# Sequel of "Impedance Matching when the Transmitter, Line and Load...."

• The Tortoise-Man
Ohm thing.In summary, @berkeman says that in general, impedance matching should be focussed on the maximization of power transfer, or not?f

#### The Tortoise-Man

Then might be regarded as continuation of discussion https://www.physicsforums.com/threa...ne-and-load-impedances-are-different.1009266/ where unfortunately it's not more possible to post further replies (why?). So I would like
to continue it here, since I think that there are some issues discussed there which require
a little bit more clarification.

@berkeman responded in the linked discussion in #25 as follws:

"I think this is pretty close to correct. If the line segments are long enough to manifest TL
effects (and thus generate reflections), it is best to use matching networks to minimize
reflections and wasted energy. If the joining sections are short, the matching networks are
probably not needed. Note though that even RF connectors are designed for a particular impedance
generally, even though they are electrically short at RF frequencies."

I'm a bit confused about the statement that "If the joining
sections are short, the matching networks are probably not needed."

As far as I understand it correctly, in general case where the source ##S## and load ##L##
have complex impedances ##Z_S## and ##Z_L## there are two standard but different impedance matching methods known:
the maximal power transfer and the minimization of reflected signal waves (they only coincide if the impedances of source and load are real, ie resistive.

But in general setting that's not the case. So if we have such source and load with complex
impedances given and our goal is to match them, we should ask ourself a basic question
depending on the context "What is for us in THIS situation more important? To
maximize the transferred power to the load or to minimize the reflected waves?

As I said in general to obtain both simultaneouly is mathematically not possible
(see my opener #1 in https://www.physicsforums.com/threa...ne-and-load-impedances-are-different.1009266/ )

And now we come back to @berkeman's statement. If we deal with the case that
joining sections (=transmission lines) are short (with resp the used wavelenghts, I guess),
then we know that the wave reflection effects are neglectable.

So in this case the impedance matching should be focussed on the maximization of
power transfer, or not?

So I not understand why berkeman said there that in case of short joining sections NO
impedance matching is needed.

Doesn't this condition only exclude the neccessarity for carring for the signal reflection issues? But then since we can exclude the neccessarity for minimization of wave reflection, we can focus ourself on maximization of power transfer only, or not?

Or did I misunderstood the point there?

Say you have a ±10V signal from an op-amp with a 10 mA output current limit, driving a module having a 10k ohm input resistance. You want to use a short 50 ohm line for the job.

If you terminate the line output with a 51 ohm resistor, the op-amp will need to deliver 10V / 50R = 200 mA. But the op-amp can only deliver 10 mA, so it will require a 200 mA line driver. Then 99.5% of the power will end up in the termination resistor. That is a waste of money, energy, and PCB real-estate.

If instead you ignore the matching, the line will look like a low-pass network, which you can make look to the low impedance op-amp output, more like the 10k load.

DaveE and berkeman

Then might be regarded as continuation of discussion https://www.physicsforums.com/threa...ne-and-load-impedances-are-different.1009266/ where unfortunately it's not more possible to post further replies (why?).
It is generally against the PF rules to re-post a locked thread. That thread was closed because of contentious debates that your questions sparked, which is not really your fault. I'll re-open this thread for a bit to see how it goes. Hopefully we can stay on-topic without too much debating this time.

That said, what specifically are you asking these questions for? Do you have a particular system or setup that you want to understand? Or are you just trying to understand general concepts involved in impedance matching? If you could narrow down your questions, that would probably help to avoid any contentious debates about generalities.

the maximal power transfer and the minimization of reflected signal waves (they only coincide if the impedances of source and load are real, ie resistive.
Most real-world situations will involve real impedances. The main one that I know of that does not is matching to an electrically short antenna...

And now we come back to @berkeman's statement. If we deal with the case that
joining sections (=transmission lines) are short (with resp the used wavelenghts, I guess),
then we know that the wave reflection effects are neglectable.
If I have a 50 Ohm source and a 50 Ohm coax cable connecting to a 50 Ohm load for an RF application, I'm not going to sweat it if I only have a 75 Ohm coax adapter/connetor to go from one 50 Ohm thing to another...

hutchphd
Very short transmission lines wouldn't need a termination because there can't really be a wave propagating to cause the undesirable effects of a mismatch (VSWR and such). Compared to the frequencies of interest, everything happens essentially instantaneously; a wave wouldn't have a significant phase shift from one end to the other. The entire source-load impedance can be well modeled as a single impedance network. Of course you may want to choose what those impedances are for various reasons, but I wouldn't call it matching a TL.

