Ultra Low Frequency Infrasonic Measurement System

Rasmus Trock Kinnerup, s052256

Master’s Thesis, July 2011

Abstract

An infrasonic measurement system is built capable of sensing acoustic signals down to 10 mHz which is advantageous for measurements of wind farm noise or sonic boom shapers. The system consists of an electric preamplifier built into a housing and a G.R.A.S. 40AZ 1 2 -inch prepolarized condenser microphone with a closed vent configuration. The total system has a dynamic range of 94 dB and a lower limiting -3 dB cutoff frequency of 8 mHz. The preamplifier connects the microphone signal directly to the input of an op-amp with an input resistance of 10 TΩ, one of the industry’s highest, which forms a high pass filter with the microphone capacitance of 20 pF. The bias current is supplied to the input node by two diode-connected FETs. The big challenge has been to sense the sound signal from the capacitive microphone with a high enough input impedance of the preamplifier to avoid an inherent cutoff of frequencies of interest. Being able to measure down to ultra low frequencies in the infrasonic frequency range will aid actors in the debate on wind turbine noise. Sonic booms from supersonic flights include frequencies down to 10 mHz and this measurement system will aid scientists trying to modify the N-shaped shock wave at high level which prohibits flights in land zones.

To my wife Cathrine and our children Alfred and Carla

Preface

This report is a Master’s Thesis in Electrical Engineering at the Department of Electrical Engineering at the Technical University of Denmark.

I have chosen the subject of this project because it deals with an electro acoustic problem. During my previous studies I have had exciting courses in both the acoustic and the electric domain. I found it natural to utilize my knowledge from both domains and to work with something that was of interest.

The project has been carried out in cooperation with G.R.A.S. Sound & Vibration A/S situated in Holte, Denmark. Working with a company have been very valuable for the project process and they have shown great interest to my project which have been a large motivating factor.

I would like to acknowledge the many individuals who have supported me during my studies. The employees in the development department of G.R.A.S. Kresten Marbjerg and Per Rasmussen have been very supportive. Also my supervisors Arnold Knott from Electron- ics Group have been encouraging and of great help.

Last but not least, appreciation goes to my family. Without their understanding, support and motivation the project would not have been the same.

Contents

1 Introduction 1 1.1 Problem Deﬁnition ...... 1 1.2 Thesis Structure ...... 2

2 Background 3 2.1 Infrasound ...... 3 2.2 Occurrences of Infrasound ...... 5 2.3 Applications ...... 7 2.4 Condenser Microphones ...... 7 2.5 Infrasonic Measurements ...... 9 2.6 Measurements with Capacitive Sensors ...... 10 2.7 Preampliﬁers for Condenser Microphones ...... 11

3 Electronic Design 13 3.1 Design Topology ...... 13 3.2 Low Leakage Op-amp ...... 14 3.3 Bias Current Circuitry ...... 14 3.4 First Prototype ...... 16 3.5 Guarding ...... 18 3.6 Analyzing Peaking ...... 20 3.7 Feedback ...... 22 3.7.1 Circuit b ...... 24 3.7.2 Circuit c ...... 25 3.7.3 Circuit d ...... 26 3.7.4 Choosing a Feedback Circuit ...... 28 3.8 Capacitive Load ...... 29 3.9 Start-up ...... 30 3.10 Noise ...... 32 3.11 Dynamic Range ...... 33 3.12 Production Component Variations ...... 34 3.13 PCB Layout ...... 35 3.13.1 Improvements for Next Version ...... 37 3.14 Final Prototype ...... 38

4 Acoustic Design 41 4.1 Choice of Microphone ...... 41 4.2 Capacitance and Voltage Variation ...... 42 4.3 Infrasound Calibration ...... 42 4.4 Leakage and Equalization ...... 43 4.5 Modeling of Vent ...... 45 4.6 New Vent Proposal ...... 46 4.7 Consequences of an Airtight Microphone ...... 49

5 Measurements 51 5.1 Electric System ...... 51 5.1.1 Damping ...... 51 5.1.2 Start-up ...... 53 5.1.3 THD and Noise ...... 55 5.2 Frequency Response of Entire System ...... 58 5.2.1 Microphone Mounting ...... 59

6 Conclusion 63 6.1 Future Work ...... 64

References 65

Appendix 69 A Various Matlab scripts ...... 69 B Microphone Calibration Chart ...... 72 C Circuit Analysis with feedback b ...... 73 D Circuit Analysis with feedback d ...... 74 List of Figures

2.1 Normal equal-loudness-level contours (ISO 226:2003) showing the threshold curve of human hearing in the lowest frequencies along with measurements from studies by Watanabe and Møller [1] ...... 3 2.2 Infrasound is produced by a variety of natural and man-made sources: exploding volcanoes, earthquakes, meteors, storms and auroras in the natural world; nuclear, mining and large chemical explosions, as well as aircraft and rocket launches in the man-made arena [2] ...... 4 2.3 The noise shape generated at the aircraft is like the shape of the aircraft but nonlinear propagation makes the sound wave at ground look like an N-shape...... 6 2.4 F-5E modiﬁed Shaped Sonic Boom Demonstration aircraft used to explore supersonic booms from aircrafts. The N-wave mentioned is painted on the side of the aircraft with a red line. The blue line painted on top is the shape of the wave from this aircraft. 6 2.5 Generic 3D model of a condenser microphone [3] ...... 8 2.6 Generic drawing of cross section of a condenser microphone [3] ...... 8 2.7 Equivalent electric circuit of a condenser microphone...... 9 2.8 Voltage sensing method measuring direct dc...... 10 2.9 Simple Capacitive Bridge circuit where the capacitance, Cx, is measured in comparison to a known capacitor C1 and with precision adjustable resistors R3 and R4. The AC null detector, D, reads 0 V when the the bridge is in balance. 11

3.1 Simplified schematic of circuit. V represents the acoustic sound pressure, Cm the variating microphone capacitance, Zb the bias circuitry supplying the bias current to the amplifier, Zf1 and Zf2 are the feedback circuitry and A the operational amplifier coupled as an impedance buffer...... 13 3.2 I-V characteristics of a P-N junction diode (not to scale) ...... 15 3.3 First prototype built into a homemade Faraday cage to protect from outside noise . . 16 3.4 The mock up of the circuit of the first prototype ...... 16 3.5 Full schematic of the first prototype. The resistor Zb shown is replaced with alternative bias circuits as shown in Figure 3.6...... 17 3.6 The different bias circuits replacing the impedance Zb from Figure 3.5. Imple- mentation a realize the high resistance with a resistor, b with two diodes in opposite direction and c with two FETs in opposite direction using the gate leakage current...... 17 13 3.7 Schematic of the simulated circuit in PSpice. Zin,cmm (10 Ω || 1 pF) is the common mode input impedance of the op-amp which is modeled along with the 15 differential input impedance, Zin,dif (10 Ω || 2 pF) to get a correct simulation in the low frequency range. Both impedances are listed in the data sheet of OPA129 as a resistance and a capacitance in parallel...... 18 3.8 Simulated and measured frequency response of first prototype (see Figure 3.7) with the different bias circuits from Figure 3.6...... 19 3.9 Simulation of the frequency response with a simple RC filter in the feedback. Peaking

is inevitable. Sweeping the value of Cf shows larger amplitude peaks for lower cut-oﬀ frequencies...... 20 3.10 Poles have very little imaginary and real values. Furthermore the stability is clearly achieved since the curve does not go beyond the point (-1,0) marked red. Component

values are Cm = 20 pF, Rb = 1000 GΩ, Cf = 16 µF, Rf = 10 MΩ...... 23 3.11 Schematic of the alternatives to the feedback circuit...... 23 3.12 Simulation showing the frequency response of the preampliﬁer with feedback circuit b

and varying Cf2. The variation shows signiﬁcant damping of the amplitude peak. . . . 24 3.13 Simulation showing the frequency response of the preampliﬁer with feedback circuit c

and varying Rf1. The variation shows an extra cutoff frequency introducing a minor attenuation before completely dropping down...... 26 3.14 Comparing simulation with circuit b with the combination of circuit a and c. Both feedback circuits in total provide a high pass filter and a voltage divider. In circuit b it’s a capacitive and in the combination of a and c it’s resistive. The simulations show comparable results...... 27 3.15 Simulation showing the frequency response of the preamplifier with feedback circuit

d, Cf2 = 0.8 µF and varying Rf1. The variation shows significant damping of the amplitude peak and no attenuation for all especially higher frequencies...... 27 3.16 Comparison of the frequency responses from the discussed 4 alternatives to a feedback circuit...... 28 3.17 Output signal of op-amp showing that the too large capacitive load in the circuit makes the op-amp reach its limitations at frequencies above 5.8 kHz. The capacitive load is 16 µF and the rated load capacitance stability of OPA129 is 1 nF up to a bandwidth of 1 MHz...... 29 3.18 The implemented circuit minimizing the start-up period in which the amplifier seeks its equilibrium potential. The switch is mechanically activated and connects a small resistance which lowers the time constant of the system. . . . 31 3.19 The time at which the input finds its DC level is decreased when the value of resistor

Rf is decreased. It also affects the frequency response, so it’s only for start-up purposes before real measurements...... 31 3.20 The noise of the transistor of the preamplifier in this case an op-amp OPA129. The noise is dominated at low frequencies by pink noise (flicker noise or 1/f noise) and above the noise corner frequency by white noise...... 33 3.21 Simulation of the frequency response of the final prototype version 1. Increased values

of Rf2 results in less peaking. A component tolerance of ±30 % results in ±0.2 dB . . 34 3.22 Simulation of the frequency response of the ﬁnal prototype version 1. Increased values

of Cf1 results in less attenuation for all frequencies. A variation of +5 % equals +19 mdB for frequencies above 100 mHz. Not shown is the variation of Cf2 which behaves opposite. This is due to the voltage division introduced by the two capacitances. . . . 35 3.23 The non-standard pinout of the chosen op-amp OPA129 makes it easy to implement a guard trace and separation of inputs and supplies minimizes leakage. 35 3.24 PCB Top layer. The board measures 44.6 mm times 10.3 mm and is 1.5 mm thick. . . 36 3.25 PCB Bottom layer. It is mirrored for easy comparison to the top layer in Figure 3.24 . 37 3.26 PCB and components in a 3D visualization. This was used to see whether the components would fit into the microphone housing...... 37 3.27 Picture of un-soldered PCB with rounded inner corners due to the process by which the board is cut using a 2 mm drill...... 37 3.28 Picture of the soldered PCB with copper guard ring and microphone housing...... 38 3.29 Picture of the entire preamplifier including LEMA plug...... 38 3.30 Full schematic of the final prototype version 1 implementing a feedback circuit with a high pass filter and a capacitive voltage divider...... 39 3.31 Full schematic of the final prototype version 2 implementing a resistive voltage divider...... 39

4.1 G.R.A.S. Type 40AZ ...... 41 4.2 The vent of 40AZ is made by putting in a spacer (green) on top of the insulator and cutting a slit in the spacer (see Figure 4.3). Equalization occurs through the slit (blue). 44 4.3 A close look of the spacer with a slit which makes equalization occur from the inner diameter to the outer...... 44

4.4 Model of the acoustic system (a) simplified to an acoustic volume (CA) and a vent for equalization of low frequencies (RA). The model is converted to the analogous electric circuit (b)...... 45 4.5 -3 dB cutoff frequency of vent as function of width and length of the slit in the spacer. The current vent/slit dimensions represent the data point in the very top...... 47 4.6 A modified vent proposal where the vent is cut skew close to a tangent of the inner radius...... 47 4.7 A new vent proposal where the vent length is increased by letting the slit run along the circumference of the spacer...... 48

5.1 Frequency response of preamplifier with 20 pF input adapter. The simulation is included for comparison. The electric lower limiting -3 dB corner frequency is clearly around 10 mHz for both versions of the preamplifier...... 52 5.2 Input adapter for supplying electric input to the preamplifier. A 15 pF version is depicted but a 20 pF also exist...... 52 5.3 Vent adapter used to seal or equalize the microphone. Both constructions are airtight from front to back. The adapter on the left has a hole which equalizes the microphone whereas the adapter to the right seals the microphone...... 52 5.4 DC offset of preamplifier version 1 with step on input through 20 pF input adapter shows the system’s settle time...... 54 5.5 Frequency response measurement of first prototype showing 2 sweeps, one with the switch off (normal operation) and one with the switch on, meaning a lower value resistor is connected in the feedback...... 54 5.6 FFT of output signal with 1 V sine at 1 kHz as input...... 55 5.7 FFT of output signal with 1 V sine at 100 Hz as input. The signal is marked red to aid the calculation of the dynamic range...... 57 5.8 FFT of output signal of version 1 with 1 kHz sine as input. 3 % distortion on the

output is reached at output voltage of 7.6 Vpp ...... 57 5.9 FFT of output signal of version 2 with 1 kHz sine as input. 3 % distortion on the

output is reached at output voltage of 28 Vpp ...... 57 5.10 G.R.A.S. 42AE low frequency calibrator with the microphone including vent inside the coupler...... 58 5.11 Measurements with version 1 showing consistency across several microphone cartridges and no or little difference whether the microphone is loosely mounted on the closed vent adapter or mounted with the open vent adapter. Lastly the measurements verify the entire system’s lower limiting frequency of around 190 mHz with a standard off- the-shelf 40AZ microphone...... 59 5.12 Measurements with version 2 and 40AZ microphone. With open vent adapter the -3 dB cutoff frequency is 190 mHz and with closed vent adapter and oil it is 8 mHz. . . . 60 5.13 Frequency response of entire system consisting of preamp v1 and 40 AZ showing the importance of ventilation. The measurements are conducted with the closed vent adapter. 61 5.14 Overpressure inside the microphone cavity results in 4 dB attenuation. The overpressure occurred when oil was applied along the thread and not only on the contact surface...... 61 List of Tables

3.1 Speciﬁcations of chosen ampliﬁer OPA129 along with its rivals...... 15 3.2 New component values in feedback circuit b which meet the requirements of the maximum load capacitance...... 30

6.1 Target speciﬁcations and obtained speciﬁcations of the measurement system . . 64

Introduction

A popular interpretation of infrasound is that it is sound at frequencies below the lower frequency limit of hearing [1]. But this implies that our hearing has a limit, which is not the case. If the sound level is high enough the sound even at frequencies below 5 Hz is audible. The lower the frequency the higher level is required for audibility.

The ability to measure acoustic noise is an important part of engineering. The noise level generated by a product has direct impact on the perception and user experience and in some cases regulations on acceptable noise levels make noise measurements inevitable. Most quality noise measurements are made with condenser microphones due to their ex- cellent all-round performance. They excel in dynamic range, frequency response, linearity, long-term stability among others [4].

Infrasonic noise has received more attention over the last few decades, especially in con- text of wind farms which produce infrasound. To measure the level of infrasound noise measurement systems must be able to cover the frequencies of interest ranging below 1 Hz. Measurement systems exist capable of measuring down into the ultra low frequency infrasonic frequency range e.g. [5], but the dynamic range is typically much less than systems operating in the traditional audio frequency range from 20 Hz to 20 kHz. Experi- ence with the B&K 2631 Microphone Carrier System capable of measuring to DC shows a dynamic range of 40-60 dB. And other similar approaches with demodulation of a carrier from Norsonic in Norway shows similar degraded results. In comparison ordinary audio measurement systems have a dynamic range of 140-150 dB.

1.1 Problem Deﬁnition This project will deal with the design and implementation of a system for measuring infrasonic noise going down to very low frequencies. Traditional infrasonic microphone systems typically cover a frequency range from 1 Hz to 20 kHz, but this system should extend down to 0.01 Hz (10 mHz). Existing systems typically have a dynamic range of 40 dB but this should be increased to 80 dB.

• Sensor: Condenser microphone

• Frequency range: 10 mHz - 20 kHz

• Dynamic range: 80 dB

• Output: analog 1. Introduction 2

1.2 Thesis Structure After this introduction relevant background information will be presented. After reading that, one should be better prepared for reading the following two design chapters. The ﬁrst design chapter describes the design from an electrical point of view, whereas the second design chapter describes the system and the design process with an acoustical view. Following the design chapters is a chapter verifying the ﬁnal prototype of the system including measurement results and comparison to simulation. Last chapter of the thesis is the conclusion including discussion of future work. 2

Background

This chapter will present background information which will put the project and its challenges in perspective.

2.1 Infrasound Infrasound is in popular terms defined as sound at frequencies below human hearing threshold. The audible frequency range is usually defined as the range from 20 Hz to 20 kHz. In other words infrasoundinterpretation is sound is that it at is sound frequencies of such low frequency below that 20 it Hz.is below The the lower IEC standard defines frequency limit of hearing, generally taken to be around 20Hz. A definition of infrasound as infrasound, found in Standards, is:

Acoustic oscillations whose frequency is below the low frequency limit of acoustic oscillation whoseaudible sound frequency (about 16Hz). is below (IEC, 1994) the low-frequency limit of audible

sound (about 16However, Hz), IEC sound 1994at frequencies below 16Hz is clearly audible if the level is high. The hearing threshold has been measured reliably down to 4Hz for listening in an acoustic chamber (Watanabe and Møller, 1990) and down to 1.5 Hz for earphone But the problem withlistening this way(Yeowart of et definingal., 1967). Fig infrasound 1 shows the hearing assounds threshold measurement below such frequency is from Watanabe and Møller between 4Hz and 125Hz together with the low frequency that sound below 20 Hzend and (20Hz even to 200Hz) 16 of Hz the isstandardized audible. hearing In Figurethreshold (ISO:226, 2.1 part 2003). of (The a standard human full range of measurements in ISO 226 is from 20Hz to 12.5kHz) There is good threshold curve is depictedcorrespondence along between with the measurements two sets of measurements by Watanabe of hearing threshold and in Møllerthe indicating overlap region in Fig 1. Rounded values are in Table 1: the extension of the curve below 20 Hz which is the lower limit of the ISO standard. This means that lower frequenciesFreq require higher level to be perceived. Frequencies down to a Hz 4 8 10 12.5 16 20 25 31.5 40 50 63 80 100 125 160 200 few hertz are provenLevel audible under certain conditions [1]. Frequencies below 20 Hz and even 16 Hz are audibledB and107 therefore100 97 92 defining88 79 69 60 infrasound 51 44 38 as32what 27 22 humans 18 14 can not hear is Table 1 Hearing threshold levels somewhat wrong. Even though no fixed frequency exists where audibility suddenly stops There is continuity of perception throughout the frequency range and no evidence for or begins for that matter,splitting into infrasound “infrasound” and” is not in infrasound” the following at around 16Hz discretely to 20Hz. However, defined as sound at frequencies below 20 Hz.there is a reduction in slope of the hearing threshold below about 15Hz from approximately 20dB/octave above 15 Hz to 12dB/octave below 15Hz. (Yeowart et al., 1967). There is also a change in perception of tonality, occurring around 18Hz. The common assumption that “infrasound” is inaudible is incorrect.

