Twin-T Notch Filter: Solve the Circuit with Node Analysis

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The discussion centers on solving a twin-T notch filter circuit using node analysis and complex impedances. The initial attempt at applying complex impedance equations led to confusion, particularly in deriving the output-to-input voltage ratio. However, after further manipulation and setting the voltage at a specific node to zero, the correct equation was successfully derived. The importance of understanding complex impedance in circuit analysis is emphasized, as it aids in simplifying the problem. Ultimately, the approach to solving the circuit was clarified through algebraic manipulation and strategic node selection.
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Homework Statement


This is a twin-T notch filter.

[PLAIN]http://l23.sphotos.l3.fbcdn.net/hphotos-l3-snc4/hs1360.snc4/163224_10150132441064992_712009991_8008832_7339032_n.jpg

Homework Equations



R = R
C = 1/sC
L = sL

The Attempt at a Solution



Not sure if my complex impedance equations are correct or even useful.

Anyhow I tried using node analysis after changing to complex impedances to see if I could get some equations to manipulate into vout/vin but it seems to get me nowhere really.

I'm fairly puzzled as far as how to approach this circuit. Any advice would be greatly appreciated.
 
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don't know if that helps.

Solution:

Yeah so I just changed to complex impedances (C = 1/sC) and used node analysis and with enough algebra I managed to manipulate the correct equation.

You just set vx=0 since it's connected to ground.
 

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