Tetrahedral Arrangement Soundeld Microphone

Thomas Allen u4123966 Simeon Baker-Finch u3938976

Riley Doust u4114397

October 24, 2006

Abstract

This report presents the design and testing of a soundeld microphone subsystem specic to the ambisonicssurround sound format. The design incorporates four uni-directional microphones in a tetrahedral array withthe aim of reproducing a sound image that accurately reects a real audio experience. The four input signalsare passed through a pre-amplier stage and are then fed into the mixing module that formats the signalsaccording to the trigonometric relationships dened by spherical harmonic theory. The four output signals,W, X, Y and Z comprise the B-format that is processed further to accommodate for a specic loudspeakerarrangement. Testing of the design was carried out in PSPICE, while the hardware was rst constructed ona breadboard and later implemented on a printed circuit board (PCB).

Contents

1 Introduction 3

2 Theory 42.1 Ambisonics and the B-Format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Encoding a Field of Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1.2 Decoding the B-Format to a Speaker Array . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Analogue Electronics Implementation Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.1 Operational Amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.2 Dierence Amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.3 Summing Amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2.4 Dierential Amplier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Design 93.1 Microphone Capsules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Microphone Preamplier Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.3 B-Format Formation Stage (Mixing Stage) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

4 Implementation 124.1 PSpice Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2 Breadboard Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2.1 Signal Interference and Breadboarding . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2.2 Capacitive Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2.3 Inductive Interference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3 Debugging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.3.1 Noise Cancellation and Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.4 Printed Circuit Board Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.4.1 The PCB Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.4.2 Design Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.5 Hybrid Final Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5 Results 145.1 General Observed Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

5.1.1 Amplier gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145.2 Results of PSpice Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.2.1 The Preamplier Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155.2.2 Mixing Stages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5.3 Results of a Streamlined Breadboard/PCB Implementation . . . . . . . . . . . . . . . . . . . 16

6 Conclusion 16

7 Appendix A: Circuit Schematic 18

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8 Appendix B: Photos 19

9 Appendix C: PSpice Schematics and Simulation Results 229.1 Preamplier Stage test Circuits and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229.2 Mixing Stage Test Circuits and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

10 Appendix D: Results of Hybrid Implementation. 28

11 Appendix E: Eagle PCB Layout 31

12 Associated Data Sheets 32

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1 Introduction

Attempts to incorporate directional information into a sound image date back to the early 19th century.Multiple telephones were spaced out across a concert hall in France in an attempt to recreate the concerthall sound elsewhere. The sound was transmitted over separate wires to the same number of telephonereceivers. [11] As microphone and loudspeaker technologies developed, researchers made various unsuccessfulattempts at surround recording and playback. Today, surround sound playback technology is commonplace inhome entertainment, cinema sound, live music venues and elsewhere. Usually, the kind of sound played backthrough these systems has been recorded by a number of mono-channel microphones, and professionallymixed into a format which mimics reality when played through a specic speaker conguration. Truesurround sound recording recreates the sound space which a human experiences - we can sense sounds fromthe left, right, high, low, far away and nearby, placing each sound at a particular point in the space aroundus.

The modern soundeld microphone concept was originally developed in the 1970s to originate ambisonicsound material. Ambisonics is a method of recording information about a soundeld and reproducing itover some form of loudspeaker array so as to produce the impression of hearing a true three dimensionalsound image. [11] Particularly important in the development of ambisonic theory is the characterisation ofthe B-Format sound signal. In this format, three reference channels (x, y and z) locate sound sources inspace, and a fourth (w) channel senses the air pressure changes that describe sound. [11]

Research continues among various academic groups who seek improvements to the ambisonic system, andapplications for a three-dimensional soundeld. Academics in music look to true surround sound in orderto reproduce concert hall sound, as well as to extend the boundaries of current musical practice. Auditorydisplay and data sonication oer a new tool in interpreting information; surround sound oers furthervariables on which to map such data. New media artists see this technology as an opportunity to build trulyimmersive environments, particularly for interactive installations. As music composers, particularly thoseinvolved in electronics-based genres, have ventured into this area, and engineers have been pushed to meetthe demands for newer, better, and more interesting sound spatialisation and diusion technologies. [12]

Ambisonic technology has found a niche in the business community also. Modern teleconference applica-tions and services attempt to make communication between participants at remote sites more eective bypresenting information in a manner which is perceived as much like natural, physical interaction as possi-ble. [4] Recording using a soundeld microphone employs technologies which have the potential to increasesuch realism.

