benny_profane
Well-known member
I’d be interested in learning more about state variable filters and biquad filters if you’d want to expand the tone stack series.
[REQUEST] State Variable Filters
- Thread starter benny_profane
- Start date
Chuck D. Bones
Circuit Wizard
ok, will do
Chuck D. Bones
Circuit Wizard
I'll keep it simple, basically tell you what you need to know without getting into the math any more than is absolutely necessary.
A State Variable Filter (SVF) and a Bi-Quadratic filter are the same thing. An SVF is basically an analog computer that solves a 2nd-order differential equation. Here's one I designed:
U1A is a buffer and is not really part of the filter. I put it there to provide a high impedance at the input and a low impedance driving the filter.
U1D is a summing amp. It combines the input signal (via R3) and two feedback signals via R5 & R7.
U1C and U1B are integrators. They are like low-pass filters with a cutoff freq at zero Hz. U1C's time constant is equal to R*C where R is R8 + the FREQ pot and C is C3. The time constant of the integrators influences the Q and cutoff frequency of the filter. Notice that in this circuit the two integrators are identical and the FREQ pots are ganged together. That's important for reasons I'll get to in a minute.
An SVF has three outputs: High-Pass at the output of the summing amp (U1D), Band-Pass at the output of the 1st integrator (U1C) and Low-Pass at the output of the 2nd integrator (U1B). S2 is a DPDT ON-ON-ON switch used to select one of the outputs. It's also possible to get a Band-Reject (notch) filter output by combining the High-Pass & Low-Pass outputs.
I mentioned that there are two feedback paths back to the summing amplifier. The path from the 1st integrator back to the summing amp provides damping. Damping is the opposite of Q. The Q pot controls the damping of the filter.
The reason we gang the FREQ pots on the two integrators is that if the two integrators have the same time constant, then Q is constant for any FREQ setting.
We make R3, R4 & R7 equal to simplify the math. We make C2 & C3 equal for the same reason. When we do this, the SVF's frequency is equal to F = 1/(2*pi*R*C) where R = FREQ pot + R8 (or R9) and C = C3 = C4. The filter shown above can be tuned from 72Hz to 7.2KHz. The Q calculation is a little more complicated. Making the integrators equal and all of the other resistors equal simplifies things immensely. I made R = R3 = R4 = R6 = 10K and Rq = R5 + VR2. Then we end up with Q = 1/2 + Rq / (2 * R). Rq varies from 15K to 265K. When the Q pot is at max resistance, Q = 1/2 + 265K/20K = 13.75. When he Q pot is at min resistance, Q = 1/2 + 15K/20K = 1.25.
For pedals, the practical limit for Q is around 20. There are three reasons for that.
1. High-Q filters require precision components. The least precise component in the SFV is the dual-gang pot. Dual-gang pots do not track very well and any imbalance can cause the Q to vary. If the Q gets too high, the filter can break into oscillation.
2. The gain of the filter at resonance is proportional to the Q. If the Q gets too high we can run into headroom problems.
3. Filters with Q over 20 just don't sound very good (IMHO).
The Tychobrahe ParaPedal contains an SVF. Some envelope filters, such as the Mutron III and Maestro FSH-1, contain SVFs.
That's about it.
If you want to get deeper into the details, there is a good article here.
A State Variable Filter (SVF) and a Bi-Quadratic filter are the same thing. An SVF is basically an analog computer that solves a 2nd-order differential equation. Here's one I designed:
U1A is a buffer and is not really part of the filter. I put it there to provide a high impedance at the input and a low impedance driving the filter.
U1D is a summing amp. It combines the input signal (via R3) and two feedback signals via R5 & R7.
U1C and U1B are integrators. They are like low-pass filters with a cutoff freq at zero Hz. U1C's time constant is equal to R*C where R is R8 + the FREQ pot and C is C3. The time constant of the integrators influences the Q and cutoff frequency of the filter. Notice that in this circuit the two integrators are identical and the FREQ pots are ganged together. That's important for reasons I'll get to in a minute.
