject. He then proceeded to givetheoretical reasons why the parametric arrayshould not be expected work in air. Orhan Berktayand I were sitting together, and we exchanged veryskeptical glances. When Peter sat down, very closeto where we were sitting, I couldn’t contain myself.I had the audacity to say, ‘Bullshit, Peter.’ I’ve of-ten wondered since then how I had the guts to saythat to the Grand Old Man of parametric arrays.Peter retorted ‘All right, you prove it!’

“The gauntlet having been thrown down, afterreturning from the meeting, I contacted MaryBeth Bennett and suggested that she do an experi-ment to demonstrate that the parametric arraydoes indeed work in air. I’m a bit hazy about theevents at this point, but I believe I consulted ElmerHixson, who had been an advisor of Mary Beth’s,before I spoke with her. He thought it was a goodidea but warned that it might be a tough experi-ment to do (he was right). I guess you could saythat Mary Beth pulled my chestnuts out of thefire.”

— David Blackstock

Soon, Mary Beth Bennett was busy with theParametric Array in Air experiments. In 1974,Mary Beth and Dr. Blackstock presented their re-sults. Parametric Array in Air, J. Acoust. Soc. Am.57 (3):562-568 (1975). They showed once and forall that the parametric array can be realized in theair.

They used an oil-filled hydrophone with outputmodes at 18.6kHz and at 23.6kHz (for a differencefrequency of 5kHz). The emitter can be seen todayin Mary Beth’s office. It has a circular center sec-tion for one frequency mode and a second concen-tric ring section for the other mode.Unfortunately, they had to deal with sphericallyspreading primary signals, and poor energy cou-pling to the air. Even so, they were still able toshow that the parametric array did indeed exist inthe air. They even showed an increasing amplitudedifference frequency signal when the propagationdistance was increased.

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Prior Art EffortsWhile working for another company, in late

1996, Jim Croft, now Sr. Vice President of Re-search & Development at ATC, provided his com-prehensive file of parametric loudspeakerhistorical papers and over the next few monthscompleted our parametric library with a group oftranslated papers on parametric theory and devel-opment.

It had now been brought to ATC’s attention thatother individuals and companies had previouslytaken an interest in the parametric array in air. Itturned out that many research papers have beenpublished on the subject. Most of the efforts di-rected at creating a practical device were based inJapan. The most notable authors of these worksare Yoneyama, Kamakura, Kumamoto, Aoki, andIkegaya.

In a paper called The Audio Spotlight: An ap-plication of nonlinear interaction of soundwaves to a new type of loudspeaker design, J.Acoust. Soc. Am. 73 (5), May 1983: pp1532-1536,Yoneyama, et al, makes an attempt at reasonableperformance with off-the-shelf components. Theauthors built a large hexagonal array of PZTbimorph emitters (547 pieces) that operate ataround 40kHz, with a secondary peak just below60kHz (typical of this type of emitter). In order toovercome the 12dB/octave frequency responseslope predicted by Berktay, they propose that theyshould equalize their incoming audio signal beforemodulating the carrier with double sideband AM.

This gives the desired frequency response (overa limited range) by decreasing the modulation in-dex for higher audio frequencies. For a doublesideband AM case with one audio frequency input,the demodulated audio signal amplitude will beproportional to m, the modulation index. The sec-ond harmonic amplitude is proportional to m2. Inorder to achieve low distortion with DSB AM, mmust be made as small as possible, at the expense ofefficiency. This is done to minimize “cross interac-tion” between the upper and lower sidebands, they

say. Since 12dB/octave is a severe slope and theaudio band is wide, a high modulation index mustbe used for the lower audio frequencies. A highamount of distortion would result for these fre-quencies.

In the actual experiment, they simply use thepeak of the emitters frequency response to equal-ize the audio signal. They achieve a flat responsefrom about 1.5kHz to about 7kHz. They also showsharp directivity for all audio frequencies. How-ever, their experiments show that the directivitydecreases for lower audio frequencies.

At the end of the paper, they state that such asystem could be used in a museum without soundbarriers between exhibits.

The next paper was from 1984, and it was pre-sented at the 10th International Symposium onNonlinear Acoustics. It’s called Developments ofParametric Loudspeaker for Practical Use(1984). They attack three problems. The optimumcarrier frequency, distortion correction, and insu-lating the listener from the ultrasound.

They state that the carrier frequency needs to beas low as possible, but not so low as to cause beamspreading. They recommend a frequency between30kHz to 70kHz. In order to correct for distortion,they introduce the concept of square-rooting themodulation signal which makes a lot of sense basedon the Berktay far field solution stating that theenvelope is squared by the air. They quickly dis-cover that this will require additional bandwidth. Aproblem we’ll explore more fully later on.

Their experimental device in this work consistsof 581 PZT bimorphs arranged in a square pack-age. They were able to show that for a few inputcases, the second harmonic output can be greatlyreduced while using square rooting. Finally, tominimize ultrasonic output, they propose anacoustic filter to attenuate the ultrasound at somearbitrary distance from the emitter.

The next paper is called A Study for the real-ization of a parametric loudspeaker, J. Acoust.Soc. Japan, June 1985. Again, they look at a few

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problems. First, the low conversion rate (fromelectrical to audio). They revisit distortion correc-tion and safety again too.

In order to improve efficiency, they suggest alower carrier frequency to make the array longer.Towards the end of the paper, they suggest 30kHzas a good trade-off between beam length, spread-ing, and safety. They also reiterate that a higherultrasonic SPL level increases gain, not just output,but they do not account for saturation effects.They do discuss how increasing the aperture sizecan be traded for a lower primary SPL. This is veryimportant.

On the distortion front, they speak in terms of asingle frequency audio signal. There are two waysto clean this up. One is square rooting, which re-sults in many sidebands. The other is by using twodiscreet primary tones (which is SSB) so the “inter-action of two sidebands” is eliminated. They don’trealize that the envelope in each case is the same,they only talk about removing the sideband inter-action. For more complex signals, they admit thatSSB distortion results from “non-linear interac-tion of the sideband itself”. This means that forcomplex signals, only square rooting with DSB willwork, but with the bandwidth penalty.

