One more thing, state variable filter is also a descriptive name for the topology.
I should probably have been more explicit than just marking it with 5V in my original schematic. I was also negligent in not pointing out that V- is connected to ground, as we are operating with a single supply.
1. The complete analysis is based on linear network theory., it's valid as long as the OPs don't run into slew rate limitations or saturation. Please consider that you assumed ideal OPs, adding finite gain and bandwidth to the simulation would be the first step towards an exact analysis.1) OP amps usually are working in linear zone where Superposition Theorem can be applicable. But how do we know that this one is not working in the non-linear zone?
2) Blocks "C" and "D" have more zeroes than poles, which is not possible in LTI (linear time invariant) systems. How is that possible ? MATLAB do not accept to implement that kind of blocks to simulate it.
2. I'm unable to identify the zeros in the post #5 schematic, I presume an analysis error.
Calculating a transfer function for the "Vin1" reference input is surely possible, but what's the purpose?
The signal flow is taking the opposite direction, there's no actual zero in the transfer function.In equation 4, I have Va(s) and Vout(s), so I can get Vd(s)
The parameters can be set independently, but not by changing a single resistor. There are slightly different double-integrator filter topologies where you can change Q and G with a single resistor, each. To tune ω independently, you need a dual variable resistor in any case.This makes it impossible to decouple Q factor, resonant frequency and gain - though I think there's a good likelihood I may have an error in my algebra. Is it possible that this configuration does not allow for separately setting Gain,Q and Wn
In my derivation, where I replace each integrator with a 1/sRC response, I am able to get a biquad equation with a single zero at DC corresponding to the R1C1 pair, but both the damping factor and natural frequency involve a combination of almost all the resistors and capacitors.
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