Studio engineers agree that even when the soundeld is not reproduced using a large number of loud-speakers, sound quality is advanced. There's no question that sounds recorded ambisonically make betterstereo. . . There are no deadspots with ambisonics. [2]

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2 Theory

2.1 Ambisonics and the B-Format

2.1.1 Encoding a Field of Sound

Systems that attempt to produce a sound experience equivalent to that experienced by a human in realityinclude wave-eld synthesis, holophony and ambisonics. All three systems attempt to recreate the wavefrontsin a sound eld, based on the Huygens Principle. [12] this physical principle is based on the fact that wavesadd constructively in the propagation direction. Of the three systems, only ambisonics can record an playbacka sound image equivalent to the real experience.

In rst-order ambisonics, sound information is transported via four channels: W, X, Y and Z. This signalconguration is known as the B-format. Each letter represents a zero order or rst order spherical harmoniccomponent of three dimensional space.

The channels of the B-format are based on the dissection of the space around the microphone into sphericalharmonics (see gure 1). Many physical functions follow Laplace's equation. These include such values asincompressible uid ow, electrostatic potential, gravitational potential and the displacement of an elasticmembrane. A solution of Laplace's equation, which is similar to both the wave equation and Schrödinger'sequation, in three dimensions is called a spherical harmonic. This complex physical phenomenon will not bediscussed further here see [9] [1] for more information.

The zero order harmonic (W) represents the sound pressure which is incident to the microphone, whilst therst order harmonics, X, Y and Z are three components of the gradient of the incident pressure. That is,the rst order harmonics are related to the velocity of air particles representing a sound pressure wave. Theinformation from these three signals precisely locates the origin of a sound in the space surrounding themicrophone as in gure 1 and gure 2.

Figure 1: The directional gain patterns of full-sphere B-Format signals.

The role of the analogue electronic circuit built for this project is to convert sound pressure information from asphere surrounding the tetrahedral array of microphones into an ambisonic B-Format signal. Discussion of the

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Figure 2: Top view of directional gain patterns of full-sphere B-Format signals. The Z-channel sphericalharmonic pattern points out of the page.

particulars of the electronics implementation follows. In principle, the role of the circuit is to appropriatelyweight and combine voltage signals which represent the sound pressures incident at each of the four elementsof the tetrahedral array, so that the output represents the four channels of the B-Format. In particular,when:

L = left, B = back, F = front,R = right, D = down, U = up,

and the four microphone input signals come from the directions:

LFU, LBD, RBU, RFD,

the following relations must be reected in the circuit output:

W = −(LFU + LBD + RBU + RFD)

X = 2√

2(−LFU + LBD + RBU −RFD)

Y = 2√

2(−LFU − LBD + RBU + RFD)

Z = 2√

2(−LFU + LBD −RBU + RFD)

2.1.2 Decoding the B-Format to a Speaker Array

A number of loudspeaker congurations will allow the ambisonic B-Format signals to be reproduced as airpressure dierentials in a three dimensional sound space. The following explanation is not central to themicrophone design and build process, but gives perspective to the practical applications of a system incor-porating both recording and playback technologies. Decoding methodology exists for sets of loudspeakersplaced at the vertices of regular polyhedrons and cuboids, as well as for diametric congurations (2n speakersarranged in diametrically opposed pairs with respect to the listener). [6] Perhaps the easiest to understandis the Cuboid Decoder Theorem, proposed by a leader in ambisonic theory, Michael Gerzon. [6, 7, 8]

For eight speakers placed at the vertices of a cube surrounding the listener, and where:

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L = left, B = back, F = front,R = right, D = down, U = up,

the following relations are true:

LBD =1

2√

2(W −X + Y − Z)

LBU =1

2√

2(W −X + Y + Z)

LFD =1

2√

2(W + X + Y − Z)

LFU =1

2√

2(W + X + Y + Z)

RFD =1

2√

2(W + X − Y − Z)

RFU =1

2√

2(W + X − Y + Z)

RBD =1

2√

2(W −X − Y − Z)

RBU =1

2√

2(W −X − Y + Z)

Figure 3: The 8 speakers forming an ambisonic cube.