120

100

ISO226:2003 Watanabe and Moller 1990 80

40 Sound pressure level dB Sound pressure level dB

0 0 20 40 60 80 100 120 140 160 180 200 Frequency Hz

Figure 2.1: Normal equal-loudness-levelFig 1. Low contours frequency hearing (ISO threshold 226:2003) showing the threshold curve of human hearing in the lowest frequencies along with measurements from studies by Watanabe and

Møller [1] 2 2. Background 4

Looking at the wavelength of infrasound elaborates one of the most obvious characteristics. Under normal conditions a sound at 20 Hz has a wavelength of 17 m and at 1 Hz it is 343 m. Going all the way down to 10 mHz the wavelength is impressive 34 km. The attenuation of infrasounds diﬀer from their higher frequency neighbors by not being aﬀected by viscous dissipation. This means that infrasonic waves can travel for very long distances (> 100 km) and still be very measurable [6].

Now that infrasound by some has been deﬁned as something humans can not hear one could ask why to bother measuring it. Along with the auditory perception through the ear, sound can to some degree be sensed by the vestibular balance system and the resonant excitation of body cavities [7]. Altogether infrasound can be perceived. Many misunderstandings about infrasound have been developed over time [1] e.g. that infrasound should be a cause of death and possessing the ability to knock down buildings. Even though these beliefs are extreme the impact of infrasound on humans is somewhat unclear. Complaints on infrasound and low frequency noise (LFN) have been made with an increasing rate and investigated in numerous articles [8, 9]. The victims search for answers of their symptoms and scientists have no straightforward answers. In some cases victims do hear sounds in the infrasonic range, but other times it seems that the sounds origin from the victim himself with some kind of tinnitus. What is proven is that some people are aﬀected by infrasound and to help solve the problem scientists need to serve methods to measure and investigate it.

Figure 2.2: Infrasound is produced by a variety of natural and man-made sources: exploding volcanoes, earthquakes, meteors, storms and auroras in the natural world; nuclear, mining and large chemical explosions, as well as aircraft and rocket launches in the man-made arena [2] 2. Background 5

2.2 Occurrences of Infrasound As just discussed some people hear or sense infrasound but most often the source of the sound is unknown. The location of infrasonic sources can be difficult to find because sounds with such long wave- lengths behave differently than high frequency sources with regards to propagation over distance and damping through different media. Nev- ertheless some sources of infrasound are known. Wind farms and wind turbines are one example, and an important source of LFN which has attracted a lot of attention in the media in recent years. The wind turbine produce noise given by RZ f = (2.1) 60 where f is the fundamental frequency, R is the rotor speed in RPM and Z is the number of blades [10]. For a classic 3 blade geared wind turbine at 10 RPM the frequency is 0.5 Hz. Talking about noise from a wind turbine can be confusing since the audible noise generated by the wind blades is different than noise at the fundamental frequency found with (2.1).

Other sources of infrasound created by mother nature include meteorological phenomena like earthquakes, volcanic eruptions, water falls and avalanches. Infrasound is generated naturally by the environment here on earth. For concrete numbers on natural occurring events, wind ﬂowing over a mountain top or massive volcanic plume injections can produce buoyancy waves with dominant very low frequencies < 0.01 Hz [6]. But also man made processes like supersonic jets, explosions both nuclear and chemical produce infrasound. And with advancing technology these man made sound sources seem to become more and more and produce more and more infrasound. And it is for the purpose of measuring these occurrences a measurement system down to 10 mHz becomes obvious.

Supersonic flight creates a sonic boom which in fact is a system of shock waves reaching ground. It is not a sound generated at the transition into supersonic speed like an explosion, but a continuous effect as long as the flight is at supersonic speeds. These shock waves are at a high level so that supersonic flights are restricted from land zones. The noise generated at the aircraft is shaped like the body of the aircraft but nonlinear distortion while propagating to ground makes the shape of a sonic boom look like an N (see Figure 2.3). Many studies have been made to know more about these sonic booms, and there exist a theory on shaping the aircraft in a clever way so that the sound propagated to ground is not seen as an N-wave. Projects like Supersonic Business Jet (SSBJ) started in th 1990s pursued an alternative to the sonic boom which should sound more like a puff. In 2000 a program called Quiet Supersonic Platform (QSP) was started and in 2003 the first demonstration was built - Shaped Sonic Boom Demonstrator (SSBD) depicted in Figure 2.4. This demonstration showed the positive result that the N-wave was changed. The program manager commented: ”In 1947 Chuck Yeager broke the sound barrier. We just fixed it.” [11]. A measurement system capable of measuring 10 mHz would aid the development of other shaped sonic booms and may help make supersonic flights possible through land zones which is of great interest to airline companies. 2. Background 6

Figure 2.3: The noise shape generated at the aircraft is like the shape of the aircraft but nonlinear propagation makes the sound wave at ground look like an N-shape.

Figure 2.4: F-5E modiﬁed Shaped Sonic Boom Demonstration aircraft used to explore supersonic booms from aircrafts. The N-wave mentioned is painted on the side of the aircraft with a red line. The blue line painted on top is the shape of the wave from this aircraft. 2. Background 7

2.3 Applications A system for measuring infrasound down to 10 mHz can be of great interest for both manufacturers and actors in the wind farm debate. To name a few Vestas A/S, Danish Ministry of Environment (and internationally equivalent) and environmental movements such as Greenpeace and The Danish Society for Nature Conservation. If not interested directly in a system capable of measuring ultra low frequency infrasound, they will for sure be interested in the results from measurements with it.

In areas with frequent meteorological phenomena of great magnitude an alert system would beneﬁt greatly from a low frequency infrasound system like this. The system can help di- agnose the occurrences like the size, location and impact of an earthquake, avalanche or volcanic eruption [6].

And lastly a clear application of this system is actors in the development of sonic boom shapers. To be able to test the theoretical solutions in practice they would need a system capable of measuring very low infrasonic frequencies. Supersonic ﬂights crossing USA are presumed to have good economy thus shaping the sonic boom is of interest for aircraft manufacturers like Airbus and Boeing.

2.4 Condenser Microphones A condenser microphone is a transducer converting acoustical energy to electrical energy. A generic model of a condenser microphone is shown in Figure 2.5 and a drawing showing the cross section in Figure 2.6. The diaphragm and backplate form a capacitor and when sound makes the diaphragm move in and out the capacitance change. The rigid backplate has holes so that the air can move back and forward between the cavities; front cavity being between the diaphragm and backplate and the much larger back cavity inside the housing of the microphone. This type of capacitive sensor is called a spacing-variation sensor because the signal represents a spacing variation. Another type of sensor is an area-variation sensor, where the plates forming the capacitance slide in a parallel direction increasing or decreasing the eﬀective capacitive area [12].

The inside of the microphone is vented so that changes in the surrounding atmospheric pressure does not make the diaphragm place itself in a outward or inward direction. The DC pressure should be equal inside and outside the microphone. The vent is typically a small tube or opening acoustically connecting the inside of the microphone with the outside.

The capacitance of the microphone is given by

A C = (2.2) m 0 d where 0 is the permittivity of vacuum, A the capacitor plate area and d the distance 1 between the plates. A typical 2 -inch microphone with a plate separation d = 20 µm and 2 an eﬀective diaphragm area A = 45 µm yields a microphone capacitance Cm = 20 pF. The microphone can be seen as an almost pure capacitance meaning that is has a very high parallel resistance in the order of 5 · 1015 Ω. The high leakage resistance ensures no attenuation of the polarization voltage of the backplate [13]. Chapter 2 — Microphone Theory Measurement Microphone Design

Chapter 2 — Microphone Theory Measurement Microphone Design

which is mainly assembled by screwing the parts together, the integrated back-plate and insulator version is assembled by pressing the parts into each other. This de- 2. Backgroundsign also deviates from the conventional design 8 by applying a backplate consisting of a metal thin-film placed directly on the surface of the insulator.

Diaphragm Diaphragm Backplate Backplate Housing Insulator Insulator Housing

(a) (b) 950573/1e

Fig.2.1Figure Classic 2.5: DesignGeneric of a Condenser 3D Measurement model of Microphone a con- FigureFig.2.2 2.6:Cross-SectionalGeneric viewdrawing of microphone of types. cross The section classic type (left) is assembled by screwing the denser microphone [3] of a condenserparts together. microphone The new type (right) [3] is assembled by pressing components together. The design is patented by Brüel & Kjær cal tension in the foil gives the diaphragm the required mechanical stiffness. The distance between the backplate and the diaphragm is typically 20 µm (± 0.8 µm). The nominal distance may vary between microphone types from about 15 to 30 µm. In practice, the first mentioned type implies more freedom for the designer to opti- mise the frequency response, while the second is advantageous during production. TheThe thickness voltage of the diaphragm V on the may capacitorvary from about can 1.5 to with 8 µm depending a given on charge the Q beThe expressed main choice which with must be made in respect to the two different design types is microphone type. The tolerance is typically less than 10 % of the nominal thickness. one of more narrow frequency response tolerances offered by the conventional design, as opposed to reduced production costs for the alternative design. The diaphragm and the front of the back-plate form the plates of the activeQ capacitor which generates the output signal of the condenser microphoneV (see= below). This2.3.3 Material and Process Requirements (2.3) capacitance which is typically between 2 and 60 pF (10-12F), depends mainlyCm on the diameter of the back-plate. The stray capacitance or the passive capacitance be- A microphone which is to be used for measurements must be stable over time and tweenThis the back-plate relation and makes the housing is clearis kept as that small when as possible, the as charge this makes is an kept constantits properties a change should preferably in microphone not vary with variations in ambient temperature, undesired load on the active capacitance. The back-plate is connected to the exter- pressure and humidity. Therefore, carefully selected, high quality materials must be used, even if they are relatively difficult to machine. nalcapacitance, contact which together ∆C withm, the will housing result make in the a concentric change output in voltage,terminals ∆V . It is usually this sensing ap- of the microphone. An alternative, microphone design is widely applied by The sensitivity of the microphone is inversely proportional to the diaphragm ten- Brüel & Kjær. This patented design employs an integrated backplate and insulator, proach which is used to measure a sound pressure as input tosion. a The microphone. tension must therefore This be kept will stable. be Normally it is a requirement that a see Fig.2.2. In contrast to the first mentioned conventional design of microphone elaborated in Section 2.6. measurement microphone has a broad frequency range and a high sensitivity. This creates a requirement for light-weight diaphragms with high internal tension and thus a very high loading of the diaphragm material. This is achieved by applying a tension of up to 600 N/mm2 (which would break most materials) to the diaphragms 2− 8 Microphone Handbook Brüel & Kjær The charge, Q, on theVol.1 microphone is kept constant by applying a high bias voltage. Either

the voltage is applied externally which is the originalBE 1447 –11 and classic construction,Microphone butHandbook also 2− 9 Vol.1 prepolarized condenser microphones exist. They are also called electret condenser microphones and the bias voltage is provided by a permanently electrically charged or polarized ferroelectric material. This makes the microphone independent of an external high voltage source, which can be a good thing especially with mobile applications.

The sensitivity is a key parameter of a microphone and it expresses the change in voltage 1 in response to a given sound pressure. A typical sensitivity of a 2 -inch microphone is 50 mV/Pa. Also the sensitivity is usually given with reference to a speciﬁc frequency, because the sensitivity is not constant for all frequencies. 250 Hz is often used as reference because the microphone frequency response is usually most ﬂat in this region.

The dynamic range of a microphone is limited by the inherent noise in the lowest end and in the highest end by distortion. With condenser microphones it is usually not the 1 microphone in a measurement system that limits the system. A typical 2 -inch microphone has thermal noise of 14 dB referenced to 20 µ Pa and 3 % distortion upper limit of 146 dB which results in a dynamic range of 132 dB.

Compared to e.g. a dynamic microphone the condenser microphone is favorable on many aspects [4]. Linearity, high and low frequency response, dynamic range, working temper- atures are among the most signiﬁcant.

An equivalent electric circuit of a microphone is illustrated in Figure 2.7. The model includes a voltage source representing the sound pressure source and a variable capacitor representing the capacitance of the moving and separated plates. The model can be ex- tended with a resistor in parallel with the capacitor, but for most practical simulations it 2. Background 9 does not inﬂuence the behavior.

Figure 2.7: Equivalent electric circuit of a condenser microphone.

2.5 Infrasonic Measurements Measurements in the infrasonic range are diﬀerent in many ways from measurements in the ordinary auditory frequency band. First of all the nature of the infrasonic frequencies diﬀer from frequencies between 20 Hz and 20 kHz as described in Section 2.1. But with all measurements comes a preceding calibration which is described in standards. Un- fortunately the standards for calibration of infrasonic measurement systems are not well established [14].

The measurements themselves are also different. Variations in the atmospheric pressure begins to play a role since they are not necessarily filtered out by the vent. Also air turbulence or rather the pressure differences causing the air turbulence begin to affect the measurement. Air turbulence can occur where sources of heat exhaust their excessive heat. That could be fans, computers or even the human body. Wind will also affect the measurement and this is again obvious since wind is caused by pressure differences guiding the air molecules from a high pressure zone to a low pressure zone.

Trying to get rid of noise in the measurement many mechanical setups have been suggested. In [15] a mechanical setup of 32 low-impedance air inlets arranged in a circle with a diameter of 16 m is proposed. Also windscreens of diﬀerent sizes and shapes are proposed. It is obvious that some kind of ﬁltering of wind disturbances will be of great importance to a good infrasonic measurement. In the IEC 61400-11:2002 standard a measurement technique for acoustic noise measurements on wind turbines is described. The standard is a part of a larger standard on wind turbine generator systems. The standard instruct the microphone to be placed on a acoustically hard sphere (Ø > 1 m) and protected by a half sphere of cell foam (Ø ≈ 90 mm). Even though this standard is well established it only measures down to around 50 Hz and it is only designed for measurements on wind turbines.

Also the data is treated differently. Specifications in audio equipment are most typically stated A-weighted which is an international standard used to relate measurement of sound pressure level to the human hearing. Unfortunately A-weighting is designed for low level sounds and for frequencies in the auditory frequency band which is not applicable here. The A weighting curve approximately follows the equal loudness curve of 40 phons. In 1995 a G-weighting was standardized (ISO 7196) designed for infrasound. Unfortunately this standard only covers from 1 Hz to 20 Hz. The curve is defined to have a gain of zero dB at 10Hz. Between 1 Hz and 20 Hz the slope is approximately 12 dB per octave. The cut-off 2. Background 10 below 1Hz has a slope of 24 dB per octave, and above 20 Hz the slope is -24 dB per octave.

All in all it is clear from previous ﬁndings and standards that this measurement system should also include some shielding of wind. And even with a properly designed equalization vent the data will contain data which is not the signal hence noise. It will be a challenging task to ﬁlter the signal from the many other noise sources like wind, atmospheric pressure variations and naturally present infrasound sources.

2.6 Measurements with Capacitive Sensors Capacitive sensors can be sensed in several ways. A thorough evaluation is found in [16]. As described in Section 2.4 the signal can be sensed by having a constant charge on the capacitor and sensing the voltage across the capacitor. This voltage reflecting the sound signal connects to an amplifier which serves the purpose of an impedance buffer and op- tional amplification (see Figure 2.8). The same node is connected to ground through a resistor to make sure the DC level does not float. And because the microphone capacitance and the input impedance of the connected amplifier forms a high pass filter, the bias resistor to ground needs to be very large. This will be discussed in details in Section 3.3. The amplifier can be a single transistor in applications where low noise is most important, but this configuration is known to have low power supply rejection. The amplifier can also be an operational amplifier (op-amp) or instrumentation amplifier (in-amp). As will be seen later these types of preamplifier circuits have a long start-up due to the large resistor values.

C + OUT A V R −

Figure 2.8: Voltage sensing method measuring direct dc.

The capacitive sensor can also be sensed with a constant voltage across meaning the microphone inputs are short circuited. This approach implies a charge ampliﬁer sensing the charge change or a current sensing transistor. Compared to the previous mentioned voltage sensing this charge sensing or current sensing method have a lower signal to noise ratio (SNR) [16].

A third possibility is to use the capacitance of the microphone in an oscillating circuit a so called oscillator. This can be implemented either by an RC circuit or LC circuit, where the microphone capacitance is the tuning element in the oscillator. This kind of a signal represented by a frequency is called frequency modulation (FM). The FM signal is sensed with a demodulator e.g. a frequency counter to linearize spacing-variation sensors. 1 By using an RC circuit the frequency is proportional to RC and with an LC circuit its proportional to √1 which is harder to linearize [12]. RC

Arranging the microphone capacitance in a bridge circuit like a simple capacitance bridge was also investigated. But that kind of circuit implies that the comparing component in 2. Background 11 the other leg of the bridge is like the device under test. In other words the bridge has best performance when the microphone capacitance and the compared capacitance are equal with respect to series resistance and capacitance value [17]. In mathematical terms the complex values of the two comparing capacitances must be equal in real and imaginary values [18]. Ideally this would only be possible if another similar microphone would be used as reference. If the two legs in the bridge are not equal the signal would be out of phase and magnitude. This is not possible for all input levels and frequencies, so this solution was trashed.

C1 Cx

V D

R3 R4

Figure 2.9: Simple Capacitive Bridge circuit where the capacitance, Cx, is measured in comparison to a known capacitor C1 and with precision adjustable resistors R3 and R4. The AC null detector, D, reads 0 V when the the bridge is in balance.

2.7 Preampliﬁers for Condenser Microphones The most commonly seen circuitry to interface a condenser microphone is by far the voltage sensing method also called Direct DC. It is very simple and thereby very small in size. The purpose of the preampliﬁer is to convert the impedance level from a very high impedance microphone to the low impedance cable which transmits the signal to whatever instrument waiting to receive.

It is usually strived to have unity gain in the preamplifier. More specifically the preamplifier is constructed to fit the application, the microphone specifications and frequency range of the system. When using an externally polarized microphone the preamplifier of course needs to be able to deliver that. Also many preamplifiers are powered by a constant current source through the signal line which is called by many names. G.R.A.S. calls it CCP (Constant Current Power supply), Bruel¨ & Kjær calls their version DeltaTron, in piezoelectric electric domains its often called IEPE and more generally it is called CCLD (Constant Current Line Drive).

