Microphones Sound Waves alternate physical compression and extension of a medium with certain frequencies A Microphone (hydrophone if in water)convert acoustic waves (pressure waves) into electrical signal Desirable Frequency Range for Audio: 20Hz to 20KHz Sound Pressure Level:⎟⎠⎞⎜⎝⎛−PaPaessureRMSLog610*20)(Pr*20 Pa610*20−: Human threshold of hearing A mechanical Structure (usually a diaphragm) converts the acoustic pressure P∆ into a displacement h∆ Mechanical Sensitivity: PhPamSM∆∆=−).(1 The displacement d∆ is converted into an electrical signal V∆ (Capacitive sensing, Piezoresistive sensing, Piezoelectric, Magnetic…) Electrical Sensitivity: dVmVSE∆∆=−).(1 Overall sensitivity of the microphone: PVSSPaVSEM∆∆==−*).(1Levels Of Sound:Mechanical Sensitivity aPht Diaphragm Equation: 43221aEthCathCP +=σ σ: Internal Stress in the membrane (Pa) 1C and 2C are geometry-dependant constants For circular membrane: 0.41=C 67.22=C If th <<, then 2214athathCPσσ≈≈ Mechanical Sensitivity: σtaphSm82=∆∆=Capacitive Microphones Principle: Measures capacitance as a function of acoustic pressure.Electrical Sensitivity In equilibrium, the voltage across the capacitor is: biasCVV =, and the electric field is:SQhVEbiasε==0 If at time 0t:hhhδ−⇒0, then for RCtt<<−0, )(tQand )(tEare almost unchanged. hEVhhEVbiasCδδ+=−= )( At the output of high pass/buffer: 0hVhhEVbiasOUTδδ== Electrical Sensitivity: 0hVEhVSbiasoute==δ 0hh =xhhδ+=00toutVhEδt)/( RCtExp−∝Sound Wave EconstExternal polarization voltage, Vbias GΩδhVout≈δxEconst ×1Q bias resistor, Rh0 Micropho High Pass / BufferOptimal Sensitivity: Sensitivity: 028*hVtaSSSbiasmeσ== But biasVcan’t be too high, or the diaphragm will collapse. Collapse voltage: 03203max27812764εεσtdSathVm== Assume maxVVbiasα= mbiasmemShhVSSSS000278*εα=== Assumptions: • Rigid backplate • Piston movement of membraneFrequency Response fLfHOpen-circuit Sensitivity (mV/Pa)Frequency (Hz)0 dB-2 dBf0 fL: Static Pressure equalization hole fO: Depends on Mechanic Resonant frequency fHOpen-circuit Sensitivity (mV/Pa)Frequency (Hz)0 dB-2 dBf0undampedlightlydampedheavilydamped ρσ202af = ρ: Density of membrane material σ: Initial Stress in membrane a: Size of membraneElectret Microphones Electrets can store permanent fixed charges: Î No Bias necessary ! The permanent fixed charge surface density can be up to 24.10−−≈ cmCelσ and is stable several years. AQDDelair=− (Gauss) Under equilibrium, 000=+=−=∫elelelairdDdDEdlVεεε SdddEeleleloelelair=+⎟⎟⎠⎞⎜⎜⎝⎛=εεεσ0 ⎟⎟⎠⎞⎜⎜⎝⎛eloeleldεεσ Plays the role of the bias voltage. Sensitivities of .2mV/Pa were demonstrated × 1 σel Vout≈δxEconstSound WaveδxGΩEconstd0