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Summary

I've designed a beamforming circuit that uses two electret condenser microphones (ECMs) in a differential end-fire array and outputs to a bluetooth module's ADC for transmission.

I explain my design below. I'm pretty confident when it comes to calculating parameters, but I lack the more practical skills and experience of circuit design. So in addition to my questions, please call out anything obviously wrong or silly mistakes.

Requirements

  1. Array parameters should be set to increase gain and directivity on an approximate bandwidth 300 Hz to 1000 Hz.
  2. Low cost. Total component cost should be less than $40.
  3. Circuit should be designed for single supply power since bluetooth module power pins will not provide dual supply.
  4. Signal-to-noise ratio as low as possible within budget.

Architecture

Architecture Block Diagram

Design

Circuit Schematic

BOM

  1. Microphone: PUI Audio AOM-5024L-HD-R ($3)
  2. Bluetooth Module: Microchip BM83 ($12)
  3. Op-amp: Analog AD8655 (<$1)
  4. Battery: 18650 ($10)

Simulation Results

Testing at 1kHz. First, putting a 233us delay on the MIC2 voltage source will simulate sound coming in from the front. The constructive interference shows that it is working as desired.

LTSpice Simulation showing audio signals constructively interfering

Next, putting a 233us delay on the MIC1 voltage source will simulate sound coming in from the back. The destructive interference shows that it is working as desired.

LTSpice Simulation showing audio signals destructively interfering

Array Performance Explanation

I used equations in DIY Microphones Blog, How Array Microphones Work, to calculate the gain and directivity of the differential end fire array with the spacing and delay described in the design. As you can see from the graphs, both show improved performance over the bandwidth in my requirements.

Array gain and directivity over frequency

Group Delay Explanation

I used the equations provided by Analog Devices' MT-202 to calculate the time constants required for the all pass filter. I also compared using a single filter (1st order) and splitting the delay among 3 filters (3rd order). As you can see from the graph, the 3rd order makes the group delay roughly constant over the bandwidth in my requirements.

Comparing group delay of 1st order and 3rd order all-pass filters

Questions

  1. Biasing the microphones: The AOM-5024L-HD-R specification recommends 3.0V and a load resistor 2.2kOhm. Since the system voltage is a nominal 3.7V, I assumed the mic's drain current should be equal to the current implied by the spec and used Ohms law to get 2.7kOhm load resistance (ie 3V / 2.2kOhm = 3.7V / 2.7kOhm). I'm concerned my reasoning is over-simplified. Is this correct way to think about biasing this microphone?
  2. Biasing the microphones: C1 is just there as a low pass filter to remove noise from the Vcc. However, should I have two capacitors after the junction, or just one where it is?
  3. LTspice microphone modeling: The AOM-5024L-HD-R specification lists the microphone output impedance as 2.2kOhm. So in LTspice, I set the "Parasitic Impedances, Series Resistance" of the voltage source to 2.2kOhm. Is this the correct way to simulate the microphones in this circuit?
  4. Using single supply: Since the module's system power only provides single supply, I selected a single supply op-amp and tried to design the circuit to accommodate. Conveniently, the signal needed to be biased anyway for mic power. You can see from Test Points 1 and 2 that the signal is biased exactly in the middle of the op-amp's output range. Furthermore, the coupling cap C3 on the negative side of the difference amp ensures that the output of the difference amplifier is also in range. Do these good results in the simulation mean that I have designed for single supply correctly? Is there anything I'm overlooking or simulating incorrectly?
  5. Noise reduction: I've read that using the same power supply for biasing signal and op-amps can lead to power supply noise amplification in the signal. However, since I'm using a battery, is this really an issue? Would putting a low-pass RC filter at the end be a smart idea or unnecessary? Any other design flaws that might increase noise?
  6. Impedance bridging: From Table 9-7 of the BM83 spec, it says that the input impedance of the module's ADC is 24kOhm. The AOM-5024L-HD-R specification lists the microphone output impedance as 2.2kOhm. So if I'm understanding impedance bridging correctly, the circuitry between the two should step up from 2.2 to 24 kOhm. I got good results out of the simulation by just setting everything to 22kOhm. Could I be implementing impedance bridging in a better way?
  7. I'd like to connect the output of this circuit to the analog input left and right (AIL/AIR) of the BM83 because this provides me more features on the software side. What is the right way to implement a mono to stereo connection with coupling cap C4? Are either of the options below correct?

Mono to stereo coupling cap ideas

Thank you! Apologies for not linking all my references. I don't have enough reputation to include all the links I wanted.

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  • \$\begingroup\$ Can't you use a stereo bluetooth transmitter and avoid the analog rigmarole? You can do the DSP on the receiving end, assuming that the compression artifacts don't mangle the signal too much. You should be able to transmit test signals not from microphones but from a dual-output function generator to assess the quality of the lossy digital channel that a bluetooth audio connection represents. \$\endgroup\$ Commented Oct 1 at 21:20
  • \$\begingroup\$ I haven't been able to find a bluetooth module that will do the beamforming DSP and has the excellent turnkey software solutions offered by Microchip for the BM83. I'm not an embedded C programmer at all. So a turnkey software solution that provides tones of bluetooth features without programming is a huge advantage for me. Do you suggest a different module? \$\endgroup\$ Commented Oct 1 at 21:49
  • \$\begingroup\$ You first need to be clear about your goals... are you trying to make a more sensitive microphone (birdwatching) or a more directive one, snr not important (voice isolation). In general with only two microphones you can't get useful gain or pattern control over a 3:1 band Remember that 3 dB of the gain you see is just by having two microphones added together, it makes them more sensitive but in all directions. (Test this by simulating with zero spacing, zero delay) \$\endgroup\$ Commented Oct 1 at 23:48
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    \$\begingroup\$ @Nolan What's the intended physical spacing of the two microphones? I skimmed, but may have missed seeing it in the TL;DR above. The greater than 3:1 ratio of 1 kHz to 300 Hz makes me wonder if you've attempted to plot out the subcardiod through hypercardiod patterns each frequency in that range yields, given any fixed spacing+inserted delay. Also, what makes you think you will get anything like 600 mV from an ecm arranged like that? \$\endgroup\$ Commented Oct 2 at 2:04
  • \$\begingroup\$ @Nolan (At 1 kHz \$\frac12\lambda\approx 17 \:\text{cm}\$ and at 300 Hz perhaps \$\frac12\lambda\approx 57 \:\text{cm}\$). \$\endgroup\$ Commented Oct 2 at 2:20

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Current is 500uA, not 3V/2K2 = 1.4mA. Function of the resistor is not intended to be current limiting - it is the impedance that the microphone (FET) drives. Without it, you would be trying to swing the supply voltage.

You need a bigger resistor if you are going to use it drop the voltage from 3.7 to 3. Maybe 3K5. This will turn the gain up, so you need to limit input swing to not take the voltage up to 3.7 when the FET goes to the "off" side.

I don't think you'll destroy the FET if you swing to 3.7V, but distortion will be worse.

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