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Distortion, Directivity and Circuit Nodeling of a Needle Array Plasma

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Distortion, Directivity and Circuit Nodeling of a Needle Array Plasma ~ Distortion, Directivity and Circuit nodeling .t..-- of a Needle Array Plasma LOudapeake51 A The~i, Pre~ented to The Faculty of the College ot Engineering and Technology Ohio University In Partial Fulfillment ot the Requirements tor the Degree ~3ter of Science Ron Sterba ~. I r~rch, 1"91 OHIO UNIV!R$Btr1r t,~~!R~'AY TABLE OF CONTENTS Page Cbapter 1: Introduction 1 Chapter 2: BackgroUDd of Plasaa Sound Production 2.1 History of Plasma Sound Production 2.1.1 Experiments of Gerald Shirley . 2.1.2 Experiments of Kiichiro ~tsuzawa . 2.1.3 Other Work . 10 2.~ Plasma Physics 2. 2. 1 Cold Plasma Sound Sources... ................ 11 .2. 2.2 Bot Ple.~.a Sound Source5.. .................. 12 2.3 Choice of Plasma Type 12 Chapter 3: Acoustic Wave Production 3. 1 Enerq1T Absorption of Weakly Ionized Geses . .. 13 3.2 Source Teras in the Wave Equation 16 3. 3 Interference Pa t terns of Four Point Sources.. 17 3.4 Results of Directional Pattern Tests 27 Chapter 4: Experiaental Apparatus 4. 1 Sound Source Construction. ................. .. 28 4.2 High Voltage nodulation Circuit 29 4.3 Choice of Operating Point5 32 4.1 Circuit Operation 33 i i Chapter 5: Circuit Dodelinq 5.1 Sound Source Characteristic Curve Analysis. .. 34 5.2 Pspice Small Signal Circuit nodel 5.2.1 Vacuum Triode nodel 42 5.2.2 Sound Source nodel 46 5.2.3 Computer nodel of Co.plete Circuit 47 5.3 Frequency Response Analysis 49 Chapter 6 BaraoDic Distortion 6.1 tleasureaent of Harmonic Components 56 6.2 Nonlinear Circuit Operation 56 6.3 Comparison of Distortion tleasurements and Computer Analysis. ..................... .. 58 Chapter 7: Test Results aDd Analysis 7.1. Results of Frequency Response Analysis 63 7.2. Results of Computer Distortion Analysis 63 7. 3 Ef f iciency Testing of Corona Sound Source.... 64 Chapter 8: S1IIlIl8.ry..................................... 66 AppendiX 1: DeriY8.tioD of the Wave Equation tor a PlaslUl........ ................... .. 68 Appendix 2: Baraon1c Distortion t ro. the SigDal Generator. ............................. .. 74 AppeDdiz 3: COJq)uter Prograa 1...................... 76 Appe.Ddiz 4: COJq)uter Prograa 2...................... 78 tt1 AppeDdi% 5: Coaputer Prograa 3.. .................. .. 80 AppeDdi% 6: Coaputer Prograa. 4. ................... .. 82 Ref.renee. 84 iv List of Figures Figure Page 2.1 Shirley's corona triode configuration . 2.2 nBtsuzawa's sound source and driving circuit . 5 2.3 Current levels through nBtsuzawa's sound source..... 6 2.4 Characteristic curve of natsuzawa's sound source 12... ................................ .. 6 2.5 natsuzswa's electrode geo.etry _. 7 :.6 Theoretical frequency responce of nBtsuzawa's sound source 9 2.7 Corona discharge between a needle and a grid 12 3.1 Four element linear array radiating in a direction g to 8 distant point C 17 3.2 Superposition of radiated signals of amplitude a and successive phase difference 0..... .......... .. 18 3.3 Relative intensity of a 2 point source array 19 3.4 Relative intensities or 4 and 8 point source arrays. ................................... .... 20 3.5 Definition of angles used in plots 21 3.6 Calculated intensity interference patterns (0.5# 1 kHz) . 21 v Figure Page 3.7 Calculated inten~ity interference patterns (2, 3, 6, 10 kHz) zz 3.8 Calculated intensity interference patterns (12, 20 kHz) 23 3.9 Directional patterns of sound pressure measured 1 .eter from the sound source at 500Hz 24 3.10 Directional patterns of sound pressure measured 1 .eter from the sound source at 1 kHz. ........... .. 24 3.11 Directional patterns of sound pressure aeasured 1 .eter trom the sound source at 3 kHz 25 3.12 Directional patterns of sound pressure measured 1 aeter from the sound source at 6 kHz 25 3.13 Directional patterns of sound pressure measured 1 aeter from the sound source at 10 kHz , 26 3.14 Directional patterns of sound pressure measured 1 aeter trom the sound source at 12 kHz. ......... .. 26 4.1 Top view of cathode assembly 28 4.2 Corona sound source 29 4.3 Sound source circuit 30 4.4 Circuit tor findinq characteristic curve of ~ound source.... ............................ .. .. 30 vi Figure Page 4.5 Sound source characteristic curve. ................ .. 31 4.6 Circuit for testing vacuum tube characteristics..... 32 4.7 6BI4 Vacuum TUbe Characteristic Curves for V~ -.5Y,-. 75V,-1V and -1.25Y 32 5.1 Vacuua diode circuit 35 5.2 Plate voltage characteristic curve of vacuua diode. .... .............................. 35 5.3 Sound Source Characteristic Curve (d = 1ea) 36 5.4 Log-Log plot of sound source characteristic curve... 37 5.5 Computer generated plot of equation 5.2 (d = 1cm) ... 36 5.6 Electrode geometry 38 5.7 Effects of vaI1~ng electrode separation d 39 5.8 Plots of Iss v» d at Vss = 4,6~6~10,12 and 14kV..... 40 5.9 Log-Log plot of Iss vs Vss at d = 8, 10 .. 