I need your help on this problem!

[semiconductor]

Can someone help me?
I need the solution to the problem below (Prob. 2.9 - Pozar’s textbook, pg 100):

A radio transmitter is connected to an antenna having an impedance 80+j04 with a 50 Ohm coaxial cable. If the 50 Ohm transmitter can deliver 30W when connected to a 50 Ohm load, how much power is delivered to the antenna.

 

[flyhigh]

Hi,

I think the solution is (if I can write this formula from the top of my head):
P=Po(1-|rho|**2)

rho=(zl-zo)/(zl+zo)

 

[semiconductor]

Yeah, maybe the solution so, but I need more explanation to this problem. I mean the complete solution include explanation!

Thank you in advance!

 

[neerajs]

Maximum power is transferred when you have load impedance = source impedance (ideal case with no reflections). Any mismatch leads to reflections.

Impedance 80+j04 means effective impedance of
sqrt (80^2+4^2) = 80.1ohm

You are feeding it with 50ohm transmission line.

Refelection Coefficient P (ratio of reflected wave to incident wave) is defined as (Zl-Z0)/(Zl-Z0)
= (80.1 - 50) / 130.1 = 0.23136

Reflection coefficient in power is a square of the reflection coefficient which means the ratio of the reflected power to the incident power in this case 0.0535 that means that 5.35% of power will get reflected. So power delivered to antenna will be ~28.4W