Solve Transmission Lines Homework: Coaxial Cable, 1kOhm, 10Ohm

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In summary, the problem involves a coaxial cable driven by a pulse source with 1kohms internal impedance and 1 V amplitude, square wave with duration of both positive and negative pulse is 800 ns, and a load impedance of 10 ohms. The characteristic impedance of the coax line is 53 ohms. The question asks for a sketch of the voltage at the end of the line as a function of time for 250 ns. The solution involves calculating the reflection coefficient at the input and output, considering the potential divider at the start of the transmission line, and understanding the behavior of the wave as it travels down the cable.
  • #1
shivik89
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Homework Statement


can someone help me solving this problem ?
A coaxial cable is driven by a pulse source with internal impedance of
1kohms, 1 V amplitude, square wave with duration of both positive and negative pulse is
800 ns, with negligible rise- and fall-time. The load impedance is 10 ohm.The characteristic ipedance of the coax line is 53 ohms.
Sketch the voltage at the end of the line as function of time for 250 ns.

Homework Equations

The Attempt at a Solution

 
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  • #2
shivik89 said:
Sketch the voltage at the end of the line as function of time for 250 ns.

nS or uS?

Forum rules require you to at least make an attempt at a solution.
 
  • #3
CWatters said:
nS or uS?

Forum rules require you to at least make an attempt at a solution.
Thanks for the reply, can you help. it is asked in ns?I tried calculating the reflection coefficent at the input and output but can't get an idea how the voltage will look like
 
  • #4
Ok what happens at the start of the transmission line - think potential divider.
 
  • #5
I guess at start.The 1V will be divided between the source resitance of 1 kohms and the characteristic impedance of the cable of 53 ohms. so the forward traveling wave is 53/(1000+53) *1 V ?
 
  • #6
Yes so a wave/step up of that magnitude sets off down the cable. What happens when it gets to the other end? And what's the voltage that end until it arrives.
 

What is a coaxial cable?

A coaxial cable is a type of transmission line used for transferring radio frequency (RF) signals. It consists of a central conductor, surrounded by a dielectric insulator, and then an outer conductor, usually in the form of a metal shield. This design allows for efficient transmission of signals while minimizing interference from external sources.

Why is 1kOhm used in transmission lines?

1kOhm is a common value used for the characteristic impedance of transmission lines. This value is chosen because it minimizes signal reflection and maximizes power transfer. It is also a value that can be easily matched to other components in the circuit.

What is the purpose of a 10Ohm resistor in a transmission line?

The 10Ohm resistor is used as a terminating impedance at the end of the transmission line. This helps to prevent signal reflections and ensures that the signal is fully absorbed by the load at the end of the line.

How do you calculate the characteristic impedance of a coaxial cable?

The characteristic impedance of a coaxial cable can be calculated using the formula Z = (138 log(D/d)) / √εr, where D is the outer diameter of the cable, d is the inner diameter, and εr is the relative permittivity of the dielectric material. This formula assumes a solid dielectric material, so adjustments may need to be made for other types of dielectrics.

What factors can affect the performance of a coaxial cable?

The performance of a coaxial cable can be affected by factors such as the type and quality of the materials used, the length and diameter of the cable, the frequency of the signal being transmitted, and external sources of interference. Proper installation and maintenance are also important for optimal performance.

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