Microphone noise

Resistance generates noise (thermal, aka Johnson noise); capacitance does not. So how is it that capacitor (historically, 'condenser') microphones have self-noise?

To answer that question we need look further than the microphone capsule itself to the circuit immediately downstream of it, often termed a preamplifier although it is more realistically viewed as an impedance converter. An example is shown in the circuit below, which is simple but includes the key elements. Namely: a field-effect transistor (FET), operated in common-drain or common-source mode, and one or more bias resistors (R) attached to the FET's gate which determine the input resistance and set the DC operating conditions:

An FET is used because field-effect transistors inherently have much higher input resistance than bipolar transistors. The importance of this is clear if we (simplistically) consider the FET to have infinite input impedance and represent the microphone capsule as a voltage source in series with a capacitance (the capacitance of the microphone capsule itself). The input circuit is then:It's clear from this that the capsule capacitance (C) and impedance converter input resistance (R) form a high-pass filter, and that to achieve flat frequency response to below audibility requires a sufficiently high input resistance relative to the capsule's capacitance. If the capsule capacitance is 20pF (typical for a half-inch diameter measurement microphone) then the input resistance needs to be 1.6 gigohm (1600 megohm) for a corner frequency of 5Hz.

In fact it's normal for the impedance converter to have an input resistance an order of magnitude or more higher than this. Not for reasons of frequency response but because of the shunting effect of the capsule capacitance. Usually it is necessary to minimise resistance to minimise noise, but in this instance increasing the input resistance reduces noise level at audio frequencies, for the reason shown in the diagram below (noise voltage and frequency both on logarithmic scales):

In this example, R2 is double the value of R1. Because a resistor's thermal noise voltage is proportional to the square root of its resistance, the thermal noise of R2 is 3dB higher than that of R1. But doubling the resistance also halves the corner frequency (F2) formed by the capsule capacitance and input resistance, above which the noise voltage reduces by 6dB per octave (20dB per decade). These effects combine to result in the noise voltage of R2 being, counter-intuitively, 3dB lower than that of R1 above the corner frequency (F1) formed by R1 and the capsule capacitance.

This also explains why capacitor microphones with larger capsules generally have lower self-noise than those with smaller capsules. The larger capsule has both greater output voltage for a given SPL and, for a given impedance converter input resistance, a lower noise corner frequency because of higher capacitance.

Let's put some hard numbers to this. For a capsule capacitance of 20pF, impedance converter input resistance of 20 gigohm, and a capsule sensitivity of 12.5 millivolts per pascal (7.89mV for 90dB SPL), the noise voltage density of the resistance is 18 microvolts per root Hz at 20C, which is -52.8dB reference the microphone's output at 90dB SPL. The noise corner frequency is 0.398Hz, so the relative noise level (for 1Hz measurement bandwidth) falls to -72.8dB at 3.98Hz, -92.8dB at 39.8Hz and -112.8dB at 398Hz. With the correct choice of FET, its noise level will be better than -130dB and its 1/f noise corner frequency less than 100Hz, So the dominant noise source at low frequencies is, or should be, the impedance converter input resistor.

The implications of microphone self-noise are discussed in the section Headphone distortion measurement.