Finally, they use some packing material (a 4 wideby 5 feet long piece) to absorb the ultrasound be-fore the instrumentation (the mic). Unfortunately,this reduces the audible sound levels too.

The next work they published appeared inAcustica: Suitable Modulation of the CarrierUltrasound for a Parametric Loudspeaker,Acustica, Vol. 73, 1991, pp215-217. This is a shortpaper, and it deals with reducing the radiationpower requirement. Specifically, they discuss re-ducing the carrier level when there is no sound orwhen there is little volume needed. We call this adynamic carrier. Where the envelope will be flat,the carrier is suppressed altogether. This can savea lot of power, but does introduce additionalnonlinearity.

For the experimental portion, they use an even

larger array of 2000 bimorphs resonating at28kHz. They used a speech for the tests (84 sec-onds of a male news announcer). It is claimed, thatwithout degradation of the demodulated signal,they were able to reduce the power requirementsby more than 64% (390 Watts average power to140 Watts average power for the dynamic carrierversion). Impressive results.

Next is their paper called Parametric Loud-speaker—Characteristics of Acoustic Field andSuitable Modulation of Carrier Ultrasound,Electronics and Communications in Japan, Part 3, Vol.74, No. 9, 1991, pp76-81. There isn’t much newground broken here. They use a large array (1.4ftdia.) of 1410 emitters working at 27kHz and30kHz to create a 3kHz audio tone.

The main item of note in this work is an asser-tion (based on Merklinger’s earlier work, Im-proved Efficiency in the ParametricTransmitting Array, J. Acoust. Soc. Am. 58 pp.784-787 (1975)) that for smaller signal levels, thedemodulated signal is proportional to the envelopesquared (Berktay). With high amplitudes, theystate that the audio signal becomes proportional tothe envelope itself. They go so far as to say that thisoccurs around 130dB.

This would mean that square-rooting require-ments for distortion correction would go awaywith primary signal levels over 130dB. We havetried to verify this in our lab with no success. Thesingle tone SSB signal sounds cleaner at all signallevels, even above 140dB. Also, in response to ourinquiry, Dr. Blackstock has given this somethought and he isn’t willing to say that they arecorrect.

Next up is a paper called Parametric SoundRadiation from a Rectangular ApertureSource, Acustica, Vol. 80, 1994, pp332-338. Themain point of the paper is to compare the results oftheir experiment using a 24cm x 44cm (9.4in x17.3in) device generating 25kHz and 30kHz, withthe KZK (Khok-hlov-Zabolotskaya-Kuznetsov)non-linear parabolic equation. The KZK equation

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combines non-linearity, dissipation, and diffrac-tion in beams. It is a successive approximationmethod. It covers the generation of harmonicsfrom single-tone primaries. The KZK equationhas been shown to have good agreement with ex-perimental results when circular apertures wereused, but the authors wanted to try a rectangularsource. They concluded that in the far-field, therectangular source gave roughly the same results asa circular source of equal area would have.

For the experiment, they used 1102 small piezobimorphs. They were driven via a two-frequencysignal as mentioned above. The source pressurewas only 116dB, so little difference tone level isexpected. However, they did get a 79dB 5kHz sig-nal at 3.5m (which was the best distance for thissetup). When they went to a 128dB source level,they got more than 100dB of 5kHz at 3.5m. Theydo say that the harmonics (distortion) predictedwith a rectangular source are lower than those pre-dicted for a circular source. Finally, they complainof the computation time for far-field KZK analy-sis.

A final paper was published by the Japanesegroup called A Parametric Loudspeaker—Ap-plied Examples, Electronics and Communications inJapan, Part 3, Vol. 77, No. 1, 1994, pp64-73. As thetitle implies, the authors tried out some actual ap-plications to see where the technology can be usedsuccessfully. They also do some theoretical workusing a transformed beam equation that is solvedby “using an implicit backward finite differencescheme based on the Richtmyer method.”

They attempt first to make a compact emitterarray (so as to be practical) so they must considerthe best possible carrier frequency to maximize theultrasound to audio conversion. As they did previ-ously, it is stated that lowering the carrier makesfor a longer beam, but spreading begins to increaseif the carrier is lowered too far. They also make thecase that shock formation is a big inhibitor of dif-ference tone generation. This would seem to beintuitive. If the waveform cannot change shapefurther, it cannot continue to effectively make au-

dio signals.They compare the audio generated by 25kHz

and 30kHz primaries with the audio generated by50kHz and 55kHz primaries. Not only is the dif-ference tone slightly stronger (in the near field)from the lower frequency primaries, but the har-monic distortion is lower too. In the far field, thedifference tone is stronger yet for the low fre-quency case.

They state that the optimal carrier frequency isabout 35kHz, but that higher frequency primariesmay be safer to humans. They then construct anarray of 91 piezo bimorphs (1cm in dia. each). Theoverall size was 11cm in diameter, and they droveit with 30Vpp. The two primaries are 38.5 and41.5kHz for a difference of 3kHz. They estimate a134.5dB source level, and a 90dB difference level atabout 0.5 meters. They then generated bird chirp-ing sounds (similar to a crosswalk signal) and usedless than 100dB of ultrasound.

Finally, they compared a larger array (2208small piezo bimorphs) against a horn loudspeakerof similar aperture in a reverberant tunnel to checkfor speech articulation. The tunnel was long(1777m) and had 52dB of background noise (78dBwhen there are idling engines). They also filledpart of the tunnel with cars and trucks. They cite asubjective intelligibility scale of which the para-metric speaker wins in monosyllable tests andthree-syllable tests (the margin in the monosyl-lable test was close, they blame the modulator).They did say that in the noisy condition, the out-put was too low. But in the quiet, the parametricspeaker communicated better. Our experienceagrees with these findings.