An SVF has three outputs: High-Pass at the output of the summing amp (U1D), Band-Pass at the output of the 1st integrator (U1C) and Low-Pass at the output of the 2nd integrator (U1B). S2 is a DPDT ON-ON-ON switch used to select one of the outputs. It's also possible to get a Band-Reject (notch) filter output by combining the High-Pass & Low-Pass outputs.
I mentioned that there are two feedback paths back to the summing amplifier. The path from the 1st integrator back to the summing amp provides damping. Damping is the opposite of Q. The Q pot controls the damping of the filter.
The reason we gang the FREQ pots on the two integrators is that if the two integrators have the same time constant, then Q is constant for any FREQ setting.
We make R3, R4 & R7 equal to simplify the math. We make C2 & C3 equal for the same reason. When we do this, the SVF's frequency is equal to F = 1/(2*pi*R*C) where R = FREQ pot + R8 (or R9) and C = C3 = C4. The filter shown above can be tuned from 72Hz to 7.2KHz. The Q calculation is a little more complicated. Making the integrators equal and all of the other resistors equal simplifies things immensely. I made R = R3 = R4 = R6 = 10K and Rq = R5 + VR2. Then we end up with Q = 1/2 + Rq / (2 * R). Rq varies from 15K to 265K. When the Q pot is at max resistance, Q = 1/2 + 265K/20K = 13.75. When he Q pot is at min resistance, Q = 1/2 + 15K/20K = 1.25.
For pedals, the practical limit for Q is around 20. There are three reasons for that.
1. High-Q filters require precision components. The least precise component in the SFV is the dual-gang pot. Dual-gang pots do not track very well and any imbalance can cause the Q to vary. If the Q gets too high, the filter can break into oscillation.
2. The gain of the filter at resonance is proportional to the Q. If the Q gets too high we can run into headroom problems.
3. Filters with Q over 20 just don't sound very good (IMHO).
The Tychobrahe ParaPedal contains an SVF. Some envelope filters, such as the Mutron III and Maestro FSH-1, contain SVFs.
That's about it.
If you want to get deeper into the details, there is a good article here.
Last edited:
fig
Village Idiot
Oh, well that clears things right up then.
What about that fourth notch filter eh?benny_profane
Well-known member
Thank you, @Chuck D. Bones, for the thorough write-up! So, the summing amp is vital to this architecture, right? What would happen if you don't feed the output of U1B and U1D back to the non-inverting input of U1D (i.e., removing the trace from pin 13 to C2)? I've seen some schematics that look like an SVF, but don't feed back to the non-inverting input.
EDIT: Inverting input.
EDIT: Inverting input.
Last edited:
Chuck D. Bones
Circuit Wizard
Pin 13 is the inverting input, so I'm not sure what you're asking.
If we break the feedback from U1B to U1D, then C4 will charge up until U1B saturates and no audio comes out of U1B. With only feedback from U1C, the filter becomes a 1st-order low-pass, pretty boring.
If we break the feedback from U1B to U1D, then C4 will charge up until U1B saturates and no audio comes out of U1B. With only feedback from U1C, the filter becomes a 1st-order low-pass, pretty boring.
benny_profane
Well-known member
Post amended. That was an error on my part.
Chuck D. Bones
Circuit Wizard
No problem. That's what I thought you meant, but wanted to clarify. My answer stands. Without all of the connections, the SVF is no longer an SVF.
Chuck D. Bones
Circuit Wizard
The notch is easy to implement, just connect two equal resistors from HP and LP to a NOTCH output. It gets much more interesting when we make those two resistors a pot so we can vary the ratio of HP to LP. This is what we get at the NOTCH output with FREQ at 6, Q at 3 and the HP/LP mix varying from 0 to 10. In a real circuit, the notches won't be quite so deep due to component tolerances. Imagine replacing a BMP TONE control with this!
Chuck D. Bones
Circuit Wizard
Right. Biquad & SVF are close cousins, but not the exact same thing.