The impedance buffer made up by the preamplifier makes sure that the signal is not attenuated by the attached cable which can be long. Without the buffering a long cable and the resulting large capacitance would attenuate the signal which can not be accepted.

Electronic Design

In the following sections the design process will be described from an electrical point of view, finishing off with the presentation of the final prototype design. The initial design considerations will be elaborated moving on to pre-verification with simulation, measurements on the first prototype and lastly manufacturing of the final prototype.

− C OUT m A +

V Zb Zf1

Zf2

Figure 3.1: Simplified schematic of circuit. V represents the acoustic sound pressure, Cm the variating microphone capacitance, Zb the bias circuitry supplying the bias current to the amplifier, Zf1 and Zf2 are the feedback circuitry and A the operational amplifier coupled as an impedance buffer.

3.1 Design Topology As described in Section 2.6 and 2.7 many topologies were considered for the design of the preampliﬁer. A bridge circuit was dismissed due to the complexity of having a perfectly matched ’other leg’ in the bridge, which is needed for a good accuracy but impractical due to the variating microphone capacitance.

A frequency modulation using the microphone capacitance in an oscillator was also dismissed. Mainly due to the disadvantages over the chosen direct DC topology which is simpler and smaller in size. Furthermore a contact was established to Norsonic, a Nor- wegian company specialized in applications for measurement of sound and vibration [19]. They shared their experience with the design of an FM system where a dynamic range of only 40 dB was achieved.

The chosen topology is a simple direct DC detection circuit. The change in capacitance is measured by charging the capacitance and connecting it to the input of an ampliﬁer. 3. Electronic Design 14

In fact the microphone is charged on forehand via the polarized material, so simply by connecting the microphone to an ampliﬁer input gives a voltage output proportional to the spacing variation between the capacitive plates.

Different amplifiers can be chosen. Most commonly found in the industry is a JFET since it has low input leakage and low noise specifications. But also op-amps and in-amps can serve the purpose of amplifying.

3.2 Low Leakage Op-amp The importance of the input leakage becomes clear when seeing that the microphone capacitance forms a high pass filter with the input resistance of the circuitry connected to it. And low input leakage is equivalent to a high input resistance. The electric -3 dB cutoff frequency is calculated using 1 f = (3.1) 2πCmRin where Cm is the microphone capacitance and Rin is the input resistance of the preamplifier. With the goal of a lower frequency limit of 10 mHz and a nominal Cm = 20 pF the required Rin is in the order of 800 GΩ. The search for an amplifier began with the primary requirement of at least 1000 GΩ or 1012 Ω.

The amplifier can be implemented in many ways and as mentioned a JFET is usually seen in microphone preamplifiers. But investigations went through the market of op-amps in various configurations and even in-amps which are the more complex solution. It became clear that the amplifier using an op-amp should be in a non-inverting configuration since it has the important property of high input resistance [20]. The in-amp has the advantage of a high common mode rejection (CMR) which is good for extracting a weak signal in a noisy environment and to minimize offsets [21]. National Semiconductor has an LMP7721 Precision Amplifier which has the industry’s lowest input bias current of 3 fA (20 fA at max). It was deselected because it only operates with a single supply voltage of maximum 5 V, which in Section 4.1 will become clear to be insufficient. Texas Instruments has produced an Ultra-Low Bias Current Difet Op-amp called OPA129 which was compared to its brother IN116 which is the same as an in-amp. Even though the IN116 had higher input resistance the choice fell on OPA129 which had better noise specifications and a simpler layout. The three rivals and their specifications are listed for comparison in Table 3.1.

3.3 Bias Current Circuitry Into any transistor and therefore also the chosen op-amp is a positive or negative leakage current. It is there because the input impedance of the terminals have a finite value and is not infinity as assumed when operating with ideal op-amps and the concept of virtual ground. Even though the leakage current of OPA129 and the other candidates is in order of fA or 10−15 A it is sufficient to cause a floating voltage on the input node. The leakage current which must flow in or out of the inputs must be supplied from a source. That is the reason why a bias current path most be established on the positive input of the amplifier. This is typically done with a high ohmic resistor connected to ground or a voltage supply. 3. Electronic Design 15

Table 3.1: Specifications of chosen amplifier OPA129 along with its rivals. OPA129 IN116 LMP7721 Texas Texas National Instruments Instruments Semiconductor Topology Op-amp In-amp Op-amp Input bias current, typical [fA] 30 3 3 Input bias current, max [fA] 100 25 20 13 15 Input impedance, differential [Ω]√ 10 10 Noise at 1 kHz [nV/ Hz] 17 28 6.5 Supply voltage [V] ±15 ±15 5.5

A problem arises because the total input impedance of whatever connected circuitry seen by the microphone must be at least 1000 GΩ. Otherwise the 10 mHz lower frequency limit is not obtained. That high a ohmic value is impractical for a traditional resistor whether it is a thin, thick or metal film resistor. Ohmite, a company specialized in manufacturing of resistors, has a 100 GΩ resistor which is a metal film resistor vacuum sealed in a long glass tube. Thin film resistors are in general not available above a couple of GΩs and thick film resistors move up in the range of 50 GΩ. It could be possible to connect a bunch of either of them in series but other solutions where sought in order to keep down the size of the design.

The leakage of the OPA129 is 100 pA at most but typical 30 pA. The bias circuitry should be able to supply that. A way to supply the leakage current is to use the leakage current of another component.

A diode has a reverse current which for specific low leakage diodes is very small. This region is active when the diode is reverse biased (see Figure 3.2) and not beyond the break- down voltage Vbr. In the forward direction the diode begins to conduct when the forward voltage Vd reaches around 0.8 V. Two diodes connected in opposite direction and in series will serve the purpose of a very large resistance. But it is only possible if the voltage across the diodes swing within Vbr and Vd. Since the input node swings according to the sound pressure the diodes can not be connected directly to ground. As calculated in Section 4.2 the voltage swing on the amplifier input can be around ±12 V at 138 SPL. There- fore the diodes are connected from the input terminal of the amplifier to a node which has the same amplitude (or close) as the input node. The output signal is used through a high pass filter which cuts off any DC present. The filter will be presented in Section 3.7.

Figure 3.2: I-V characteristics of a P-N junction diode (not to scale) 3. Electronic Design 16

Several diodes came into play. NXP Semiconductors have a low leakage diode BAS116 which has a typical reverse current, IR, of 3 pA. Recalculating the reverse current to a equivalent resistance is not straight forward since the characteristics is not well defined and nonlinear around the transition between reverse and forward region around 0 V. Another aspect of choosing a diode as a low leakage component is that diodes essentially is designed for rectifying and not for low leakage. Some transistors on the other hand are designed specifically for low leakage through the gate. This property was looked into. Especially the NXP Semiconductors BFR31 which has a gate cut-off current of 200 pA. The gate cut-off current is the reverse current of the internal gate-source diode when drain-source is shorted. One argument for looking at FETs over diodes is that FETs are available at much lower prices than diodes, the reason being that they are produced in far larger numbers than diodes and the production costs thereby minimized. Even though the leakage current of BFR31 is larger than the reverse current of BAS116 the designed purpose of low leakage and not rectifying makes better for the application.

Measurements where conducted on the first prototype with the mentioned diodes and FET and will be presented in the next section. While working with the different bias circuits it became clear that the voltage across Zb indeed has an effect. Because the preamplifier has gain of about -1 dB (a factor 0.89) the feedback voltage is always less in amplitude than the input voltage. At 10 V input the feedback voltage is 8.9 V and thus the voltage across Zb is 1.1 V. This is beyond the forward voltage of the diode which starts to conduct hence the high ohmic resistance it emulates decreases. Using leakage currents of FETs does not seem to fall for the same issue since it is designed for low leakage. This problem will be discussed further in Section 5.1.

3.4 First Prototype

To be able to build a working prototype a small box of aluminium was made. The enclosure works in practice as a Faraday cage which blocks out external static electric ﬁelds. The box thereby work as a ﬁlter for the noise present in the world around us. In cooperation with the mechanical department at G.R.A.S. the box was equipped with a thread arrangement 1 for mounting of a 2 -inch microphone, two BNC connectors, a power switch and a second switch which will be presented later. The box measures 188x120x57 mm and is provided with rubber studs on the bottom side. A top-view picture of the box is shown in Figure 3.3.

Figure 3.3: First prototype built into a Figure 3.4: The mock up of the circuit of homemade Faraday cage to protect from out- the ﬁrst prototype side noise 3. Electronic Design 17

The circuit shown in Figure 3.5 is implemented in a quick and dirty mock up on a copper plate. The feedback impedances Zf1 and Zf2 are chosen as an RC circuit with a cutoﬀ frequency of 1 mHz. The component values are Zf1 = Cf = 16µF and Zf2 = Rf = 10MΩ. The power supply for the circuit is two 9 V batteries each with a decoupling capacitor of 100 nF placed close to the pins on the op-amp.

V + 100 nF

− C OUT m A +

V − 100 nF V Zb

Cf 16 µF Rf 10 MΩ

Figure 3.5: Full schematic of the ﬁrst prototype. The resistor Zb shown is replaced with alternative bias circuits as shown in Figure 3.6.

The first prototype was fixed with respect to feedback circuitry and was used to test the circuit in general, the performance of the op-amp and the bias circuits shown in Figure 3.6. The initial step was to simulate the circuit using PSpice. The simplified model build in PSpice is shown in Figure 3.7 and differs from the already presented schematic by having an ideal op-amp. To get a correct response of the model in the low frequency range the input impedance of the op-amp is modeled as a finite impedance. This impedance is stated in the data sheet of OPA129 both as a differential input impedance, Zindiff and a common mode input impedance, Zincmm . A spice model of OPA129 was tried implemented but it turned out to give very incorrect results. It became obvious that the spice model is a behavioral model and not necessarily correct for all applications. Thus it was decided to work with an ideal op-amp and modeling the input impedance manually.

a b c

Figure 3.6: The diﬀerent bias circuits replacing the impedance Zb from Figure 3.5. Im- plementation a realize the high resistance with a resistor, b with two diodes in opposite direction and c with two FETs in opposite direction using the gate leakage current.

In Figure 3.8 the result of the simulations are shown. For all measurements the feedback circuit is as illustrated in Figure 3.11. As mentioned the feedback is a simple RC circuit with low cutoﬀ frequency of 1 mHz. The diﬀerence between the measurements/simulations 3. Electronic Design 18

− OUT Cm Zincmm A +

Zindif V Zb Zf1

Zf2

13 Figure 3.7: Schematic of the simulated circuit in PSpice. Zin,cmm (10 Ω || 1 pF) is the common mode input impedance of the op-amp which is modeled along with the diﬀerential 15 input impedance, Zin,dif (10 Ω || 2 pF) to get a correct simulation in the low frequency range. Both impedances are listed in the data sheet of OPA129 as a resistance and a capacitance in parallel. is the bias circuitry.

Initially a BAS216 diode was tested even though the reverse current is 30 nA which is far too much to meet the requirements. It is worth mentioning that the component models used in the simulation are spice models downloaded directly from the manufacturer’s web- sites. Simulation and measurement shows similarities with a peak around 0.4 and 0.7 Hz. The remarkable attenuation of around 8 dB for the measurement is due to wrong guarding which will be described later.

Then a BAS116 low leakage diode was tested. Unfortunately the match between simulation and measurement is not as good as with the BAS216. Simulation shows a peak below 10 mHz whereas the measurement shows one at 150 mHz. It is not investigated further why this mismatch occurred. Either the spice model of the diode is not perfect for this usage or the measurement has introduced some kind of error. Maybe the previously mentioned problem with voltage across the diodes due to attenuation of the feedback voltage causes the higher cutoﬀ frequency.

Lastly the FET BFR31 was tried. This shows a very good match with a peak in simulation at 5.5 mHz and a measured at 8 mHz. Again the attenuation in the measurement is due to introduced capacitances as will be elaborated in the next section. The results show that using two FETs coupled in opposite direction to supply the bias current is suﬃcient to achieve a high enough resistance and thereby a low enough cutoﬀ frequency.

3.5 Guarding Ultra-low input bias current op-amps introduce the need for extra careful layout to achieve the documented performance. The output signal of the microphone needs to be guarded on its way to the input of the op-amp. A guard is a low impedance conductor that surrounds an input line and the potential of this guard must be similar to the input line’s voltage. Without guarding large stray capacitances will be introduced which will attenuate the signal. The BFR31 FETs have an input capacitance of 4 pF. The input capacitance of a FET 3. Electronic Design 19

Frequency response of first prototype with different bias circuits 40 Simulation: BAS216 30 Simulation: BAS116 Simulation: BFR31 Measurement: BAS216 20 Measurement: BAS116 ] Measurement: BFR31

RMS 10

−10 Amplitude [dB V −20

−30

−40 −3 −2 −1 0 1 10 10 10 10 10 Frequency [Hz]

Figure 3.8: Simulated and measured frequency response of first prototype (see Figure 3.7) with the different bias circuits from Figure 3.6. is defined as the sum of the gate-source capacitance and the gate-drain capacitance. And as mentioned the OPA129 has a differential input capacitance of 2 pF. These introduced capacitances can not be removed but stray capacitance like introduced by wiring without guarding can be dealt with.

In Figure 3.8 the attenuation in the measurements can be explained by stray capacitance in the wiring. For the BAS216 case the guard following the microphone signal from the inside wall of the microphone thread to the input of the op-amp on the copper board was connected to ground. This correspond to no guarding since the guard’s voltage level is not equal to the input signal. This introduces a lot of the -8 dB gain which is seen on the BAS216 measurement. After connecting the guard correctly to the output signal of the op-amp the gain in the same setup was -2.5 dB which is more like the other measurements.

The guard also needs to be present on the PCB since leakage current on the surface of the board can exceed the leakage current of the pin. For example, a circuit board resistance of 1012 Ω from a power supply pin to an input pin produces a current of 15 pA - more than 100 times the input bias current of the op-amp [22]. A guard trace is surrounding the input pins on the ampliﬁer. This ensures that a current will not as likely ﬂow from the input pin to somewhere else since the voltage level everywhere else is at the same potential. 3. Electronic Design 20

3.6 Analyzing Peaking Now with a first prototype which seems to be able to meet the requirement of measuring down to 10 mHz another problem arises. The peaking at the low cutoff frequency is not acceptable. In Figure 3.9 it is seen that decreasing the cutoff frequency by variating the feedback capacitor will only make the matter worse. To better understand what causes this an analytical expression of the transfer function is sought.

Frequency response with variation of C in the feedback f 20

5 33 pF 0 59 pF 104 pF −5 186 pF 330 pF −10 587 pF Amplitude [dBV] −15 1 nF 1.9 nF −20 3.3 nF 5.9 nF −25 10 nF 19 nF −30 −3 −2 −1 0 1 10 10 10 10 10 Frequency [Hz]

Figure 3.9: Simulation of the frequency response with a simple RC ﬁlter in the feedback. Peaking is inevitable. Sweeping the value of Cf shows larger amplitude peaks for lower cut-oﬀ frequencies.

First Kirchhoff’s Current Law (KCL) is used on the node connected to the positive input of the amplifier. For simplicity the concept of virtual ground is assumed meaning that the voltage on the two inputs are equal and no current flow in or out of the inputs. Furthermore the bias circuitry is assumed to be a very large resistor, Zb.

1 1 0 = (VO − VA) + (VO − VIN ) ⇔ (3.2) Zb Zm 1 1 1 1 VA = VO + − VIN (3.3) Zb Zm Zb Zm where VA is the voltage at the node connecting the bias circuitry to the feedback circuitry. And Zm is the impedance of the microphone. And now using KCL on the node VA yields

1 1 1 0 = (VO − VA) + (VO − VA) − VA (3.4) Zb Zf1 Zf2 3. Electronic Design 21

Rearranging coeﬃcients of VO on one side and of VA on the other

1 1 1 1 1 VO + = VA + + Zb Zf1 Zb Zf1 Zf2

Isolating VA

1 + 1 Zb Zf1 VA = VO (3.5) 1 + 1 + 1 Zb Zf1 Zf2

Substituting (3.5) into (3.3) yields

1 + 1 ! Zb Zf1 1 1 1 1 VO 1 1 1 = VO + − VIN + + Zb Zm Zb Zm Zb Zf1 Zf2

Rearranging all coeﬃcients of VO on one side and VIN on the other

1 + 1 !! 1 1 1 1 Zb Zf1 VIN = VO + − 1 1 1 Zm Zm Zb Zb + + Zb Zf1 Zf2

Rearranging and isolating VO on one side VIN

V Z O = b (3.6) 1 1 V Z + Z IN Zb b f1 Zm + 1 − 1 1 1 Zm + + Zb Zf1 Zf2

Now it’s time to insert Laplace transformed expressions instead of complex impedances. They are transformed as follows

1 Zb = Rb Zf1 = (3.7) sCf 1 Zm = Zf2 = Rf (3.8) sCm

Substituting the expressions from (3.7) and (3.8) in (3.6) yields

VO Rb = 1 +sCf VIN 1 Rb sRbCm + 1 − 1 1 sCm + +sCf Rb Rf sRbCm = 1 +sCf Rb sRbCm + 1 − 1 1 + +sCf Rb Rf 1 1 sRbCm( + + sCf ) Rb Rf = 1 1 1 1 1 sRbCm( + + sCf ) + + + sCf − − sCf Rb Rf Rb Rf Rb 2 s Rf Cf RbCm + s(Rf + Rb)Cm = 2 (3.9) s Rf Cf RbCm + s(Rf + Rb)Cm + 1 3. Electronic Design 22

The expression in (3.9) is the transfer function of the circuit and relates the output voltage to the input voltage. It is a second order system which is normally written on the standard form:

b Y (s) b 2 = = ωn (3.10) 2 2 s2 s U(s) s + 2ζωns + ωn 2 + 2ζ + 1 ωn ωn where Y (s) is the output, U(s) the input, b the static gain, ζ the damping ratio, ωn the natural frequency [23].

Directly comparing (3.10) to (3.9) yields the system’s natural frequency s 1 ωn = (3.11) Rf Cf RbCm

And its damping ratio

s 1 1 ζ = (Rf + Rb)Cm (3.12) 2 Rf Cf RbCm

For all practical component values ζ is below 1 which makes it an under-damped system with complex poles with a negative real value. With Cm = 20 pF, Rb = 1000 GΩ, Rf = 10 MΩ and Cf = 16 µF the damping ratio is ζ = 0.18. This implies that the system is stable. For a better understanding on the location of poles and zeros a Nyquist diagram is made. See Figure 3.10.

