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I am reading through a PDF of a book on transmission lines, and ran into a question in the book that kind of stumped me.

A transmission line driven by 2.4 GHz generator has a Thevenin equivalent impedance of 50 ohms. The transmission line is lossless, infinite, and has a characteristic impedance of 100 ohms. The maximum power that can be delivered to any load from the generator is 1W.

  1. What is the total (phasor magnitude) voltage at the input of the transmission line?
  2. What is the forward-traveling voltage at the generator side of the transmission line?
  3. What is the forward-traveling current at the generator side of the transmission line?

Using the maximum power equation, I determined that the generator amplitude is 20 V (let Rl = Rs = 50). $$\frac{\frac{1}{2}|E|^2R_L}{(R_S+R_L)^2} = P_{max}$$

I know I can solve (2.) because I can treat an infinite transmission line as a "load", so I can determine V+ with a simple voltage divider between the 50 ohm impedance of the generator and the characteristic impedance of the transmission line.

$$20V\frac{100}{50+100} = 13.33 V$$

What is the difference between (1.) and (2.)?

If the transmission line is infinite, there is never a reverse-traveling voltage, right?

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    \$\begingroup\$ Note, the maximum power delivered to the load is 1 W \$\endgroup\$
    – Chu
    Commented Sep 6, 2022 at 7:19
  • \$\begingroup\$ Difference between 1 and 2 <-- none as far as I can tell. \$\endgroup\$
    – Andy aka
    Commented Sep 6, 2022 at 8:22

2 Answers 2

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If the transmission line is infinite, there is never a reverse-traveling voltage, right?

Correct, end-reflection is ignored but not source mismatch.

In a matched impedance network, half the power is always dissipated in the source. Such is the case for RF systems.

other info

One exception is a PV current source where the photoelectric conversion is a high impedance current source that supplies max power or MPT at a matched impedance of Voc/Isc. The PV does not heat up if there is no load.

Even if the end was matched, in theory, there is no reflection regardless. In practice, nothing is perfectly matched and there is no such lossless infinite line or zero ohm conductor in ambient temperatures.

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  • \$\begingroup\$ So how will mismatch impact the magnitude of the voltage seen at the front of the transmission line? I'm guessing a reflection will exist between source impedance and this transmission line, which Increases the total magnitude of the voltage seen at the front of the transmission line, even though it doesn't impact the forward-traveling voltage? \$\endgroup\$
    – JohnnyMac
    Commented Sep 6, 2022 at 0:26
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100/(100+50) is known as the "emitting" coefficient Ke=2/3.
It is the part of "voltage" that will travel (and stay also at the input of the line)) into the 100 Ohm line ... without reflection at the "infinite" end.

There is no reflection (at input) when the generator sends "voltage", only Ke.
Reflexion appears only when there is reflected voltage (if one ) ...
And the reflection coefficient is then Kr,g=(Zg-Zo)/(Zg+Zo)=-1/3.

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