Decoding the recorded B-Format allows the listener to experience the complete spatial sound experiencewhich was incident upon the tetrahedral array microphone at recording time.

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2.2 Analogue Electronics Implementation Theory

2.2.1 Operational Amplier

The internal block diagram of an op-amp (gure 4) shows that the input stage consists of a dierentialamplier. A gain is applied to the output of this stage. Stemming from the identication of the op-ampinput stage as a dierential amplier is following basic relationship:

vout = Aol(v+ − v−). (1)

Figure 4: Operational amplier internal arrangement.

When a feedback network is introduced (when the op-amp output is connected, possibly through a numberof electrical components, to one of the two op-amp inputs), the closed loop gain, Acl can be calculated. Theclosed loop gain depends on the nature of the feedback network, and the op-amp characteristic equationbecomes:

vout

vin= Acl. (2)

In this case, vin is used, since in most common congurations, one of the two op-amp input terminals isgrounded.

2.2.2 Dierence Amplier

A dierence amplier employs an opamp in dierential mode to obtain an output proportional to the dif-ference between two scaled inputs. [3] For the conguration shown in gure 5, the following relationshiprepresents the ideal circuit characteristic equation.

vout =R2

R1(v1 − v2). (3)

Figure 5: The dierence amplier. [3]

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2.2.3 Summing Amplier

A summing amplier can be used to calculate a weighted sum of a number of input voltages. For example,for the three input conguration shown in gure 6, the following relationship exists between the outputvoltage and the inputs.

vout = −(RF

R1vin1 +

RF

R2vin2 +

RF

R3vin3). (4)

Figure 6: The summing amplier. [3]

2.2.4 Dierential Amplier

A dierential amplier circuit (gure 7) can provide high voltage gain and common-mode rejection. [5]

Figure 7: The dierential amplier. [5]

Considering applications in which a non-zero signal is applied to both inputs, the dierential amplier is saidto be in either dierential or common-mode conguration. The characteristics of both modes stem from thekey concept that the dierential amplier outputs an amplied signal representing the dierence betweenthe two inputs. For dierential mode, the two inputs are the same, but perfectly out of phase. In this case,the output is a signal with the same frequency, but twice the amplitude of the input. In the common-modecase, both inputs are identical, thus no signal is amplied and the output of the dierential amplier is zero.This is known as common-mode rejection. The role of the dierential amplier in the soundeld microphonecircuit is explained later.

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3 Design

Initial design was chosen from a website (see [13]) which oers circuit schematics for a range of unique,interesting analogue electronics applications. First, the circuit was modelled using PSpice software. Somedesign faults were noted at this stage - particularly the presence of circuit noise at a frequency of between1 and 2MHz at the output for a clean input signal. Changes were made in both modelling and prototypingstages to enhance the performance of the circuit. Making such changes allowed the design team to be moreinvolved in the analogue electronics at the heart of the device, and to learn about real world limitations interms of component performance. The team noted that sometimes bandaid solutions were the best way toconfront a challenge in electronics implementation given restraints in both budget and time.

3.1 Microphone Capsules

The most basic requirement for building an eective tetrahedral array soundeld microphone is four unidi-rectional, cardoid pattern microphone capsules. A good signal to noise ratio characteristic is desirable forrecording purposes, and the microphones must be small in size, since they need to be mounted as close aspossible to the others in the array for best ambisonic performance. All breadboard testing was done usingcheap, omnidirectional capsules, available from any hardware store (see data sheet [15]). These capsuleswere not mounted in the correct tetrahedral conguration. For the nal implementation, low-noise, unidirec-tional capsules (see datasheet [16]) were obtained from Ariose Technologies (Taiwan) via Crest Technologies(Nunawading, Victoria). The capsules were mounted on a somewhat primitively fashioned tetrahedron on asmall stand (see gure 8).

