Design Goals

Design Description

This circuit uses a non–inverting amplifier circuit configuration to amplify the microphone output signal. This circuit has very good magnitude flatness and exhibits minor frequency response deviations over the audio frequency range. The circuit is designed to be operated from a single 5V supply.

Design Notes

1. Operate within the op amp 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 amps for low noise designs.
5. The common mode voltage is equal to the DC bias voltage set using the resistor divider plus any variation caused by the microphone output voltage. For op amps with a complementary pair input stage it is recommended to keep the common mode voltage away from the cross over region to eliminate the possibility of cross over distortion.
6. Resistor R₁ is used to bias the microphone internal JFET transistor to achieve the bias current specified by the microphone.
7. The equivalent input resistance is determined by R₁, R₂, R₃. Use large value resistors for R₂ and R₃ to increase the input resistance.
8. The voltage connected to R₁ to bias the microphone does not have to be the same as the op amp supply voltage. Using a higher voltage supply for the microphone bias allows for a lower bias resistor value.

Design Steps

This design procedure uses the microphone specifications provided in the following table.

1. Convert the sensitivity to volts per Pascal.
   ${\text{ 10}}^{\frac{-\text{35dB}}{\text{20}}}=\text{17.78}\frac{\text{mV}}{\text{Pa}}$
2. Convert volts per Pascal to current per Pascal.
   $\frac{\text{17.78}{\displaystyle \frac{\text{mV}}{\text{Pa}}}}{\text{2.2kΩ}}=\text{8.083}\frac{\text{μA}}{\text{Pa}}$
3. Max output current occurs at max pressure 2Pa.
   ${\text{I}}_{\text{Max}}=\text{2Pa × 8.083}\frac{\text{μA}}{\text{Pa}}=\text{16.166μA }$
4. Calculate bias resistor. In the following equation, Vmic is microphone standard operating voltage.
   ${\text{R}}_1=\frac{{\text{V}}_{\mathrm{cc}}-{\text{V}}_{\mathrm{mic}}}{{\text{I}}_{\mathrm{s}}}=\frac{\text{5V-2V}}{\text{0.5mA}}\text{=6kΩ≈5.9kΩ (Standard Value)}$
5. Set the amplifier input common mode voltage to mid–supply voltage. The equivalent resistance of R₂ in parallel with R₃ is 10 times larger than R1 so that a majority of the microphone current flows through R₁.
   $$\begin{gathered} {\text{R}}_{\mathrm{eq}}=\text{R2||R3}\mathrm{ }\text{>10 × R1}=\text{100kΩ} \\ {\text{Choose R}}_{\text{2}}={\text{R}}_{\text{3}}=\text{200kΩ} \end{gathered}$$
6. Calculate the maximum input voltage.
   $$\begin{gathered} {\text{R}}_{\text{in}}={\text{R1||R}}_{\text{eq}}=\text{5.9kΩ}|\text{|100kΩ}=\text{5.571kΩ} \\ {\text{V}}_{\text{in}}={\text{I}}_{\text{max}}{\text{ × R}}_{\text{in}}=\text{16.166uA × 5.571kΩ}=\text{90.067mV} \end{gathered}$$
7. Calculate gain required to produce the largest output voltage swing.
   $\text{Gain}=\frac{{\text{V}}_{\text{outmax}}}{{\text{V}}_{\text{in}}}=\frac{\text{1.228V}}{\text{90.067mV}}=\text{13.634}\frac{\text{V}}{\text{V}}$
8. Calculate R₄ to set the gain calculated in 7. Select feedback resistor R₅ as 10kΩ.
   $$\begin{gathered} {\text{R}}_4=\frac{{\text{R}}_5}{\text{Gain-1}}=\frac{\text{10kΩ}}{\text{13.634-1}}=\text{791Ω}\approx \text{787Ω (Standard Values)} \\ \text{The final gain of this circuit is:} \\ \text{Gain}=\text{20log}\left(\frac{\text{Vout}}{\text{Vin}}\right)=\text{20log}\left(\frac{\text{16.166uA} \times \text{ 5.571kΩ} \times \left(\text{1+}\frac{\text{10kΩ}}{\text{787Ω}}\right)}{\text{2V}}\right) = \text{-4.191dB} \end{gathered}$$
9. Calculate the corner frequency at low frequency according to the allowed deviation at 20Hz. In the following equation, G_pole1 is the gain contributed by each pole at frequency "f." Note that you divide by three because there are three poles.
   ${\text{f}}_{\mathrm{c}}=\text{f}\sqrt{{\left(\frac{1}{\text{G\_pole1}}\right)}^2-\text{1}}=\text{20Hz}\sqrt{{\left(\frac{\text{1}}{{\text{10}}^{\frac{\text{-0.5/3}}{\text{20}}}}\right)}^{\text{2}}-\text{1}}=\text{3.956Hz}$
10. Calculate C₁ based on the cut off frequency calculated in 9.
    ${\text{C}}_1\text{=}\frac{\text{1}}{{\text{2π×Req×f}}_{\mathrm{c}}}=\frac{\text{1}}{\text{2π×100kΩ×3.956Hz}}=\text{0.402μF≈0.33μF (Standard Value)\hspace{0.17em}}$
11. Calculate C₂ based on the cut off frequency calculated in 9.
    ${\text{C}}_{\text{2}}=\frac{\text{1}}{{\text{2π×R4×f}}_{\mathrm{c}}}=\frac{\text{1}}{\text{2π×787Ω×3.956Hz}}=\text{51.121μF≈47μF (Standard Value)}$
12. Calculate the high frequency pole according to the allowed deviation at 20kHz. In the following equation, G_pole2 is the gain contributed by each pole at frequency "f."
    ${\text{f}}_{\mathrm{p}}=\frac{\text{f}}{\sqrt{{\left(\frac{\text{1}}{\text{G\_pole2}}\right)}^2-1}}=\frac{\text{20kHz}}{\sqrt{{\left(\frac{1}{{\text{10}}^{\frac{-\text{0.1}}{20}}}\right)}^2-1}}=\text{131.044kHz}$
13. Calculate C3 to set the cut off frequency calculated in 12.
    ${\text{C}}_{\text{3}}\text{=}\frac{\text{1}}{{\text{2π×R}}_{\text{5}}{\text{×f}}_{\mathrm{p}}}\text{=}\frac{\text{1}}{\text{2π×10kΩ×131.044kHz}}\text{=121.451pF≈120pF (Standard Value)}$
14. Calculate the output capacitor, C₄, based on the cut off frequency calculated in 9. Assume the output load R₆ is 10kΩ.
    ${\text{C}}_4=\frac{1}{{\text{2π×R}}_6\text{×}{\mathrm{f}}_{\mathrm{c}}}=\frac{\text{1}}{\text{2π10kΩ×3.956Hz}}=\text{4.023μF≈3.3μF (Standard Value)}$

Design Simulations

AC Simulation Results

Transient Simulation Results

The input voltage represents the SPL of an input signal to the microphone. A 1V_rms input signal represents 1Pa.

Noise Simulation Results

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

References:

Texas Instruments, Simulation for Non-Inverting Microphone Amplifier Circuit, SBOC525 SPICE simulation file

TI Precision Designs Single-Supply, Electret Microphone Preamplifier, TIPD181 reference design

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