Transmission Line attenuation

Question

Suppose I have an experimental lossy transmission line, being fed a sine voltage wave of known frequency and amplitude, with a known characteristic impedance that is terminated by a perfectly matched load impedance. With the aid of R', G', L', and C', how can I find the amplitude at the end of the transmission line? It is fair to assume that there are no reflections.

I have already found the phase difference, but am struggling to get the correct answer for amplitude. I've found the propagation constant (K) and attempted to find V~(z) = V0+ * e^(-Kz), where z is the length of the transmission line, and then taking the modulus of V~(z), but am getting a much smaller value compared to an experimentally determined value. Thanks for any help.

Answer 1

1. Check your calculation

A propagation constant is composed with attenuation and phase constants.

$$ \gamma = \alpha + i\beta $$

, where α is the attenuation constant and β is the phase constant.

Your goal is to get the amplitude of the signal at the given position z, which can be calculated like this,

$$ A_z = A_0 \times e^{-\gamma z} = A_0 \times e^{- (\alpha + i\beta)z} $$ $$ \left| \frac{A_0}{A_z} \right| = e^{\alpha z} $$

In your question, there was not mentioning about the attenuation constant. Thus, I cannot assure if you calculated the amplitude correctly using the attenuation constant, which is the real term of the propagation constant.

2. Check your experiment setup

Note that the above calculation is only valid for the infinite length transmission line with correct impedance matching between instruments and the transmission line. Did you check impedance of signal generator, spectrum analyzer (or oscilloscope), and the transmission line itself?

For example, if the instrument's input impedance doesn't match to the transmission line, there will be reflections and will lead you to incorrect result.