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Is oscillation bad for an active audio filter?

Super-Dave

Member
I am TRYING to build a 5 band audio spectrum analyzer for my car. I'm still in the design phase, working out resistor & capacitor values for the bandpass filters. I've chosen to go with 3rd order(single op-amp) Sallen Key low pass filters cascading into a 3rd order(also single op-amp) Sallen Key High pass filters due to their steep roll-off and flat pass band characteristics, but also reduce the component cost, complexity & real estate needed for the circuit board layout. I intend to use one quad op-amp as a buffer, and a single quad op-amp for each bandpass (this is going to be a stereo display, with left & right being handled by each half of the quad op-amp). This way I'll only need a total of 6 op-amp chips. I've found numerous websites to help me calculate the low pass & high pass filters, yet most of them spit out insane values that I don't possess in my assortment kits.

However, I have found one site that will crank out actual values I do have (mostly), the final results are close to the frequencies I want and it even shows a bode plot.

http://sim.okawa-denshi.jp/en/Fkeisan.htm

It even tells me if it oscillates and at what frequency.

A couple questions I want to know is:
1) Is oscillation bad for an audio filter? Will it create wonky strobing or glitchy performance in the LED display? Or is it just a momentary transient thing that I need not be concerned with? This is just for a visual display, not speakers so if there's distortion, I won't hear it.
2) I've discovered that I can input MATCHING values (all caps & resistors being the same), and it won't oscillate, but the bode plot no longer resembles a sharp 3rd order response. The "knee" frequency at the -3db point is right, but it doesn't give a sharp enough dive for my liking. Or maybe I don't understand how to read it properly, the frequencies are listed in scientific notation, not actual hertz. Can you make cascading filters (low pass or high pass) with matching values and get the performance desired?


Thank you in advance for your replies.
Super-Dave
 

audioguru

Well-Known Member
Most Helpful Member
A properly designed audio filter does not oscillate.
You need a filter with parts values that produce a sharp corner and a flat response before or after the filter that is called Butterworth. I cannot remember what is its "damping" number.
 

audioguru

Well-Known Member
Most Helpful Member
He is making 3rd-order filters. 3rd order lowpass filter.PNG
 

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audioguru

Well-Known Member
Most Helpful Member
The 1st stage of a Sallen-Key 3rd-order filter does not have an opamp with R1 and R2 setting its gain. Instead it is passive.
 

danadak

Well-Known Member
Most Helpful Member
Prior prior post was based on this, a cascade of a 2 pole active and a passive (Ra2, Ca2) -

1646997310546.png


The order of stages, in this topology, 1 passive pole first or 1 passive pole last, is irrelevant.
Unless of course one is taking output at intermediate stage as well as output stage, for
some other purpose.

Regards, Dana.
 

LvW

New Member
2) I've discovered that I can input MATCHING values (all caps & resistors being the same), and it won't oscillate, but the bode plot no longer resembles a sharp 3rd order response. The "knee" frequency at the -3db point is right, but it doesn't give a sharp enough dive for my liking. Or maybe I don't understand how to read it properly, the frequencies are listed in scientific notation, not actual hertz. Can you make cascading filters (low pass or high pass) with matching values and get the performance desired?
Yes - it is correct that Sallen-Key-topologies can be realized with equal components (2 equal R and two equal C). However, in this case the non-inverting gain must not be larger than "3" - and the whole transfer function is very sensitive to gain variatons/tolerances. This is the price you have to pay for these "matching conditions".
There is an alternative with much better properties - this is the "gain-of-two" alternative.
 

danadak

Well-Known Member
Most Helpful Member
Sensitivity analysis for the SK filter -




Regards, Dana.
 

audioguru

Well-Known Member
Most Helpful Member
A Butterworth filter has the RC values producing critical damping that has a flat response and a sharp corner.
A 2nd-order Bessel filter with a gain of 1 has equal RC values producing over damping with a drooping response and a gradual corner. Adding a 3rd RC to a Bessel Filter makes it more droopy.
A 2nd-order filter with equal RC values can have a gain of 1.586 to have a sharp Butterworth response.
 

audioguru

Well-Known Member
Most Helpful Member
Prior prior post was based on this, a cascade of a 2 pole active and a passive (Ra2, Ca2) -

The order of stages, in this topology, 1 passive pole first or 1 passive pole last, is irrelevant.
Unless of course one is taking output at intermediate stage as well as output stage, for
some other purpose.