Returning to the origin of this analysis, it was suppose to help understand why the system has an amplitude peak and how to avoid it. Introducing damping will minimize the peak and with a critical damped system (ζ = 1) it would disappear. Unfortunately the expressions derived in (3.12) shows that it is not possible with only two degrees of freedom being the feedback components, Rf and Cf . But when the cutoﬀ frequency is to be maintained and Cm and Rb are rather ﬁxed it is actually only Rf that is adjustable to maximize the damping. But as explained in Section 3.3 the resistor values quickly become impractical. Especially when Rf occur as a sum together with Rb which is in the order of 1000 GΩ. So to have a say in this matter it should be very large and impractical.

To round up, this analysis show that another approach to the circuit must be considered.

3.7 Feedback Different variations of feedback circuits can be implemented and to deal with the amplitude peak as just described, some alternatives are investigated. The alternatives are shown in Figure 3.11. Circuit a shows the simple RC filter which proved to be insufficient. Circuit b is one alternative where a capacitor is put in parallel with the feedback resistor. The capacitor introduces a capacitive voltage divider together with the existing feedback capacitor, Cf , now named Cf1. Another possibility is circuit c which is a resistive voltage divider. The last investigated alternative is a filter modifying circuit b with an extra resistor connected in parallel with the original feedback capacitor. 3. Electronic Design 23

Nyquist Diagram 5 0 dB 4

3 −2 dB 2 2 dB

4 dB −4 dB 1 6 dB −6 dB 10 dB −10 dB 0

Imaginary Axis −1

−2

−3

−4 Poles Zeros −5 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3 Real Axis

Figure 3.10: Poles have very little imaginary and real values. Furthermore the stability is clearly achieved since the curve does not go beyond the point (-1,0) marked red. Component values are Cm = 20 pF, Rb = 1000 GΩ, Cf = 16 µF, Rf = 10 MΩ.

Rf1 C C f1 f1 Rf1

Cf1

Rf2 Cf2 Rf2 Rf2 Cf2 Rf2

a b c d

Figure 3.11: Schematic of the alternatives to the feedback circuit.

Simulations where made in PSpice to see what results could be achieved with the 4 diﬀer- ent alternative feedback circuits. The simulations are conducted with a circuit model as shown in Figure 3.7 and the bias circuit of Figure 3.6 c, and the variating feedback circuits of Figure 3.11. 3. Electronic Design 24

3.7.1 Circuit b

The first simulation involves circuit b where a capacitive voltage divider is added by connecting a capacitor in parallel with the existing resistor in the feedback. In Figure 3.12 simulation results from this setup is shown. The effect of the voltage divider is clearly seen by the increasing attenuation at higher frequencies. With the chosen interval of values for Cf2 the amplitude varies from -0.9 dB to -3.5 dB. When trying to make sure not to compromise the low frequency cutoff frequency it is obvious that the best curve without peak is with 4 µF. This value correspond to a fourth of the original feedback capacitor, Cf1. This choice introduces -0.6 dB of gain relative to the dB level without the extra capacitor. With the chosen extra capacitor the total gain is -1.5 dB. Introducing more attenuation leads to another issue. Loading the microphone introduces distortion and nonlinearities which is why preamplifiers are usually designed to have a gain as close to 0 dB as possible. But some attenuation is acceptable and is seems a good trade off to accept some attenuation and get rid of the peak.

Frequency response with variation of C in the feedback f2 10

−5

−10 128 nF

Amplitude [dBV] 405 nF −15 1.28 µF 4.05 µF 12.8 µF −20 40.5 µF 128 µF −25 −3 −2 −1 0 10 10 10 10 Frequency [Hz]

Figure 3.12: Simulation showing the frequency response of the preampliﬁer with feedback circuit b and varying Cf2. The variation shows signiﬁcant damping of the amplitude peak.

As in the analysis in Section 3.6 the expressions for the cutoﬀ frequency of circuit variation b is

s 1 ωn = (3.13) Rf2(Cf1 + Cf2)RbCm 3. Electronic Design 25 and its damping ratio

s 1 1 ζ = (Cf2Rf2 + (Rf2 + Rb)Cm) (3.14) 2 Rf2(Cf1 + Cf2)RbCm

The equations deriving these expressions can be found in Appendix C.

Lets try to put in real numbers to see that components can alternate the damping

The frequency ωn is ﬁxed to 2π · 0.01 Hz

1 ζ = · 2π · 0.01 Hz · (C R + (R + R )C ) (3.15) 2 f2 f2 f2 b m

The bias resistance, Rb, is 1000 GΩ and the microphone capacitance, Cm, is 20 pF

1 ζ = · 2π · 0.01 Hz · (C R + (R + 1000 GΩ) · 20 pF) (3.16) 2 f2 f2 f2

Simplifying by saying Rf2 Rb

1 ζ = · 2π · 0.01 Hz · (C R + 1000 GΩ · 20 pF) (3.17) 2 f2 f2

Rearranging to isolate the unknown with ζ < 1

1 C R < − 1000 GΩ · 20 pF (3.18) f2 f2 π · 0.01 Hz Cf2Rf2 < 11.831s (3.19)

Using Rf2 = 10 MΩ as in the original circuit a

Cf2 < 1.2 µF (3.20) which is not far from what the simulations in Figure 3.12 shows (damped scenario with Cf2 = 4.05 µF). If Rb is not quite as large as 1000 GΩ and the cutoﬀ frequency is a bit lower than 1 mHz the value of Cf2 will increase to something closer to 4 µF which is what the simulation shows.

3.7.2 Circuit c The result from the previous section with circuit b were done by introducing a capacitive voltage divider. Circuit c has a resistive voltage divider and no frequency dependence. The simulations with varying attenuation in the voltage divider is shown in Figure 3.13. It shows that with a voltage divider feeding back half the amplitude of the output voltage (Rf1 = 100 GΩ) the response drops 1 dB at 0.1 Hz and cuts oﬀ completely above 10 mHz. Referring back to Section 3.3 the diodes inside the FETs require the voltage node VA to be equal or close to equal in magnitude and phase. The extra cutoﬀ introduced in this scenario might be due to the internal diodes beginning to conduct larger current beyond the voltage limits Vbr and Vd. In the other 10 scenarios in Figure 3.13 the extra 3. Electronic Design 26

Frequency response with variation of R in the feedback f1 0

−1

−2

−3 1 GΩ −4 1.6 GΩ 2.5 GΩ −5 4.0 GΩ Ω −6 6.3 G

Amplitude [dBV] 10 GΩ −7 16 GΩ 25 GΩ −8 40 GΩ Ω −9 63 G 100 GΩ −10 −3 −2 −1 0 1 10 10 10 10 10 Frequency [Hz]

Figure 3.13: Simulation showing the frequency response of the preampliﬁer with feedback circuit c and varying Rf1. The variation shows an extra cutoﬀ frequency introducing a minor attenuation before completely dropping down.

cutoﬀ is also present but not as profound. With the choice of Rf1 = 10 GΩ the extra cut- oﬀ introduces only 0.3 dB of attenuation and still has a -3 dB frequency limit of a 2.5 mHz.

Circuit b has a ﬁlter and a capacitive voltage divider. Circuit c has only the voltage divider but by combining circuit a and c the total feedback circuit should treat the signal the same. A comparison of the two cases is shown in Figure 3.14 and it is clearly seen that the results are similar. So it is just as good with a capacitive voltage divider as with a resistive voltage divider.

3.7.3 Circuit d The last variant of a feedback circuit is that of Figure 3.11 d. The analytic expression of the transfer function is a third order system as seen in Appendix D. This makes is it a lot more diﬃcult to extract useful tuning parameters. So for this feedback circuit only PSpice simulations are used to validate the performance.

Varying Cf2 changes the overall gain in the transfer function as was seen with feedback circuit b in Figure 3.12. A higher value introduces more attenuation. Varying Rf1 changes the peak and also the roll off below the cutoff frequency. For lower values the peak dis- appears but the slope below the cutoff frequency gets smaller. It makes sense that for an infinite resistance the peak is as with circuit b and with no resistance the high pass filter is not existing meaning direct feedback. In Figure 3.15 the variation of the resistor Rf2 is shown. This is with a fixed value of Cf2 = 0.8 µF. 3. Electronic Design 27

Comparing frequency response of circuit b with combination of circuit a and c 0

−1

−2

−3

−4

−5

−6 Amplitude [dBV] −7

−8

−9 Circuit b Combination of Circuit a and c −10 −3 −2 −1 0 1 10 10 10 10 10 Frequency [Hz]

Figure 3.14: Comparing simulation with circuit b with the combination of circuit a and c. Both feedback circuits in total provide a high pass ﬁlter and a voltage divider. In circuit b it’s a capacitive and in the combination of a and c it’s resistive. The simulations show comparable results.

Frequency response with variation of R in the feedback f1 4

1 100 kΩ 0 159 kΩ 251 kΩ −1 398 kΩ Ω −2 631 k

Amplitude [dBV] 1.0 MΩ −3 1.6 MΩ 2.5 MΩ −4 4.0 MΩ Ω −5 6.3 M 10 MΩ −6 −3 −2 −1 0 1 10 10 10 10 10 Frequency [Hz]

Figure 3.15: Simulation showing the frequency response of the preampliﬁer with feedback circuit d, Cf2 = 0.8 µF and varying Rf1. The variation shows signiﬁcant damping of the amplitude peak and no attenuation for all especially higher frequencies.

Introducing the resistor Rf1 does not seem to have the great eﬀect. Minimizing Cf2 decreases the overall gain but reveals the amplitude peak, and by adjusting the resistor Rf1 to a no-peak situation there is nothing achieved compared to the feedback circuit b. On the contrary the slope below the cutoﬀ frequency is decreased compared to circuit b. And 3. Electronic Design 28 this is not desired.

With Cf2 = 0.4 µF (10 times smaller than circuit b) there is -0.9 dB in overall gain compared to -1.5 dB in circuit b. But the amplitude has only dropped to -5 dB at 1 mHz where the choice of resistor results in a no-peak situation. In comparison the amplitude has dropped to -25 dB in a similar situation with circuit b. With Cf2 = 0.8 µF (5 times smaller than circuit b) there is -1.0 dB in overall gain and the amplitude has dropped to -7 at 1 mHz. With Cf2 = 2 µF (2 times smaller than circuit b) there is -1.2 dB in overall gain and the amplitude has dropped to -13 dB at 1 mHz.

3.7.4 Choosing a Feedback Circuit In the previous couple of subsections 4 variants of a feedback circuit are presented. To more easily compare the performance they can be seen together in Figure 3.16. Circuit a is clearly not desired and the arguments already presented says enough. Circuit c has a somewhat mysterious second cutoff frequency which for a relatively small frequency range drops the amplitude. But for the chosen component values this drop is very small. Circuit d has has the best gain performance for the flat part of the frequency response, but like circuit c the slope below the cutoff frequency is too small. Circuit b has a desired large slope below the cutoff frequency and a flat response for higher frequencies even though it introduces a bit of attenuation. For the final prototype there will be presented two versions. Version 1 implements circuit b and Version 2 implements circuit c. The reason for making two different versions is to be able to test both and to have two different alternatives to match the simulations.

Frequency response with all the proposed feedback circuits

−5

−10 Amplitude [dBV] −15

−20 a − simple RC b − parallel capacitor c − resistive voltage divider −25 d − cap and res in parallel

−3 −2 −1 0 1 10 10 10 10 10 Frequency [Hz]

Figure 3.16: Comparison of the frequency responses from the discussed 4 alternatives to a feedback circuit. 3. Electronic Design 29

3.8 Capacitive Load The op-amp is specified to have a load capacitance stability of 1 nF with a gain of 1. This parameter lead to a problem which was noticed when looking at the output signal with a sinusoid at different frequencies as input. The graphs in Figure 3.17 show 5 different scenarios measured on the first prototype with circuit a in the feedback. The graphs have been scaled along the frequency axis for easy comparison. They have also been shifted along the amplitude axis to better distinguish then from one another. The top graph shows a 100 mHz perfect sinusoid which is also what is fed to the input. But as the frequency is increased the sinusoid is distorted and at 7.1 kHz it looks like a triangular wave. The deformation of the sinusoid happens because the op-amp is not rated to operate with the implemented capacitive load at those frequencies. It is the slew-rate limitation which is reached meaning that the op-amp can not change the voltage quick enough.

Output signal with sinus input

100 mHz 10 Hz 1 kHz 5.8 kHz 7.1 kHz Voltage (shifted level)

Relative time

Figure 3.17: Output signal of op-amp showing that the too large capacitive load in the circuit makes the op-amp reach its limitations at frequencies above 5.8 kHz. The capacitive load is 16 µF and the rated load capacitance stability of OPA129 is 1 nF up to a bandwidth of 1 MHz.

The rated maximum load capacitance of 1 nF is given that the full bandwidth of 1 MHz is utilized or under full power response only 47 kΩ. This is not the case for this application which is why it could be of interest to calculate the maximum load capacitance for this application. The maximum output current of the op-amp, Imax is 10 mA and the maximum load capacitance can be calculated with

1 Cload,max = (3.21) 2π · BW · Vmax Imax 3. Electronic Design 30

where BW is the bandwidth and Vmax is the maximum voltage on the load.

(3.22)

When this application needs performance up to 20 kHz and can expect voltages of 26 V the resulting maximum load capacitance is 1 Cload,max = 26 V (3.23) 2π · 20 Hz · 10 mA Cload,max = 3.06 nF (3.24)

This leads to a problem with the presented feedback components. In feedback circuit a the load capacitance is 16 µF and for circuit b 20 µF. Therefore the new values with the implemented circuits is tuned to continue providing the same results but also to meet the requirement of the maximum load capacitance. The new component values for circuit b are listed in Table 3.2.

Table 3.2: New component values in feedback circuit b which meet the requirements of the maximum load capacitance.

Cf1 Rf2 Cf2 Circuit b 3.2 nF 50 GΩ 470 pF

3.9 Start-up When operating a system with a very large time constant it takes a long time for the system to stabilize after turning on. This is inherent in such a system. When the op-amp is turned on and the input nodes are floating at unknown potentials there is only a little chance that the input nodes will be 0 V. In fact the voltages will most likely be different than 0 V. And when powered on the op-amp will have a period where it will try to stabilize and reach 0 V or the potential of the DC offset.

This start-up period is large due to the time constant which is between 100 and 1000 seconds. The system could be left like that but it would require the user to wait for a very long time before every measurement. That is not a desired feature of any measurement system so to avoid the waiting period the system is provided with a circuit to decrease the time constant brieﬂy.

The circuit implemented is illustrated in Figure 3.18 and connects a resistor in parallel to the existing resistor in the feedback circuit. The added resistor has a much lower resistance which makes the total feedback resistance decrease to a level close to the resistor added. By connecting a 100 kΩ resistor through a switch to the existing 50 GΩ the total equivalent resistance is 100 kΩ. And with a new smaller feedback resistor the new time constant of the feedback circuit becomes a much more friendly value.

The eﬀect of the circuit is clearly seen in simulation in Figure 3.19 where the blue curve shows start-up without using the switch and the green curve shows the start-up activating the switch. For the situation without activating the switch the voltage reaches 0 V after approximately 300 s and when activating the switch it decreases to 25 s. The simulation is made by applying a step function on the input and looking at the voltage level at the 3. Electronic Design 31

3.3 nF

470 pF 50 GΩ 100 kΩ

Figure 3.18: The implemented circuit minimizing the start-up period in which the ampliﬁer seeks its equilibrium potential. The switch is mechanically activated and connects a small resistance which lowers the time constant of the system. output.

Simulated offset with step on input 1 R = 50 GΩ f2 R = 100 kΩ f2

0.5 Voltage [V]

−0.5 0 50 100 150 200 250 300 Time [s]

Figure 3.19: The time at which the input ﬁnds its DC level is decreased when the value of resistor Rf is decreased. It also aﬀects the frequency response, so it’s only for start-up purposes before real measurements.

It was also considered adding the switch and the resistor directly on the input node in parallel with the bias current circuit. But it was unclear what consequences it might introduce. The ampliﬁer circuit is much more sensitive on that node and anything connected to the input node will have to have the leakage or high resistance. Various data sheets from diﬀerent switch manufacturers where examined but none promised an insulation resistance high enough. They all write ’minimum 100 MΩ’ which was quite odd. It might be that mechanical engineers thinks such a resistance value is rocket high and therefore does not bother to state a real value. Or else all switches does in fact only insulate that value. 3. Electronic Design 32

Either way connecting a switch to the input node was not done. The switch might also have parasitics which could attenuate the signal or distort it.

3.10 Noise The preamplifier has inherent noise which will be discussed in this section. Normally the most dominant noise sources of a preamplifier are the bias resistor and the transistors (JFET, op-amp or similar). But as we will see in a bit the dominant source of noise for this preamplifier is the op-amp. Noise of the microphone will be dealt with in Section 4.1. In general the noise in an audio measurement system is dominated at high frequencies by the microphone and at low frequencies by the preamplifier [3].

In [24] noise from a similar direct DC circuit as this is calculated and the bias resistor noise is given as

2 4KT 1 Vn,bias = 2 (3.25) Rbias (ω · Cm) where K is Boltzmann’s constant 1.38−23 and T is the temperature in Kelvin. This relation shows that with increasing bias resistance the noise is moved to lower frequencies. Rbias in this preamplifier is as discussed not straight forward since the reverse current of two diodes are used and not a resistance. But the relation also holds for decreasing reverse current resulting in noise at lower frequencies. Furthermore the noise from the resistor is shunted by the microphone capacitance which forms a low pass filter which ensures decreasing resistor noise above the cutoff frequency [3]. So in this circuit the bias circuitry does not contribute significant to the total noise.

The noise of the transistor on the other hand is responsible for most of the noise of the electric circuit. At low frequencies flicker noise or 1/f noise is dominant and at higher frequencies white noise establishes a noise floor. The noise corner frequency, fnc, is where the two different noise colors (pink and white) are equal and in this preamplifier it is just below 1 kHz.

In the data sheet of OPA129 the noise of the op-amp is given both in numbers in the speciﬁcation but more accurately in a graph shown in Figure 3.20.

To calculate the total voltage noise of the op-amp, the spectral density is integrated over the bandwidth. This is done with (3.26) [25]. s fmax Vn,F ET = Vn,floor fnc · ln + (fmax − fmin) (3.26) fmin where Vn,floor is the noise density of the white noise above fnc, fmax and fmin are the frequencies in each end of the bandwidth of interest. For this application Vn,floor = 15 √nV , f = 500 Hz, f = 20 kHz and f = 0.01 Hz. This yields a V = 2.47 Hz nc max min n,F ET µVRMS.

