antenna-theory.com

[Nihm]

Hi,

First THANK YOU for this AMAZING web site so easier to read and understand than all the books I have (tried) to digest.

My question is about the transmission lines introduction, when we can read
(as in so many books), the relationship between the voltage and current on the left and right side of a small transmission line, using oridinary circuit theory:





Weel,
Despite all my efforts using Ampere' circuital law, I would like to write
… + G' V(z+dz,t) + C' dV(z+dz,t)/dt = 0
… in the second equation.

Could you help me to understand my mistake?
Thank you in advance,
Nihm

[bigSteve]

Looks like you have it right! if you follow circuit theory you get it exactly right as you have stated.

What happens is we take the limit as z->0 in the next step, so that the bracketed terms become partial derivatives.

Then dV(z+dz,t)/dt = dV(z, t)/dt so it all ends up working out.

If you want to spend more time thinking about calculus you can figure out why it is ok to do dV(z+dz,t)/dt = dV(z, t)/dt but not I(z+dz,t)=I(z,t) as dz goes to zero.....

no mistake on your end.

Cheers