Figure 8: The microphone and stand.

According to the datasheet for the electret microphone inserts 16, a certain conguration of resistor andcapacitor must be connected at the output terminal for proper operation. The +bat supply voltage isheavily ltered by the combination of 2.2kΩ resistor and 100µF capacitor. These leftmost components on

9

the schematic layout also act to provide the required 1.5V bias to each capsule, rather than the 9V railvoltage.

3.2 Microphone Preamplier Stage

Each of the four microphone capsules which make up the tetrahedral array are attached to a preampliercircuit. Preampliers are commonplace in circuits using microphones, because the low voltage output ofthe microphone must be converted into a relatively high voltage input to a recording device. Contemporarymicrophone amplier design can be categorised into four types, based on active elements: discrete semicon-ductor, vacuum tube, integrated circuit, and hybrid. Within these categories are found FETs, BJTs, ICfunction modules, IC opamps, discrete opamps, among other components. [10]

The circuit implemented in this project incorporates four separate preamplifer stages one for each micro-phone capsule. Each uses a simple discrete transistor dierential amplier connected to an op-amp withfeedback. This gives low noise from using good quality cheap discrete transistors congured to provide somegain, and good linearity provided by the high open-loop gain of the op-amp with overall feedback. [13]The TL074 is a low-noise, JFET-input operational amplier, designed to have low input bias and osetcurrents, and fast slew rate. [17] Unfortunately, the input noise of this IC is too high to be used alone as amicrophone preamplier, and must be coupled with the discrete transistor dierential amplier to achievethe best possible performance in minimising circuit noise.

The original design [13] called for the use of 2N4403 BJTs in the dierential amplier stage. 2N2905 PNPswitching transistors were chosen based on availability, and proximity to the characteristics of the preferredcomponent. See ( [18] and [19]) to conrm that the two transistors are interchangeable for the purposes ofthe soundeld microphone circuit.

The trimpot variable resistors in each preamplifer stage can be used to adjust the voltage gain of eachmicrophone input signal. Some microphones are more sensitive than others. The trimpots can be varied toensure equal level inputs. In advanced usage, the shape of the soundeld being recorded can be changedby altering the gain pattern which is directly controlled by the four variable resistances. See [7, 13] fordiscussion of advanced topics.

3.3 B-Format Formation Stage (Mixing Stage)

The ambisonic B-format is realised as the circuit output according to a weighted sum of the inputs, followingthe relationships described above for encoding soundeld information. The mixing stage of the circuit isessentially an opamp set up in an arithmetic conguration. A combination of summing and dierenceamplier is used so that both negative and positive weightings can be applied to the input waveforms. Notethat the capacitors in parallel with the feedback resistors for each opamp in the mixing stage have very smallcapacitance. They are present to form an active low pass lter, which eliminates any high frequency noisegenerated by the circuit from the output. These capacitors do not have a signicant eect on the opampsummer or dierence congurations, except that they limit the circuit frequency response to an appropriaterange.

Mixing together the four amplied signals for the W component of the B-format is relatively simple. We

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need:W = −(LFU + LBD + RBU + RFD). (5)

Summing amplier theory suggests that for the conguration shown in gure 9,

voutW= −20kΩ

10kΩ(vLFU + vLBD + vRBU + vRFD). (6)

Figure 9: The mixing stage for the W channel of the B-Format.

For the X,Y and Z channels, both sum and dierence operations are required. Focusing on the X channel,theory suggests that the electronic circuit must reect:

X = 2√

2(−LFU + LBD + RBU −RFD). (7)

Combining summing and dierence amplier theory, for the conguration shown in gure 10, note that theinputs to the opamp (+) and (-) terminals are rst summed, and then the dierence is taken between them.So:

voutX=

56k

10k[(vLBD + vRBU )− (vLFU + vRFD)]. (8)

Figure 10: The mixing stage for the X channel of the B-Format.