Very often the peak-to-peak value of the voltage noise is of interest and in the data sheet of OPA129 this value is also stated to 4 µV pp for the bandwidth 0.1 Hz to 10 Hz. To compare TYPICAL PERFORMANCE CURVES (Cont.) ° At TA = +25 C, +15VDC, unless otherwise noted.

COMMON-MODE REJECTION vs INPUT COMMON-MODE VOLTAGE COMMON-MODE REJECTION vs FREQUENCY 120 140

120 110 100

100 80

60 90 40 80 Common-Mode Rejection (dB) Common-Mode Rejection (dB) 20

70 0 1510505 10 15 110 100 1k 10k 100k 1M 10M Common-Mode Voltage (V) Frequency (Hz)

BIAS AND OFFSET CURRENT BIAS AND OFFSET CURRENT vs TEMPERATURE vs INPUT COMMON-MODE VOLTAGE 100pA 10

10pA

1 1pA IB and IOS

100 0.1

10 Bias and Offset Current (fA) Normalized Bias and Offset Current 1 0.01 Ð50Ð25 0 25 50 75 100 125 Ð15 Ð10 Ð5510150 ° Ambient Temperature ( C) Common-Mode Voltage (V)

3. Electronic Design 33

INPUT VOLTAGE NOISE SPECTRAL DENSITY FULL-POWER OUTPUT vs FREQUENCY 1k 30 ) Hz) PP √ 20

100

10 Output Voltage (V Voltage Density (nV/

10 0 1 10 100 1k 10k 100k 1k10k 100k 1M Frequency (Hz) Frequency (Hz)

Figure 3.20: The noise of the transistor of the preampliﬁer in this case an op-amp OPA129. The noise is dominated at low frequencies by pink noise (ﬂicker noise or 1/f noise) and above the noise corner frequency by white noise.

the result of (3.26) which is in RMS the expected peak-to-peak value can be calculated. The instantaneous4 value of noise will be equal to or less than 6 times the RMS value 99.7 OPA129 SBOS026A % of the time [26]. For the calculated RMS value the peak-to-peak voltage noisewww.ti.com is 14.9 Vpp.

Now the noise is discussed from a theoretical view and it has been explained that the dominant source of noise in the preampliﬁer is the op-amp. No simulations have been made with respect to noise, and the measurements will be presented in Section 5.1.

3.11 Dynamic Range The dynamic range of the preamplifier is the ratio of the maximum output voltage the preamplifier can handle to the lowest output voltage. The maximum output voltage is limited by the maximum input voltage of the op-amp which is again limited by the supply voltage. Furthermore the maximum output voltage can be limited by maximum current and maximum slew rate, but that is mostly important when combining high frequencies and high signal levels [3]. In acoustic systems it is common to state the upper limit of the dynamic range by the level at which a certain percentage of distortion is present. For this preamplifier 3 % distortion is defined as the upper limit.

The lowest output voltage is set by the noise which has been discussed in Section 3.10. The highest output voltage is 13 V stated by the op-amp when supplied with ± 15 V. It is expected that some attenuation in the op-amp conﬁguration is inevitable, an estimate is 1 dB which yields an output voltage of 11.6 Vp. With a maximum of 23.2 Vpp and a minimum of 14.9 µVpp the dynamic range is theoretically 124 dB, which is quite impressive if succeeded. 3. Electronic Design 34

Everything until now has been un-weighted numbers. As described in Section 2.5 it is better to use no weighting than some weighting not designed for the speciﬁc purpose.

3.12 Production Component Variations Even though simulations have already been presented showing the eﬀect of variating component values, it is still of interest to see how the component tolerances impact the system. In Figure 3.21 the simulation of the circuit is shown with variation of the resistor Rf2 which has a tolerance of ±30 %. It can be seen that the smallest component value is least desired since the peak appears. To avoid this possible variation in a production a resistor with a lower tolerance must be chosen.

Frequency response with variation of R in the feedback f2 0

−0.5

−1

−1.5

−2

−2.5

−3

Amplitude [dBVrms] −3.5

−4 35 GΩ Ω −4.5 50 G 65 GΩ −5 −3 −2 −1 0 10 10 10 10 Frequency [Hz]

Figure 3.21: Simulation of the frequency response of the ﬁnal prototype version 1. Increased values of Rf2 results in less peaking. A component tolerance of ±30 % results in ±0.2 dB

In Figure 3.22 the simulation of a variating feedback capacitor, Cf1 which have a tolerance of ±5 %. This possible variation of capacitance will result in a ±19 mdB difference in amplitude. The variation will also affect the cutoff frequency which will decrease for higher values of Cf1.

All in all the tolerances pointed out do not have huge impact on the performance of the circuit. 3. Electronic Design 35

Frequency response with variation of C in the feedback f1 −1

−1.1

−1.2

−1.3

−1.4

−1.5

−1.6

Amplitude [dBVrms] −1.7

−1.8 3.135 nF −1.9 3.3 nF 3.465 nF −2 −3 −2 −1 (1) 0 ABSOLUTE MAXIMUM10 RATINGS 10 PACKAGE10 INFORMATION 10 Power Supply Voltage ...... ±Frequency18V [Hz]PRODUCT PACKAGE-LEAD PACKAGE DESIGNATOR Differential Input Voltage ...... VÐ to V+ OPA129P DIP-8 P Input VoltageFigure Range 3.22: ...... Simulation of the frequency VÐ to responseV+ ofOPA129PB the ﬁnal prototype DIP-8 version 1. Increased P Storage Temperature Range ...... Ð40°C to +125°C OPA129U SO-8 D Operatingvalues Temperature of Cf 1Rangeresults ...... in less attenuationÐ40°C to for+125 all°C frequencies.OPA129UB A variation of SO-8 +5 % equals +19 mdB D Output Short Circuit Duration(1) ...... Continuous for frequencies above 100 mHz. Not shown is the variation of Cf2 which behaves opposite. This is ° Junction Temperature (TJ) ...... +150 C NOTE: (1) For the most current package and ordering information, see the due to the voltage division introduced by the two capacitances.Package Option Addendum at the end of this data sheet, or see the TI website NOTE: (1) Short circuit may be to power supply common at +25°C ambient. at www.ti.com.

3.13 PCB Layout CONNECTION DIAGRAM ELECTROSTATIC Top View DIP/SO The ﬁnal prototype circuit shown in Figure 3.30 and 3.31DISCHARGE have been implemented SENSITIVITY on a PCB and there are NC 1 8 Substrate a couple of important design considerations regard- ÐIn 2 7 V+ Any integrated circuit can be damaged by ESD. Texas OPA Instrumentsing the recommends layout which that all integrated will be discussedcircuits be in this sec- +In 3 6 Output handledtion. with appropriate precautions. Failure to ob- NC 4 5 VÐ serve proper handling and installation procedures can cause damage. As already mentioned guarding of the input signal is very FigureNC: No internal 3.23: connection. The non- ESD damageimportant. can range The from guard subtle also performance needs to bedeg- present on the standard pinout of the chosen radation to complete device failure. Precision inte- PCB which is easily done with the non-standard pinout of op-amp OPA129 makes it grated circuits may be more susceptible to damage the op-amp shown in Figure 3.23. The guard is connected easy to implement a guard becauseto thevery output small parametric in order to changes have a lowcould voltage cause diﬀerence be- the device not to meet published specifications. trace and separation of in- tween the input and the guard it self. The guard trace puts and supplies minimizes connects pin 1, pin 4, pin 6 and pin 8 and surrounds the leakage. input pins 2 and 3. The guard copper tube connects to this node and thereby the input signal is guarded all the way to the input of the op-amp. This minimizes the stray capacitance which is not wanted in the circuit.

Placing of the components have also been considered and especially the components connected to high impedance nodes like the op-amp and the bias circuitry. These components are placed under the guard ring which helps to ensure the high impedance. TYPICAL PERFORMANCE CURVES ° At TA = +25 C, +15VDC, unless otherwise noted.

OPEN-LOOP FREQUENCY RESPONSE POWER SUPPLY REJECTION vs FREQUENCY 140 140

120 45 120 Gain 100 100 θ 80 90 80 +PSRR 60 Phase 60 Margin ÐPSRR

Voltage Gain (dB) 40 ≈90° 135

Pulse Shift (degrees) 40

20 Power Supply Rejection (dB) 20

0 180 0 110 100 1k 10k 100k 1M 10M 110 100 1k 10k 100k 1M 10M Frequency (Hz) Frequency (Hz)

OPA129 3 SBOS026A www.ti.com 3. Electronic Design 36

Another issue is the board surface resistance which is usually not an issue. But when dealing with resistances in the 1000 GΩ range it can be something creating troubles. For instance with the normally used board material FR4 the surface resistivity is 30 GΩm [27]. This means that implementing a 50 GΩ resistor on the board needs careful placement not too close to nodes different in potential. Another possible issue with the FR4 material is its volume resistivity which has the same effects and need the same precautions. For moisture tolerant applications FR4 board can also be troublesome since it has only got a moisture absorbency of .05 to .07 (% 24h). Other board materials exist which are more expensive but will minimize these problems. The author of [27] has developed an extreme board material with superb parameters for high demanding applications. Actually it is a dielectric film which have low moisture absorption and a surface resistance of 40 PΩ (40 · 1015). Ceramic materials can also be used to achieve higher performance than the standard FR4 material. For extreme moisture tolerant applications the entire board can be molded in anti-moisture-epoxy or something similar. Even though the problem with surface resistivity exist and moisture can be a problem this prototype is manufactured on standard FR4 material and measurements does not show signs of problems.

Regarding the placement of the wires on the PCB special care have been taken to the pads and how wires connects to them. Wires can not have sharp angles of incidence to a pad because the manufacturing process can possibly break the connection. The pads for the feedback components are arranged so that all the proposed feedback circuits can fit to them. And since the 50 GΩ resistor is a size 0805 the pads for this component are modified so both a 0805 component and a size 1206 can fit. With respect to the previously mentioned problem with surface resistivity the distance from Cf2 pads to other nodes are maximized. It was also considered to drill out the space between the two pads which would make the board leakage path longer and thereby the board resistance larger.

A practical issue in the manufacturing process is the shape of the board which has 4 inner corners making it ﬁt into the microphone housing. The board is cut out by a milling machine which in a standard setup has a drill with a diameter of 2 mm. This leaves no room for sharp inner corners which is why they where ﬁled by hand after receiving the PCBs.

The ﬁnal PCB layout is shown in Figure 3.24 and 3.25 top layer and bottom layer respectively. In Figure 3.26 a 3D model of the PCB including components is shown. This model was used to see if the components especially the bias FETs and the switch could ﬁt into the housing and under the guard ring. And in Figure 3.27 the manufactured PCB is shown.

Figure 3.24: PCB Top layer. The board measures 44.6 mm times 10.3 mm and is 1.5 mm thick. 3. Electronic Design 37

Figure 3.25: PCB Bottom layer. It is mirrored for easy comparison to the top layer in Figure 3.24

Figure 3.26: PCB and components in a 3D Figure 3.27: Picture of un-soldered PCB visualization. This was used to see whether with rounded inner corners due to the pro- the components would ﬁt into the micro- cess by which the board is cut using a 2 mm phone housing. drill.

3.13.1 Improvements for Next Version When soldering a prototype something often shows to be inconveniently designed. Here are listed some of the suggested improvements that would make the next version of the PCB a better one.

• The text labels (V+, V-, GND and OUT) are too small in font size.

• The pads for contacts (V+, V-, GND and OUT) have solder mask on them by mistake which should be removed.

• That also applies for the guard trace (reference to data sheet of 3 fA Input Bias Op-amp LMP7721)

• The pads for supply voltages are moved to the bottom layer because the wires collide with the switch on the center of the PCB. This could also be solved by having shorter wires, but they are advantageous when assembling the housing.

• Mounting the microphone spring contact to the PCB was tricky because the contact was made to ﬁt a board of 1 mm in thickness. Using a 1 mm thickness instead of a 1.5 mm would also make the guard ring ﬁt more easily. 3. Electronic Design 38

3.14 Final Prototype The components where soldered to the PCB and two versions of the ﬁnal prototype was made. Version 1 implements feedback circuit b and Version 2 implements feedback circuit c - a resistive voltage divider. The guard ring is soldered directly to the board connected to the guard trace on the PCB like shown in Figure 3.28. Also a spring connector for the microphone is mounted. It is located inside the guard ring and interface the microphone with a copper pad on a spring.

Figure 3.28: Picture of the soldered PCB with copper guard ring and microphone housing.

To be able to activate the switch used during or after start-up a drill hole is made in the housing. This makes it possible with a pen or a pair of tweezers to push the button and thereby quickly discharge the input node of the op-amp. In a production the switch would be equipped with some kind of nob which would stick out the hole for activation without further tools.

After soldering the PCB it was fitted into a housing like shown in Figure 3.29. The housing is of aluminium which gives the preamplifier a nice feel but also shields from electric fields like in the first prototype. In the left of the picture you see the thread for mounting a microphone and the guard ring protrude the housing for correct guarding all the way from the microphone to the op-amp.

The electric interface for power supplies and output signal is done through a high quality push-pull circular connector made by LEMA. They are commonly used for audio equipment and measurement systems in other domains.

Figure 3.29: Picture of the entire preampliﬁer including LEMA plug.

The complete schematics of both versions of the preampliﬁer is seen in Figure 3.30 and 3.31. 3. Electronic Design 39

V + 100 nF

− C OUT m A + OPA129 100 nF Zb V − V BFR31 Cf1 3.3 nF 470 pF Cf2 Rf2 50 GΩ

Figure 3.30: Full schematic of the ﬁnal prototype version 1 implementing a feedback circuit with a high pass ﬁlter and a capacitive voltage divider.

V + 100 nF

− C OUT m A + OPA129 100 nF Zb V − V BFR31 Rf1 10 GΩ Rf2 100 GΩ

Figure 3.31: Full schematic of the ﬁnal prototype version 2 implementing a resistive voltage divider.

Acoustic Design

This chapter deals with the acoustic design of the measurement system. To begin with details on the microphone will be elaborated and from there how the system acoustically performs at ultra low frequencies. In the end proposals for modiﬁcations of the present microphone will be presented.

4.1 Choice of Microphone ½″ Free-fi eld Microphone, Infra-sound Type 40AZ 1 The microphone chosen for this measurement system is a 2 -inch free-field microphone, Type 40AZ made by G.R.A.S.Product shown Data in Figure 4.1. It is made specifically for infrasound measurementsTypical applications but unfortunately the acoustic lower limiting frequency is not stated ■ Precision in the acoustic data measurements sheet directly. The data sheet states the -3 dB low-frequency ■ limitType 0 and of 1 0.2SPL measurements Hz when the 40AZ is connected to a preamplifier type 26CG with ■ Free-fi an eld input measurements impedance of 40 GΩ. ■ Low-frequency measurements 0.2 Hz could be the electric -3 dB low frequency ■ Infra-sound measurements limit because (3.1) yields Fig. 1 ½″ Free-fi eld Microphone Type 40AZ exactly that value with Cm = 20 pF and Rin = 40 GΩ. But it is for sure (inset shows true size) The G.R.A.S. ½″ Free-fi eld microphone Type 40AZ Figure 4.1: that the acoustic frequency limit is equalis a to precision or below condenser 0.2 microphone Hz. for The low-fre- lower The G.R.A.S.G.R.A.S. 1/4″ High Impedance preamplifi er quency (incl. infra-sound) measurements in open limiting frequency of a complete measurement chain is determined by theType 26CG (input impedance = 40 GΩ)* is avail- acoustic fi elds. It is a pre-polarized free-fi eld micro- Type 40AZ able for use with Type 40AZ (see data sheet for Type highest of either the electric or acousticphone lower with limiting a large dynamic frequency. range and a wide Another fre- 26CG). The mounting thread (11.7 mm - 60 UNS-2) quency response. characteristic of the 40AZ is that it is prepolarized i.e. the polarization volt-is compatible with microphone preamplifi ers for age is supplied internally by a charged material.As a free-fi eld microphone, This implies Type 40AZ thatis designed the terminalsWS2P/F microphones. where essentially to measure the sound pressure as it All G.R.A.S. microphones comply with the specifi - would appear if the microphone were not present, the preamplifier connects are 0 V with a sound signal on top. cations of IEC 1094: Measurement Microphones, the sound fi eld pointing towards the microphone. Part 4: Specifi cations for working standard micro- At low frequencies, the disturbing effects of its pres- phones. Being a free-field microphone means thatence it inis the designed sound fi eld are to minimal have (large an wave-electrical output volt- Non-corrosive, stainless materials are used in manu- lengths compared to the size of the microphone). age that is proportional to the acoustic pressure which would exist at thefacturing position these microphones of the to enable them to with- diaphragm in the absence of the microphone.At higher The frequencies microphone (>1 kHz), the effects is designed of dif- stand to rough compensate handling and corrosive environments. fractions generally cause microphones to measure G.R.A.S. WS2P/F microphones are guaranteed for for the effects of acoustic reflections at itssound diaphragm pressure levels at increasing an angle with of frequency. incidence equal to zero 5 years, and each microphone is individually cali- Fig. 2 shows corrections to be made for various degree, which begin to matter above 1 kHz. Below that frequency wavelengthsbrated, calibration are chart long supplied. angles of incidence. In a free-fi eld microphone, the compared to the microphone dimensionseffects and of therefore diffraction are compensated diffractions for to provide do not * playFor the microphone a role. capsule capacity of Type 40AZ a fl at frequency response in a free-fi eld for 0º inci- (20 pF), the high input impedance of Type 26CG

dence. For Type 40 AZ, this compensation is shown (40 GΩ) leads to a low-frequency 3-dB limit fL= 0,2 Hz. The nominal capacitance of the microphonein Fig. 3. is 20 pF and it is rear-vented i.e. the equalization of atmospheric pressure occurs backwardsSpeciﬁ cations or in the direction of the preampliﬁer connected to it. The dynamic range of theFrequency microphone response: alone is limited byPolarization 3 % distortion voltage: ...... 0 V 0.5 Hz - 20 kHz: ...... ± 2.0 dB Dynamic range: at 146 dB and by thermal noise at 14 dB.1 This Hz - 10 kHz: yields ...... a. . . dynamic...... range. . ± 1.0 dB of 132Upper limit dB. (3% distortion): ...... 146 dB re. 20 µ Pa Resonant frequency: Microphone thermal noise ...... 14 dB re. 20 µ Pa 90 ° phase shift:...... 4 kHz Capacitance: Nominal sensitivity: Polarized:...... 20 pF Each microphone has a serial number andat 250 the Hz:. primarily...... used ...... 40AZ. . . 50 mV/Pa in this project has ...continued overleaf 111305. Each microphone also comes with a calibration chart which shows the frequency response for frequencies above 250 Hz along with the sensitivity, S, which for 40AZ serial Vers. 18.03.2009 Vers. Skovlytoften 33, G ..R A .S. 2840 Holte, Denmark SOUND & VIBRATION www.gras.dk - [email protected] 4. Acoustic Design 42

111305 is 52.57 mV/Pa or -25.59 dB re. 1V/Pa. The calibration chart is found in Appendix B.

