Communication Q: Answers to Reflection Coefficient, VSWR & Power

[Matt007]

Hi there,

This is my first post so I hope that I am doing this correctly. I have put the question below and i am having troubles with numbers 3,5 and 6. Any help would be great.

Cheers


A transmitter with an output power of 200W operates at a frequency of 20MHz. It feed an antenna with an impedance of 30 Ω. The cable has a characteristic impedance of 50 Ω and a velocity factor of .90. Cable loss will be ignored and power rating is adequate for the application.

Load is not matched to the transmission line so there will be some reflection of the incident wave energy when it arrives at the load. The incident wave and the reflected wave will both combine to produce an interference phenomenon known as a stationary wave or standing wave.


1. Calculation the Reflection Coefficient at the load

Г = (Rl-Zo)/(Rl+Zo)

Г = (30-50)/(30+50) = 20/80 =1/4 or 0.25

* How do you convert this to dB??


2. What does the sign mean of the reflection coefficient value

+ve Maximum positive reflection when the line is open circuited
-ve Maximum negative reflection when the line is short circuited
0= perfectly matched

3. Would there be a Maximum or Minimum in the standing wave



4. Calculate the voltage standing wave ratio (VSWR) on the line

VSWR = Zo/Rl = 50/30 = 1.6667

VSWR = (1+ Г)/(1- Г) = (1+0.25) / (1-0.25) = 1.6667

5. What is the distance between adjacent minima in the standing wave pattern.



6. Calculate the actual amount of reflected power and the actual amount of power few to the load.

Г^2 = Pref/Pinc

 

[berkeman]

Hi there,

This is my first post so I hope that I am doing this correctly. I have put the question below and i am having troubles with numbers 3,5 and 6. Any help would be great.

Cheers


A transmitter with an output power of 200W operates at a frequency of 20MHz. It feed an antenna with an impedance of 30 Ω. The cable has a characteristic impedance of 50 Ω and a velocity factor of .90. Cable loss will be ignored and power rating is adequate for the application.

Load is not matched to the transmission line so there will be some reflection of the incident wave energy when it arrives at the load. The incident wave and the reflected wave will both combine to produce an interference phenomenon known as a stationary wave or standing wave.


1. Calculation the Reflection Coefficient at the load

Г = (Rl-Zo)/(Rl+Zo)

Г = (30-50)/(30+50) = 20/80 =1/4 or 0.25

* How do you convert this to dB??


2. What does the sign mean of the reflection coefficient value

+ve Maximum positive reflection when the line is open circuited
-ve Maximum negative reflection when the line is short circuited
0= perfectly matched

3. Would there be a Maximum or Minimum in the standing wave



4. Calculate the voltage standing wave ratio (VSWR) on the line

VSWR = Zo/Rl = 50/30 = 1.6667

VSWR = (1+ Г)/(1- Г) = (1+0.25) / (1-0.25) = 1.6667

5. What is the distance between adjacent minima in the standing wave pattern.



6. Calculate the actual amount of reflected power and the actual amount of power few to the load.

Г^2 = Pref/Pinc

Welcome to the PF. You have a sign error in #1, which affects your answer in #4. What is the range of values for VSWR? Knowing that, you should have caught the error in #4 right away.

And in #1, you could have caught the sign error as well. When you have a load with a lower impedance than the transmission line that feeds it, do you get a postive or negative reflection?

 

[Matt007]

Hi Berkeman,

Thanks for the info, I missed that sign error in the first post. I have since re-worked the question and found that the Г to equal -4


1. Calculation the Reflection Coefficient at the load

Г = (Rl-Zo)/(Rl+Zo)

Г = (-30-50)/(-30+50) = -80/20 = -4

3. Would there be a Maximum or Minimum in the standing wave

Does the max and min refer to the VSWR which has been worked out to be

VSWR = -3/5 = -0.6

So the max = -3
and the min = 5

4. Calculate the voltage standing wave ratio (VSWR) on the line

VSWR = Zo/Rl = 50/30 = 1.66667

VSWR = (1+ Г)/(1- Г) = (1+(-4)) / (1-(-4)) = -0.6

* If I use both the VSWR equations how come I get two different answers, I am only assume that i have done something incorrect.


5. What is the distance between adjacent minima in the standing wave pattern.

*From the VSWR would this equal -0.6 ??

6. Calculate the actual amount of reflected power and the actual amount of power few to the load.

* Do i use the Г value and sub into this formula
Г^2 = Pref/Pinc and use the 200W given in the question?


Thanks for your help

 

[berkeman]

Hi Berkeman,

Thanks for the info, I missed that sign error in the first post. I have since re-worked the question and found that the Г to equal -4


1. Calculation the Reflection Coefficient at the load

Г = (Rl-Zo)/(Rl+Zo)

Г = (-30-50)/(-30+50) = -80/20 = -4

3. Would there be a Maximum or Minimum in the standing wave

Does the max and min refer to the VSWR which has been worked out to be

VSWR = -3/5 = -0.6

So the max = -3
and the min = 5

4. Calculate the voltage standing wave ratio (VSWR) on the line

VSWR = Zo/Rl = 50/30 = 1.66667

VSWR = (1+ Г)/(1- Г) = (1+(-4)) / (1-(-4)) = -0.6

* If I use both the VSWR equations how come I get two different answers, I am only assume that i have done something incorrect.


5. What is the distance between adjacent minima in the standing wave pattern.

*From the VSWR would this equal -0.6 ??

6. Calculate the actual amount of reflected power and the actual amount of power few to the load.

* Do i use the Г value and sub into this formula
Г^2 = Pref/Pinc and use the 200W given in the question?


Thanks for your help

AFAIK, there is no such thing as a negative VSWR. Look at the definition of $$\rho$$ at this wikipedia page (note the page has some math formatting issues at the moment...):

http://en.wikipedia.org/wiki/VSWR

.

 

[DeeNos]

Pref = Г^2 * Pinc = (0.25)^2 * 200W = 12.5W

Pload= Pinc - Pref = 200W - 12.5W = 187.5W


I would like to provide a thorough explanation and clarification of the concepts involved in this question.

Firstly, the reflection coefficient (Г) is a measure of how much of the incident wave is reflected at the load. It is a complex number, with both a magnitude and a phase. To convert it to dB, we can use the formula ГdB = 20log(|Г|), where |Г| is the magnitude of the reflection coefficient. In this case, ГdB = 20log(0.25) = -12.04 dB.

The sign of the reflection coefficient indicates the direction of the reflected wave. A positive sign means that the reflected wave is in phase with the incident wave, while a negative sign means that the reflected wave is out of phase. In this case, the positive sign indicates that the reflected wave is in phase with the incident wave.

In terms of the standing wave pattern, there will be both a maximum and a minimum. The maximum will occur at the load, where the reflected wave is in phase with the incident wave. The minimum will occur at a distance of λ/2 from the load, where the reflected wave is out of phase with the incident wave.

The voltage standing wave ratio (VSWR) is a measure of how well the load is matched to the transmission line. A VSWR of 1 indicates a perfect match, while higher values indicate a mismatch. In this case, the VSWR is 1.6667, which indicates a moderate mismatch.

The distance between adjacent minima in the standing wave pattern can be calculated using the formula λ/2 = (v/f) * λ, where v is the velocity factor and f is the frequency. In this case, the distance between adjacent minima would be 15 meters (λ/2 = (0.90*3*10^8)/(20*10^6) = 15m).

Finally, we can calculate the actual amount of reflected power and power delivered to the load using the formula Pref = Г^2 * Pinc and Pload = Pinc - Pref, where Pinc is the incident power. In this case, 12.5W of power