Transmission Line Problem

[cdeguzma]

I'm trying to find the power dissipation in each resistor. I don't know how Rm effects the circuit/characteristic impedance of the 2nd section. Please help.


Thanks so much!!!

 

[leap]

If there is no Rm, the impedance of 2nd section couldn't be equal to 50.

 

[sergio mariotti]

25 uW by Rm
100 uW by RL

Are you a student?
There are many solutions:
1) use Spice, the most complicated.
2) use ADS or other freq. domain simulator and "normalize" the exiting voltage to 1.

3) use the brain as follow:
3a) "move" to left RL across the 2nd lamda/4 line... RL became R1=50^2/100=25 Ohm. R1 is shunted to Rm.
3b) calculate the parallel Rm//R1. Rm//R1=R2=100//25=20 Ohm.
3c) move to left R2. R3=50^2/R2 = 2500/20 = 125 Ohm
3d) since le lines are loss free, they cannot dissipate any power, so for energy conservation law, the power dissipate into R3 is the sum of the power dissipate into Rm and RL
3e) find power dissipate into R3
P3=(0.2/(75+125))^2*125=125 uW
3f) find Voltage applied to Rm.
Vm=(20*125uW)^.5= 50mV
3g) find power dissipated by Rm: Pm=0.05^2/100=25uW
3h) find power dissipated by RL: 125uW-25uW=100 uW

 

[Element_115]

If your Frequency is low you can just use an O-Scope and measure
Vrms across each Resistor and (V^2/R) = P.
Hope this helps