4.2 Capacitance and Voltage Variation The microphone is a spacing-variation capacitive transducer meaning that the capacitance change when the diaphragm moves in and out with respect to the rigid backplate. It is of interest to know how much the capacitance change and to begin with the voltage signal generated by a given sound pressure level (SPL) is calculated √ dBSPL/20 Vs = 20 µP a · 10 · S · 8 (4.1)

√where dBSPL is the upper and lower limits of the dynamic range (146 dB and 14 dB) and 8 converts RMS values to peak-to-peak assuming sinusoids. This yields Vs ranging from 14 µVpp at 14 dB SPL to 56 Vpp at 146 dB SPL.

It is realized that an SPL of 146 dB is quite a lot for an audio measurement system especially one designed for noise measurements. Furthermore the chosen electrical design is limited by the maximum input voltage of the op-amp about ±12 V or 24 Vpp . This correspond to a maximum of 138 dB SPL which should be more than enough.

To calculate the change of capacitance, the relation from (2.3) is initially used to calculate the charge of the microphone

Q = Vpol · Cm (4.2) where Vpol is the polarization voltage of the permanently electrically charged material. With Cm = 20 pF and Vpol = 200 V (estimated)

Q = 4 nC (4.3)

Now the capacitance can be calculated using the relation

Q Cm = 1 (4.4) Vpol ± 2 Vs The relation states that the capacitance to varies between 17 and 23 pF at 146 dB SPL resulting in a ∆Cm around 3 pF at max input. At 14 dB SPL the change of capacitance −18 is so small that it only makes sense to state the ∆Cm which is 0.7 aF (10 F).

4.3 Infrasound Calibration Like any other measurement system a calibration is needed to prove a system’s performance compared to a known system. For infrasound measurement systems this is no different, and the procedure is as follows. The ventilation which equalizes the slow variations in atmospheric pressure has a great influence on the low frequency response. The time constant of the ventilation is a compromise between the frequencies you would like to measure and the frequencies you do not (noise). Also the placement of the vent is important e.g. if the vent is exposed to the sound field or not. 4. Acoustic Design 43

A minor effect on the low frequency response is due to the ambient pressure causing the impedance of the cavity to vary. The air stiffness of the microphone is relatively low compared to the stiffness of the diaphragm which causes the change of impedance to alter the low frequency response [28]. This effect is not as pronounced on ground as when measuring at other altitudes like diving tanks or aircrafts.

Lastly the compression of air is usually assumed to be adiabatic meaning no heat is trans- ferred between the system and the surroundings. But at low frequencies it actually changes into an isothermal compression which increases the sensitivity [28]. This eﬀect is very important below 1 Hz but not so often taken into consideration. Normally the transducer is thought as linear and inverse with respect to SPL but that implies that it is an adiabatic compression of air which occurs in the microphone.

Also the preampliﬁer plays a signiﬁcant role in the measurement chain and thereby the calibration. The acoustic lower limiting frequency is dependent on the microphone, but the system’s total lower limiting frequency contains both the acoustic and the electric lower limiting frequency. A way to extract the two frequencies is to measure the total response and then compare to the electric which can reveal the acoustic lower limiting frequency.

4.4 Leakage and Equalization As mentioned Section 4.3 the lower limiting frequency is primarily determined by the ventilation. However, equalization can also occur through leaks in the construction. Leakage through the diaphragm seems strange but nevertheless diaphragms can have pin holes of the size of large molecules. A standard way to test the diaphragm is to flush it with helium whereby the very small molecules will penetrate any pin holes revealing them. Hydrogen can be used for better results due to the smaller molecular size but the risk of explosion is high. Also the assembly of the different parts of the microphone (see Figure 2.6) are a great source of possible leakage. To ensure a completely airtight microphone all parts are carefully checked for flaws and oil is applied on the contact surfaces before assembly. These precautions will minimize leakage of air. However, it is not possible to make a 100 % airtight construction.

Without ensuring a very airtight microphone the effect of a designed vent is difficult to control. And a well controlled ventilation is required when operating at that low frequencies. The more controlled the vent is the more accurately the results will be since you know exactly what frequencies you have measured. Sealing the construction of the microphone by minimizing leakage makes the design and manufacturing of a vent more easy since it takes less effort to ensure a certain total leakage. If a designer seeks a total equalization of 1 unit, the amount left for the vent it self is made smaller and thereby more difficult when leakage elsewhere in the microphone is present. Designing a vent for frequencies in the order of 10 mHz, is in such a small physical scale compared to the size of molecules.

In the chosen 40AZ microphone the vent is made by putting a spacer on top of the insulator and cutting a slit in the spacer which is illustrated in Figure 4.2 and 4.3. The spacer is 20-25 µm thick and measures 1.5 mm from the from inner to outer radius. In the end of the slit at the inner radius the back cavity is acoustically connected. And at the outer Chapter 2 — Microphone Theory Measurement Microphone Design

which is mainly assembled by screwing the parts together, the integrated back-plate and insulator version is assembled by pressing the parts into each other. This design also deviates from the conventional design by applying a backplate consisting of a metal thin- lm placed directly on the surface of the insulator.

4. Acoustic Design 44

radius the preampliﬁer connects and by its leaky construction the atmospheric pressure. The length of the slit equals the length of the vent and the cross section is determined by Diaphragm the thickness of the spacer times the width of the slit. With a width of 90 µm the slit has a cross section of 1.8 · 10−9 m2. Backplate Insulator Housing

Insulator

Air in/out Spacer

Air in/out

Figure 4.2: The vent of 40AZ is made by(a) putting in a spacer (green) on top of the insulator and (b) 950573/1e cutting a slit in the spacer (see Figure 4.3). Equalization occurs through the slit (blue).

l h w

Figure 4.3: A close look of the spacer with a slit which makes equalization occur from the inner diameter to the outer. In practice, the rst mentioned type implies more freedom for the designer to opti- mise the frequency response, while the second is advantageous during production. The main choice which must be made in respect to the two dierent design types is one of more narrow frequency response tolerances oered by the conventional design, as opposed to reduced production costs for the alternative design.

2.3.3 Material and Process Requirements

A microphone which is to be used for measurements must be stable over time and its properties should preferably not vary with variations in ambient temperature, pressure and humidity. Therefore, carefully selected, high quality materials must be used, even if they are relatively dicult to machine.

The sensitivity of the microphone is inversely proportional to the diaphragm tension. The tension must therefore be kept stable. Normally it is a requirement that a measurement microphone has a broad frequency range and a high sensitivity. This creates a requirement for light-weight diaphragms with high internal tension and thus a very high loading of the diaphragm material. This is achieved by applying a tension of up to 600 N/mm 2 (which would break most materials) to the diaphragms

BE 1447 –11 Microphone Handbook 2 − 9 Vol.1 4. Acoustic Design 45

4.5 Modeling of Vent The inﬂuence of the vent just presented will now be calculated. To start with the physical or acoustic system parts are converted into analogous electric circuit elements where voltage is equal to pressure and current to volume velocity. This is called impedance analogous circuits [29]. A simpliﬁed acoustic model of the vent system includes a volume and a resistance. Normally a tube (in this case the slit) models as a resistance and a mass but the mass term is inverse proportional to frequency so for this ultra low frequency scenario it is neglected. The acoustic system is illustrated in Figure 4.4 a. And the converted analogous electric circuit is illustrated in Figure 4.4 b.

RA RA

CA CA

a b

Figure 4.4: Model of the acoustic system (a) simpliﬁed to an acoustic volume (CA) and a vent for equalization of low frequencies (RA). The model is converted to the analogous electric circuit (b).

The resistance of the vent, RA, is calculated with 12 · η · l R = (4.5) A w3 · h

−5 N·s where η is the viscosity coeﬃcient (ηair = 1.86 · 10 m2 ) and l, w and h are the length, width and height of the vent respectively. The acoustic compliance of the air inside the volume is calculated with

V CA = 2 (4.6) ρ0 · c

−3 ◦ where V is the volume of the cavity, ρ the density of air (ρ0 = 1.204 kg · m at 20 C) and c is the velocity of sound at 20◦C.

With the component values of the electric circuit deﬁned it is easy to calculate the cutoﬀ frequency with (3.1). The two missing values are the width of the slit and the volume of the cavity. None of them are known. But the data sheet of 40AZ states the volume of the front cavity to 50 mm3 and a rough estimate is that the back cavity is 100 times larger [29] which yields V = 5 · 10−6 m3. From the measurements which will be presented in Section 5.2 the acoustic lower limiting frequency is 190 mHz. Reverse engineering yields a width of the slit of 0.09 mm. 4. Acoustic Design 46

4.6 New Vent Proposal As mentioned designing a vent to achieve a well controlled cutoff frequency at ultra low frequencies is a very delicate business. In this section the present type of construction will be analyzed with the purpose of finding dimensions which will meet the requirement which is a -3 dB cutoff frequency below 10 mHz. An overlap of the low pass filter of the vent and the lower limiting frequency of the preamplifier is not desired. Therefore the design parameter for the lower limiting frequency of the vent is set to 5 mHz. In the end of this section other possible ways of constructing a vent will be discussed.

An obvious way to start searching for modifications of the existing construction that will lead to a lower cutoff frequency is to start with the parts that are easiest to modify. To decrease the cutoff frequency either the resistance of the vent or the compliance of the volume needs to increase. The volume of the cavity is difficult to alter since it will require a completely new microphone design. The vent on the other hand can be modified and for increased resistance either the length of the vent can increase or the cross-section decrease (see (4.5)). And since the width is in power of 3 it should be clear that modifying this will have greatest impact.

In Figure 4.5 the cutoﬀ frequency is plotted with two changing parameters namely the width and length of the vent. The width is linearly decreased to 10 µm and the length increased linearly to 33.5 mm. The choice of these numbers are not random. Laser cutting is a common manufacturing process employed to cut many types of materials e.g. metal. The process can produce cuts with a kerf down to 1 µm in organic materials [30, 31] or 2 µm in steel [32]. The kerf is the material removed by the laser beam hence the dimension of the smallest possible slit. These speciﬁcations on laser cutting and a belief that laser cutting the spacer is possible support the choice of the variation of the width. The variation of the length becomes clear when presenting the new vent in Figure 4.7.

Minimizing only the width of the slit to 26 µm shows that the -3 dB cutoﬀ frequency is decreased to 4.7 mHz (see data mark in Figure 4.5). This suggests that laser cutting the vent and maintaining the very simple construction will make it possible to alter the 40AZ with an acoustic lower limiting frequency which will match the electric lower limiting frequency. But it depends on the manufacturing process.

If the vent length is thought as a better parameter to tune an easy way to make it longer is to make a skew cut across the spacer illustrated in Figure 4.6. The maximum length achievable with the given dimensions of the spacer are calculated using the Pythagorean theorem as follows q 2 2 l = r2 − r1 (4.7) where r1 and r2 are the inner and outer radii of the spacer respectively 1 r = · 11.7 mm = 5.9 mm (4.8) 2 2 r1 = r2 − 1.5 mm = 4.4 mm (4.9) which yields

l = 3.9 mm (4.10) 4. Acoustic Design 47

0 10

−1 10

−2 10

f [Hz] −3 X: 2.6e−005 10 Y: 0.0015 Z: 0.004734

−4 10

−5 10 90.0 74.0 1.5 58.0 7.9 42.0 14.3 20.7 26.0 27.1 10.0 33.5 l [mm] w [µm]

Figure 4.5: -3 dB cutoﬀ frequency of vent as function of width and length of the slit in the spacer. The current vent/slit dimensions represent the data point in the very top.

l h w Figure 4.6: A modiﬁed vent proposal where the vent is cut skew close to a tangent of the inner radius. 4. Acoustic Design 48

Another new vent proposal increasing the length of the vent tremendously is the construction illustrated in Figure 4.7. A circular cut around the spacer would make it possible to increase the length to a value close to the circumference of the spacer. The maximum length is then close to

l = lold + c (4.11) where c is the circumference of the spacer

r + r c = 2πr = 2π 1 2 = 2π · 5.1 mm = 32 mm (4.12) 2 which yields

l = 33.5 mm (4.13)

h w Figure 4.7: A new vent proposal where the vent length is increased by letting the slit run along the circumference of the spacer.

This proposal depends even more on the manufacturing process because it is thought as a challenging task to cut a slit around the surface of such a small spacer. Without knowing the manufacturing process by which the current slit is made it might be possible to use the same process and hence the same slit width and cut the circular vent in the spacer. From Figure 4.5 in the most left data point an unchanged width and a length increased to 33.5 mm yields a cutoﬀ frequency of 8.8 mHz.

Designing vents on standard microphones with cutoﬀ frequencies in the order of 1 Hz has an important rule to obey. The vent must be shorter than one quarter of a wavelength. But with the low frequencies dealt with in this case this will never be a problem. The wavelength of a 10 mHz tone is 100 m.

To round up this section it must be said that designing an acoustic vent for equalization of the microphone is more a mechanical problem than an acoustic. That is especially true with respect to the challenges. The acoustic challenge is rather straight forward; the equations yield the design parameters. The true challenge at this point is the physical construction and what is possible and not. Engineers dealing with nanotechnology might have valuable information regarding this. Using laser cutting to make the slit in the spacer will probably be able to lower the cutoﬀ frequency suﬃciently. 4. Acoustic Design 49

4.7 Consequences of an Airtight Microphone Working with a microphone with a very slow equalization like the one being designed comes with some precautions which must be known by the user. It is related directly to the large time constant and the equalization of the pressure inside the cavity. When measuring, the atmospheric pressure must not change to fast. If this is the case then the diaphragm will find an inbound or outbound resting position which will compromise the measurement system e.g. by introducing distortion. This requirement entails that measuring while moving up or down with high speed is not allowed. This could be in an elevator, on an escalator, or during liftoff or landing with a spacecraft. The atmospheric pressure might change too fast for the vent to cope with the pressure difference. This must be considered when relevant.

This altitude problem also exists when the measurement system is not in use. If the outside pressure is increasing very fast the pressure inside might pop out the diaphragm before the vent is able to equalize it. This means that when transporting the measurement system in fast changing pressure environments it needs to be more ventilated or sealed. A solution to the problem could be a second vent which is activated during transportation. Or it could be an airtight transportation box. If the issue is not handled correctly one could imagine that the microphone would break by running up a few stairs or taking a fast elevator.

The precautions mentioned in Section 2.5 regarding infrasonic measurements will of course also be relevant for this system and for some of them more pronounced with an almost airtight microphone.

Measurements

This chapter will verify the performance of the design by presenting measurements both electric and acoustic and elaborating on these. The measurements will be compared to the speciﬁcations stated in Section 1.1.

For most measurements both versions of the preampliﬁer are measured, and to summarize version 1 incorporates a high pass ﬁlter and a capacitive voltage divider in the feedback whereas version 2 has a resistive voltage divider alone. Besides the feedback circuit both versions are alike.

5.1 Electric System The most important design parameter of the measurement system is the lower limiting frequency. Electrically this is veriﬁed by measuring the frequency response with a sinusoid sweep on the input. The measurement is conducted on a Dynamic Signal Analyzer SR785 by Stanford Research Systems which is noted for having a generator able to produce signals down in the ultra low infrasonic frequency range. The output signal of the analyzer is connected through an input adapter serving as a capacitive microphone (see Figure 5.2). The input adapter has a BNC connector at one terminal, a female microphone thread at the other and a 20 pF capacitor in between which is equal in value as the nominal capacitance of the microphone. Even though the capacitance does not change with voltage level like the microphone does the measurement gives a good approximation to the electric lower limiting frequency.

In Figure 5.1 the measurements are shown along with the simulations. Version 1 of the preampliﬁer shows a -3 dB cutoﬀ frequency of 10 mHz and version 2 something similar. Unfortunately the number of measured data points are in some cases kept at a minimum and in this case not far enough down in frequency. This is because every data point takes a very long time to measure. The analyzer uses one period of the signal to settle the level and at least one period to measure. Ideally more periods should be averaged to make the measurement more precise, but at 10 mHz one period is 100 seconds resulting in 3 minutes for one single data point. Doing a sweep from 100 Hz to lets say 1 mHz with 30 data points will take hours.

5.1.1 Damping Another important parameter of any preampliﬁer is the overall attenuation or the damping. Ideally the gain should be 0 dB meaning no damping as the op-amp is coupled as a voltage follower. But as described the gain is not 0 dB due to feedback and nonidealities. 5. Measurements 52

Frequency response of preamplifier with 20 pF input adapter 0

−0.5

−1

] −1.5

RMS −2

−2.5

−3

Amplitude [dB V −3.5

−4 Measurement: Version 1 Measurement: Version 2 −4.5 Simulation: Version 1 Simulation: Version 2 −5 −2 0 2 4 10 10 10 10 Frequency [Hz]

Figure 5.1: Frequency response of preampliﬁer with 20 pF input adapter. The simulation is included for comparison. The electric lower limiting -3 dB corner frequency is clearly around 10 mHz for both versions of the preampliﬁer.

The evaluation of the damping is done with a pistonphone, a calibrated microphone and calibrated preampliﬁer.

Figure 5.2: Input adapter for supplying Figure 5.3: Vent adapter used to seal or electric input to the preampliﬁer. A 15 pF equalize the microphone. Both constructions version is depicted but a 20 pF also exist. are airtight from front to back. The adapter on the left has a hole which equalizes the microphone whereas the adapter to the right seals the microphone.

The arrangement is that a known and calibrated preamplifier and microphone is used as reference and then the same calibrated microphone is used on the unknown preamplifier (both version 1 and 2). The pistonphone produces a 250 Hz tone at 114 dB re. 20 µPa 5. Measurements 53 equal to 10 Pa. The sound signal is connected to the microphone through the coupler of the pistonphone and is converted into a voltage by the microphone. This voltage is calculated by the sensitivity stated in the calibration chart and fed to the input of the preamplifier. The output of the preamplifier is connected to the SR785 analyzer which yields a total damping at 250 Hz (third octave band) of the total measurement chain.