As mentioned earlier, most of the prior art hasbeen from Japan, but there has been some workdone in other parts of the world, and domesticallyas well. While there haven’t been any recent papersthat break significant new ground regarding para-metric arrays, it is worth citing one more paper of

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note.It is titled: The Use of Airborne Ultrasonics

for Generating Audible Sound Beams, AudioEngineering Society, Presented at the 105th Con-vention, 1998 San Francisco, CA, by F. JosephPompei of the MIT Media Lab.

In this paper there is some mention of the priorart but, as it was with ATC in the early days, he ap-pears to be unaware of much of the work that hadbeen done previously. The paper goes on to pro-vide a good discussion the challenges of perform-ing the standard preprocessing scheme. That is,double integration and square rooting. It is notedthat infinite bandwidth is needed for a perfectimplementation of this scheme, consistent with theJapanese view, but it is considered that the side-bands decrease in level as they are further removedfrom the carrier such that a reasonably widebandultrasonic device may suffice.

A large array (≈ 35cm) of 60kHz (center fre-quency) wideband devices is used. Since the fre-quency response in this paper is a near-perfectmatch to the Polaroid single-ended electrostaticranging devices, referred to in early ATC experi-ments, it is assumed that these are most likely thedevices utilized. The main theme is the need forwideband ultrasonic devices to recreate the square-rooted audio DSB spectrum. The distortion re-duction achieved with square-root preprocessing issignificant and consistent with the expected resultsbased on the earlier Japanese research.

Figure 5 in his report is curious in that it showshigher SPL at 400Hz than it does at 5kHz. This islikely due to experimental error. Using a flat (ornearly so) response emitter results in about 12dB/octave of rolloff in the audio signal. A microphonecan be fooled (even a good one like the B&K 4138or the new 4939). It may be that the radiation pres-sure of the ultrasonic wavetrain is giving a falsereading. The radiation pressure will change at anaudio rate when doing AM, and will deflect a mi-crophone diaphragm at lower frequencies showingwhat appears to be much more extended low fre-

quency bandwidth than what is measured with aproperly filtered microphone or perceived audibly.

By the last half of 1997 research at ATC com-bined with the knowledge gained by the pre-1990papers gave the R&D group at ATC a knowledgebase for parametric arrays that allowed effectivemovement forward in pursuing and creating novelsolutions for the remaining problems inherent inparametric technology.

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Parametric Problems Remaining tobe Solved in 1997

With the state of the parametric loud-speaker art well defined and further advancementshaving stalled over ten years ago, it was now clear,through exposure to the body of previous paramet-ric investigation combined with extensive researchat ATC, what problems remained and what im-provements had to be made in each of the threemain system categories if a practical and usefuldevice were to be realized.

Some Significant Problems of Prior ArtSystems

1) Double Sideband and Preprocessed DoubleSideband Signal Processing

• high distortion or,

• low modulation index causing low conversionefficiency, or

• unrealistically wide bandwidth and high carrierfrequency requirements to achieve the idealmodulation envelope which when imple-mented causes reduced output and/or correc-tion terms appearing in the audible range asanother form of very audible, non-harmoni-cally related distortion;

• upper-to-lower sideband asymmetries limitingthe effectiveness of preprocessing

2) Piezoelectric Bimorph Transducer Arrays• mismatched transducers in multi-unit arrays

• sideband amplitude aberrations

• out-of-band subharmonics falling into theaudible range

• expensive multi-transducer arrays (500 ormore units)

• high distortion

• unreliable for sustained outputs of the requiredlevels

• insufficient ultrasonic bandwidths

3) Linear Ultrasonic Power Conversion• high dissipation of sustained half voltage

carrier operating at lowest efficiency

• very high dissipation due to reactive loadtransducer interaction

• poor load matching/power transfer

Types of Solutions Required1) Signal Processing

• A method for modulation and distortionreduction that:

a) is able to minimize distortion by creatingoutput that matches the ideal modulationenvelope while simultaneously;

i) does not increase bandwidth require-ments (preferrably even reduces band-width)

ii) allows high modulation index for goodconversion efficiency

iii) allows the lowest possible ultrasonicoperating frequency for greatest output

iv) eliminate the problem of upper to lowersideband symmetry

2) Emitter Design• An emitter that removes the limitations of the

prior art multiple bimorph transducers by:

a) eliminating the multi-transducer unit-to-unit variations

b) exhibiting very high efficiency, particularlyat the carrier and low frequency correlatedsideband frequencies

c) having adjustable resonant frequencyadaptive to various carrier frequencies &modulator types

d) elimination of out of band (audio range)subharmonics of the prior art devices

e) a monolithic structure for matched outputover surface and repeatable, simplifiedconstruction

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f) having ultrasonic bandwidth at least equalto that of the audio source

g) having greater than 140dB large signal ca-pability

h) having inherent low distortion

3) Ultrasonic Power Conversion• An ultrasonic power converter system that

provides:

a) good efficiency at low crest factors

b) efficient drive into ultrasonic reactive loads

c) impedance matching for efficient powerconversion into the load

Further it is important to work across the tech-nology areas to:

• integrate a narrow band modulation schemewith a transducer technology such that thecombination eliminates any unwantedaudioband artifacts

• integrate the power amplification intimatelywith the emitter load to maximize efficiencyand effective energy transfer

• correlate emitter resonant frequency, modula-tion carrier frequency, and amplifier matchingat those frequencies through an integratedrather than independent development

Through extensive research significant ad-vancements have been made in each area ofparametric loudspeaker system design, solving theabove listed problems and providing furtherimprovements.

A Partial List of Key ATCProprietary Solutions1) SIGNAL PROCESSING

• Half bandwidth modulation w/unprocessedzero distortion simple signals

• Zero bandwidth distortion correction

• Psychoacoustically favorable modulationmethod

2) EMITTER DESIGN• Monolithic film ultrasonic transducers

Electrostatic, Piezo-electric Film, andPlanar magnetic emitters

Pressure based PVDF

3) POWER CONVERSION• High efficiency ultrasonic power amplifiers

• Switching frequency/carrier frequency corre-lation

• Reactive power regeneration

• Switching filter/transducer impedance match-ing integration

Signal ProcessingIn order to convert the source program material

to ultrasonic signals, a modulation scheme is re-quired. In addition, error correction is needed ifdistortion is to be reduced without loss of effi-ciency. The goal, of course, is to produce the audioin the most efficient manner while maintainingacceptibly low distortion levels.