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4 Implementation

4.1 PSpice Simulation

Before construction was initiated, the soundeld microphone circuit was simulated using PSpice software.Figure 11 details the structure of the top level schematic. Detail for each block is attached, appendix C.

Figure 11: Top level schematic of PSpice implementation.

4.2 Breadboard Implementation

The rst physical realisation of the soundeld microphone circuit was achieved on a breadboard. Various dif-culties were encountered during this process, as detailed below. A photo of the breadboard implementationis attached, appendix B.

4.2.1 Signal Interference and Breadboarding

Throughout the whole implementation process it was realised that achieving hi-delity results from the pre-amp stage of the design was very much dependent on the circuit layout on the breadboard. Over the courseof the prototyping stage of the circuit two critical factors had to be addressed to achieve the desired output.

4.2.2 Capacitive Interference

Capacitive interference will propagate through a circuit when wires at dierent voltages are placed closedto each other. When voltage changes in one wire, a voltage can be induced in the neighboring one throughcapacitive coupling. Higher frequency source interference results in larger capacitive interference. Throughresearch it was determined that the best way to prevent capacitive interference is to shield all wires andcomponents with a Gaussian surface. [14] The shield would be connected to ground, protecting the innersignal carrying conductor from the interference. However, for our purposes, having signal carrying wires anddevices placed at distance signicantly apart generally suced to eliminate the problem.

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4.2.3 Inductive Interference

Inductive interference is the result of collapsing and reforming magnetic elds associated with time varyingcurrents carried by a conductor. The magnetic elds created by the alternating signal induce similar currentsin neighboring wires. [14] It is not always easy to prevent this interference during breadboard implementation.Preventative measures that were taken to avoid inductive interference included keeping the breadboard designcompact, and ensuring that no wires were running parallel to each other; running wires perpendicular toeach other eectively nullies the potential for inductive interference due to the direction of the magneticeld vector.

4.3 Debugging

4.3.1 Noise Cancellation and Filtering

Despite the meticulous bread-boarding techniques that were followed, high frequency noise in the order of 2MHz was being propagated through three out the four pre-amps initially constructed. This noise was mostlikely a result of capacitive coupling of the transistors used in the pre-amp stage of the design. The outermetal casing of each BJTs was not electrically isolated from the device (the casing was found to be thecollector of the BJT 19). We found that the noise was eliminated when we physically touched the casingof the BJTs. The body's capacitive eects de-coupled the devices, eliminating the high frequency gain. Toreplicate this eect, capacitors were placed in parallel with the 18kΩ collector resistors. This limited thegain of the 2MHz signal. A more eective method was to directly place a capacitor between the collectorsof the BJTs. A low pass lter was implemented on the output to eliminate any other noise.

The specications of all of the lters that were implemented were garnered from the equation:

f =1

2πRC(9)

The cut-o frequency of the lters was always set to 20 kHz, the upper limit of the audible frequencyspectrum of the human ear. Being an audio application, all frequencies greater then 20 kHz are necessarilyunwanted noise.

The introduction of lters and noise minimisation measures during the implementation of the soundeldmicrophone circuit on breadboard resulted in a more robust design. Resolving circuit anomalies throughoutthe course of prototyping is an eective method for increasing circuit performance.

4.4 Printed Circuit Board Implementation

4.4.1 The PCB Design

Designing the printed circuit board (PCB), after observation of the circuit analog electronic theory andbreadboard implementation, further considers physical and practical considerations. Like most analog cir-cuits, the microphone pre-amp serves to manipulate signals. Particularly in this audio application, thequalities of signals are an important consideration, and as was clear from the bread board implementationresults, an acceptable standard of signal quality was not achieved with the original circuit design. Howeverimplementation of the circuit on PCB was expected to inherently improve the signal performance at thetime of designing the PCB the noise problem was thought to be primarily caused by the wiring, rather than

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transistor case interference. Therefore the design for the PCB as sent to the manufacturer did not includenoise alleviation components.

