# doubt on cutoff frequency

Discussion in 'Homework Help' started by prescott2006, Mar 13, 2010.

1. ### prescott2006 Thread Starter Active Member

Nov 8, 2008
72
1
1.base on calculation, the cutoff frequency of the multiple feedback filter is around 106Hz, but base on simulation, the cutoff frequency is not even reach 100 Hz. Can anybody explain to me?
2.even if it is 106Hz, it is also not make sense.because this is a guitar tuner circuit, and it should capture the frequency range between 82.4Hz to 329.6Hz. if cutoff frequency is 106Hz,then it would not be possible to detect the higher frequency.anyone got idea?
3. is it the gain of the inverting amplifier is -21? because it is using single supply, so i not sure whether my answer is correct or not.
4.if the gain is -21,why i input ac voltage 10mV p-p,then the output i obtain is only 42.23mV rms(simulation result)?

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2. ### steveb Senior Member

Jul 3, 2008
2,433
469
It's not clear to me why your simulation does not show something near 106 Hz for a peak response. I would suggest double checking the inputs to your simulation.

As far as I can tell, this circuit should have peak near 106 Hz and it should be fine for guitar.

Your input stage is a high pass filter with 500 Hz cutoff frequency. Your second stage is a bandpass filter with resonance at 106 Hz. Based on this, I expect a very sharp roll off at low frequency (60 dB per decade). Then you should see a peak response near 106 Hz. Then you should see a mild roll off above 106 Hz because the bandpass is rolling off as a second order response rate, while the high-pass is increasing at first order response rate. Then above 500 Hz. the high pass filter flattens out and you should see a 40 dB per decade roll off above 500 Hz, from the bandpass filter.

Hence, you will have acceptable response for a guitar. This circuit will help boost the low frequency end for the bass strings, but your high notes will still be heard fine. Upper harmonics on notes will be reduced substantially, so you may or may not like the sound. What ultimately matters is how this circuit combines with other elements in the system to produce the final sound.

3. ### prescott2006 Thread Starter Active Member

Nov 8, 2008
72
1
my first stage is configured as a inverting amplifier, why you say it is a high pass filter? and the second stage supposed is a low pass filter. care to explain more?

4. ### steveb Senior Member

Jul 3, 2008
2,433
469
The capacitor on the input of the first stage turns it into a high pass filter. A quick calculation reveals the cutoff frequency as follows.

$f_c={{1}\over{2\pi R_1 C_1}}$ where R and C are the input capacitor and input resistor. In this case you have 68 nF and 4700 ohms which yields a 500 Hz cutoff frequency.

I believe you are correct about the second stage. It does appear to be a second order low pass filter. Sorry about that mistake. The formula for the cutoff frequency is

$f_r={{1}\over {2\pi \sqrt{R_6 C_3 R_7 C_4}}}$

Based on this, I expect the net effect of both filters to behave like a bandpass filter with resonance at 106 Hz, and then an additional first order roll off will kick in at 500 Hz.

This should still be acceptable for guitar, but will likely create a bass-heavy sound, unless other compensation is put in.

5. ### prescott2006 Thread Starter Active Member

Nov 8, 2008
72
1
the best i can think is the first stage is act as inverting amplifier beside is a high pass filter. because the guitar input amplitude is very small, it's not make sense if does not have an amplifier.am i correct? by the way, so the two filter will capture the range between 106 -500 HZ? but the 6 guitar string should be from 82.4 -329.6Hz. then how come the circuit will work? very confuse about this.

6. ### steveb Senior Member

Jul 3, 2008
2,433
469
First, you are correct about the amplification. I didn't mean my comment to imply that the first stage did not amplify as well as filter. I thought that the amplification factor is obvious and didn't think to comment on it.

Second. I think a guitar requires more than 329 Hz response. Consider that the A note on the first string (5th fret) is 440 Hz, and the 17th fret is 880 Hz. Also, there is a need to reproduce the upper harmonics which implies that often 2000 Hz or 4000 Hz is needed for good quality.

However, if other system components have their own response, or if you are trying to get a particular sound/effect, a circuit like this one is not out of the question. It's hard to say more without more details. Keep in mind that you will still hear sounds above 500 Hz, it's just that they may sound attenuated.