The pistonphone is a G.R.A.S. 42AP (serial 68449) with build-in barometer showing the necessary correction for the atmospheric pressure, which for all mentioned measurements is -0.04 dB. The known preampliﬁer is a G.R.A.S. 26CA (serial 122012) and with the setup just described the analyzer reads -5.9 dB at 250 Hz. The calibration chart of the microphone states a sensitivity of -25.59 dB re. 1 V/1 Pa equal to -5.59 dB re. 1 V/10 Pa (see Appendix B) which is exactly as referenced to the output of the pistonphone. The known preampliﬁer is therefore accounting for −5.9 − (−5.59) − 0.04 = −0.35 dB gain which is close to -0.25 dB stated in its calibration chart.

The preamplifier version 1 is then placed in the measurement chain replacing the known preamplifier and the analyzer yields a total damping at 250 Hz of -6.35 dB. That leaves the preamplifier with a gain of -0.80 dB.

For version 2 the damping of the total measurement chain reads -6.64 on the analyzer which yields a gain of -1.09 dB.

5.1.2 Start-up Another important parameter of the preampliﬁer is the start-up described in Section 3.9. The switch connects a resistor minimizing the total resistance in the feedback circuit. To verify the eﬀect of this start-up circuit the output signal during start-up is measured and compared to simulations.

The setup was quite easy but the execution of the measurement was difficult. To be able to compare one measurement to another it would be favorable for the voltage level to start at the same value every time. Unfortunately the level at the input reaches a random level at start-up. A rather fixed voltage was introduced to the input through the 20 pF input adapter (see Figure 5.2). Measuring the time signal on a Tektronix TDS2024B digital os- cilloscope shows the measurements in Figure 5.4. Without the switch being activated the system show a very long settle time of 220 seconds. Simulations show a bit longer which is possibly due to the real resistances implemented by the feedback circuit and the bias circuitry. Simulations conducted but not shown show faster settling times with decreasing feedback resistance. The scenario where the switch is activated on the other hand shows very fine correspondence between simulation and measurement. Both have a settling time of around 25 s which proofs the effect of the start-up circuit.

The frequency response is dramatically altered when the switch is activated which is shown in Figure 5.5. When the switch is activated the lower limiting frequency of the preamplifier increases to around 1 Hz. If the switch did not have an effect on the frequency response it could be argued why not connecting the resistor permanently. The measurement is conducted on the first prototype of the preamplifier which has a 16 µF capacitor and a 10 MΩ resistor in the feedback. The switch interconnects a 10 kΩ resistor in parallel to the existing causing the cutoff frequency of the feedback circuit to increase from 1 mHz to 1 Hz. At frequencies below the cutoff frequency of the feedback circuit the bias circuitry 5. Measurements 54

Offset with step on input, preamp version 1 2 Measurement: switch off Measurement: switch on Simulation: switch off 1.5 Simulation: switch on

Voltage [V] 0.5

−0.5 0 50 100 150 200 250 300 Time [s]

Figure 5.4: DC oﬀset of preampliﬁer version 1 with step on input through 20 pF input adapter shows the system’s settle time. does not behave like a resistance because the voltage across it is beyond the diode limitations mentioned in Section 3.3.

Frequency response with switch on and switch off −3 Switch off −4 Switch on

−5

−6

−7

Amplitude [dB] −8

−9

−10

−11 −4 −2 0 2 4 10 10 10 10 10 Frequency [Hz]

Figure 5.5: Frequency response measurement of ﬁrst prototype showing 2 sweeps, one with the switch oﬀ (normal operation) and one with the switch on, meaning a lower value resistor is connected in the feedback. 5. Measurements 55

5.1.3 THD and Noise Measuring the output signal for a given input signal tells a lot about the performance of the preamplifier. The noise can be estimated along with total harmonic distortion (THD). In the following measurements a Fast Fourier Transform (FFT) is done on the output signal when a sinusoid is on the input through the 20 pF input adapter. The measurements are done with a Rohde & Schwarz UPV Audio Analyzer which generates the sinusoid, feeds it to the input adapter and reads the output signal from the preamplifier. The UPV Audio Analyzer is made for regular audio and hence the generator is not designed to produce ultra low frequencies, but it extends down to 100 mHz. The analyzer can measure down to DC but unfortunately the measurements where conducted measuring only down to 200 mHz. And also the acquisition time was to short resulting in the data points at low frequencies being of little value. At the time when this was realized the UPV had been returned to Rohde & Schwarz from whom it had been borrowed. The Stanford SR785 was used but trouble with windowing and the fact that the number of FFT lines is limited to 800 made the measurements difficult to conduct and the results not convincing. The measurements in Figure 5.6 show the output of the preamplifier with a 1 V sinusoid at 1 kHz on the input. Both version 1 and 2 of the preamplifier are measured with the UPV.

FFT of output signal with 1 kHz sine as input 0 Version 1 −20 Version 2

−40

−60

−80

−100

−120 Amplitude [dB] −140

−160

−180

−200 0 1 2 3 4 10 10 10 10 10 Frequency [Hz]

Figure 5.6: FFT of output signal with 1 V sine at 1 kHz as input.

From both measurements the noise of the preampliﬁer discussed in Section 3.10 can be seen. The noise corner frequency is about 500 Hz, where pink noise (below fc) is replaced by white noise (above fc). Pink noise has a slope of approximately -10 dB/decade and white noise is ﬂat. Also the harmonics of the input signal can be seen with the levels being quite small for this input voltage level.

The measurements can also be used to estimate the dynamic range of the preampliﬁer. 5. Measurements 56

Figure 5.7 will support the explanation on how to calculate the signal to noise ratio (SNR) from an FFT. The dynamic range is comparable to the maximum achievable SNR because the noise is constant with respect to input voltage and with the signal increasing to its maximum leads to the deﬁnition of the dynamic range being the ratio of the maximum output to the minimum output.

The amplitude of the frequency bins containing the signal are squared and summed in order to get the power of the signal, Ps. The remaining frequency bins are also squared and summed to get the power of the noise, Pn. The FFT gain, AFFT, in dB also needs to be subtracted which is equal to dividing by the number of frequency bins in the sample. In math this looks like

f2 X 2 Pn = Ak (5.1) k=f1

fs+b X 2 Ps = Ak (5.2) k=fs−b where f1 and f2 is the frequency range, Ak the amplitude of frequency bin k and b indicates the number of neighboring bins to include in the signal to get all the power. To calculate the SNR Ps SNR = 10 · log − AFFT (5.3) Pn where

AFFT = 10 · log(ktotal) (5.4)

With the data from Figure 5.7 and the relatively low input voltage of 1 V the SNR is -95 dB. Which is an approximation because the noise power is not suﬃcient due to the low acquisition time and lower frequency limit of 200 mHz.

To get a better estimation of the dynamic range of the preampliﬁer the output voltage is measured when it reaches 3 % distortion. This along with a better estimation of the total noise voltage will result in the dynamic range. The input voltage is increased until 3 % distortion is reached on the output voltage. For version 1 the output voltage is 7.6 Vpp and for version 2 it is 28 Vpp. The measurements are shown in Figure 5.8 and 5.9. It came as a surprise that version 1 reached distortion at so low voltages. And the reason is probably that the attenuation in the preampliﬁer makes the voltage across the bias circuitry increase and thereby the equivalent resistance decreases. From Figure 5.8 and 5.9 the output voltages are indicated, and with the input voltages being 8.6 Vpp and 33 Vpp respectively, the voltage across the bias circuit is more than 1 V. The reason why it does not happen with version 2 is that the feedback capacitor in version 1 of 3.3 nF has a resistance of 48 kΩ at 1 kHz. That resistance is much smaller than the 10 GΩ which is in the feedback circuit of version 2.

The noise voltage is estimated by√ a measurement on the SR785.√ The white noise voltage density is around -125 dBVrms/ Hz equal to 560 nVRMS/ Hz. The noise corner frequency is estimated to 500 Hz from Figure 5.7. The noise of the preampliﬁer is calculated 5. Measurements 57

FFT of output signal with 100 Hz sine as input 0 Version 1 Version 2 Signal

−50 Amplitude [dB] −100

−150 0 1 2 3 4 10 10 10 10 10 Frequency [Hz]

Figure 5.7: FFT of output signal with 1 V sine at 100 Hz as input. The signal is marked red to aid the calculation of the dynamic range.

FFT of output signal with 1 kHz sine as input FFT of output signal with 1 kHz sine as input 20 20 Version 1 Version 2

0 0

−20 −20

−40 −40

−60 −60 Amplitude [dBVrms] Amplitude [dBVrms]

−80 −80

−100 −100 2 3 4 2 3 4 10 10 10 10 10 10 Frequency [Hz] Frequency [Hz]

Figure 5.8: FFT of output signal of ver- Figure 5.9: FFT of output signal of version 1 with 1 kHz sine as input. 3 % dis- sion 2 with 1 kHz sine as input. 3 % distortion on the output is reached at output tortion on the output is reached at output voltage of 7.6 Vpp voltage of 28 Vpp

using (3.26) which yields 92 nVRMS. Calculating the ratio of the maximum output voltage and the noise voltage yields the dynamic range of version 1 of 84 dB and 94 dB for version 2.

To round up this section on measurements of dynamic range it would be of interest to make a new measurement with the UPV. The acquisition time should be at least 100 s for the slow 10 mHz signals to be sensed, and the analyzer should measure down to 10 mHz. But the two estimates of the dynamic range of the preampliﬁer show believable values yet far from the theoretical value of 124 dB calculated in Section 3.10. 5. Measurements 58

5.2 Frequency Response of Entire System Measuring the frequency response of both the microphone and preamplifier is the most obvious and important verification of the system. The measurement system is supposed to operate in its entirety and not in parts separately. The measurement is done with a low frequency calibrator G.R.A.S. 42AE which is an acoustic source using a constant force to ensure a constant sound pressure level inside the calibration chamber. The microphone attached to the preamplifier is fitted into one of the holes down into the coupler, so both the diaphragm and the vent of the microphone are exposed to the sound field inside the coupler. This ensures that the measurement setup (see Figure 5.10) includes the total system and measures both the electric and the acoustic lower limiting frequencies. The calibrator ensures a constant sound pressure level down to very low frequencies about 0.01 Hz and is in theory only limited by any air leakage of the system. The sound pressure level is determined by the input signal which is supplied by the SR785 Analyzer. The output signal of the preamplifier is also returned to the SR785.

Figure 5.10: G.R.A.S. 42AE low frequency calibrator with the microphone including vent inside the coupler.

The first measurements presented in Figure 5.11 show the low frequency response with several setups. To make sure the vent of the microphone is exposed to the sound pressure in the coupler and not equalized to the ambient pressure a vent adapter like shown in Figure 5.3 was mounted between the microphone and the preamplifier. The first adapter used is the closed vent adapter which seals the measurement setup. The inside of the microphone is equalized to the sound pressure of the coupler through the thread connecting the microphone to the preamplifier which is not tightened. The equalization occurs into the microphone through the vent and not through the preamplifier because the vent adapter is sealed. To verify that venting through the thread was sufficient the open vent adapter was made. This adapter is like the other airtight back towards the preamplifier, but it has a hole on the side (a large vent) equalizing the cavity. 5. Measurements 59

Also shown in Figure 5.11 are measurements with two other 40AZ microphones. One of the three 40AZ microphones show a -3 dB lower limiting frequency of 70 mHz. The microphone used through the entire project along with one other 40AZ have a -3 dB frequency of 190 mHz. This cutoff frequency is determined by the vent in the microphone and as we shall see in the next section the mounting of the microphone to the preamplifier can have significant impact on the total response.

Frequency response of preamplifier version 1 with 40AZ 0 ] −5 RMS

−10 Amplitude [dB V Mic not tightened to closed vent adapter Mic not tightened to closed vent adapter Another 40AZ (Serial: 111320) not tightened Another 40AZ (Serial: 111312) not tightened Mic on open vent adapter −15 −2 −1 0 1 2 10 10 10 10 10 Frequency [Hz]

Figure 5.11: Measurements with version 1 showing consistency across several microphone cartridges and no or little diﬀerence whether the microphone is loosely mounted on the closed vent adapter or mounted with the open vent adapter. Lastly the measurements verify the entire system’s lower limiting frequency of around 190 mHz with a standard oﬀ-the-shelf 40AZ microphone.

The measurements of version 2 of the preampliﬁer are shown in Figure 5.12 and again the acoustic lower limiting frequency is 190 mHz. When sealing the setup with oil in the thread the cutoﬀ frequency lowers to 8 mHz. The ripple on the closed vent adapter measurement can be due to overload. Auto range of sensitivity is disabled on the SR785 analyzer which might allow low frequency spikes and other disturbances.

5.2.1 Microphone Mounting The mounting of the microphone to the preamplifier has a great impact on the response. Like discussed in Section 4.4 leakage can occur many places in the microphone construction but also the connection to the preamplifier is of importance since the vent equalized backwards into the cavity between the microphone and the preamplifier. The more airtight the connection is the lower the acoustic lower limiting frequency becomes. This is illustrated by the measurements in Figure 5.13. 5. Measurements 60

Frequency response of preamplifier version 2 with 40AZ −2

−4

−6 ]

RMS −8

−10

−12 Amplitude [dB V −14

−16 Open vent adapter Closed vent adapter and oil −18 −3 −2 −1 0 1 2 10 10 10 10 10 10 Frequency [Hz]

Figure 5.12: Measurements with version 2 and 40AZ microphone. With open vent adapter the -3 dB cutoﬀ frequency is 190 mHz and with closed vent adapter and oil it is 8 mHz.

When the microphone is loosely mounted to the preamplifier the ventilation occurs through the vent and through the thread. This results in the cutoff frequency just below 200 mHz. Tightening the thread as much as possible by hand results in a cutoff frequency decreased to 90 mHz. The last measurement shows the lower limiting frequency when the contact surface between the microphone and the vent adapter is lubricated with oil to ensure no ventilation. This decreases the -3 dB frequency to 6 mHz. With this measurement all frequencies are attenuated 0.3 dB which is due to unequalized pressure explained next.

Before the just mentioned lubrication with oil another measurement was made where the oil was applied on the thread and not on the contact surface. This had the eﬀect that the cavity of the microphone was sealed before the thread was screwed on all the way. And when screwing on the microphone the enclosed air inside the cavity made the pressure rise and the diaphragm establish a new equilibrium position. The phenomenon is illustrated in Figure 5.14 where this introduces 4 dB attenuation because of overpressure in the microphone cavity.

To summarize the results of the entire measurement system it is clear that the 10 mHz lower limiting frequency can be achieved when the microphone is sealed. The electric lower limiting frequency is in this case the limiting parameter. When the microphone is vented the limiting parameter of the entire measurement system is the acoustic lower limiting frequency which is 190 mHz. Sealing of the microphone introduces precautions to be taken with respect to overpressure in the microphone cavity. This occurs when the microphone is screwed on with oil in the contact surface and when the atmospheric pressure changes due to altitude changes or weather changes. 5. Measurements 61

Frequency response of preamplifier version 1 with 40AZ 0

−1

−2 ] RMS −3

−4

Amplitude [dB V −5

−6 Loose mounted Tightened Sealed with oil −7 −3 −2 −1 0 1 2 10 10 10 10 10 10 Frequency [Hz]

Figure 5.13: Frequency response of entire system consisting of preamp v1 and 40 AZ showing the importance of ventilation. The measurements are conducted with the closed vent adapter.

Introduced attenuation due to overpressure in the microphone cavity 0

−2

−4 ] RMS −6

−8

Amplitude [dB V −10

−12 Oil along thread Oil on contact surface −14 −3 −2 −1 0 1 2 10 10 10 10 10 10 Frequency [Hz]

Figure 5.14: Overpressure inside the microphone cavity results in 4 dB attenuation. The overpressure occurred when oil was applied along the thread and not only on the contact surface.

Conclusion

Measurement of infrasound is important because noise at frequencies below 20 Hz is audible thus most commonly tried avoided at high levels. And to avoid noise in a design process or in an established setup it is advantageous to be able to measure it. Sources of infrasound include wind turbines which are best placed where the generated noise level does not disturb or damage the environment and nearby living people. Other infrasonic sources containing ultra low frequencies are the sonic boom - an N-shaped shock wave formed from a supersonic flight. Modifications of the aircraft shape makes it possible to reshape the shock wave so flights in land zones will be allowed.

The noise measurement systems widely available typically measures down to 1 Hz which is not suﬃcient for measurement of ultra low frequency infrasound. Some systems exist measuring down into the mHz range but they have very poor dynamic range of about 40 dB. The design of a measurement system capable of measuring down in the ultra low frequencies with good dynamic range has been presented. The system consisting of a condenser microphone and a preampliﬁer will aid stakeholders in the wind farm noise debate and sonic boom shapers.

The acoustic part of the measurement system has been analyzed and a new vent conﬁgu- 1 ration of the G.R.A.S. 40AZ 2 -inch microphone has been proposed. Acoustically the lower limiting frequency can be pushed to 10 mHz by either sealing the microphone resulting in numerous precautions to take when measuring. Another solution is the modify the equalization vent by increasing its length or decreasing its cross section area.

Electrically the system connects the capacitive microphone directly to an op-amp resulting in an electric lower limiting frequency determined by the capacitance of the microphone and the input impedance of the preamplifier. The design parameter of 10 mHz and a 20 pF microphone capacitance yields an input resistance of 1 TΩ which is obtained by a OPA129 op-amp. The bias circuit preventing a floating input voltage due to leakage current in or out of the op-amp is constructed with two diode-connected FETs. They em- ulate a sufficiently large resistance which in parallel with the input impedance of OPA129 determines the total input impedance of the preamplifier and thereby the electric lower limiting frequency of the system.

The challenges encountered in the design was the mentioned bias circuitry which plays an important role on the lower limiting frequency. Also the feedback circuit was presented in four alternative ways which had disadvantages as peaking below the cutoﬀ frequency and unwanted attenuation through the preampliﬁer. 6. Conclusion 64

The final prototype have been measured and the target specifications of the design stated in Section 1.1 have been fulfilled. For comparison they are stated in Table 6.1.

Table 6.1: Target speciﬁcations and obtained speciﬁcations of the measurement system Target Obtained Note -3 dB lower limiting frequency 10 mHz 8 mHz When microphone is sealed Dynamic range 80 dB 94 dB With version 2

6.1 Future Work During the project a number of aspects have come up which were out of the scope of this project. Further research could go in the direction of any of them which would either benefit this specific measurement system or benefit the concept of measuring ultra low frequency infrasound in general.

Choosing a condenser microphone as the sensor is obvious since they exhibit great specifications with respect to e.g. humid conditions. These specifications characterizing condenser microphones would be natural to test on the preamplifier. It would be good to perform environmental tests such as performance under humid conditions. This way not only the microphone but the entire measurement system can be characterized with high quality.

