Impedance matching with complex source and load impedances

[rude man]

I can't recall which, maybe several, but I've seen in some ARRL books that characteristic impedance of a line can be visualized by sticking the probes of an ohmeter on the end of a transmission line that extends to infinity. I'll do a bit of digging.
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Edit: Radio Amateur's Handbook 1975 edition. It was on top of the pile, didn't look any farther.

That is correct.

 

[rude man]

Baluncore was illustrating how the concept of "impedance matching" can be misused if you don't consider the whole system. A low-power opamp can drive a 10k Ohm load no problem (up to the output voltage constraints of the opamp), so it would be strange to put a long 50 Ohm TL between the opamp and the 10k Ohm load to propagate the opamp signal to the load (a long enough TL so that at the frequencies of operation the TL characteristic impedance comes into play*).

A low-power opamp is not designed to drive a 50 Ohm load (you use a buffer amp for that), and a 10k Ohm load is not usually placed at the end of a 50 Ohm TL all by itself, since it's badly mismatched. Instead, if you were designing a system where an opamp output were driving a 10k Ohm load over long distances, you would use a buffer amp at the far end to preserve signal integrity and not waste boat-loads of power.

* And low-power opamps only have a bandwidth of 100kHz or so (a little more for the more expensive opamps), so any TL that was a couple wavelengths long would have a lot of resistive loss.

If the source impedance (op amp $Z_{out}$ + complementary series resistor) matches the cable $Z_0$ and the far end load is high then there is no distortion of the source signal at the load, just a time lag, and not a function of cable length. No wasted power.

 

[sophiecentaur]

What is this 51 ohm resistor? Does it play the role of a "matching device" in following sense:

Yes. If you want to terminate the 50Ω transmission line then your termination must be 50Ω. 51Ωin parallel with the 1k load will achieve that - but there would be other, better ways of doing it so it may look confusing. But how 'short' is the 'short' in the question?
A suitable line receiver for a 50Ω system would have 50Ω input impedance if the line were to be of significant length to ensure that all the received signal power gets into the circuitry. Signal to noise ratio is relevant in many cases.

 

[sophiecentaur]

For us slow-witted folks, visualizing the ohmeter probes on the transmission line that extends forever helps.

If you look at the display on a (50Ω) Time Domain Reflectometer you see an initial horizontal line - corresponding to start of the 50Ω section of the line - there will be a step in the line, corresponding to any change in impedance - when the signal, reflected by the discontinuity gets back to the sending end.
In that case, the TDR circuit is fast enough not to need the 'infinite' line that the simple Ohm meter. It will easily show the effect over a few cm of line. Of course, the source impedance of the TDR needs to be a good resistive 50Ω with an accurate 50Ω line on the way out etc. etc.. Measurements need picosecond resolution too.