# Complex Circuit Analysis Simplification

1. Feb 9, 2012

### jonlg_uk

I have the following circuit....

I have managed to derive an equation for U2:

Now I want to substitute U2 into U1, in order to derive equation for U1

I have defined U1 as:

Now I substitute U2 into the above equation. This is how far I get.....I am stuck...

My circuit simulator is saying that U1 is equal to:

However I cannot simplify to get this equation. Can someone please help I have spent hours trying to get U1 to look like the U1 that the simulator produces.

2. Feb 9, 2012

### Jony130

Have you try to replace R1, R2 and E2 with his Thevenine equivalent circuit ?
Eth = R2/ ( R1 + R2 ) * E1 and Rth = R1||R2

V3 = I * R3

$$I = \frac{Eth}{\sqrt{(Rth + R3)^2 + Xc^2)}} = \frac{E1*\frac{R2}{R1+R2}}{\sqrt{(R1||R2 + R3)^2 + Xc^2)}}$$

And

$$V3 = \frac{E1*R2*R3}{(R1+R2)\sqrt{(R1||R2 + R3)^2 + Xc^2)}}$$

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Last edited: Feb 9, 2012
3. Feb 9, 2012

### jonlg_uk

No I haven't tried this before, but I did just try it and I still can't derive U1. Perhaps I am being stupid...

4. Feb 9, 2012

### Jony130

A made a small error instead of V3 I should write U1

What is the name of your simulation program?

5. Feb 9, 2012

### jonlg_uk

Thanks for your help Jony, the simulator is giving me this equation:

I haven't derived that myself^. When I expand out the equation you derived:

$$V3 = \frac{E1*R2*R3}{(R1+R2)\sqrt{(R1||R2 + R3)^2 + Xc^2)}}$$

I still not can get a the equation looking like the simulator one.