Consider Vg

Let Vg be the voltage of the supply voltage source.

So that we can instantly get the value of V+

Input impedence (Zin)

We consider z=-l as the point which is the entry
of the transmission line.
Now, by the general equation the impedance in
transmission line, we are going to get a particular
solution for Zin.
Applying general equation,

Recall


Notice That

Then we have

Characteristic Impedence Zo

Characteristic Impedence Zo indicates the impedence of a single transmission line.
Since R & G are small, we assume them as neglgible parameters.

Voltage Standing Wave Ratio (VSWR)

Recall the voltage equation with repect to z,





Notice That :
(1) VSWR =1 means no reflection
(2) VSWR =infinity means wave is totally reflected

That implies that if one of the points in the figure |V|/|V|(max) touches zero,
VSWR -> infinity

In other words, when VSWR= infinity, there exists some/a point(s) such that the wave is total cancelled due to suposition between incident wave and reflected wave.


Important Notes:
(1)Once again VSWR is a ratio comparing between
Max and Min e.g VSWR= n means VSWR= n:1 etc.
(2)The particular representation
for |V|/|V|(max), you may consider


Then, by the consideration of different z, you can get the values
of each point one by one and at the end obtain the figure.

Reflection Coefficient in terms of impedence

Derive for load impedence

Notice that Load is in z=0 ,


Where

Transmission line

We may simply consider what happen inside a single transmission line as a pair of travelling waves going into or out of the the transmission line.

Theory Of Electromagnetic Wave

Due to the phase difference in the transmittion line, the same wave in the same direction in different point may have different magnitude, given by a phasor:

The former expotental function represents the drop of amplitude,where the latter one indicates
the phase angle of a particular wave.