We know that, for a DSB system, the modula-tion index can be reduced to decrease distortion,but this comes with a cost of reduced conversionefficiency. The other choice that has been exploredby us is so-called “square-rooting” of the audiobefore modulation. This gives the proper envelopefor a DSB system and allows for a high modulationindex, but it requires large bandwidths whenimplemented properly. In fact, since the lowersidebands extend out so far below the carrier, the

15


carrier frequency needs to be pushed much higherin order to keep sidebands out of the audio range.On the upper sideband, ultrasonic absorption,among other impediments, limits the ability toproduce the desired bandwidth. But, a high carrierfrequency is also less efficient for parametric con-version than a lower one.

The three signal processing performance issues/problems with parametric loudspeakers are: highdistortion, low efficiency/output, and an unreason-able bandwidth requirement. Any two of these canbe easily overcome, but as a direct result the thirdproblem will be maximized. This quandary is ex-plored in the following paper: Parametric Arrayin Air: Distortion Reduction by Preprocessing,Thomas D. Kite, John T. Post, and Mark F.Hamilton. Proceedings of the 16th International Con-gress on Acoustics and the 135th Meeting of the Acous-tical Society of America, 20-26 June 1998 p1091.

They explore the theoretical results of raisingand lowering the modulation index, the carrier fre-quency, and the use of square-rooting. It is as-sumed in the paper that the only way to get asquare-rooted envelope is to use an audio square-rooter before the modulation step. One of the au-thors (the faculty advisor to this paper), MarkHamilton, had even said that the only way to get asquare-rooted envelope was with an audio square-rooter. This is not the case, as will be demonstratedbelow. Mark Hamilton, David Blackstock, andElmer Hixson were all shown how it could be doneduring a presentation by Joe Norris (co-author ofthis document) while presenting ATC’s technologyat the University of Texas.

Since there is a direct relationship between themodulation index and the resulting conversionefficiency, a high modulation index is desirable. Sohow can we achieve low distortion without a highbandwidth requirement? If square-rooting werethe only option, ideal distortion reduction of a fullband audio signal would be very difficult toachieve. Remember, Berktay’s solution says thatthe audio signal will be proportional to the enve-lope, not the spectrum. While each spectrum has

only one envelope, fortunately, there is more thanone spectrum that can be used to achieve the idealenvelope shape. How this can be turned into anadvantage will be explored below.

In the prior art parametric loudspeakers, twobasic approaches have been utilized; double side-band amplitude modulation and double sidebandamplitude modulation with square root prepro-cessing (always with a carrier when used for para-metric conversion).

In terms of general approaches to amplitudemodulation for non-parametric uses, there is an-other scheme called Single Sideband (SSB) ampli-tude modulation. While previous parametricloudspeaker design has been substantially limitedto DSB, SSB should also be analyzed and com-pared to determine the advantages and disadvan-tages of each. Since optimal demodulated audiosignals depend only on the envelope shape (andnot the ultrasonic spectrum), there is substantialfreedom in choosing the modulation scheme. As-suming Berktay’s Far-Field solution for the non-linear wave equation is valid, it turns out that asingle-sideband amplitude modulation schemeholds some interesting and important advantagesover a double-sideband AM scheme.

The ideal envelope shape can be determinedquite easily. It is simply the square-root of the de-sired audio output, plus any equalization factors.The goal of any modulation scheme should be togenerate a modulation envelope that matches asclosely as possible this ideal envelope. It is instruc-tive to compare the modulation schemes and theirresulting envelopes with the ideal envelope. Foreach test case evaluated below, a 40kHz carrier willbe used for simplicity. The maximum modulationindex will also be used (because the differencesbetween the modulation schemes are less dramaticat low modulation indexes). Note: The two time-derivative operations in Berktay’s solution trans-lates to a 12dB/octave high pass slope in theparametric audio output. This will be ignored fornow since it can be corrected independent of themodulation scheme.

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For DSB, the resulting spectrum is simple, be-ing just two equal-amplitude sidebands at 38kHzand 42kHz, centered around the 40kHz carrier. Itwill be assumed that the envelope function is pro-portional to (or the same as) the modulation signalshape. To achieve this, the DC off-set modulationsignal is simply multiplied by the carrier. For ex-ample, a 2kHz audio signal (used as the modula-tion signal) would result in a 2kHz sinewaveenvelope. The following is the time-domain signalof these three frequencies, 38kHz, 40kHz, and42kHz:

When this envelope is squared by the process inthe medium of air, the 2nd harmonic ends up withthe same amplitude as the fundamental or 100%THD as was mentioned earlier in the paper.

For SSB, it will be assumed that the incomingaudio signals will be frequency “up-shifted” by thecarrier value. For example, a 2kHz audio tone willbe up-shifted by 40kHz, resulting in an upper-sideband frequency of 42kHz (in addition to theever-present carrier). For the single audio tonecase (40kHz carrier, 2kHz audio input) the result-ing spectrum will be simply two equal-amplitudesinewaves at 40kHz and 42kHz. The followingplot shows the time-domain signal of these twofrequencies in green, and the resulting envelope inmagenta.

When this signal is squared by the process in themedium of air, you get back your original audiofrequency of 2kHz, with zero distortion becauseno other frequencies are present. In other words,for a single-tone case, SSB gives a distortion-freesignal with no pre-processing or additional signalconditioning.

So in the case of no preprocessing, SSB is vastlysuperior to DSB. It has half the bandwidth require-ment and no distortion compared to 100% THD.

As disclosed by the Japanese papers from the1980s, the DSB signal can be pre-processed toeliminate distortion by running the audio signalthrough a square-root processor before it is uti-lized to modulate the carrier. This makes the enve-lope into a square-rooted sinewave. This comeswith a price, though: bandwidth, in fact, theoreti-cally, infinite bandwidth in both the upper andlower sidebands.

