Hi all

I have to obtain the transfer function,ie Vout/Vin, of this circuit:

I am aware of the y-delta transformation, and I eventually get a structure like this:

I tried to perform nodal analysis at the ground since I don't know what current flows into or out of the Vin and Vout terminals.
(Vin-0)/Zb = (Vin-0)/Zc, but since Zb=Zc in my case, the transfer function obtained is something stupid like Vin=-Vout which is obviously wrong.

Alternatively I can y transform that into this:

The impedances are not important, I know how to get them, but I don't know how to form nodal equations. It seems no matter whether I have the original big circuit, or these smaller ones, I still don't know where to start and what conditions are valid.



We used to do exercises on closed circuits with a bunch of resistors and batteries. The way to do those exercises was to put one reference ground, and use nodal analysis to solve all voltages relative to the arbitrary reference ground. But those examples always feature closed circuits.

-So is this twin T circuit a closed circuit, ie is there no current flowing in and out of Vin and Vout? If it is closed, then what's the point of doing the y-delta transform in the first place? I could just do a bunch of nodal analyses (I doubt this is the case).

-What was wrong with my nodal analysis of the simplified delta circuit? Is it because current 'flows into' the ground?
Sorry for the long read, I am trying to learn some fundamental concepts.

Thank you very much.

 

Your "Vin" is driven by a signal source, right?

So draw a signal source (a voltage source whose value is Vin) connected between your Vin node and your reference ground.

You also generally have some kind of a load at the output, but you can treat that as a very high impedance load (for instance, it might be a unity gain opamp buffer) and leave it as an open circuit.

 

Your "Vin" is driven by a signal source, right?

So draw a signal source (a voltage source whose value is Vin) connected between your Vin node and your reference ground.

You also generally have some kind of a load at the output, but you can treat that as a very high impedance load (for instance, it might be a unity gain opamp buffer) and leave it as an open circuit.

Thank you very much, this makes sense and made the problem solvable, both with and without the y-delta transforms.