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I'm asked to find the order, type, number of poles and zeroes and the dc gain of the following filter:

enter image description here

Since the output of each integrator is the input both of the following and the preceding integrators, this filter is a leapfrog filter. In particular, I know from the theory that it is a low-pass filter implementing an all-pole low-pass ladder. As a consequence, there are no zeroes. The number of poles (and thus the order of the filter) is given by the number of integrators: 4.

I then have this equivalent circuit:

enter image description here

Now, I draw the corresponding flowgraph:

enter image description here

Considering the red loop, then by multiplying all the incoming branches by R and dividing all the outcoming branches by R, I can transform the currents into voltages. In particular, the state variables I2 and I4 become V2' and V4', respectively.

enter image description here

Question: is there an error in the exercise? Indeed, if you consider for example the output of the second integrator V2':

  • according to my flowgraph, V2' should go directly (+1) as input of the following integrator, and should be swapped (-1) at the input of the preceding integrator;
  • according to the exercise scheme, V2' gets swapped at the input of the following integrator, and goes directly (without swapping) at the input of the preceding integrator.
Stefanino
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    In recreating the schematic with RC cells, don't forget that the opamps provide buffering, which means that the output of the previous stage is not affected by the input of the next one. – a concerned citizen Nov 01 '20 at 23:18
  • For which purpose did you create the flowgraph? Are you interested, finally, in the transfer function? – LvW Nov 02 '20 at 08:39
  • Because in the slides of my Professor at first a passive all pole ladder is given. Then, by using flowgraphs, he finally comes to this leapfrog implementation. In this exercise it is the opposite: the final implementation is given. I thus tried to do the reverse operation (from active to corresponding passive implementation). Yes, I'm interested in the transfer function, which I thought to get from the corresponding passive implementation – Stefanino Nov 02 '20 at 09:42

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