(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given the coupled RC network shown below (see attachment), show that the voltage transfer function is

[tex]\frac{Vout}{Vin}=\frac{1}{(1-\omega^2C^2R^2)+3j\omega CR}[/tex]

Hint: [tex]\frac{Vout}{Vin}=\frac{V1}{Vin}\frac{Vout}{V1}[/tex]

2. Relevant equations

For Capacitor, [tex]Z=\frac{1}{j\omega C}[/tex]

General Potential divider equation [tex]Vout=\frac{Z2}{Z1+Z2}Vin[/tex]

3. The attempt at a solution

I find this all a bit confusing :( I know that the second filter is acting as a load for the first filter, so I know I just can't write

[tex]V1=\frac{1}{j\omega C}\frac{1}{R+\frac{1}{j\omega C}}Vin[/tex]

So would I need to combine the total impedance of the second filter with the impedance of the first capacitor?

Actually, could someone clear up impedance and reactance? For a capacitor reactance is

[tex]X=\frac{1}{\omega C}[/tex]

while its impedance is

[tex]Z\frac{1}{j\omega C}[/tex]

So if a resitor is connected in series, how/what would I combine to obtain the total resistance/impedance?

Anyhelp would be appreciated, I think you can tell that my ideas are a bit muddled :s

thanks

SG

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# Cascaded low pass filters problem

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