# How are the gain and corner frequencies calculated for this speech bandpass filter?

This speech bandpass filter circuit appears in the TI OPA344 datasheet. It says "G = 100" and passband is 300 Hz to 3 kHz. How is the gain and corner frequencies calculated from the various component values? I'd like to try this circuit but I only need a gain of 5 and I might want to tweak the passband. I think I see that R7 and C2 form a first order low pass filter with a corner frequency of 3120 Hz. And I believe R6 and R5 produce a gain of (1 + R6/R5) = 6. But I don't understand the rest of the circuit. Where is the rest of the gain and the high pass filter?

• By initial inspection the gain seems to me to be 50, not 100. To calculate the transfer function start with 6*Vin at the left side of R7, and Vin at the right side of R8. Write KCL at the junction of R7 + R8, then use the voltage across C3 to get another expression linking Vout to the voltage on C2 and solve the whole mess for Vo/Vin. – John D Mar 21 '14 at 18:13
• Brian is correct, I overlooked R4 when I first glanced at the circuit, pretty close to a gain of 100. – John D Mar 21 '14 at 18:43

## 1 Answer

The main part of the filter (sectioned in red below) is a modified MFLP filter and not a Sallen-key filter: - I've used Mr. Okawa's web site for doing the analysis and it tells me that the cut-off frequency is about 3.2kHz and there should be no peaking because the Q (or damping ratio if you did the math) is about optimum for flat response ($\frac{1}{\sqrt2}$).

The high pass stage is at the input with C1 and R2//R3. This works out at 318 Hz for it's 3dB point.

One slight modification to the general type of circuit is the 2nd op-amp (that forms the MFLP filter) receives mid-rail bias from R2 and R3 but also a smidgin' of input signal. This doesn't alter the frequency response too much but does subtract 1 from the calculated gain of the 2nd stage. Okawa calculated it at 10 when I believe, with the modification it will be 9. The first op-amp stage gain is 11 and the total gain (at mid-frequency) will be 99 and not 100!

• Thank you. I mistakenly ignored C1, R2, and R3 because I've seen that repeatedly (as a coupling capacitor and setting the mid-rail voltage) in other electret mic preamp circuits. But now I see that it is also a high pass filter. And the MFLP is new to me. – kkrambo Mar 22 '14 at 2:55