Transmission line relative amplitude question

In summary, a low frequency signal is fed into an air spaced coaxial transmission line with an annular sheet of thickness 1mm and resistivity 0.5 Ohm m connecting the inner and outer conductors at a point on the line. The relative amplitude of the wave reflected from the resistive sheet is calculated using the formula for reflection coefficient. The impedance at that point is determined to be the parallel combination of the characteristic impedance and the impedance of the annular sheet. This understanding is based on the concept of resistors in parallel.
  • #1
timhunderwood
12
0

Homework Statement


An annular sheet (i.e. a flattened ring) , of thickness t = 1mm and made of a material of resistivity 0.5 Ohm m connects the inner and outer conductors of an air spaced coaxial transmission line at a point on the line. A low frequency signal is fed into one end of the line and the other is terminated by its characteristic impedance. Calculate the relative amplitude of the wave reflected from the resistive sheet.

Homework Equations


The Attempt at a Solution


I firstly calculated the resistance/impedance of the annular sheet which i found to be:

Z(sheet)= ln(r2/r1)*p/(2*Pi*t) where r2 and r1 are radii of coaxial cable, t is thickness of sheet and p is conductivity.

I then used the formula
Reflection coefficient = (Z(sheet)-Z(characteristic))/(Z(sheet)+Z(characteristic))
from which the unknowns nicely cancel.

But this gives the wrong answer by a factor of about 1/2.

Am I missing something? I assumed that the termination by characteristic impedance completely absorbed all waves reaching end of transmission line... Is my derivation of the impedance of the annular sheet correct?

Thanks
 
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  • #2
Should the impedance at that point be the parallel combination of Zs and Zc?
 
  • #3
Thank you very much, this gives the right answer...

However, could you explain why?

I don't think I really understand why the impedance at that point should be considered as the parallel combination of Zc and Zs, although I recognise that the circuit looks like resistors in parallel...
 
  • #4
Resistors in parallel is the correct mental picture for this problem.
 

Related to Transmission line relative amplitude question

1. What is a transmission line relative amplitude question?

A transmission line relative amplitude question is a question that asks about the change in amplitude of a signal as it travels along a transmission line. This is important in understanding the behavior of signals and the performance of a transmission line.

2. How is relative amplitude calculated in a transmission line?

The relative amplitude in a transmission line is calculated by taking the ratio of the amplitude at a certain point along the line to the amplitude at the source of the signal. This can be expressed in decibels (dB) or as a percentage.

3. What factors can affect the relative amplitude in a transmission line?

There are several factors that can affect the relative amplitude in a transmission line, including the length and type of the line, the frequency of the signal, and the presence of any impedance mismatches or losses in the line. Environmental factors such as temperature and humidity can also have an impact.

4. Why is relative amplitude important in transmission line design?

Relative amplitude is an important consideration in transmission line design because it affects the overall performance and efficiency of the line. It can impact the quality of the signal, as well as the amount of power that is lost during transmission. Properly managing relative amplitude can help optimize the performance of a transmission line.

5. How can the relative amplitude in a transmission line be improved?

The relative amplitude in a transmission line can be improved by using proper line design techniques, such as minimizing the length of the line, using appropriate types of transmission line, and ensuring proper impedance matching. Additionally, using signal amplifiers and filters can also help improve the relative amplitude of a signal in a transmission line.

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