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I am using the below circuit to amplify the signal from an electret condenser microphone for analysis by a microcontroller to detect short bursts of sound. The circuit runs off a ~4.5V supply from 3 AA batteries, so options for opamps are limited. I am using an NJM4580D. Datasheets for microphone and opamp linked below:

https://www.cuidevices.com/product/resource/cma-4544pf-w.pdf

https://www.njr.com/electronic_device/PDF/NJM4580_E.pdf

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Circuit includes a potentiometer to adjust gain on second stage. The circuit is working fine at low gains with louder sound bursts, but I am having an issue with the noise at the higher gains required to detect fainter sound bursts.

Low Gain

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Higher Gain

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The noise appears to be approx 580Hz. The room is quiet prior to sound bursts. The circuit is built on protoboard, and size is somewhat limited. Photo below:

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So, given the limitations on power supply and construction, is there anything I could do to reduce the amplitude of the noise while maintaining the signal strength at higher gains?

Appreciate any feedback.

EDIT 1

Brian appears to be correct. I removed the microphone circuit board and powered directly from 4.5V batteries. At max gain, the noise was acceptable:

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The rest of the circuit board that this device is connected to is fairly straightforward. I don't have a presentable schematic at the moment but it is constructed in a manner similar to the microphone circuitand made up of the following components:

The microcontroller is an ATMEGA328P https://ww1.microchip.com/downloads/en/DeviceDoc/ATmega48A-PA-88A-PA-168A-PA-328-P-DS-DS40002061B.pdf

MAX7219 driven 8-digit segmented display https://datasheets.maximintegrated.com/en/ds/MAX7219-MAX7221.pdf

Pair of SN74HC165N shift registers for keypad input (momentary pushbutton array) https://www.ti.com/lit/ds/symlink/sn74hc165.pdf?ts=1607932478460

SN74HC125N buffer on SPI MISO line https://www.ti.com/lit/ds/scls104e/scls104e.pdf?ts=1608013220070

100nF decoupling is provided at each IC power pin and I have a couple of 100uF electrolytic capacitors on the power rails.

Any thoughts as to what might be causing instability/interference?

EDIT 2

As suggested by Andy, I tried a different op-amp, the MCP6022, which I was able to drop into the existing circuit and the difference in output range is remarkable:

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In addition to this, I took Brian's advice and added a 470uF capacitor to the power rails at on the mic board, which also helped significantly:

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Finally, I added a 10ohm resistor in series with the power supply to the mic board and it also produced a noticeable reduction:

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Original op-amp with the additional capacitor and resistor, for reference:

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    \$\begingroup\$ Try putting a 10k resistor in series with C3 and increasing R5 to 100k. You may not then have enough gain so it would be better to convert the first gain stage to a non-inverting amplifier and feed the mic output into the non-inverting input via C3 (biased to mid supply). \$\endgroup\$ – James Dec 11 '20 at 7:41
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    \$\begingroup\$ A poor op-amp for this design I must say. \$\endgroup\$ – Andy aka Dec 11 '20 at 9:23
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    \$\begingroup\$ Use a small, reduced feature size n-jfet as a source-follower with its source fed by another n-jfet operating as a current source. This matches the capacitance of the electret and reduces noise. That should by followed by another, larger n-jfet also as a source follower. Burkhard, 1970, disclosed the use of back to back diodes to avoid the use of a large resistor in biasing the gate and to exchange shot noise for Johnson noise, favorably. \$\endgroup\$ – jonk Dec 11 '20 at 12:13
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    \$\begingroup\$ That's not noise, that's either instability or interference, perhaps on the PSU. Start by arranging a perfectly clean 4.5V supply. \$\endgroup\$ – user_1818839 Dec 11 '20 at 14:43
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    \$\begingroup\$ @pat there are literally thousands of them. Try the usual vendors like farnell, RS, digikey and mouser. They all have sophisticated search engines. \$\endgroup\$ – Andy aka Dec 15 '20 at 9:47
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OK, from comments:

That's not noise, that's either instability or interference, perhaps on the PSU. (The regularity of the waveform shows this. Start by arranging a perfectly clean 4.5V supply for the mic amp, and see how it goes.

Having seen that a separate battery supply improves performance, I'd suggest improving the quality of power fed to the mic amp. Simplest approach would be an R-C low pass filter : 100 ohms would drop a fraction of a volt at the current required, and 1000uF (giving an 0.1 second time constant) should attenuate the power supply noise adequately. These values can then be tuned for size, cost, headroom, attenuation to suit your goals.

Andy also deserves credit for suggesting an improvement in opamp selection.

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