Lets look at a square-rooted DSB signal and anuncorrected SSB signal in the time domain:

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The blue DSB line lies on top of the red linewhen their values are the same, so when only theblue line can be seen, the red trace is underneath it.Both of these methods give the same envelope thatwill demodulate into a single, distortion-free audiosignal (in this case, 2kHz). However, the spectrumsrequired to generate these two envelopes are vastlydifferent. Lets look at them. Here is the SSB spec-trum with two frequencies:

For a 2kHz audio signal, only 2kHz of ultra-sonic bandwidth is required.

Here is the DSB spectrum:

More than 30kHz of bandwidth is required toget the same ideal envelope to reproduce a mere2kHz signal. For a 20kHz audio tone, the square-rooted DSB method requires some serious band-width that can’t be realized in practice. In fact witha 20kHz signal the ideal DSB method would notonly require an upper sideband of over 150kHz ofbandwidth above the carrier, which is very difficultto realize, the least of which is building a widebandtransducer. What is particularly problematic aboutthis approach is the lower sideband would requiredistortion correction terms down into the audiblerange which would then become very audible asnon-harmonically related distortion. The distor-tion correction terms themselves become distor-tion! A clear catch-22.

Fortunately, an effective square-rooted DSBsystem can still be made reasonably effective bytruncating the bandwidth of the correction terms,even to the extent of not allowing any of the cor-rection terms to fall outside the audio bandwidth.Theoretically, this would incur substantial distor-tion penalties and with equal amplitude signals itdoes. But, due to the nature of real world signals,the peak amplitudes of the audio spectrum willtend to fall in level for frequencies above 2 to4kHz. Also, due to the inherent 12dB/octave high

18


pass characteristic of the parametric output, sub-stantial equalization will normally be used, at leastdown to some low frequency limit, and this willfurther reduce the high frequency output com-pared to the lower frequencies. These two thingscontribute to a very low modulation index for allhigh frequencies and therefore reduced distortionfor those same high frequencies.

Even so, the distortion is still greater than whatand ideal bandwidth could achieve and the singlesideband system will always have less than half ofthe basic bandwidth of the processed double side-band approach.

So, let’s look at some examples of the error termsthat do occur when complex signals are used witha SSB system and how they can be suppressed.First, is a 40kHz carrier modulated to make 7kHzand 9kHz audio tones. SSB provides two uppersidebands with frequencies of 47kHz and 49kHz.The time domain signal looks like this:

Next, the ideal envelope (square-rooted audio)for equal-amplitude 7kHz and 9kHz signals isshown on the same plot as the uncorrected SSBenvelope:

It is apparent that these two functions are simi-lar, but not the same.

The resulting error spectrum (between the twoenvelopes) is shown below:

You can see that the only error term is at 2kHz.It can be proven mathematically that the only errorterm that results in the SSB envelope is in fact the2kHz signal shown. However, if a 2kHz “correc-tion term” (with the proper phase and amplitude)is injected into the modulator, the unwanted 2kHzerror term can be suppressed completely.

19


Thus, a third sideband is added at 42kHz (inaddition to the original 47kHz and 49kHz side-bands that normally occur) with the following re-sults:

You can see that the 2kHz error term is gone,but a new one at 9kHz has appeared. However, thenew error term is approximately 10dB lower inamplitude than the original 2kHz error term was.

If a 9kHz correction term (ultimately resultingin a modified 49kHz sideband) is inserted, with theproper phase and amplitude, into the modulator(in addition to the 2kHz, 7kHz, and 9kHz terms),the 9kHz error term can be suppressed completely,but a new term at 5kHz will appear at an evenlower SPL:

This suggests that by utilizing a recursivescheme we can correct a SSB envelope withoutrequiring any additional bandwidth. Note, as op-posed to DSB, all of the correction sidebands fallwithin the bandwidth of the original audio inputsignal. Also, as can be seen, the amount of error oc-currence, as a percent, falls with each recursive cor-rection step used.

It is worth mentioning that a third modulationtype has also been explored. We call this approachtruncated double sideband. In this scheme a DSBmultiplier is used and the lower sidebands are trun-cated with a filter and/or the transducer. The givesa hybrid between DSB and SSB. It allows for asimple multiplier but substantially retains the lim-ited bandwidth of SSB. Moreover, it gives a con-trolled measure of self equalization to thedemodulated audio.

For example, a DSB system with carrier at30kHz could be high pass filtered at 28kHz so thatit operated with a full 20kHz upper sideband but atruncated, 2kHz lower sideband. A 500Hz audiotone would result in upper and lower sidebandsboth being created equally around the carrier (fora high modulation index). A 5kHz tone would re-sult in a strong upper sideband and a very weaklower sideband so the modulation index would belower (the spectrum looks very similar to SSB).This lower modulation index results in a loweraudio level for the upper frequencies. This servesto inherently equalize the audio for flatter responseat lower frequencies.

The truncated DSB system can be used effec-tively with a recursive error correction scheme toeliminate distortion in the same way that the SSBscheme does.

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A Further Novel and AdvantageousApproach to SSB

Obviously, with SSB, one can choose to use ei-ther the upper sideband or the lower sideband.Generally, upper sidebands are used in SSB modu-lators.

In parametric loudspeaker use, the lower side-band (LSB) system has a number of advantagesover upper sideband SSB or DSB, systems.

Ideally, double sideband systems require sym-metrical outputs above and below the carrier fre-quency. Unless the transducer response isabsolutely flat over at least a 40kHz range, prepro-cessed distortion correction will be less than ideal.Flat transducer systems are usually too low in effi-ciency to generate enough carrier output for para-metric loudspeakers. To meet the requirement offrequency linear symmetry, equalized systemsmust utilize corrective factors that are linear withfrequency rather than logarithmic, which is verydifficult to realize, so even a smoothly peakedtransducer will not be linearly symmetrical aboveand below the resonance/carrier frequency.

Therefore, the theoretically ideal square rooteddouble sideband system cannot be fully realized.

