Answer: Calculating Average Power Delivered to Load Resistors on 50 Ohm Line

[Tush123]

A 50 ohm transmission line is terminated with 60 ohm and 30 ohm resistors in parallel. The voltage at the input to the line is V(t) = 100 cos (5X10 ^ 9 t) and the line is 3/8 th of a wavelength long. What average power is delivered to each load resistor ?

My ans is getting 81.6 but actual ans given is 69 . I simply used the formula P = (V^2) (1-L^2) / 2 Z
where L = reflection coefficient
Z = characteristic impedance

 

[.Scott]

If I understand this:
The terminating resistance is 1/((1/60)+(1/30)) = 20 ohms
The RMS voltage will be 100 * sqrt(2) = 70.71 volts
The length of the transmission line doesn't make a difference because we have a voltage source at one end.

So:
The RMS voltage at the resistor end will be 70.71 * 2(20)/(20+50) = 70.71 * (4/7) = 40.41 V
So the power that the resistors are dissipating would be V*V/r = 40.41*40.41/20 = 81.63 watts

Well, that's your answer.

I think the bad assumption is about the way the input voltage source is connected to the transmission line. It would normally be connected through a 50 ohm resistor. Once you put that 50 ohm resistor in, then you will need to take into consideration the effects of the 3/8 wavelength.

 

[rude man]

1. Get the correct formula for the load voltage E₂ as a function of source voltage E₁, line chas. impedance Z₀, load impedance Z₂, and length of line expresed as a fraction of wavelength.

2. Then, power to the two load resistors is P = |E₂|²/R
where R = 30 ohms and 60 ohms.

 

[rude man]

ohms
The RMS voltage will be 100 * sqrt(2) = 70.71 volts
The length of the transmission line doesn't make a difference because we have a voltage source at one end.
.

Uh-uh.

 

[rezeew]

I would first double-check my calculations and make sure that all units are correct. I would also consider the possibility of any errors in the given values or formula used. Additionally, I would make sure that the voltage and resistance values are in the same units (e.g. all in volts or all in ohms).

If the calculations and units are correct, I would then look at the physical interpretation of the results. Is it possible that the actual power delivered to the load resistors is lower than the calculated value due to losses in the transmission line or other factors? Are there any assumptions made in the formula that may not be applicable in this specific scenario?

I would also consider alternative methods of calculating average power, such as using the average voltage and current at the load resistors or using the Poynting vector. It is important to consider all possible factors and methods in order to accurately determine the average power delivered to the load resistors.

In conclusion, as a scientist, I would carefully double-check my calculations and consider all possible factors and methods in order to accurately determine the average power delivered to the load resistors.