Dispersion relation of a transmission line - questions

[Matej Kurtulik]

Hi,

I have transmission line with dispersion relation ω=sin(kx), so then means that for one value of ω I have two values of k. I apply voltage with some frequency with is allowed to move in the line. First question is, how can I influence what k will be generated inside the line. The another question is, if there is somehow possible to generate a wave not with generating frequency ω like in the first example but to generate wavelength, basically k.

Thank you

 

[marcusl]

The only way to change k without changing the line construction is to vary ω.

 

[Matej Kurtulik]

and I see from dispersion formula that each ω has two k, so what key will be inside the line, and how can I switch is for another one.

 

[marcusl]

Are you using a lumped-element model (discrete L's and C's) for the transmission line?

 

[Matej Kurtulik]

Yes

 

[marcusl]

You are seeing the effects of aliasing, as it is called in digital signal processing. It arises in any discrete or sampled system. In the present case, you can't see a continuous sine wave travel down your transmission line model because voltage is defined (sampled) at only a finite number of points--namely across each capacitor, if it's a low-pass transmission line. For spatial frequencies above a certain maximum k_0, the pattern of sampled voltages looks the same as that for a lower frequency--that is, two values of k appear to have the same ω. As a result, there is no point in considering the upper, degenerate part of the k spectrum. It is conventional to limit the argument of sin to the range 0 to π/2. This is called the "reduced zone."