Transducer response is very predictable whentransducers are used below resonance. In thisrange they operate in their stiffness mode and fora critically damped system the high pass character-istic is consistently 12dB per octave. Forunderdamped systems, with much greater effi-ciency at the resonant frequency, the high passcharacteristic is greater than 12dB per octave downto a given frequency after which it shifts back to12dB per octave down to dc which, as will be seenlater in this paper, more closely matches the idealequalization for ultrasonic to audio parametricconversion. For the distortion correction systemsto be effective they depend on the linear responseof the transducer to be a simple function to achievesignificant distortion reduction. The stiffness con-trolled, high pass function of most transducertypes is quite predictable and repeatable.

Upper sideband, above resonance, mass con-trolled region frequency response of most trans-ducers can be somewhat erratic.

Further, the lower sideband has program mate-rial peak energy factors that fall with frequency.This means that in a 20 kHz bandwidth, the side-band information that is displaced 20kHz from thecarrier will be very low level. If we were to use a40Khz carrier for LSB, the spectral content of theprogram material would guarantee significantlyreduced output at all frequencies below 30kHz,with the spectrum falling between 3 and 6dB per(audio) octave below 38kHz depending on pro-gram type. Further, the parametric conversionprocess demands another 12dB per octave of rolloff with ascending audio or descending LSB ultra-sonic. This results in at least a 15dB per octave“audio” attenuation which translates to more than90dB per octave from 40kHz down to 20kHz inthe ultrasonic. (This assumes a 300Hz to 20kHzaudio bandwidth.)

Below resonance/carrier in a LSB system thesaturation levels and attenuation levels are minimalwith decreasing ultrasonic and ascending audiofrequencies. In an upper sideband system, be itSSB or DSB, above resonance/carrier the ultra-sonic attenuation and saturation levels both in-crease with frequency.

Even though the DSB systems have outputs thatcan descend down into the upper audio frequen-cies, that output is greatly attenuated since it is themirror of the high frequency audio. Even thoughthe upper SSB system has no lower sideband,which should allow a lower carrier frequency, thecarrier is at very high levels so it may still need tobe placed at a higher frequency than just above theaudible range.

Band limited, in band corrected, LSB systemsshould provide the best of both worlds with thepotential for greater output and much more effec-tive distortion reduction.

Also, there are many higher efficiency trans-ducer techniques, such as tuned pipes, that in-crease output at the fundamental resonant

21


frequency but cause many problems with frequen-cies above that range. Interestingly, these high ef-ficiency, resonant devices remain well behavedbelow resonance. This implies, that if the uppersideband is eliminated, there may be further im-provements in efficiency available in emitter de-sign without sacrificing linearity.

Lower sidebands are also be better because thelow audio frequencies are at higher ultrasonic fre-quencies and therefore have greater directivity as-sociated with them and visa versa for high audiofrequencies, further helping to maintain high di-rectivity at low audio frequencies.

Because attenuation and saturation effects in-crease with higher frequencies, minimizing anysignificant upper sideband extension requirementis significant in achieving higher performance in aparametric array.

Ultimately, the narrower the bandwidth thegreater the system efficiency can be.

Besides being effective from a distortion reduc-tion standpoint, as will be seen in the next section,ATC’s proprietary, narrow bandwidth, recursive,lower single sideband system can provide muchgreater parametric output by interacting more ef-fectively with the associated ultrasonic transducer.

Utilizing the information disclosed above, it canbe seen that the system that provides significantadvancement over the prior art, while eliminatingpreprocessing side effects, is a single sideband pro-cessor utilizing a square rooted envelope referenceto calibrate a recursive, zero bandwidth distortioncanceller operating as a lower sideband modulator.This is the basis for the proprietary parametricprocessor currently being implemented at Ameri-can Technology Corporation.

Transducer TechnologyGeneral RequirementsIn order to make a parametric loudspeaker

work, ultrasonic energy must be emitted into theair. Electrical signals are converted into theseacoustic signals by means of an ultrasonic trans-ducer.

Acoustic transducers or emitters can designed tocover a certain frequency range, and to have a cer-tain dispersion patterns. The optimum parametricemitter would have bandwidth from around20kHz to infinity, and a sharp dispersion pattern(one that gives a collimated beam of ultrasound),and unlimited output capability. Unfortunately,this is not physically possible to achieve. What wehave to shoot for is 20kHz of useable bandwidth(for use with SSB modulation giving 20kHz ofaudio bandwidth), a resonant peak where the car-rier will be placed, and a falling output level withfrequency to provide a measure of self-equalizationin the system (to overcome the 12dB/octave roll-off of the demodulation mechanism).

The optimal slope that the frequency responseshould fall off can be computed by applyingBerktay’s solution to see what ultrasonic signals areneeded to give uniform audio response. In order toachieve a flat audio response from 20Hz to 20kHz,the upper sideband level must fall by 20*Log(4)dBor 12.04dB per audio octave. Here audio octavemeans going from an upper sideband who’s fre-quency is, say, f0+1kHz to an upper sideband who’sfrequency is f0+2kHz. For example, if the carrier,f0 is 40kHz and 120dB and the upper sideband is41kHz and 120dB too, a 1kHz audio signal willappear at a given level. To have the same level ap-pear for a 2kHz tone, the carrier can be left alone,and the upper sideband needs to be changed to42kHz and 107.96dB. So in order to equalize thelevels of the entire audible range (20Hz to 20kHz),the following transducer frequency responsewould be required:

22


Notice that the level difference between thecarrier at 40kHz and the 60kHz upper end is120dB. Since the audio range is 10 octaves wide,severe equalization is needed to achieve uniformresponse. Equalization generally means bringingpeak output levels down to match the lowest levelspresent. The toughest sound to make is the 20Hztone, so the transducer would be driven at its maxi-mum level when making this tone. All the othertones are generated more efficiently, so less modu-lation level (meaning less upper sideband power) isused to bring these other tones down in level to theachievable level of the 20Hz.

Such an arrangement would give very poor au-dio output levels. If the transducer could be drivenharder, say to 200dB at its resonance, one wouldthink the performance should improve dramati-cally. It would not. The air column in front of theemitter would be “saturated”, and much of theenergy would be dissipated as heat, rather thanturning it into sound. With the current state ofthe art in parametric loudspeakers it can be seenthat the lowest audio frequencies are too inefficientto generate in a practical manner. If we need tohave them, it is currently, best left to a conven-tional bass module.