berkeman
I think the op needs to eliminate transmission lines from his thinking as @DaveE had implied. After @The Tortoise-Man has his head wrapped around everything that happens with various loads on amplifiers with various output impedance, including reactive loads, then transmission lines can explored. @The Tortoise-Man send me a PM if you like.

berkeman
I am very confused by this entire exercise. Perhaps my understanding is amiss so I will ask simple questions: Isn't the impedance of a cable only defined for a cable of infinite length? By what token can you apply it to this circumstance?
The supposition that the two ends of the cable don't see the other external impedances might be ok in certain circumstances but needs justification IMHO.

Isn't the impedance of a cable only defined for a cable of infinite length?
I think this may be a semantic issue. I can define a characteristic impedance for anything that can resonate, like a simple L-C, or a very short line. Granted, Zo isn't that useful away from resonance for networks or short lines, but it exists mathematically. Anyway, infinity isn't required. It's useful for TLs as a descriptive parameter. For example, in LTspice if you want to simulate a lossless TL, you would normally input the time delay and impedance.

The supposition that the two ends of the cable don't see the other external impedances might be ok in certain circumstances but needs justification IMHO.
Or it might just be wrong.

But the"it looks like a 50 ohm resistive load" is only because the "dissipated" energy is actually heading on down the line to infinity yes? So a shorter section of coaxial cable will look like some sort of "pi" or "T" L-C filter? Are there standard ways to choose the characterizations or is this a black art? Apologies for my ignorance.

Are there standard ways to choose the characterizations or is this a black art?
You use the length of cable required to connect the modules.
You then consider it more carefully if the length of cable is over about 1/20 wavelength.
Otherwise, you just call it a small lump of capacitance, or a series inductor.

Isn't the impedance of a cable only defined for a cable of infinite length?

##Z_0## is well defined in the literature, and I use it every day. One way to measure the ##Z_0## of a TL with length of a couple of wavelengths is to connect a potentiometer at the end and turn the little dial thing until there are no reflections for an input waveform drive. There are no infinities involved in that measurement, no?

sophiecentaur and DaveE

https://web.mst.edu/~kosbar/ee3430/ff/transmissionlines/z0/index.html

Isn't the impedance of a cable only defined for a cable of infinite length?
It is a transmission line if the capacitance and the inductance are distributed over the length of the line. If you make a ladder network out of many series inductors and parallel capacitors, it will behave like a transmission line, with Zo = √(L/C).
You can calculate Zo from the physical cross section of the line, without knowing the length.
You can measure Zo of 1" of line with a TDR.
https://en.wikipedia.org/wiki/Time-domain_reflectometer

DaveE
https://en.wikipedia.org/wiki/Coaxial_cable
Please see sec 6 in particular 6.3 where this is derived (for an infinite cable). I think that method of measurement allows the meter to assure a node at the end of the cable and extrapolate. But I am not at all expert here and this is a dark art!

You can measure Zo of 1" of line with a TDR.
But I don't really understand the definitionof ##Z_0## except for an infinite cable...can you help?

##Z_0## is well defined in the literature, and I use it every day. One way to measure the ##Z_0## of a TL with length of a couple of wavelengths is to connect a potentiometer at the end and turn the little dial thing until there are no reflections for an input waveform drive. There are no infinities involved in that measurement, no?
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.

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Snapped a few pix of the subject matter. I don't think the ARRL will throw any fuss about me snapping some pix out of a 1975 handbook.

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When defining Zo, we need to get away from infinite lines and standing waves.
Simply calculate the capacitance and inductance of 1” of line, then compute Zo = √(L/C).
That will be the dot in the middle of a Smith Chart.

Remember Ohms law? Impedance = Voltage / Current.
For a transmission line, conceptually;
Series inductance reduces the line current, while increasing the line voltage.
Parallel capacitance increases the line current while reducing the line voltage.
Zo is the geometric mean of the two parameters. Zo = √(L/C).

