Rasmus Trock Kinnerup, s052256 Ultra Low Frequency Infrasonic Measurement System 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 elec- tric 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 stud- ies. 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 jj 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 jj 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 ampli- fier 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.