# Kirchhoff's Law

1. Oct 21, 2011

### SMOF

Hello,

I am hoping someone can break down an equation for me. I am used to Kirchhoff's law in the form of i1 + i2 + i3 = 0 etc. But recently in a High Frequency class, we were told ...'Let us apply the Kirchhoff's law to the equivalent circuit of a transmission line segment of length $\delta$z. Using the voltage law, we get

V(z,t) = R$\delta$z * I(z,t) + L$\delta$z * ($\delta$I(z,t)$/$$\delta$t) + V(z + $\delta$z,t)'.

If anyone could help me break this down, or explain who it relates to the general form of the equation, that would be amazing.

Seán

2. Oct 21, 2011

### BackEMF

An infinitesimal piece of transmission line would look as follows:

Now say the current flowing into the left side of this circuit is $I(z,t)$ and the voltage across the two input terminals is $V(z,t)$. Likewise, say the current flowing out of the right side is $I(z+\delta z,t)$, and the voltage across the output terminals is $V(z+\delta z,t)$. Just as in the diagram (except it uses x as the distance variable, and upper case delta symbols - but hopefully you get the idea).

Now simply apply the usual KVL equation, Ohm's Law and the inductor equation: $V = L \frac{\text{d}I}{\text{d}t}$. This will yield your equation above.

3. Oct 23, 2011

### SMOF

Hey,

That's great! Thanks for the reply and the information.

Seán

4. Oct 23, 2011

### BackEMF

No problem Seán. If you need any more help just let me know.