Design Goals

Design Description

This circuit uses an op amp in a transimpedance amplifier configuration to convert the output current from an electret capsule microphone into an output voltage. The common mode voltage of this circuit is constant and set to mid–supply eliminating any input–stage cross over distortion.

Design Notes

1. Use the op amp in the linear output operating range, which is usually specified under the A_OL test conditions.

2. Use low–K capacitors (tantalum, C0G, and so forth) and thin film resistors help to decrease distortion.

3. Use a battery to power this circuit to eliminate distortion caused by switching power supplies.

4. Use low value resistors and low noise op amp to achieve high performance low noise designs.

5. The voltage connected to R₁ to bias the microphone does not have to match the supply voltage of the op amp. Using a larger microphone bias voltage allows for a larger value or R₁ which decreases the noise gain of the op amp circuit while still maintaining normal operation of the microphone.

6. Capacitor C₁ should be large enough that its impedance is much less than resistor R₁ at audio frequency. Pay attention to the signal polarity when using tantalum capacitors.

Design Steps

The following microphone is chosen as an example to design this circuit.

1. Microphone parameter	Value
   Sensitivity at 94 dB SPL (1 Pa)	–35 ± 4 dBV
   Current Consumption (Max)	0.5 mA
   Impedance	2.2 kΩ
   Standard Operating Voltage	2 Vdc

2. Convert the sensitivity to volts per Pascal.
   ${\text{10}}^{\frac{-35\mathrm{dB}}{20}}=17.78\mathrm{mV}/\mathrm{Pa}$
3. Convert volts per Pascal to current per Pascal.
   $\frac{\text{17.78mV}/\mathrm{Pa}}{\text{2.2kΩ}}=8.083\mathrm{\mu A}/\mathrm{Pa}$
4. Max output current occurs at max sound pressure level of 2Pa.
   ${\text{I}}_{\mathrm{Max}}=2\mathrm{Pa}\times 8.083\mathrm{\mu A}/\mathrm{Pa}=16.166\mathrm{\mu A}$
5. Calculate the value of resistor R₄ to set the gain
   $$\begin{gathered} {\text{R}}_4=\frac{{\mathrm{V}}_{\max }}{{\mathrm{I}}_{\max }}=\frac{\text{1.}228\mathrm{V}}{\text{16.}166\mathrm{\mu A}}=75.961\mathrm{k}\mathrm{\Omega }\approx 75\mathrm{k}\mathrm{\Omega } (\mathrm{Standard} \mathrm{value}) \\ \mathrm{The} \mathrm{final} \mathrm{signal} \mathrm{gain} \mathrm{is}: \\ \mathrm{Gain}=20\times \log \left(\frac{{\mathrm{V}}_{\mathrm{out}}}{{\mathrm{V}}_{\mathrm{in}}}\right)=20\times \log \left(\frac{\mathrm{16.}166\mathrm{\mu A}\times 75\mathrm{k}\mathrm{\Omega }}{2\mathrm{V}}\right)=-4.347\mathrm{dB} \end{gathered}$$
6. Calculate the value for the bias resistor R₁. In the following equation, Vmic is the standard operating voltage of the microphone
   ${\text{R}}_1=\frac{{\mathrm{V}}_{\mathrm{cc}}-{\mathrm{V}}_{\mathrm{mic}}}{{\mathrm{I}}_{\mathrm{s}}}=\frac{5\mathrm{V}-2\mathrm{V}}{\text{0.5}\mathrm{mA}}=6\mathrm{k}\mathrm{\Omega }\approx 5.9\mathrm{k}\mathrm{\Omega } (\mathrm{Standard} \mathrm{value})$
7. Calculate the high frequency pole according to the allowed deviation at 20 kHz. In the following equation, G_pole1 is the gain at frequency f.
   ${\text{f}}_{\mathrm{p}}=\frac{\mathrm{f}}{\sqrt{{\left(\frac{1}{\mathrm{G}\_\mathrm{pole}1}\right)}^2-1}}=\frac{20\mathrm{kHz}}{\sqrt{{\left(\frac{1}{{10}^{\frac{\text{-0.1}}{20}}}\right)}^2-1}}=131.044\mathrm{kHz}$
8. Calculate C₃ based on the pole frequency calculated in step 6.
   ${\text{C}}_3=\frac{1}{2\mathrm{\pi }\times {\mathrm{f}}_{\mathrm{p}}\times {\mathrm{R}}_4}=\frac{1}{\text{2π×131.0}44\text{kHz×75kΩ}}=16.194\mathrm{pF}\approx 15\mathrm{pF} (\mathrm{Standard} \mathrm{value})$
9. Calculate the corner frequency at low frequency according to the allowed deviation at 20 Hz. In the following equation, G_pole2 is the gain contributed by each pole at frequency f respectively. There are two poles, so divided by two.
   ${\text{f}}_{\mathrm{c}}=\mathrm{f}\times \sqrt{{\left(\frac{1}{\mathrm{G}\_\mathrm{pole}2}\right)}^2-1}=20\mathrm{Hz}\times \sqrt{{\left(\frac{1}{{10}^{\frac{\text{-0.5}/2}{20}}}\right)}^2-1}=4.868\mathrm{Hz}$
10. Calculate the input capacitor C₁ based on the cut off frequency calculated in step 8.
    ${\text{C}}_1=\frac{1}{2\mathrm{\pi }\times {\mathrm{R}}_1\times {\mathrm{f}}_{\mathrm{c}}}=\frac{1}{2\mathrm{\pi }\times \text{5.9kΩ}\times \text{4.868}\mathrm{Hz}}=5.541\mathrm{\mu F}\approx 4.7\mathrm{\mu F} (\mathrm{Standard} \mathrm{value})$
11. Assuming the output load R₅ is 10 kΩ, calculate the output capacitor C₄ based on the cut off frequency calculated in step 8.
    ${\text{C}}_4=\frac{1}{2\mathrm{\pi }\times {\mathrm{R}}_5\times {\mathrm{f}}_{\mathrm{c}}}=\frac{1}{2\mathrm{\pi }\times 10\mathrm{k}\mathrm{\Omega }\times \text{4.868}\mathrm{Hz}}=3.269\mathrm{\mu F}\approx 3.3\mathrm{\mu F} (\mathrm{Standard} \mathrm{value})$
12. Set the amplifier input common mode voltage to mid–supply voltage. Select R₂ and R₃ as 100 kΩ. The equivalent resistance equals to the parallel combination of the two resistors:
    ${\text{R}}_{\mathrm{eq}}={\mathrm{R}}_2\left|\left|{\mathrm{R}}_3=100\mathrm{k}\mathrm{\Omega }\right|\right|100\mathrm{k}\mathrm{\Omega }=50\mathrm{k}\mathrm{\Omega }$
13. Calculate the capacitor C₂ to filter the power supply and resistor noise. Set the cutoff frequency to 1 Hz.

Design Simulations

AC Simulation Results

Transient Simulation Results

The input voltage represents the SPL of an input signal to the microphone. A 2 V_rms input signal represents 2 Pascal.

Noise Simulation Results

The following simulation results show 22.39 µV_rms of noise at 22 kHz. The noise is measured at a bandwidth of 22 kHz to represent the measured noise using an audio analyzer with the bandwidth set to 22 kHz.

References:

1. Analog Engineer's Circuit Cookbooks
2. SPICE Simulation File SBOC526
3. TI Precision Designs TIPD181
4. TI Precision Labs

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