8.2.1.2 Detailed Design Procedure

In this circuit, the op amp is configured as a transimpedance amplifier which converts the signal current of the microphone into an output voltage. The bandwidth of this circuit is limited to the vocal range as is common in telephony systems. The gain of the circuit is determined by the feedback resistor (R_FB), which must be calculated according to the microphone sensitivity. For this design, a microphone output current of 8 µA per Pascal (Pa) of air pressure was selected. Using this value, the output current for a sound pressure level of 100 dB_SPL, or 2 Pa air pressure, is calculated in Equation 1.

Equation 1.

R_FB is then calculated from this current to produce 1-V_RMS output for a 100-dB_SPL input signal in Equation 2.

Equation 2.

The feedback capacitor (C_FB) is calculated to limit the bandwidth of the amplifier to 3 kHz in Equation 3.

Equation 3.

R_BIAS is necessary to divert the microphone signal current through capacitor C_IN rather than flowing from the power supply (V_CC). Larger values of R_BIAS allow for a smaller capacitor to be used for C_IN and reduces the overall noise of the circuit. However, the maximum value for R_BIAS is limited by the microphone bias current and minimum operating voltage.

The value of R_BIAS is calculated in Equation 4.

Equation 4.

Input capacitor C_IN forms a high-pass filter in combination with resistor R_BIAS. The filter corner frequency calculation is shown in Equation 5 to place the high-pass corner frequency at 100 Hz.

Equation 5.

The voltage divider network at the op amp noninverting input is used to bias the op amp output to the midsupply point (V_CC / 2) to maximize the output voltage range of the circuit. This result is easily achieved by selecting the same value for both resistors in the divider. The absolute value of those resistors is limited by the acceptable power-supply current drawn by the voltage divider. Choosing 50 µA as an acceptable limit of supply current gives a value of 100 kΩ for the resistors in the divider, as Equation 6 shows.

Equation 6.

Finally, to minimize the additional noise contribution from the voltage divider, a capacitor is placed at the op amp noninverting input. This capacitor forms a low-pass filter with the parallel combination of the voltage divider resistors. Selecting a filter corner frequency of 20 Hz minimizes the noise contribution of the voltage divider inside the amplifier passband; see Equation 7.

Equation 7.