I was asked to find out why this Treble Boost Filter is really a 3khz sinewave oscillator?
I think I can figure out why it's an oscillator:
The negative feedback set up of the circuit means the output is 180 deg out of phase with the inverting input at low to mid frequencies (assuming non inverting terminal grounded), but as the frequency gets even higher the op amp introduces a 90 deg phase shift meaning the output becomes a total of 270 deg out of phase. The RC network introduces another 90 deg phase shift at frequencies above cut off (usually in the region of 10xFo from simulations) and so you've got a total phase shift around the feedback loop of 360 deg which will reinforce the oscillation, is this right?
Also im thinking the RC network will attenuate the signal and so the open loop gain of the Op amp at the oscillation frequency must be high enough to counter this. If all this is correct, I'm not sure how we get to the actual value of 3khz for oscillation. I checked the data sheet on the 741 op amp and it appears to introduce a 90 deg phase lag way before 3 khz so again im not sure where 3khz comes from.
I've found some other examples on the web of formulas which look like they contain 2*pi*RC*sqrt(n) where n is the number of filters in the feedback loop, but I'm not sure if this applies.
Finally I tried looking at the RC network from an impedance point of view and worked out the capacitor behaves like a 530 ohm resistor at 3khz. In the potential divider this means it degrades the voltage of the op amp by a factor of 5000. This feels like the right ball park, because the open loop gain of the op amp at 3khz looks to be about 60db = 1000. Still a factor of 5 off though? The RC network is still degrading the signal integrity by a factor of 5 even after the op amp boosts it. So i'm a bit stuck now, what should I try next?
Thanks In advance,
Megamox
I think I can figure out why it's an oscillator:
The negative feedback set up of the circuit means the output is 180 deg out of phase with the inverting input at low to mid frequencies (assuming non inverting terminal grounded), but as the frequency gets even higher the op amp introduces a 90 deg phase shift meaning the output becomes a total of 270 deg out of phase. The RC network introduces another 90 deg phase shift at frequencies above cut off (usually in the region of 10xFo from simulations) and so you've got a total phase shift around the feedback loop of 360 deg which will reinforce the oscillation, is this right?
Also im thinking the RC network will attenuate the signal and so the open loop gain of the Op amp at the oscillation frequency must be high enough to counter this. If all this is correct, I'm not sure how we get to the actual value of 3khz for oscillation. I checked the data sheet on the 741 op amp and it appears to introduce a 90 deg phase lag way before 3 khz so again im not sure where 3khz comes from.
I've found some other examples on the web of formulas which look like they contain 2*pi*RC*sqrt(n) where n is the number of filters in the feedback loop, but I'm not sure if this applies.
Finally I tried looking at the RC network from an impedance point of view and worked out the capacitor behaves like a 530 ohm resistor at 3khz. In the potential divider this means it degrades the voltage of the op amp by a factor of 5000. This feels like the right ball park, because the open loop gain of the op amp at 3khz looks to be about 60db = 1000. Still a factor of 5 off though? The RC network is still degrading the signal integrity by a factor of 5 even after the op amp boosts it. So i'm a bit stuck now, what should I try next?
Thanks In advance,
Megamox