### MMR-40 Active Audio Filter U8b

## MMR-40 Active Audio Filter U8b

U8b of the MMR40 provides a band pass audio filter, which has a peak at around 600 hz.

It consists of the following components:

- U8b Op Amp
- R42 Feedback Resistor
- C72, C73 Feedback Capacitors
- R40, R41 Input Resistors

In this circuit, S1 bypasses u8b for wide response, or includes u8b for narrow.

R42 and C73 form a high pass filter, while C72 and R40,R41 form a low
pass filter. These two filters combine to create the bandpass filter.

From http://www.ecircuitcenter.com/Circuits/MFB_bandpass/MFB_bandpass.htm, we can see some formulas to help evaluate this circuit.

Rin = (R40*R41)/(R40+R41) = (47k*1.5k)/(47k+1.5k) = 70.5k/48.5k = 1.45k

So, in this case, our center frequency:

Co = 1/(2*PI*C*(sqrt(100000*1450)))

C0 = 1/(2*PI*C*12041.6)

C0 = 1/(0.000000138*12041.6) = **600.77 hz**

Q = 0.5 *(sqrt(R42 /Rin))

Q = 0.5 *(sqrt(100000/1450)

Q = 0.5 * 8.30

**Q = 4.15**

The expected bandwidth given various Q factors are given here:

- Q = 1 = 6db per octave
- Q = 5 = 18 db per octave
- Q = 10 = 24 db per octave
- Q = 50 = 40 db per octave

So Iâ€™m guessing **about 15 db rolloff** for a Q of 4??

**The gain should be approximately equal at 300hz and 1200 hz at about 15db down from the peak.**

BW = 2/(R42*C)

BW = 2/(100000*0.000000022)

BW = 2/0.0022

**BW = 909 hz**

This agrees with our Q calculation bandwidth (1200hz - 300 hz = 900hz)

So, we would expect a **bandpass centered on 600 hz, with the the gain at about 0.707 of the center at 300hz and 1200hz**

Midband Gain H0 = R42/(2*Rin)

H0 = 100k/(2*47k) = **~1.0
**This stage provides no gain, the signal is no louder with the filter in than it is with the filter out.

So lets see if this all works out in a ltSpice model

The Spice plot shows that the signal at the following levels:

- 300hz -93db
- 603hz-76db
- 1200hz-89db
**Difference from passband edges to center 13db - 17db**

That's pretty close to what we predicted. The bandwidth might be a little bit narrower than predicted, but it's not too far off.

Then lets see how the real world looks, compared to our theoretical world

Inputting our noise source into u8b input gives the following output:

The absolute levels are different due to the amount of input signal we put in, vs how much we used in the spice simulation.

Only their relative level to each other is important.

Our Real World results:

- 300hz -60db
- 600 hz -45db
- 1200hz -61db
**Difference from passband edges to center 15db**

So that's pretty good correlation from basic electronics math to real-world results. It's always good to see that.

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