# Possible to use varicap in a Sallen Key filter?

#### Angakok Thoth

Joined Sep 5, 2016
16
I designed a special audio filter (unusual filter for unusual purpose. to make it short, I will not go into details, but I attached the schematic).
I would like to control one "parameter" (won't go into details) of the filter using a control voltage and I found, that using the Sallen-Key topology, exactly that parameters changes when I am changing the values the C1=C2 capacitors. **
So I wonder - would it be somehow possible to use varicaps (sometimes also called varactor diodes) in the place of C1 and C2 and control their value by adding DC bias voltage to the audio signal?
How would I do that?
Do I add the control voltage/bias to the audio signal? Or should I feed it into some node next to the vari-capacitors?
Also, I use bipolar supplies and so the audio is between -5v and +5v... and while the varicap is really a diode, that could also be a problem, as only half-waves would get through such vari-capacitor.

** or also when changing values of all the resistors, while sustaining the ratio between them. there are 5 resistors per stage and there will be at least 8 stages in the final circuits, so using VCA or a transconductance amplifier instead of each resistor would be quite insane.

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#### kubeek

Joined Sep 20, 2005
5,796
Applying bias to the input might work, but I am not sure how this will affect the bias on the output. Anyway, the signal will need to have very low amplitude in order not to change the capacitances.

#### AlbertHall

Joined Jun 4, 2014
12,396
You can separate the varactor bias from the rest of the circuit by adding C1 and R2 as below. C1 should be large compared to the diode capacitance, perhaps 0.01uF and the resistor should be large compared to the other resistances in the circuit, perhaps 1-10M but check the diode leakage current and how much voltage that would drop across R2.

#### crutschow

Joined Mar 14, 2008
34,840
The trick is to find a varactor with sufficient capacitance to have a significant effect on the filter parameters at audio frequencies.

#### Angakok Thoth

Joined Sep 5, 2016
16
The trick is to find a varactor with sufficient capacitance to have a significant effect on the filter parameters at audio frequencies.
That shouldn't be a problem, because I am able to redesign the filter to use resistors of higher values and capacitors of lower values.

#### Angakok Thoth

Joined Sep 5, 2016
16
You can separate the varactor bias from the rest of the circuit by adding C1 and R2 as below. C1 should be large compared to the diode capacitance, perhaps 0.01uF and the resistor should be large compared to the other resistances in the circuit, perhaps 1-10M but check the diode leakage current and how much voltage that would drop across R2.
View attachment 113082
Thanks a lot.
So the C1 will have zero effect on the audio filter if the capacitance is high enough?
But what about the D1 in audio path and the fact, that the audio input of the circuit is bipolar (between -5V and +5V) ?
(+i assume that you did not ground the GND node on the diagram just by mistake and not for some purporse.)
Going to try it in simulations.

#### AlbertHall

Joined Jun 4, 2014
12,396
The input voltage must be small compared to the diode bias voltage as otherwise the capacitance will change with the signal voltage so a 10V P-P input is definitely a no-no.

#### kubeek

Joined Sep 20, 2005
5,796
It might be better to use analog switches and switch capactiors in an out instead of doing it with varicaps. This setup will probably be very noisy since it needs very low signal levels (maybe 10mVpp?).

#### Angakok Thoth

Joined Sep 5, 2016
16
It might be better to use analog switches and switch capactiors in an out instead of doing it with varicaps. This setup will probably be very noisy since it needs very low signal levels (maybe 10mVpp?).
Thanks for your answer. I have to say that I thought about that already and tried to find some info, but everywhere I looked, the switched capacitors were used only instead of a resistor and not instead of a capacitor.
So how exactly would I do that? Lets assume I want a variable capacitor in 220pF to 1220 pF range. (moved the range higher, to make the parasitic capacitance of analog switches less significant).

Using 220pF fixed capacitor with SPST switch + 1000pF capacitor in parallel and control the switch using PWM?
So when the PWM is 0%, switch is off all the time => capacitance 220pF
When PWM is 100%, switch is off all the time => capacitance 1220pF
PWM 50% and switching fast enough above audio range, I would perhaps kind of get (1220+220)/2=610 pF
But only in my imagination and I was not sure how to verify in simulation without complex breadboarding. I tried, but was never successful simulating these switching things in LTspice. (Also the tutorials which i found about switching in LTspice were about the traditional frequency controlled switching capacitor used as resistance filters.).

So, would that work?
And even if it does (or does not), what are other possible ways of implementing a switching capacitors that act like a variable capacitor?

Thanks a lot.

#### crutschow

Joined Mar 14, 2008
34,840
Here's a varactor with a relatively high maximum capacitance and a high adjustment range ratio.

Below is an LTspice simulation of a Sallen-Key HP filter using two of those varactors, showing the variation in corner frequency for varactor DC voltages of 1.2V, 3.5V, 6V and 8V reverse bias.

