5
\$\begingroup\$

Consider a transmission line with characteristic impedance of Z₀ and electrical length of λ/4. One end of the transmission line is terminated in a load of impedance (lets assume) 2Z₀. The other end is connected to an ideal voltage source Vsrc. Will the reflection from the load end of the transmission line (due to the impedance mismatch) affect the functioning of the source? Will the reflected wave from the load end get again reflected from the source end or does it get absorbed there so that the source can provide the same voltage of Vsrc?

\$\endgroup\$
2
  • 2
    \$\begingroup\$ have you considered an ideal voltage source plus the correct termination resistor (at the source end), rather than zero ohm? This would be a more realistic model. \$\endgroup\$
    – Rodney
    May 18, 2022 at 8:47
  • \$\begingroup\$ @Rodney When a source resistance is added will that stop reflections from the source end. I did not include the resistor in my simulation. I will try that out. Thank you. \$\endgroup\$ May 19, 2022 at 3:05

3 Answers 3

8
\$\begingroup\$

An ideal voltage source has 0 impedance. If a transmission line is terminated at one end with an ideal voltage source, it will reflect any incoming waves in the same manner as a short-circuit would reflect the waves, with one difference. While a short circuit termination holds the voltage at 0, and reflects the wave, an ideal voltage source would hold the voltage at whatever level it is specified at (and reflect the wave).

A good way to visualize this, is to imagine a jump rope that is held fixed at one end. If one applies motion to the other end, the motion will cause a wave to travel down the rope, and reflect off the fixed end. Now imagine that the fixed end is higher than originally. The same thing will happen, only the fixed end holds the wave at a higher elevation. But the wave will still be reflected.

\$\endgroup\$
5
\$\begingroup\$

Will the reflected wave from the load end get again reflected from the \$\color{red}{\text{ideal }}\$source end or does it get absorbed there so that the source can provide the same voltage of Vsrc?

There will be a total reflection from the ideal source, because there is a total impedance mismatch; the initial reflection from the load travels back to the ideal source under controlled impedance conditions (dictated by the transmission line) and, when that reflection reaches the ideal source, its energy cannot be dissipated and is fully reflected.

Here's a simulation of a 25 metre 50 Ω t-line terminated in 100 Ω. The initial voltage step is 1 volt and is applied at t = 50 ns: -

graphs showing voltages and currents at different points in the circuit

  • A 1 volt step is applied at t = 50 ns
  • The 1st reflection from the load occurs 125 ns after the 1 volt is applied.
  • The 1st reflection from the source occurs 250 ns after the 1 volt is applied. You see that reflection in the current waveform of R1.
\$\endgroup\$
2
\$\begingroup\$

Normally we don't use ideal voltage sources and transmission lines together. Ideal voltage sources are an approximation from circuit theory, and (continuous) transmission lines are a step beyond circuit theory. The right model to use with transmission lines is an ideal voltage source in series with an output impedance.

If (for some reason) you want to use a bare ideal DC voltage source, you can replace it with a short circuit at AC, just like with lower-frequency circuits.

\$\endgroup\$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.