Find S/E in Filtres & OPAMP Circuits: A Complex Schema

[ace130]

So this is the circuit of a filtre and it's complex schema :

The question was find the fonction S/E .In order to find S/E , I had to sum up impedances in serie or parallel, for example R2 and Z2 have the same current so we put R2+Z2=Z', but can I sum Z1+Z' ? since they have different current and voltage,The rule says that serie means same current and parallel means same voltage .
My first attempt is to consider Z1 and Z' are in parallel but the result was weird.
I want to know if that green statement is correct , and if you wish you can give me a hint or solution the find S/E.

 

[phyzguy]

(1) The green statement is correct.
(2) Assuming no current flows out of S, then you are correct that R2 and Z2 are in series.
(3) The correct next step is to consider Z1 and Z'=R2+Z2 in parallel. What was "weird" about this?
(4) Do you then see how to incorporate R1?

 

[ace130]

I'm a little confused, here is my friend attempt (E=Ve, S=Vs , Z'=Zeq1) , considering that his part 2 is correct , so the voltage at Z1(Zc1) is V1 , but the voltage at Z' is obviously V1-S

 

[donpacino]

I'm a little confused, here is my friend attempt (E=Ve, S=Vs , Z'=Zeq1) , considering that his part 2 is correct , so the voltage at Z1(Zc1) is V1 , but the voltage at Z' is obviously V1-S

View attachment 219463

not quite.
R2 and Z2 are in series. so Zeq(1) will be R2 + Z2, note the other end of Zeq(1) has to be tied to ground.

By doing this you "lose" your Vs node. You will have to resolve for this later.

Then Zeq(1) is in parallel with Z2, the combo of which is in series with R1. You should then be able to use ohms law to find Ie = Ve / (R1 + (Zeq || Z2)). You then solve for the current through Zeq, and go from there!

note: there are other easier ways to solve this, but you likely have not learned them yet.

 

[ace130]

well, I knew that Vs would cause problems when adding R2 and Z2 , so I tried to find E/S without sum up any component , instead I wrote E/S= (V1/S)*(E/V1) and calculate each expression , it takes more time but the result seems to be more convenient , the problem is I can't find a "stable" solution , I don't know which method is correct

 

[donpacino]

instead I wrote E/S= (V1/S)*(E/V1)

that is not a true statement though. where did you get it?

DO you know what a voltage divider is?

 

[ace130]

that is not a true statement though. where did you get it?

DO you know what a voltage divider is?

It is ! it's simple math ? I just inverse it , because I'm using a Right-to-left Keyboard... my bad