[SOLVED] Transfer function - some very long and tricky computation

[Phoibus]

Hello.

I am designing a general FLF filter topology. I need it for filter design with genetic algorithms, so I thought the topology should be as general as possible. Consequently, I added leap=-frog connections of all possible orders (2, 3...etc).

I have attached my schematic for a FLF with 8 integrators.

Now, I was trying to write the transfer function (hand calculation), and get a general equation so as to extend it to n integrators. Mathematical induction seemed to be the solution, but at some point I lost track.

If you have a solution to this "exercise", could you please help me?

Thanks a lot!!!

 

[LvW]

Hi PHOIBUS,

I don't know if it helps, please find attached (pdf-doc) a block diagram and the corresponding transfer function for a generic
Follow-the-leader topology.

 

[Phoibus]

OK, finally I've got it

The best solution is actually with Mason's rule. OpAMP + C form a losless integrator which will be the direct gains of a block diagram/signal flow graph. Feedback gains are the feedback resistor values (assuming the resistors at the OpAMP inputs are unity). Then Mason's rule is straightforward.