12, 14 :ram. .. 41 5.10 5aall signal model of 6BK4 vacuum tube 42 5.11 Characteristic curve of Ip vs Vp at bias voltage V~ = -O.75V 43 "ii Figure Page 5.12 Plot of plate current vs grid-cathode voltage for the 6BK4 45 5.13 Sound source circuit .odel. ....................... .. 47 5.14 !xperiaental sound pressure trequency response. ... .. 49 5.15 Siaulation frequency responce of the sound source capacitance current 50 5.16 Siaulation frequency responce of the sound source resistance current.... ".......................... .. 50 5.17 Siaulation frequency responce of the sound source plate voltage. ................................... .. 51 5.18 Simplified small signal model of sound source circuit..................................... 51 5.19 General Form of Bode Plot of Eq. 5.23 55 6.1 Operating points of sound source 60 6.2 Calculated sound pressure haraonic levels at different dc bias points 61 6.3 ~easured haraonic sound pressure levels at different de bias points 61 A.6.1 Node numbers tor Pspice ac small signal circuit .ooel 80 Chapter 1: Introduction The object of thi~ the~i~ i~ to explore aco~tical propertie5 ot a corona loudspeaker inclUding ha~anic distortion and directivity of sound pressure. A corona loudspeaker of the type used here consists of several .etal points in front of 8 .etal screen, biased with a high voltage to produce a corona. When the high voltage across the air gap is aodulated, sound is produced. This work examines the characteristic curve of such a device and uses it to predict distortion. The results of this analysis show the optiaum operating point to achieve low distortion ie near maximum current. Since the source has several points of acoustic energy generation, an interference pattern is set up. neasureaents were made on this in two di.ensio~ and it was compared to the theoretical interference patte~. A saall signal circuit model for the sound source and amplifier circuit was created using Pspsice. The frequency response of the sound source is compared to the frequency response of the .odel. 2 Cbapter 2: Background of PlaslI8 SoUDd Production 2.1 History of Plasma Sound Production The following sections review previous experiaents with plas.e sound sources. 2.1.1 Experiments of Gerald Shirley ~rald Shirley pre~ented a paper on his studies of corone wind loudspeakers to the New York section of the Audio Engineering Society in June 1957. (1) Shirley described the construction of 8 corona triode in which e ring is .ounted coaxially around one of two needle electrodes which point toward each other. This corona. triode was the basis for his loudspeaker design. Shirle1' claimed that . having no aovmq parts, this speaker has definite advantages over conventional loudspeakers. , control r"ino / . ~"'? f!llectrodes Figure 2.1 Shirley's Corona Triode Configuration Shlrley observed that the particles composinq the plasM. of a corona discharge have a net drift velocity which he teraed a 'corona windI. He stated that the darectron. Jaagnitude and pattern of the corona wind could be observed by injectinq a smoke streaa at low velocities into the plas.a. Fro. these test he found that that the .agnitude of this wind can be controlled by a coaxial ring set at the proper controlling potential between the ring and its concetric electrode. Shirley also noted that the electrical current can also 3 be controlled by the voltage on the ring just as the plate voltage contro15 the current through a vacuum triode. He plotted the characteri~tic curve~ for different geo.etrie~ and grid potential~ or the corona t r rode. Shirley noted that the sound produced by a single triode is very faint and described the construction of a sound source with 144 triodes operating in parallel. Needles in a grid pattern were mounted in a 6 inch square fraae and interlaced vires spaced one­ half inch apart were placed over the needles which are centered in the spaces between the wires. Shirley liaited his discussion of this sound source to the practical considerations of its operation and did not explore the theoretical means of sound production. He then I18de soae coaparasons between the corona. wind loudspeaker (CiLS) and. electrostatic speakers. 1) Botb are extended rather than point sources of sound. 2) The corona wind loudspeaker can reproduce a wider frequency range .. and should be able to create a greater aap11tude of air aotion at any trequency. 3) Electrostatic speakers require a high pover audio 5ignal while C\~S can be driven by a ~aall voltage signal which is m.odulated onto the polarizing higtl voltage circuit by 8 tube amplifier. Shirley did not verify his second point. With regard to point number three he should add that the polarizing high voltage source supplies the operating power. Due to the absence of ]loving aechanica.l parts (and assocaeted suspensions) the overall audio frequency response curve of the ClLS was in general aucb smoother than that obtained f roa a typical cone­ type speaker.
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