Resonant Filters

[Gobotak]

I've been using the ssi2164 for high pass and low pass filters and am trying to add resonance.  My goal is to have separate low pass and high filters each with their own variable cutoff and resonance controls. I would be fine with each filter being a first order filter if that saves on the number of required components. 
This is what I have drawn up for the low pass filter:

I'm going for bandpass resonance to avoid passband attenuation when using increased resonance.  I'm wondering if the polarity of my resonant signal matters.  If I am understanding correctly, each filter stage results in a 45 degree phase shift at the corner frequency so I would get a phase shift of 90 degrees from the filters. I am using a VCA for the resonance so I get another 180 totaling 270.  If I added another inverter that would give me 450. Since neither is an integer multiple of 360 I would not get self-oscillation but would there be a difference between the two?
This is the high pass filter:

Again I am going for bandpass resonance but I am not sure if it is needed.  Would there be an attenuation of high frequencies with an increase in resonance? And do I need to be concerned with polarity if self-oscillation is not needed?
As is I would need 2 ssi2164s using 6 of the 8 VCAs leaving me two extra VCAs for other purposes.

[Gobotak]

I forgot to put this in the first post:  https://www.soundsemiconductor.com/downloads/AN701.pdf
There is a lot of great information in this document that I have been using as a guide.

[Digital Larry]

Not sure about the other details but you can't get resonance with a first order filter.

[Gobotak]

Since I'm new to filter design would you be willing to elaborate on that a bit more?  In the low pass example my thought was that having second order band-pass feedback would give me resonance but it just would not self-oscillate.  As for the high pass filter would feeding the output back into the input not achieve any resonance?  Would there be resonance if there was second order band-pass feedback like in the example?

[Matthew Sanford]

I don't know enough, but you made me think to comments on Tom's FilterFX project page. He had stated " e.g. bigger resistance = less signal = less damping = more resonance.". For that pedal, it is a dual lpf for lp, bp, and hp options.

at here, hope it helps lead you along with ideas

[PRR]

Don Lancaster Active Filter Cookbook is a good basic practical (and best selling) filter theory reference.
https://www.tinaja.com/ebooks/afcb.pdf

[ElectricDruid]

It looks a lot like you've been reading the SSI application note about designing analog filters with the SSI2164:

https://www.soundsemiconductor.com/downloads/AN701.pdf

...and quite right too! It's a fantastic document! It's pretty much a summary of about 30 years of synth filter history in about as many pages.

I would be fine with each filter being a first order filter if that saves on the number of required components.

No, I think you've taken the right path going with 2-pole filters in both cases. You won't get effective feedback with a single pole filter.

This is what I have drawn up for the low pass filter:

I'm going for bandpass resonance to avoid passband attenuation when using increased resonance.  I'm wondering if the polarity of my resonant signal matters.

The filter looks good to me. It's basically two stages of the classic four-stage synth filter, with the pole-mixing bandpass feedback from Fig.33 in the app note.
I notice you've halved the value of your R56 feedback resistor though. What's the purpose of that?
In general, the polarity of the resonant signal *always* matters! If it's not right, it won't resonate!

If I am understanding correctly, each filter stage results in a 45 degree phase shift at the corner frequency so I would get a phase shift of 90 degrees from the filters.

Correct.

I am using a VCA for the resonance so I get another 180 totaling 270.

No. The *VCA* itself is inverting, but it's followed by an I-to-V op-amp stage (U4.2 in your lowpass schematic) which is also inverting, so there's no net inversion through the typical whole 2164 VCA schematic. <later note>I'm wrong! see further down the thread!
Whether 90 degrees is better than 270 I can't tell you. I agree with you that it doesn't *seem* like it matters, but a practical experiment would be the way to know for sure. Theory's great n'everyfing, but you can't beat a real-world bench test...

This is the high pass filter:

Again I am going for bandpass resonance but I am not sure if it is needed.

