Transmission Line attenuation

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.

• What Andy said. Also note that transmission line formulae often use nepers for loss, rather than decibels, which changes the calculations. Feb 24 at 22:09

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.