Now, if we give up on trying to generate equal-level signals below, for example, 500Hz, we have amuch better chance of providing good output overthe rest of the range. The frequency response of atransducer designed for 500Hz to 20kHz flat audioresponse would look like the following:

As you can see, this is much more realistic. Be-cause the upper sideband levels are so muchhigher, the overall performance will be much bet-ter. In fact, the output levels will be increased bymore than 56dB over the band of concern. Such anemitter is realizable. Also remember that there willbe output below 500Hz, just not at the same levelas the rest of the bandwidth.

As mentioned earlier, a collimated beam is amust. Conversely, with a point source the inversesquare law holds. This means that the intensity andSPL drop by ≈ 6dB for every doubling of distancefrom the source. This is because the wavefronts areexpanding spherically around the source, so theintensity falls as the surface area of the spheregrows (intensity is power/unit area). With a planewave source (where the radiating surface diameter>> a wavelength being emitted), the wavefronts donot spread appreciably and a collimated beam re-sults. The only losses in intensity occur due tomolecular friction. The attenuation is gradual overdistance. For example, at 68° F and 80% relativehumidity, a 40.0kHz signal loses 3.1dB in ten feet.This attenuation grows with increasing frequencyso lower operating frequencies are desirable forminimizing losses.

23


(For the full table of attenuation values vs. fre-quency, see section 14 in a CRC Handbook ofChemistry & Physics.)

It also necessary to make the emitter about0.5ft2 in surface area to ensure that there is a suffi-ciently large ultrasonic column. Berktay’s solutionsays that the demodulated level will be propor-tional to the area of the beam. Using a broad beamis also a way to avoid saturation. Efficiency isgained by spreading the output power over a largerarea. Since a large area and the short wavelengthsneeded are not generally compatible requirements,an array of small elements is generally used to getboth.

Other emitter essentials include reliability overa 5-10 year life span and manufacturability, reason-able cost, and a high output capability (>140dB re.20µ Pa at resonance).

The design used in virtually all of the prior artbefore 1998 is based upon a PZT “bimorph”. Thisis a two-layer wafer of poled PZT material ar-ranged in such a way that it bends from concave toconvex as the AC is applied. This gives large dis-placements in the center of the element. To coupleto the air load and give the PZT a mechanical load,

a lightweight cone about 8mm in diameter is at-tached to the center of a load matching plate whichis bonded to the bimorph. The cone has a funda-mental vibration mode at the bimorph’s loadedresonance. To produce more output, the bimorphis mounted over a l/4 cavity. See the drawing be-low.

When a voltage is applied across the pins (thatare protruding downward), the red element getslonger while the blue one shortens, causing a bendin the bimorph. When the polarity changes, theopposite bend occurs. The maximum displace-ment change is in the center of the element wherethe cone is attached. This way, the cone undergoesmaximum displacements. Also, the outer edge ofthe cone moves as much as three times further thanthe inner portion as it flexes.

These devices are good for many applications,but their parametric ability is limited. The fre-quency response is okay for approximately 10 kHzabove resonance (a sloping roll-off above 40kHz),and the efficiency is not bad. The total output isgood also (123dB for the Nicera AT40-12P at30cm with 10Vrms drive). Unfortunately, they arevery small (about 7mm in cone diameter) so nearlya hundred have to be used to make a decent arraywith enough beamwidth for effective parametricconversion. Worse, they are fragile and whendriven to the required levels, a few in a given array

24


begin to squeal and create subharmonics almostimmediately. This seems to occur because the coneflex required for high-output results in fatiguingand cracking around the center weld spot.

Also, there is a large electrical phase shift a reso-nance. This would not be problematic, but eachdevice has a slightly different peak frequencywhich limits their arrayability. If a carrier is set atthe average peak frequency of a group of emitters,many will be out of phase with their neighbors.Because of this, it was found that they work bestwhen the carrier frequency is set slightly off-peakvalue.

Advancements in ParametricEmitter Development

It was clear that there was no “on the shelf”transducer available that would allow this technol-ogy to reach its potential. In light of the dearth ofprior art transducers for effective use in paramet-ric loudspeakers early on ATC began research intonew types of transducers that would advance theperformance of parametric systems.

Early experiments produced very high outputdevices, capable of producing over 155 dB of out-put at the ultrasonic carrier frequency. Thesetransducers were fairly small, with a diaphragmdiameter of approximately 30 mm. It was quicklydiscovered that even though there was significantlymore output than any previous device the para-metric conversion was very weak.

In referring back to the Berktay solution it isfound that the output is proportional to the col-umn area. While this would seem obvious, as anyloudspeaker output is directly related to radiatingsurface area, greater surface area plays a muchmore significant role in parametric systems. Be-cause of the inherent parametric output restric-tions, due to the saturation of the medium at highintensities, a larger ultrasonic emitter with lessoutput per unit of radiating area will significantlyout perform a smaller device with greater outputper unit area.

Various experiments were performed with varia-tions in packing density of individual PZTbimorphs and it was found that much greater con-version efficiencies were available from lower den-sity configurations such as an open ring topology,which was found to have significantly greater para-metric output per driving area while using less thanhalf the devices to create a larger diameter ultra-sonic column.

What was needed was a transducer that did nothave the inherent limitations of the PZT bimorphand would further lend itself to large area paramet-ric column generation. With this in mind we

25


moved away from individual, high output devicesand explored large, monolithic, thin film transduc-ers topologies based on electrostatic, planar mag-netic and piezoelectric films. At ATC there isongoing research into many types of ultrasonic de-vices, but of the thin film transducers, the piezofilm generates the greatest ultrasonic output perunit area while providing easily scalable singularstructures of any diameter desired for a given ap-plication.

