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# State Variable active filter

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Hi,
I am trying to design a low pass state variable filter (non inverting) and i have no clue how to do it! Gain must be 20dB max, cut off at 1k, roll off at 40dB/decade. Does anybody have any design equations or circuits to assist me with this!

Thanks

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A roll-off of 40db can be stable. This will occur at a higher frequency. A capacitor affects the phase margin. The capacitor is also a gain element. A state variable device is just a filter with gain. Try not to confuse the 40db of the opamp with the 40db realized from the state variable filter.

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Designing your own filters requires a bit of calculation. You need to know what you expect for damping factor, Q, bandwidth, and gain as well as the center frequency. The standard State variable filter design uses 3 op-amps, which I think will give you an inverted output. If your design gives you an inverted output, all you have to do is add an op-amp buffer stage to change it. How much time do you have to learn this? You said you are trying to design one. What do you have so far?

MP

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Shmitt, here is the basic template for a state variable filter with gain. The 4th op-amp determines gain.
All of the calculations are on the schematic. All you have to do is plug in your frequency and a few other values and you have a state variable filter.

MP

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There is a simpler solution than the opamp. This sounds like a transistor capacitor transistor capacitor solution. Actually, I believe the filter should be of the inductor capacitor type. This way you can get rid of the resistors. Just remember that it is harder to measure the voltages with reactive components.

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It would take far too many transistors for a similar circuit to make such a design feasible, stable, and allow this kind of control to bandwidth, center frequency and damping factor.

MP

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An opamp is the amplifier of choice because it satisfies a few main requirements associated with electronics signal handling in general. Stability is normally dealt with as a result of the high frequency. The reactive components work better with discrete transistors.

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Here is what is inside the common LM741 op amp. With this in mind, your post does not really make a lot of sense. Perhaps I misunderstand?

MP

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High input impedance, high gain, differential input. This is what separates the opamp circuit from the discrete components. Why use the opamp if you don't need to utilize one of these characteristics?

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...as he said, he needed gain up to 20dB and roll off at 40dB/decade. Op amps are the best way to go to achieve this. If you can provide a similar circuit as you have mentioned using only transistor capacitor transistor capacitor, please post it so that we can see.

I think that it is only fair on this forum to ask if you are going to argue with proven design or a posted schematic that you should post your alternative method. Electronics deal in fact, not opinion.

MP

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A 40db per decade occurs at a high frequency and is the result of the transistor characteristics. Each capacitor section will give you 20db per decade. When you incorporate capacitors and inductors in various areas the db per decade can be tricky. I would first build the circuit, then determine the gain and the reduction of gain per decade. You will find that the inductor and the capacitor will give you the attenuation you need.

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Great! When do you think you will be posting the schematic for us?

MP

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I am aware of some of the problems with designing a circuit. You want one thing, but you turn around and end up negating it. You have meaing to the signal in one part, then you lose meaning when you make additions. I have an idea to correct for the nonlinearity of the transistor curve using it's inverse function. But I don't know how it can be done. Anyway, doesn't an LC filter give you 40db reduction. I really think trial and error helps a lot when determining db. If you head in the right direction and not worry exactly about the db then you can just test it with the circuit built. It must be a sorry situation when it comes time to guess because of the limitations of the measuring oscilloscope.

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• 2 weeks later...

Hi MP,

Thanks for the State Variable filter tutorial. As an audio engineer, I encountered this design a lot of times, however mostly with different values of C1 and C2.

Could you please explain me what's the effect of using different values for C1 and C2 and how it would be possible to determine the bandpass center frequency out of a given design with different values of C1 and C2?

PS I just got to know this forum; really inspiring!

Greetz,

Rogy

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Hi Rogy, welcome to the group!
Fc is the frequency of cut off for high and low pass, but it is the center frequency when you are using the band pass output.
The following formula applies to this filter:
Fc - 1 / (6.28 * R * C) where Fc is the centeror cut off freq., R is R2 through R9 in ohms and C = C1 = C2 is in farads. So, if you are looking for the relationship to C, you can rewrite the formula as C = 1/ (6.28 * R * Fc). If you have a filter that has already been built, you can plug in the R and C numbers and find the Fc from this formula.

MP

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I really like how someone posted the opamp schematic next to the state variable filter. I have been able to draw some conclusions about the opamp circuit in the past. I have guessed that the input transistors are low current. Am I right? So the variable filter really stumps me. I think this one of those circuits where the results are just good enough. I still don't see output bias. But I know that once again they will throw anything around an opamp. Sometimes you can get extra current by using low value resistors, but the impedance will be too low. Any suggestions?

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Tone control takes a very stable circuit. A circuit which just barely passes would not be workable in the audio field. It certainly would not allow you the ability to change a resistor or capacitor value and cover a wider range of frequencies.
Output bias is not needed.
You need more study of the op-amp before drawing such conclusions about how workable a design is. To answer your queries, look over the data sheet for the LM741. This is a pretty common op-amp. BTW, not low current transistors, high input impedance.

MP

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There exists more than one design for the opamp. I can't remember which part of the opamp is the high gain. Was it a pushpull at the front end or the middle part?

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It looks as though it is the front end. Am I right?

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• 15 years later...

There are three gain stages in a 741.  First stage is a differential.  Second stage is high gain as a darlington.  Third stage is a class AB power amplifier.  There are a few other features such as current limiting and a miller capacitor that helps to reduce oscillation.  There's a 39 kΩ resistor that sets the bias for the entire opamp.  It's pretty much genius and yet looks so simple.  Multiple current mirrors to keep everyhing just right... it's beautiful.

the SV filter is a biquad consisting of a summing amplifier and two integrators it is has second order response.  The integration of a HP creates a BP and the integration of the BP creates a LP.  Each stage is out of phase with one another... it again is simple to conceptualize but work of genius.  It gives you the ability to have 3 different filter output to TAP while giving you independent control over Q and ω.   You can also change Av but it will affect Q.  If you add another summing stage you can sum the LP and HP and get a great notch filter also.  This is a great filter for audio use with it's versatile controls and different filters.  It is also used in analog synthesizers due to it's versatility and the high Q you can achieve.

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