Reducing a circuit to a single impendence value

[cowmoo32]

Homework Statement

Find V_out over a range of frequencies

Homework Equations

V = IZ

The Attempt at a Solution

I'm trying to equate V_in to V_out using equivalent impedences. I have some python code to handle the numbers but want to be sure my algebra and circuit reudction are correct because I'm getting good-ish values from the script but I'm still not positive they're right.


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edit: I just saw that I'm missing a bridge between the upper and lower lines on the second to last diagram. Z_EQ and Z₃ should be in parallel.

 

[Nugso]

Hi cowmoo32, I'm no expert, but it looks like in your equivalent circuit(2nd circuit, that is) R3 and C1 have the same current, but in the first circut it's clear that R3's current is 'higher' than C1's.

 

[cowmoo32]

I could kick myself. For some reason I've had it in my head that the voltage drop would be across the two V_in leads and the two V_out leads, but you're right. I should be measuring voltage across V_in to V_out.

edit: Seeing that makes things even harder. Now I have no idea how to reduce it.

 

[cowmoo32]

Does this work?

 

[Nugso]

Hi. Well, I don't see why Z1 and ZR1 are parallel.

 

[cowmoo32]

Right again. It was a long day yesterday. Thanks!