Piezoelectric Film Parametric Trans-ducerThe most active piezo film is polyvinylidene

diflouride or PVDF for short (also sometimes re-ferred to PVF2). This film is commonly used inmany industrial and chemical applications and forsuch applications, the raw film is used. In order tobe useful for ultrasonic transduction, the film mustbe polarized, or activated. This is done by one oftwo methods. One method yields a “uniaxial” filmthat changes length along one axis when an electricfield is applied through it. The other methodyields a “biaxial” film that shrinks/expands alongtwo axes. Finally, the film needs to have a conduc-tive electrode material applied to both sides in or-der to achieve a uniform electric field through it(by having the same potential at all points on oneside).

The first proof of concept devices created forparametric use utilizing this material were com-pleted in late 1996 and the initial results were verypromising.

Piezoelectric films operate as transducersthrough the expansion and contraction of the Xand/or Y axes of the film surface. For use as anemitter rather than a sensor or receiver, the filmwill not create effective motion in the Z axis unlessit is curved or distended in some what so that theexpansion and contractions can be converted intoZ axis movement and create displacement generat-ing acoustic output.

In one of the simplest implementations of this

concept, one takes a sheet of PVDF and lays it overa metal plate with an array of holes in it. One canthen apply pressure or vacuum to one side of theplate to create an array of PVDF diaphragms, eachwith the diameter of the hole under it, which areunder uniform tension and can be driven in paral-lel. A schematic cross section of such a device isshown below.

To achieve a resonant frequency correspondingto a parametric carrier frequency, distended piezofilm emission areas were created by placing thefilm over a plate containing an array of openingsthat were sized for a 40 KHz resonant frequencyand a differential pressure was applied to the sur-face facing into the plate of openings. It was calcu-lated that for a 40 kHz resonant frequency, with a14.7 psi pressure differential, a hole size of 0.140"was needed. A vacuum was used to distend the filminstead of a positive pressure so as to eliminateback wave effects.

The first device to be built was 1.75" in diameterwith 85 9/64" holes (selected to use a standard sizedrill bit) arranged in a tight hexagonal pattern withcenter-to-center spacing of 0.160". 28 micron filmwas used and with nearly a full vacuum behind thefilm, the resonance frequency was 37.23 kHz. Theoutput was 136.5 dB with 73.6VPP drive. A veryencouraging result for a first try.

Because of the flexibility in calibrating the oper-ating resonant frequency, we could explore a widerange of frequencies for parametric operation. Anumber of experimental devices were built withoperating center frequencies ranging from 25 kHzto over 100 kHz. (Using specialized emitters para-metric arrays have been tested at ATC up to fre-quencies greater than 500 kHz.)

The measured results of a typical, early proof ofconcept device showing a resonant frequency of

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approximately 93 kHz is shown below. This deviceutilized 25 micron PVDF film on a plate with 1mm holes with a back pressure of 1 atm.

In ATC’s early days of developing ultrasonicemitters with PVDF there were a number of issuesto over come, such as, containing a vacuum, unit tounit variation control, selection of metalizationmaterial and optimum processing of the piezo filmfor maximum output and reliability. Through theuse of a new type of proprietary PVDF film pro-duction process, the current emitter is a stable,repeatable and very practical device to manufac-ture.

Through the use of differential pressure dis-tended PVDF film, we now have the first purposebuilt emitter for use as a parametric loudspeaker.With this device a solution now exists to solve theprior art parametric transducer problems with anultrasonic emitter that:

• eliminates multi-transducer unit -to-unit vari-ability through the use of a single monolithic,thin film for the entire array

• exhibits very high efficiency at the carrier fre-quency with attenuated, self equalizing slopesat the sideband frequencies

• has an adjustable resonant frequency adaptableto various carrier frequencies and modulatortypes

• eliminates out of band (audio range) sub har-monics of the prior art devices

• has ultrasonic bandwidth at least equal to thatneeded to reproduce the widest band audio

• a monolithic structure for matched output overthe active surface with repeatable, simplifiedconstruction

• has greater than 140 dB ultrasonic output capa-bility

• has inherently low distortion

When matched with the zero bandwidth para-metric processor, a practical, reliable, advancedparametric loudspeaker system of low distortioncan be realized for a wide variety of applications.

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Parametric Loudspeaker Facts andLimits

• Maximum parametric output throughout theaudio range is always slightly less than themaximum volume velocity of the emitter at thecarrier frequency. i.e. 12 dB reduction perdescending octave in output relative to pri-mary, ultrasonic frequency output

• Parametric output is proportional to the areaof the ultrasonic column

• When used below saturation, the parametricoutput increase is proportional to the square ofthe increase in carrier level

• Ultrasonic directivity is based directly on emit-ter diameter

• Parametric directivity is based indirectly on theultrasonic directivity and directly on thelength of the ultrasonic column or virtual end-fired array

• Lower modulation index reduces distortion

• Greater modulation index increases paramet-ric gain

• Single Sideband envelope is equal to squarerooted envelope for a single tone

• Emitter linear errors (ultrasonic amplitude re-sponse) can translate to parametric non-linearerrors in any error correction scheme

• Square root correction is needed less for highfrequencies in real world program material dueto:

• Spectral power attenuation above 2kHzcausing lower modulation index and thereforelower inherent distortion

• Harmonic distortion for signals above 7to 10kHz tend to be inaudible

• Saturation sets in at levels 6 dB lower for eachoctave of increased ultrasonic operation

• Output volume velocity is decreased 12 dB foreach octave of increased ultrasonic operation

• Human Factors:

• Studies of intense airborne ultrasoundexposure so far have found that any noticeableeffects of ultrasonic outputs have been due tothe unwanted high-frequency audible signalsthat can accompany ultrasonic equipment andnot the ultrasonic signals themselves. The un-wanted audio frequencies can be essentiallyeliminated with zero bandwidth correctionschemes combined with using emitters that donot generate sub-harmonics.

• For any heating effects to occur, the para-metric systems would have to operate at morethan ten times the power output of an effectiveparametric loudspeaker.

• For ultrasonic levels above 135 dB, at 40 kHz,saturation of the air creates diminishing re-turns relative to the effectiveness of any furtherincrease in ultrasonic level achieving signifi-cant increases in parametric output

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