Originally the system was supposed to deliver a digital output signal for easy connection to e.g. a computer. This was given a low priority on the cost of unforeseen challenges. It could be a plus to the measurement system to incorporate an analog to digital converter.

The offset performance of the preamplifier has not been investigated. A DC offset can degrade the performance of both the microphone linearity and the preamplifier maximum allowed output voltage thus the dynamic range. Using an in-amp e.g. IN116 show better offset performance and this should be investigated. An offset correction circuitry could also be designed for the current OPA129.

The start-up circuit of the preampliﬁer ensuring quick discharge of the input nodes of the op-amp is implemented using a switch. No indication exist to show when the measurement system is stabilized and ready for use. This could be solved by a light emitting diode and maybe a sensing circuit indicating when the system is ready.

Lastly speciﬁcally on this design it would be of interest to see the performance of the entire measurement system on real infrasound sources. It was originally intended to establish a setup at a wind turbine and measure real data. But realizing that infrasound measurement is a challenging task in it self and the fact that the system only measures down to 10 mHz when the vent is closed with precautions in result, the ﬁeld measurement was deemphasized.

On a more general level looking into the manufacturing processes involved with the design of microphone vents would be interesting. Laser cutting has been mentioned but it should be investigated what it is capable of manufacturing. To a start the proposed vent conﬁgurations presented should be tested. References

[1] Geoﬀ Leventhall. Low frequency noise. what we know, what we do not know, and what we would like to know. Low Frequency Noise and Vibration and its Control, 2008.

[2] Preparatory Commission for the Comprehensive Nuclear-Test-Ban Or- ganization. http://www.ctbto.org/verification-regime/ monitoring-technologies-how-they-work/infrasound-monitoring/ page-1/.

[3] Bruel¨ & Kjær A/S. Microphone handbook, volume 1: Theory, 1996. BE 1447 –11.

[4] P. V. Bruel¨ and W. J. Parker. The condenser microphone and some of its uses in laboratory investigations. Electro-Acoustic Group, 1963.

[5] Allan J. Zuckerwar and William W. Shope. A solid-state converter for measurement of aircraft noise and sonic boom. IEEE Transactions on Instrumentation and Mea- surement, 1974.

[6] Jeﬀrey B. Johnson, Jonathan M. Lees, and Hugo Yepes. Volcanic eruptions, lightning, and a waterfall: Diﬀerentiating the menagerie of infrasound in the ecuadorian jungle. Geophysical Research Letters, 33, 2006.

[7] Howe Gastmeier Chapnik Limited (HGC Engineering). Wind turbines and infrasound. Canadian Wind Energy Association, 2006.

[8] Frits van den Berg. Low frequency noise can be a phantom sound. Low Frequency Noise and Vibration and its Control, 2008.

[9] Christian Sejer Pedersen, Henrik Møller, and Kerstin Persson Waye. Low-frequency- noise complaints: an investigation of twenty-one cases. Low Frequency Noise and Vibration and its Control, 2008.

[10] Takanao Sugimoto, Kenji Koyama, Yosuke Kurihara, and Kajiro Watanabe. Measure- ment of infrasound generated by wind turbine generator. SICE Annual Conference, 2008.

[11] Kenneth J. Plotkin. Sonic boom: From bang to puﬀ. Echoes, The newsletter of The Acoustical Society of America, 20(3), 2010.

[12] Larry K. Baxter. Capacitive Sensors Design and Applications. IEEE Press, 1997.

[13] Bruel¨ & Kjær A/S. Condenser microphones and microphone preampliﬁers for acoustic measurements, data handbook, 1982. BP 0100, 2-044 01 00-2A. References 66

[14] Gunnar Rasmussen and Kim M. Nielsen. Low frequency calibration of measurement microphones. Low Frequency Noise and Vibration and its Control, 2008.

[15] Benoit Alcoverro and Alexis Le Pichon. Design and optimization of a noise reduction system for infrasonic measurements using elements with low acoustic impedance. Acoustical Society of America, 2004.

[16] Jelena Citakovic Haas-Christensen. New Technology-Driven Approaches in the Design of Preampliﬁers for Condenser Microphones. PhD thesis, Technical University of Denmark, 2009.

[17] David A. Bell. Electronic Instrumentation and Measurements. Prentice Hall Career & Technology, Englewood Cliﬀs, New Jersey, USA, 2nd, edition, 1994.

[18] Bernard M. Oliver and John M. Cage. Electronic Measurements and Instrumentation. McGraw-Hill Book Inc., 1971.

[19] M.Sc. Ole-Herman Bjor Senior Scientist. Norsonic as, norway, 2011. http://www. norsonic.com.

[20] Adel S. Sedra and Kenneth C. Smith. Microelectronic Circuits, International Student Edition. Oxford University Press, Inc., New York, NY, USA, 5th edition, 2004.

[21] Charles Kitchin and Lew Counts. A Designer’s Guide to Instrumentation Ampliﬁers. Analog Devices, Inc., 3rd edition, 2006.

[22] Burr-Brown Products from Texas Instruments. Datasheet of texas instruments opa129 ultra-low bias current difet operational ampliﬁer, 2007. SBOS026A.

[23] Ole Jannerup and Paul Haase Sørensen. Reguleringsteknik. Polyteknisk Forlag, 4th edition, 2006.

[24] Claus Erdmann Furst.¨ A low-noise/low-power preampliﬁer for capacitive microphones. IEEE, 1996.

[25] Ron Mancini. Op amps for everyone. Design Reference, Texas Instruments, SLOD006B, August 2002.

[26] Texas Instruments. Noise analysis in operational ampliﬁer circuits. Application Re- port, SLVA043B, 2007.

[27] Robert Tarzwell. Xtreme resistance and impedance circuits. DMR LTD, February 2009.

[28] Erling Frederiksen. Low frequency calibration of acoustical measurement systems. Bruel¨ & Kjær Technical Review No. 4 1981, 1981.

[29] Jr. W. Marshall Leach. Introduction to Electroacoustics and Audio Ampliﬁer Design. Kendall/Hunt Publishing, 3rd edition, 2003.

[30] Nick Rau et al. Limits of very small manufacturing processes. http://inst.eecs. berkeley.edu/~ee245/fa97/small.html, 2011.

[31] Wikipedia. Excimer laser. http://en.wikipedia.org/wiki/Excimer_laser, 2011. References 67

[32] Engineers Edge LLC. Laser cutting review. http://www.engineersedge.com/ manufacturing/laser_cutting.htm, 2011.

Appendix

A Various Matlab scripts cap change.m - calculating change of capacitance of the microphone

1 % How much does the capacitance of the microphone change during operation? 2 clc; clear all; 3 format longEng; 4 5 % Microphone specific data 6 dyn_max = 146% Maximum dB SPL(where distortion takes over) 7 dyn_min = 14% Minimum dB SPL(where noise floor takes over) 8 sens = 50e-3% Sensitivity inV/Pa 9 cap = 20e-12% Capacitance when charged inF 10 polV = 200% Polarization voltage inV 11 12 % Voltage swing(Vpp) 13 Vpp_max = 20e-6*10^(dyn_max/20)*sens*sqrt(8)% sqrt(8) requires sinusoid 14 Vpp_min = 20e-6*10^(dyn_min/20)*sens*sqrt(8)% sqrt(8) requires sinusoid 15 16 % Charge when polarized 17 Q = cap*polV 18 19 % Capacitance when max outswing(plus/minus half of Vpp) 20 Cmax = [Q/(polV+Vpp_max/2) Q/(polV-Vpp_max/2)] 21 22 % Capacitance when min outswing(plus/minus half of Vpp) 23 Cmin = [Q/(polV+Vpp_min/2) Q/(polV-Vpp_min/2)] 24 25 % Capacitance change 26 deltaC_max = Cmax-cap 27 deltaC_min = Cmin-cap 28 29 %%%% Result %%%% 30 % with input of 146 dB SPL cap changes from 17.5 pF to 23.3 pF 31 % with input of 14 dB SPL cap changes 0.7 aF- 10^(-18) 32 33 % Capacitance ofa microphone 34 eps0=8.85e-12;% Permittivity of vacuum 35 d=20e-6;% Plate distance[m] 36 A=45e-6;% Capacitor plate area[m^2] 37 Cm = eps0*A/d Appendix 70

mic vent.m - calculations of vent design

1 clc; clear all; 2 close all; 3 format longEng; 4 5 rho0 = 1.204;% Density of air at 20 ◦C 6 c = 343;% Velocity of sound at 20 ◦C 7 eta = 1.86e-5;% Viscosity coefficient of air at 20 ◦C and 0.76m Hg 8 9 Vf = 50e-9;% Volume of front cavity[m^3](ref. datasheet) 10 V = 100*Vf;% Volume of back cavity[m^3](ref. Leach) 11 12 % Spacer dimensions 13 w = 90e-6;% Width of slit in spacer[m] 14 h = 20e-6;% Thickness of spacer[m] 15 l = 1.5e-3;% Length of slit in spacer[m] 16 17 l = linspace(l,33.5e-3,11)’;% Increasing the length 18 w = linspace(w,10e-6,11);% Decreasing the width 19 20 C = V./(rho0*c.^2);% Acoustic compliance of back cavity[m^5/N] 21 %R= [8 *eta*l./(pi.*a.^4)]’% Acoustic resistance of vent(tube) 22 %R= [12 *eta*l*1./(w.^3*h)]’;% Acoustic resistance of vent(slit) 23 24 % Plotsf as function ofw andl 25 [W, L] = meshgrid(w,l); 26 R = [12*eta*L./(W.^3*h)];% Acoustic resistance of vent(slit) 27 f = 1./(2*pi*R*C); 28 29 figure1 = figure; 30 axes1 = axes(’Parent’,figure1,’ZScale’,’log’); 31 view(axes1,[-125 18]); 32 box(axes1,’on’); 33 grid(axes1,’on’); 34 hold(axes1,’all’); 35 surf(W,L,f,’Parent’,axes1);% Plots3D 36 colormap hsv % Determines colors 37 xlim([min(W(1,:)) max(W(1,:))]) 38 ylim([min(L(:,1)) max(L(:,1))]) 39 xlabel(’w[\mum]’) 40 ylabel(’l[mm]’) 41 zlabel(’f[Hz]’) 42 % Defining labels 43 xl=fliplr(W(1,:)); 44 xl=xl(1:2:end);% Selects every second for label 45 yl=L(:,1); 46 yl=yl(1:2:end);% Selects every second for label 47 xl = sprintf(’%3.1f|’,xl*1e6); 48 yl = sprintf(’%3.1f|’,yl*1e3); 49 if ispc 50 xl = strrep(xl,’e-00’,’e-’); 51 yl = strrep(yl,’e-00’,’e-’); 52 end 53 % Defining ticks 54 xt=fliplr(W(1,:)); 55 xt=xt(1:2:end); 56 yt=L(:,1); 57 yt=yt(1:2:end); 58 set(gca,’XTick’,fliplr(W(1,:))) 59 set(gca,’YTick’,L(:,1)) 60 set(gca,’XTick’,xt) 61 set(gca,’YTick’,yt) 62 set(gca,’XTickLabel’,xl) 63 set(gca,’YTickLabel’,yl) 64 65 % Max length of skew slit in spacer 66 r2 = 11.7e-3/2;% Outer radius of spacer 67 l_old = 1.5e-3;% Difference between inner and outer radius 68 r1 = r2-l_old;% Inner radius of spacer Appendix 71

69 l_skew = sqrt(r2^2-r1^2);% Max length of slit with skew cut 70 71 % Max length of circular slit in spacer 72 r = (r1+r2)/2;% Radius in the midle of the spacer 73 circ = 2*pi*r;% Circumference of the slit 74 l_circ = l_old+circ;% Max length of slit with circular cut

sys analysis v1b.m - transfer function of circuit of ﬁrst prototype

1 % This circuit is as of April4th 2011- version 1. This hasa simple high 2 % pass filter in the feedback. 3 clc; clear all; 4 close all; 5 format longEng; 6 7 f = [[1e-3:1e-6:1e-1] [1e-1:1e-3:1] [1:1e2:100e3]]; 8 omega = f*2*pi;% Angular frequency 9 s=i*omega;% Laplace transformed frequency 10 Cm=20e-12;% Capacitance of microphone 11 Rb=500e9;% Equivalent resistance of bias circuit 12 Cf=16e-6;% Feedback capacitor 13 Rf=10e6;% Feedback resistor 14 15 omegaN=(1/(Cf*Rf*Cm*Rb))^(1/2);% Natural frequency of system 16 fn=omegaN/(2*pi)% In Hertz 17 zeta=0.5*omegaN*Cm*(Rf+Rb)% Damping of system 18 19 % Poles and zeros of system(calculated using the bottom three lines) 20 pole1 = -(Cm*Rb - (Cm^2*Rb^2 + 2*Cm^2*Rb*Rf + Cm^2*Rf^2 - 4*Cf*Cm*Rb*Rf)^(1/2) + Cm*Rf) /(2*Cf*Cm*Rb*Rf) 21 pole2 = -((Cm^2*Rb^2 + 2*Cm^2*Rb*Rf + Cm^2*Rf^2 - 4*Cf*Cm*Rb*Rf)^(1/2) + Cm*Rb + Cm*Rf) /(2*Cf*Cm*Rb*Rf) 22 zero1 = 0 23 zero2 = -(Rb + Rf)/(Cf*Rb*Rf) 24 25 % Transfer function written on standard form 26 H = (s.^2*Cf*Rf*Cm*Rb + s*Cm*(Rf+Rb)) ./ (s.^2*Cf*Rf*Cm*Rb + s*Cm*(Rf+Rb) + 1); 27 % System in form for nyquist plot 28 sys=tf([Cm*Rb*Cf*Rf Cm*(Rf+Rb) 0],[Cm*Rb*Cf*Rf Cm*(Rf+Rb) 1]) 29 nyquist(sys) 30 hold all; 31 p1=plot(pole1,’bx’,’LineWidth’,2,’MarkerSize’,10) 32 p2=plot(pole2,’rx’,’LineWidth’,2,’MarkerSize’,10) 33 z1=plot(zero1,’bo’,’LineWidth’,2,’MarkerSize’,10) 34 z2=plot(zero2,’ro’,’LineWidth’,2,’MarkerSize’,10) 35 legend([p2 z2],{’Poles’,’Zeros’},4) 36 grid 37 % Savinga pdf 38 set(gcf,’PaperUnits’,’centimeters’); set(gcf,’PaperSize’, [15 10]); 39 set(gcf,’PaperPosition’,[0 0 15 10]); 40 print(gcf,’-dpdf’,’-r300’,’../Latex/graphics/peaking_nyquist.pdf’); 41 42 figure() 43 subplot(2,1,1); 44 semilogx(f,20*log10(abs(H))) 45 grid on 46 ylabel(’|H(j\omega)|’); 47 title(’Magnitude in dB’); 48 subplot(2,1,2); 49 semilogx(f,unwrap(angle(H))*180/pi); 50 grid on 51 xlabel(’f[Hz]’); 52 ylabel(’\angleH(j\omega)[\circ]’); 53 title(’Phase in degrees’); 54 55 % syms Cm Rb Cf Rfs; 56 % poles=solve(’s^2*Cm*Rb*Cf*Rf+s*Cm*(Rf+Rb)+1=0’,’s’)% poles of system 57 % zeros=solve(’s^2*Cm*Rb*Cf*Rf+s*Cm*(Rf+Rb)=0’,’s’)% zeros of system Appendix 72

B Microphone Calibration Chart

Test Frequency Measured Level Measured Level Uncertanty [Hz] [mV/Pa] [dB re. 1V/Pa] [dB] 250 52.57 -25.59 ±0.06

4 2 0 -2 -4 -6 [dB] -8 -10 -12 -14 -16 100 1000 10000 20000 Frequency [Hz] Appendix 73

C Circuit Analysis with feedback b The starting point is (3.6) which is repeated here. Naming is with reference to Figure 3.1 and Figure 3.11 b.

V Z O = b (1) 1 1 V Z + Z IN Zb b f1 Zm + 1 − 1 1 1 Zm + + Zb Zf1 Zf2

Now it’s time to insert Laplace transformed expressions instead of complex impedances. They are transformed as follows

1 Zb = Rb Zf1 = (2) sCf1 1 1 Rf2 Zm = Zf2 = Rf2||Cf2 = 1 = (3) sCm + sCf2 1 + sRf2Cf2 Rf2 which by insertion yields

VO sCm = 1 (4) sCf1+ VIN 1 Rb sCm + − 1 1 Rb Rb(sCf1+sCf2+ + ) Rb Rf2

Extending the fraction by multiplying with Rb

VO sRbCm = 1 (5) sCf1+ VIN Rb sRbCm + 1 − 1 1 sCf1+sCf2+ + Rb Rf2

Another extending of the fraction

1 1 sRbCm(sCf1 + sCf2 + + ) VO Rb Rf2 = 1 1 1 1 1 (6) VIN sRbCm(sCf1 + sCf2 + + ) + sCf1 + sCf2 + + − sCf1 − Rb Rf2 Rb Rf2 Rb

Collecting coeﬃcients of s

2 1 1 V s RbCm(Cf1 + Cf2) + sRbCm( R + R ) O = b f2 (7) 2 1 1 1 VIN s RbCm(Cf1 + Cf2) + sRbCm( + ) + sCf2 + Rb Rf2 Rf2

Writing to the standard form with 1 as coeﬃcient to s0

2 VO s RbCmRf2(Cf1 + Cf2) + s(Rf2 + Rb)Cm = 2 (8) VIN s RbCmRf2(Cf1 + Cf2) + s((Rf2 + Rb)Cm + Cf2Rf2) + 1

Now on its standard form (see (3.10)) the natural frequency and damping can easily be read as stated in (3.13) and (3.14). Appendix 74

D Circuit Analysis with feedback d The starting point is (3.6) which is repeated here. Naming is with reference to Figure 3.1 and Figure 3.11 d. V Z O = b (9) 1 1 V Z + Z IN Zb b f1 Zm + 1 − 1 1 1 Zm + + Zb Zf1 Zf2 Now it’s time to insert Laplace transformed expressions instead of complex impedances. They are transformed as follows

1 Rf1 Zb = Rb Zf1 = Rf1||Cf1 = 1 = (10) + sCf1 1 + sRf1Cf1 Rf1 1 1 Rf2 Zm = Zf2 = Rf2||Cf2 = 1 = (11) sCm + sCf2 1 + sRf2Cf2 Rf2 which by insertion yields...... a very long and nasty 3rd order expression which is not used for further analysis and therefore omitted.