Regards, Dana.
I have never seen a 3rd-order Sallen-key filter with an extra opamp.
 

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Super-Dave

Member
Yes - it is correct that Sallen-Key-topologies can be realized with equal components (2 equal R and two equal C). However, in this case the non-inverting gain must not be larger than "3" - and the whole transfer function is very sensitive to gain variatons/tolerances. This is the price you have to pay for these "matching conditions".
There is an alternative with much better properties - this is the "gain-of-two" alternative.
So I should test the components with a multimeter 1st and make sure they match to, what, say 2 decimal places?

I'm going non-inverting unity gain on all my filters. My opamp of choice is a TH074, supposedly they are susceptible to phase inversion if the low end of the sine wave swings too close to the lower power rail. Since I'm using a +/- 15v split power supply and the input is coming from a 12v automotive stereo head unit pushing 50w max thru 4 channels (maybe 13w RMS), I figure I'm within the safe margin of those opamps. I am aware that Sallen Key topology becomes unstable over a gain of 3.

I am also aware that the higher frequencies may not have a much voltage behind them due to their limited "area under the curve", resulting in less LEDs lighting up. In such a case, it may become necessary to bump the gain up, possible as much as double. We will see during breadboard testing. I'm thinking I may boost it at the buffer stage then use trim pots to attenuate the signal before going into the bandpass filters.
 

Super-Dave

Member
So what is the difference between Bessel & Butterworth? Both look the same in that the resistors & caps are placed identically. Is it the math? The values of the caps &/or the resistors? I don't understand.
 

Super-Dave

Member
And what IF they weren't a dead on match & it became unstable? What would that mean? How would that manifest in the display? Would it quit working altogether? Explode? Or would it rip another hole in space-time like what happened when I programmed my laptop computer to divide by zero?
1647092517204.jpg
 

danadak

Well-Known Member
Most Helpful Member
So what is the difference between Bessel & Butterworth? Both look the same in that the resistors & caps are placed identically. Is it the math? The values of the caps &/or the resistors? I don't understand.

Above might help.

Regards, Dana.
 

danadak

Well-Known Member
Most Helpful Member
So I should test the components with a multimeter 1st and make sure they match to, what, say 2 decimal places?

I'm going non-inverting unity gain on all my filters. My opamp of choice is a TH074, supposedly they are susceptible to phase inversion if the low end of the sine wave swings too close to the lower power rail. Since I'm using a +/- 15v split power supply and the input is coming from a 12v automotive stereo head unit pushing 50w max thru 4 channels (maybe 13w RMS), I figure I'm within the safe margin of those opamps. I am aware that Sallen Key topology becomes unstable over a gain of 3.

I am also aware that the higher frequencies may not have a much voltage behind them due to their limited "area under the curve", resulting in less LEDs lighting up. In such a case, it may become necessary to bump the gain up, possible as much as double. We will see during breadboard testing. I'm thinking I may boost it at the buffer stage then use trim pots to attenuate the signal before going into the bandpass filters.
Looks stable, example G = 5. But design is not your freq.....

1647096528123.png




Number tools refed in article - https://www.edn.com/a-sallen-key-low-pass-filter-design-toolkit/

Regards, Dana.
 
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audioguru

Well-Known Member
Most Helpful Member
So what is the difference between Bessel & Butterworth? Both look the same in that the resistors & caps are placed identically. Is it the math? The values of the caps &/or the resistors? I don't understand.
When the opamp gain is 1, a 2nd-order Sallen-Key Butterworth filter has the feedback capacitor value for a lowpass filter twice the value of the capacitor to ground, or the feedback resistor for a highpass filter half the value of the resistor to ground.

When a Butterworth filter or an equal values Bessel filter has gain then there is a peak in the frequency response that oscillates when the gain is a little higher than 3 times.
 

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Super-Dave

Member
Well then, the answer seems obvious. To avoid instability, ripple or oscillation, any gain desired should be outside the filters, either in the buffer stage or afterwards. Since I intend to keep all the filters at unity gain, it shouldn't be a problem.

Let me see if I get this straight, the big difference from Bessel & Butterworth are mainly dependent on the ratios of the caps or resistors in the feedback loop vs ground? A ratio of 2:1 or better is Butterworth, less is Bessel? Then what is a sub-Bessel?
 

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