Actually transformed in quarter wave transformer

antennamicrowavetransmission line

I'm reviewing some stuff on quarter wave transformer for a transmission line but since I have not had any experienced in handling these type of stuff, I am struggling to understand this concept intuitively

What I don't get is that all the calculation involved in this "quarter wavelength transformer" is to calculate the input impedance Zin at a quarter wave length away from the load. What is the point of that?

What is actually done in the field to change the transmission line network into a matched network using quarter length transformer?

Best Answer

This is the formula that is interesting: -

\$Z_{IN} = \dfrac{Z_1^2}{R_L}\$

As George has "said" in a comment - if you have a 75 ohm system feed and you want to deliver the full power to a 33 ohm load, use a quarter wavelength of 50 ohm cable and the formula numerically becomes: -

\$Z_{IN} = \dfrac{50^2}{33}\$ = 75.75 ohms. (Near enough)