Transmission line reflection coefficient

In summary, the conversation is about a calculation for the reflection coefficient of a transmission line using the formula ((ZL - ZO) / (ZL +ZO)). The last part of the calculation (0.355e^j) is a misprint and should be (0.354 + 0.030j). The magnitude of this complex number is 0.355 and the ej must be a misprint for ejθ, where θ is unknown.
  • #1
fran1942
80
0
Hello, I am looking at the following calculation for the reflection coefficient of a transmission line using the formula ((ZL - ZO) / (ZL +ZO)
I can understand it all apart from the last part (0.355e^j).
Can someone please tell me how that figure was gained from (-0.354 + 0.030j)

(216 + j15 - 452.38) / (216 + j15 + 452.38)

= (236.38 + j15) / (668.38 + j15)

= -0.354 + 0.030j

= 0.355e^j
 
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  • #2
hello fran1942! :smile:

(try using the X2 button just above the Reply box :wink:)
fran1942 said:
= -0.354 + 0.030j

= 0.355e^j

0.355 is the magnitude (the modulus) of the complex number -0.354 + 0.030j (use Pythagoras :wink:)

the ej must be a misprint for e,

where θ is … ? :smile:
 

FAQ: Transmission line reflection coefficient

1. What is the transmission line reflection coefficient?

The transmission line reflection coefficient is a measure of the amount of energy reflected from a transmission line back towards the source due to impedance mismatches. It is represented by the Greek letter gamma (Γ) and is a complex number that includes both magnitude and phase information.

2. How is the transmission line reflection coefficient calculated?

The transmission line reflection coefficient, Γ, can be calculated using the following equation: Γ = (ZL - Z0) / (ZL + Z0), where ZL is the load impedance and Z0 is the characteristic impedance of the transmission line. This calculation takes into account the impedance mismatch between the load and the transmission line and can be used to determine the amount of energy reflected back towards the source.

3. What is the significance of the transmission line reflection coefficient?

The transmission line reflection coefficient is an important parameter in understanding the performance of a transmission line. A high reflection coefficient can result in signal loss and distortion, while a low reflection coefficient indicates good impedance matching and efficient transmission of energy.

4. How does the transmission line reflection coefficient affect signal integrity?

The transmission line reflection coefficient can greatly impact signal integrity. A high reflection coefficient can cause signal degradation, resulting in attenuation and distortion of the transmitted signal. This can lead to errors in data transmission and decrease the overall performance of the system. A low reflection coefficient indicates good impedance matching and results in better signal integrity.

5. What factors can affect the transmission line reflection coefficient?

The transmission line reflection coefficient can be affected by various factors such as the impedance of the load and the transmission line, the length and type of the transmission line, and any discontinuities or impedance mismatches along the line. Temperature and frequency can also have an impact on the reflection coefficient. It is important to properly design and match the impedance of a transmission line to minimize the effects of the reflection coefficient.

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