A schematic of a circuit is laid out to maximise visual understanding of the component relationships. Thelayout for the PCB therefore was dissimilar to the schematic optimised to create the shortest leastcomplicated path for signals and power supply and practically utilise available space. The rst and secondstages were realised on separate boards, with four signal wires joining each. Each stage utilised the fourop-amps contained in a single TL074 IC. The tracks that carry V+, V− and earth are designed to bethicker in order to carry more current with less resistance and potentially damaging heat dissipation. Thethickness of the track at a given point is proportional to the number of component pads that the 'rail' willbe sourcing/sinking current to. The earth track is thicker overall than the V+ and V− tracks, because in theimplemented circuit, the single connection to earth must carry all current owing through V+ and V−.

4.4.2 Design Errors

The PCB was not designed perfectly to match the schematic the series of outputs to cable jacks thatconnect the second stage to the recording device omits the ground connection. This was remedied in theimplementation by connecting an additional lead from the cable jack ground to the power ground. Addi-tionally, the EAGLE library components nominated for the 100uF capacitors were much smaller than theavailable capacitors, which caused diculty in tting the components to the PCB.

4.5 Hybrid Final Implementation

The nal implementation of the soundeld microphone was achieved using a mix of breadboard and PCBcircuit components. A tetrahedral structure was built to house the four unidirectional microphones. Theoutput of each microphone was attached to one circuit input. The B-format output was taken from thecircuit and connected to two stereo wires for input into a computer. See appendix D for a photo and theresults of this implementation.

5 Results

The following details a number of tests carried out to characterise the operation of the soundeld microphoneanalogue electronic circuit in both simulation (using PSpice software) and in physical reality modes. Thecentral goal of the experimental procedure dened below was to ensure that the microphone achieved properencoding of the surrounding sound pressure into the B-format. Noise performance is a key indicator in audioapplications much time was spent on eliminating unwanted circuit noise from the output voltage signals.

5.1 General Observed Behaviour

5.1.1 Amplier gain

The following voltage gains were observed for the two stages of the circuit design. The gain for the mixingstage is chosen to be a multiple of the intended gain 1 for the W-channel and 2

√2 for the other channels.

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Gain stage PSpice simulated Breadboard observedPreamplier 11.5 10 to 20Mixing stage 2 1 to 3

5.2 Results of PSpice Simulation

For PSpice simulation, the circuit was subdivided into blocks. Note that the circuit block diagram (gure 11)contains four identical preampliers, and four separate channel mixers.

5.2.1 The Preamplier Stage

Three variations of the preamplier stage were tested using transient analysis. The circuits and graphicaloutputs are shown in appendix C. As mentioned above, the key performance parameter considered here wasthe noise performance of the circuit.

The rst circuit to be simulated was a replica of the preamplier stage outlined in the design schematic (seeappendix A). A sine wave was applied at the microphone input terminal, and the output was plotted at theright hand side of the 47µF capacitor, across a load resistor. The key observation made from this simulationwas that a noisy signal appeared at the output. The noise oscillates at a frequency of around 1.5MHz. Seegure 18, appendix C.

For the second simulation, a capacitor was attached in parallel with each resistor which joins the collectorof a BJT with the negative power supply rail. This is intended to limit high frequency gain. Choosing acapacitance of 44nF eectively eliminates the circuit noise. Instability does appear at the output for theinitial stages of the transient response. See gure 20, appendix C.

As another, more simple approach to eliminate the high frequency noise initially found at the output, a singlecapacitor (68nF ) was attached between collector terminals of the BJTs in the dierential amplier circuit.This oered a more stable transient response than the solution discussed above. For detail, see gure 22,appendix C.

Finally, a simple rst order lter, designed to have a cuto frequency of 20kHz (ideal for an audio applica-tion), was applied to the output of the preamplier. This had a signicant eect in noise reduction, but didnot fully eliminate the 1.5MHz circuit noise. See gure 24, appendix C.

