Problem with Pozar Derivation For Transmission Lines

[HPRF]

Hi

I am reading through the proof for transmission line theory in Pozar and have a basic derivation step question that I am wondering if anyone can answer.

In the derivation Kirchoffs Voltage and Current laws are applied to give

V(z,t)-R*(delta)z*i(z,t)-L*(delta)z*(d/dt)i(z,t)-V(z+(delta)z,t)

for the voltage and something similar for the current.

The problem is that there is no explanation for where V(z+(delta)z,t) and I(z+(delta)z,t) go to when (delta)z-->0. They just seems to disappear from the derivation, without explanation, instead of cancelling with V(z,t) and I(z,t).

Any ideas would be much appreciated.

Thanks in advance.

 

[Element_115]

Not sure what you mean. Can you post the EQ ? (or Book & pg #)
If "(Delta)z" is the Calculus dz then it is most likely an integration, as dz goes to 0 .

 

[msokey]

look into the definition of differentiation in a calculus book. as dz goes to zero, the equation you mention turns into a differential equation. you'll be able to find this in a calculus book for sure.

 

[HPRF]

Thanks, that solved it. A basic error.