Transmission and Reflection Coefficients

So I've been told that transmission coefficient in general I_s

$$\gamma = \alpha + j\beta = \sqrt{(R+j \omega L)(G + j \omega C)}$$

Written in polar form, $|\gamma| \angle \phi$ helps us get $\phi$, which is used to calculate $\beta$ or something? Wait that doesn't make sense. I'll investigate.

This is the normal case. I think lossless has something simplified, and distortionless also has something simplified. I'll look at it later.

Now reflection coefficient is this:

$$\Gamma = \frac{Z_L - Z_o}{Z_L + Z_o}$$ $$\Gamma = |\Gamma|\angle\phi$$

Why are they both Phi? I'll investigate again.

But more, about SWR (is VSWR the same thing? IDK(yet))

$$SWR = \frac{1 + |\Gamma|}{1 - |\Gamma|}$$

Results of investigation:

1. SWR is a concept, VSWR is the Voltage Standing Wave Ratio whatever. But in numerical, both should mean the same thing.

2. Listen, there is an important thing I need to tell you:

$$\beta = \frac{2\pi}{\lambda}$$

but

$$\lambda = \frac{v}{f}$$

thus

$$\beta = \frac{2\pi f}{v}$$

Where $f$ is the circuit frequency, and $v$ is the velocity of em wave in the medium ($c$ if free space).