For the classic 4-pole case, the highpass version of the filter has the same problem as the lowpass version - the fed-back passband signal cancels the signal coming through the filter. So yes, I'd guess the bandpass feedback improves the situation for the highpass circuit just the same too.

As is I would need 2 ssi2164s using 6 of the 8 VCAs leaving me two extra VCAs for other purposes.

Yep! 3 VCAs needed for each two-pole filter with VC-resonance, and two left over for actual VCA duties, maybe?!

[Gobotak]

Thanks for the help and suggestions!

It looks a lot like you've been reading the SSI application note about designing analog filters with the SSI2164:
https://www.soundsemiconductor.com/downloads/AN701.pdf
...and quite right too! It's a fantastic document! It's pretty much a summary of about 30 years of synth filter history in about as many pages.

Yep! It has been a great resource for learning how to set up filters with this chip.

I notice you've halved the value of your R56 feedback resistor though. What's the purpose of that?

I copied from a different schematic and forgot to change the value.  Whoops.

No. The *VCA* itself is inverting, but it's followed by an I-to-V op-amp stage (U4.2 in your lowpass schematic) which is also inverting, so there's no net inversion through the typical whole 2164 VCA schematic.

I was thinking the VCA itself was not inverting from page 4 of the ssi2164 datasheet:
https://www.soundsemiconductor.com/downloads/ssi2164datasheet.pdf
"For audio level applications where the VCA is used only to vary the signal level (e.g., mixer automation, synthesizer VCA module, etc) the combination of SSI2164 VCA and
opamp (Figure 1) produces an output whose phase is inverted."
Am I misunderstanding this?

Regarding phase shift, would the phase shift of a high pass filter be 45 degrees or 90 degrees?  The document states that single pole filter stages are 45 and an all pass is 90.  A high pass and all pass are identical except for one resistor being halved.

[ElectricDruid]

I was thinking the VCA itself was not inverting from page 4 of the ssi2164 datasheet:
https://www.soundsemiconductor.com/downloads/ssi2164datasheet.pdf
"For audio level applications where the VCA is used only to vary the signal level (e.g., mixer automation, synthesizer VCA module, etc) the combination of SSI2164 VCA and
opamp (Figure 1) produces an output whose phase is inverted."
Am I misunderstanding this?

No, I've checked and you're right and I'm wrong. Sorry about that. The VCA itself doesn't invert, but the whole thing does. I had it back-to-front.

Regarding phase shift, would the phase shift of a high pass filter be 45 degrees or 90 degrees?

45 degrees at the cutoff freq.

The document states that single pole filter stages are 45 and an all pass is 90.  A high pass and all pass are identical except for one resistor being halved.

That's true, but that one resistor value makes a big difference to the overall frequency response, as well as the phase!
Perhaps a more intuitive way of thinking of it is that halving that value doubles the amount of that signal in the mixture. That makes the significant change a lot more comprehensible (to me, at least ).

[Gobotak]

No, I've checked and you're right and I'm wrong. Sorry about that. The VCA itself doesn't invert, but the whole thing does. I had it back-to-front.

45 degrees at the cutoff freq.

That's true, but that one resistor value makes a big difference to the overall frequency response, as well as the phase!

Thanks for clarifying!

I drew up a few more examples with the goal of achieving self oscillation:
The first one is a low pass filter.  It is the same one as the first one I posted but with an extra all pass filter added in the resonance path to get the required 360 degree phase shift.  With this setup I would have a one/two pole low pass filter with second order resonance capable of self oscillating?


This one is the high pass version:


The last one is a one/two pole high pass filter with 4th order resonance that should still be capable of self oscillation:


The down side is it requires an extra VCA.  If I were to do a low pass version I think I would just use figure 32 from the application note.

I have a lot of experimenting to do.  There could be a more elegant or clever way of doing things but I want to make sure my head is at least a little bit in the right place.