5.2.2 Mixing Stages

PSpice simulation was used to conrm that the arithmetic amplier immediately before circuit output wasdesigned correctly for each channel. Key outcomes of this simulation were that the circuit output the correctsignal according to the weighted sum and dierence equations described in the theory, above.

A sine wave signal was applied at each of the four inputs to each mixing stage. Each input was assigned halfthe frequency of the last, in the order LFU, LBD, RBU, RFD. This way, the mixing stage is tested for alarge range of values in particular, note the similarity of this type of test input to a four-bit binary count.A transient analysis was set up to display the changing waveform over time this is the key mode in whicha microphone is used (recording sound over time). The results of these tests conrmed the correct design ofthe mixing stages for each channel. See appendix C for details of the simulation.

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5.3 Results of a Streamlined Breadboard/PCB Implementation

A streamlined circuit was built in the latter stages of the project to achieve the best possible circuit operationfrom the resources available. A combination of breadboard (used for the preamplier stages) and PCB (usedfor the mixing stages) was connected to the tetrahedral array of four unidirectional microphones. The fouroutput channels, W, X, Y and Z were paired and connected to two 3.5mm jack stereo leads. These leadswere plugged into two separate sound cards in a single computer. Trial software (Adobe Audition) was usedto observe and record the B-format waveforms. Once recorded, one may use appropriate software to decodethe B-Format into a cuboid array of 8 loudspeakers.

The process of connecting the circuit to a computer allowed the group to conrm that the circuit wasoperating correctly and accurately. The results of some recordings are shown in appendix D. It is interestingto note the phase and amplitude dierences in the waveforms displayed in these results.

6 Conclusion

Recording audio information in a surround sound format is an interesting application of analogue electronicsthat is prevalent in modern society. The team designed and built a subsystem specic to the ambisonicssurround sound format. Four uni-directional microphones in a tetrahedral array were constructed to replicatethe sound image that accurately represents a real audio experience. The four input signals are passed througha pre-amplication stage, consisting of a dierential amplier and an operational amplier; the dierentialamplier being added to the design to reduce the output noise and to achieve gain distribution. A capacitorwas added to the design to eliminate the high frequency noise propagating through the circuit.

The signals X, Y and Z were outputs of the mixing module, formatted according to the trigonometricrelationships that describe the position of the sound according to the rst order spherical harmonic theorymentioned in the report. The remaining W channel conveys the actual compression wave characteristicssurrounding the microphones during recording. This 4 channel output is called the B-format. Furtherprocessing is required to convert this audio format into information that can be reproduced through aspecied loudspeaker arrangement.

The implementation of audio processing circuits requires consideration of noise and interference character-istics that should inuence the circuit design at the schematic and PCB design stage. In this application itwas necessary to remedy problems that only became apparent when using the circuit for its intended purpose- the audio application. PSPICE and EAGLE simulation is not sucient to gauge the extent of radiatednoise. The function generator signals were also more stable inputs than the inputs from the microphone.

All design considerations mentioned above mean that an analogue electronics application must be closelymonitored, tested and redesigned throughout the prototyping stage.

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References

[1] Arfken, G. (1985) Spherical Harmonics, in Mathematical Methods for Physicists, 3rd ed. Orlando, Aca-demic Press.

[2] Cromer, Ben (1992) Nimbus Brings Ambisonic Recording Home, in Pro Audio 104,4.

[3] Durrani, S. (2006) Lecture Notes for Analogue Electronics: ENGN3227. ANU, Canberra.

[4] Evans, Michael James (1997) The Perceived Performance of Spatial Audio for Teleconferencing Universityof York, England.

[5] Floyd, T.L & Buchla, D. (2002) Fundamentals of Analog Circuits. Prentice-Hall, USA.

[6] Gerzon, M.A. (1992) General Metatheory of Auditory Localisation, presented at the 92nd Convention ofthe Audio Engineering Society. AES, USA.

[7] Gerzon, M.A. (1980) Practical Periphony: the reproduction of Full-Sphere Sound, presented at the 65thConvention of the Audio Engineering Society. AES, USA.

