Calculate the reflection coefficients of the load and the source impedances

In summary, the conversation discusses a new member joining the forum and taking online courses to obtain a degree. The problems all involve a transmission line with a characteristic impedance of 50 ohms and a source voltage of 1.0 volt peak sine wave. The load and source impedances vary for each problem. The conversation then goes on to discuss different problems and their solutions involving reflection coefficients, peak voltages, and transmission line properties. The members of the forum remind the new member that they must show their assumptions and workings before receiving help.
  • #1
battal
1
0
Hi there,
I am new member to this forum.
I am taking online courses, in order to get my degree.

For all of the problems, the transmission line in the problem has a characteristic impedance of 50 ohms and is one quarter wavelength (an electrical length of 90 degrees) at the frequency of the source.

Likewise for all problems, the source voltage is a 1.0 volt peak sine wave. However, note that the source impedance varies from problem to problem.

1a. Calculate the reflection coefficients of the load and the source impedances if the load impedance is 75 ohms and the source impedance is 25 ohms.

1b. Calculate the peak voltage at the load and the peak voltage at the input of the transmission line.

2. Repeat problem 1 for a load impedance of 50 ohms and a source impedance of 75 ohms.

3. Repeat problem 1 for a load impedance of 25 ohms and a source impedance of 50 ohms.

4. A 75 cm length of coaxial transmission line has a characteristic impedance of 50 ohms. The capacitance per unit length of the line is 1pf/cm.

a. Calculate the inductance per unit length.
b. Determine the relative dielectric constant of the material separating the inner conductor from the outer conductor.

5. The reflection coefficient of a load is 0.5+j.5
a. Plot the location of the reflection coefficient on the complex plane.
b. Plot the location of the complex conjugate of the reflection coefficient on the complex plane.
c. What is the reflection coefficient seen at the input of a transmission line connected to this load if the line is 90 degrees long (quarter wavelength).

Thanks
Battal H. Al-Qahtani
 
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  • #2
Welcome to the Forum.

The forum rules is that you have to show you assumptions and workings before we help you.
Check the rules on the Homework section it will give a proformer.

Trying not to be patronising, but if we just give you the answer you won't learn how to do it.
 
  • #3
Moved to Homework Help forums. And as Panda says, you need to show us your attempts at the solutions before we can offer out help, Battal.
 

1. What is the purpose of calculating the reflection coefficients of the load and source impedances?

The reflection coefficients of the load and source impedances help us understand the behavior of electrical signals in a circuit. They indicate how much of the signal is reflected back from the load or source, and how much is transmitted. This is important in determining the overall performance and efficiency of a circuit.

2. How do you calculate the reflection coefficient of a load impedance?

The reflection coefficient of a load impedance can be calculated using the formula: ΓL = (ZL - Z0) / (ZL + Z0), where ΓL is the reflection coefficient, ZL is the load impedance, and Z0 is the characteristic impedance of the transmission line.

3. What is the relationship between the reflection coefficient and standing wave ratio?

The standing wave ratio (SWR) is a measure of how well a transmission line is matched to its load. It is directly related to the reflection coefficient, with the formula: SWR = (1 + |Γ|) / (1 - |Γ|), where |Γ| is the magnitude of the reflection coefficient. A lower SWR indicates a better match and less signal loss in the transmission line.

4. Can the reflection coefficient of a load impedance be negative?

Yes, the reflection coefficient can have a negative value. This indicates that the reflected signal is out of phase with the incident signal. A negative reflection coefficient can occur when the load impedance is greater than the characteristic impedance of the transmission line.

5. How can the reflection coefficient be minimized in a circuit?

The reflection coefficient can be minimized by ensuring that the load impedance is matched to the characteristic impedance of the transmission line. This can be achieved through impedance matching techniques such as using a matching network or adjusting the length of the transmission line. A lower reflection coefficient results in less signal loss and better overall performance in the circuit.

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