The NTE618 model here is one for which I empirically generated values for Cjo, M, and Vj to approximately match the capacitance versus reverse bias voltage on the data sheet. The other parameters are not necessarily accurate.
.model NTE618 D(Is=1.365p Rs=1 Cjo=800p M=15.2 Vj=30 Isr=16.02p Nr=2 Bv=16 Ibv=10u Vpk=16 mfg=NTE type=varactor)

#### crutschow

Joined Mar 14, 2008
34,840
................................
Using 220pF fixed capacitor with SPST switch + 1000pF capacitor in parallel and control the switch using PWM?
So when the PWM is 0%, switch is off all the time => capacitance 220pF
When PWM is 100%, switch is off all the time => capacitance 1220pF
PWM 50% and switching fast enough above audio range, I would perhaps kind of get (1220+220)/2=610 pF
But only in my imagination and I was not sure how to verify in simulation without complex breadboarding. I tried, but was never successful simulating these switching things in LTspice. (Also the tutorials which i found about switching in LTspice were about the traditional frequency controlled switching capacitor used as resistance filters.).

So, would that work?
And even if it does (or does not), what are other possible ways of implementing a switching capacitors that act like a variable capacitor?
No, you can't use PWM with a capacitor to get a variable capacitance.

You would need to use the standard switched-capacitor configuration to substitute for the resistors in the circuit.
Changing the switching frequency changes the equivalent resistance of the switched-cap.

#### kubeek

Joined Sep 20, 2005
5,796
That is not what I meant at all. My idea was to have a set of say 6 capacitors, something like 1000pF, 500pF, 250pF, 125pF, 62.5pF and 31.25pF and use analog switches to connect them in parallel in order to get any value from ~30pF to ~2000pF in 64 steps.

#### crutschow

Joined Mar 14, 2008
34,840
That is not what I meant at all. My idea was to have a set of say 6 capacitors, something like 1000pF, 500pF, 250pF, 125pF, 62.5pF and 31.25pF and use analog switches to connect them in parallel in order to get any value from ~30pF to ~2000pF in 64 steps.
All those exact values are not standard of course.

#### Angakok Thoth

Joined Sep 5, 2016
16
That is not what I meant at all. My idea was to have a set of say 6 capacitors, something like 1000pF, 500pF, 250pF, 125pF, 62.5pF and 31.25pF and use analog switches to connect them in parallel in order to get any value from ~30pF to ~2000pF in 64 steps.
Thanks for an idea, but I need it to be as smooth as possible.

No, you can't use PWM with a capacitor to get a variable capacitance.

You would need to use the standard switched-capacitor configuration to substitute for the resistors in the circuit.
Changing the switching frequency changes the equivalent resistance of the switched-cap.
I see. Controlling resistances is possible more ways, but there are too many resistors. Would prefer achieving voltage controlled (non-stepped) capacitance somehow. Is varactor the only way to do that, or do I have some other options?

#### kubeek

Joined Sep 20, 2005
5,796
Thanks for an idea, but I need it to be as smooth as possible.
How smooth?

#### crutschow

Joined Mar 14, 2008
34,840
.....................
I see. Controlling resistances is possible more ways, but there are too many resistors. Would prefer achieving voltage controlled (non-stepped) capacitance somehow. Is varactor the only way to do that, or do I have some other options?
Not if you want to vary the capacitance electronically.

#### OBW0549

Joined Mar 2, 2015
3,566
I stand corrected.
Well, maybe not: the OTA's in the VCF-1 circuit aren't really varying the effective capacitances in the two integrators in the state-variable filter, they're varying the effective resistances at the inputs of the integrators.

THAT Corporation's line of Blackmer cell VCA's can also be used to make voltage-tunable filters, as in this application note. While that note only describes a first-order filter, extending it to a second-order filter is just a matter of adding another integrator stage.

#### Angakok Thoth

Joined Sep 5, 2016
16
I stand corrected.
That VCF doesn't have variable capacitance. It uses OTA (operational transconductance amplifier) instead of a resistor. That is the standard approach in synthesizezrs since the Moog times - replacing some Fc defining resistor with OTA (or nowdays more often with a VCA chip), or sometimes an opto-resistor coupled with LED. It works well within simpler 1st order filter topologies where changing one resistor changes the cutoff frequency. And yes, I could realize my filter that way too, but I would need twice as much opamps and also I would need as many OTAs as opamps. The parts count would increase dramatically as my final circuit has many stages. And the OTAs are also not hassle-less - they cannot stand high input voltages, so I would have to attenuate audio anyway. And they are current out devices, so more parts to convert that to voltage...
So what I am trying to achive is some more efficient way. In the topology I use, I need just one opamp to get 2 poles+2 zeroes (instead of two opamps). It's just that in this topology I can either voltage control 6 resistors at the same time (doable using the standard OTA way, but crazy as 6 is too much) or 2 capacitors (something I haven't seen done in this kind of circuits...maybe for some reason. maybe it won't be doable but at least i will learn).

Anyway, Thanks a lot for all the ideas.
I am designing a prototype PCB aleady.