[8] Gerzon, M.A. (1992) Psychoacoustic Decoders for Multispeaker Stereo and Surround Sound, presented atthe 93rd Convention of the Audio Engineering Society. AES, USA.

[9] Groemer, H. (1996) Geometric Applications of Fourier Series and Spherical Harmonics. New York, Cam-bridge University Press.

[10] LaGrou, John. The Design of Microphone Preampliers, originally published in R-E-P Magazine. Online:http: // www. mil-media. com/ docs/ articles/ preamps. shtml Last accessed: 20/10/06

[11] Malham, D.G. (1998) Spatial Sound Mechanisms and Sound Reproduction. University of York, England.

[12] Malham, D.G. (2001) Toward Reality Equivalence in Spatial Sound Diusion, in Computer Music

Journal. 25,4.

[13] Make your own ambisonic soundeld type microphone. (2003) Online:http: // homepage. ntlworld. com/ henry01/ cheap_ soundfield/ cheap_ soundfield. htm Lastaccessed: 20/10/06

[14] Wolf, S. (1995) Guide to Electronic Measurements and laboratory Practice. Prentice-Hall, USA.

[15] AM4011-Electret Microphone Insert (Datasheet). Electus Distribution, Sydney.

[16] Specication for Back Electret Condenser Micrphone (Datasheet). Ariose Electronics, Taiwan.

[17] Low-Noise JFET-Input Operational Ampliers (Datasheet). Texas Instruments, Texas.

[18] PNP General Purpose Amplifer (Datasheet). Fairchild Semiconductor Corporation.

[19] PNP Switching Transistors (Datasheet). Philips Semiconductors.

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7 Appendix A: Circuit Schematic

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8 Appendix B: Photos

Figure 12: Breadboard implementation. The leftmost board houses two preamplier stages, the right andsecond from right house one each. The second board from the left is the mixing stage for the B-Formatchannels.

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Figure 13: Breadboard implementation of the mixing stage. TL074 opamp terminals are as shown in theschematic. Inputs LFU, LBD, RBU, RFD are applied at the middle four connected lines, from bottom totop.

Figure 14: Breadboard implementation of preamplier. The dierential amplier is characterised by the twosilver 2N2905 transistors.

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Figure 15: PCB implementation. The board on the right is the PCB realisation of the four preamp stages.On the left is the mixing circuit.

Figure 16: PCB implementation with collector-collector capacitors attached to limit high frequency gain.

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9 Appendix C: PSpice Schematics and Simulation Results

9.1 Preamplier Stage test Circuits and Results

Figure 17: Preamplier: PSpice simulation of initial design.

Figure 18: PSpice simulation results for circuit of gure 17

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Figure 19: Preamplier: PSpice simulation with capacitors added across collector resistors.

Figure 20: PSpice simulation results for circuit of gure 19

Figure 21: Preamplier: PSpice simulation with bridging capacitor between two collector terminals.

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Figure 22: PSpice simulation results for circuit of gure 21

Figure 23: Preamplier: PSpice simulation of initial design with rst order lter on the output.

Figure 24: PSpice simulation results for circuit of gure 23

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9.2 Mixing Stage Test Circuits and Results

Figure 25: W-channel output test circuit.

Figure 26: Results of simulation: w-channel.

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Figure 27: X-channel output test circuit.

Figure 28: Results of simulation: x-channel.

Figure 29: Y-channel output test circuit.

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Figure 30: Results of simulation: y-channel.

Figure 31: Z-channel output test circuit.

Figure 32: Results of simulation: z-channel.

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10 Appendix D: Results of Hybrid Implementation.

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Figure 33: The hybrid implementation of the soundeld microphone.

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Figure 34: Adobe Audition recorded waveform: a nger click

Figure 35: Zoomed in on the nger click in gure 34

Figure 36: Adobe Audition recorded waveform: some ambient noise

Figure 37: Zoomed in version of gure 36

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11 Appendix E: Eagle PCB Layout

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12 Associated Data Sheets

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