Averagesupernova
When defining Zo, we need to get away from infinite lines...
For us slow-witted folks, visualizing the ohmeter probes on the transmission line that extends forever helps.

hutchphd
But I don't really understand the definitionof ##Z_0## except for an infinite cable...can you help?
I think part of the confusion here may be the difference between characterizing a TL as a circuit element (with a characteristic impedance), and the input impedance of a real TL including it's termination. An ideal matched termination makes the line appear at the input as if it's infinite in length, which would have an input impedance equal to the characteristic impedance. Any other termination requires analysis of the input impedance which is a function of the characteristic impedance, length, and termination. So, the characteristic impedance of just the TL is still well defined, but it's not necessarily the input impedance of the network (TL + termination).

hutchphd
Another way of saying this is that the characteristic impedance of a (finite length) TL is the value of the termination that makes it appear from it's input as if it is infinite in length. i.e. no reflections.

alan123hk
My understanding of the characteristic impedance of the transmission line is very simple. It is the ratio of the corresponding voltage and current caused by the wave passing through the transmission line. This has nothing to do with the length of the transmission line, source impedance and load impedance, input and output impedance. Therefore, the characteristic impedance is only related to the material and structure of the transmission line itself. But of course it needs to be noted that there may be waves propagating forward and waves propagating in the opposite direction at the same time on the transmission line.

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DaveE
This has nothing to do with the length of the transmission line, source impedance and load impedance, input and output impedance.
Of course it has nothing to do with the length of the line so long as we cease our voltage/current measurements before the wave has arrived at the opposite end of the line. Hence the infinite length description. It helps us understand what is happening before saying: "Ok, now we give the line a specific length and describe what happens when we drive a line with a shorted, open, or terminated (properly or improperly), end, etc. etc."
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It's called characteristic impedance for a reason. Because it's a characteristic of the line, that's it.

Of course it has nothing to do with the length of the line so long as we cease our voltage/current measurements before the wave has arrived at the opposite end of the line.
If the load impedance of the transmission line does not match the characteristic impedance of the transmission line, the input impedance at the other end of the transmission line is not equal to the characteristic impedance, as described in Post 21. But this will affect the input impedance (what I call it), not the characteristic impedance. I just want to say that the characteristic impedance is not affected.

DaveE
Say you have a ±10V signal from an op-amp with a 10 mA output current limit, driving a module having a 10k ohm input resistance. You want to use a short 50 ohm line for the job.

If you terminate the line output with a 51 ohm resistor, the op-amp will need to deliver 10V / 50R = 200 mA. But the op-amp can only deliver 10 mA, so it will require a 200 mA line driver. Then 99.5% of the power will end up in the termination resistor. That is a waste of money, energy, and PCB real-estate.

If instead you ignore the matching, the line will look like a low-pass network, which you can make look to the low impedance op-amp output, more like the 10k load.

Sorry for my dumbness but I'm sure if I understand your example. What you mean by the formulation
"terminate the line output with a 51 ohm resistor"?

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

Or do you have another configuration in mind?

What you mean by the formulation
"terminate the line output with a 51 ohm resistor"?

What is this 51 ohm resistor? Does it play the role of a "matching device" in following sense:
Yes, if you want to fix the large mismatch between the 50 Ohm TL and the 10k Ohm load, you would use a matching network that has 50 Ohm input impedance and 10k Ohm output impedance.

But this is obviously a bad thing to do, and the whole system should be re-engineered to make it work better without dissipating lots of un-needed power. Driving a 10k Ohm load with a transmission line would probably not be the way that you would handle that situation in real life. More likely you would use a low-power 50 Ohm TL with a separate low-power amplifier at the output to drive the high-Z load.

It is generally against the PF rules to re-post a locked thread. That thread was closed because of contentious debates that your questions sparked, which is not really your fault. I'll re-open this thread for a bit to see how it goes. Hopefully we can stay on-topic without too much debating this time.

Sorry, you are right, presumably sending a PM to you about how to continue the discussion there would have been a better option. I will keep that in mind.

That said, what specifically are you asking these questions for? Do you have a particular system or setup that you want to understand? Or are you just trying to understand general concepts involved in impedance matching? If you could narrow down your questions, that would probably help to avoid any contentious debates about generalities.

Right, at the moment I'm just trying to understand general concepts. I will try to make my questions concise.

berkeman
Sorry, you are right, presumably sending a PM to you about how to continue the discussion there would have been a better option. I will keep that in mind.
Thank you very much.

Right, at the moment I'm just trying to understand general concepts. I will try to make my questions concise.
Thanks. The issue of impedance matching for signal integrity is important, since we use it all the time in designing and setting up instrumentation and industrial communication systems.

The issue of maximum power transfer is very important in power generation and transfer. See for example Maximum Power Point Tracking (MPPT) in solar generation systems and other power generation/transfer systems:

https://en.wikipedia.org/wiki/Maximum_power_point_tracking

And as I mentioned, it is true that maximum power is transferred when the load matches the complex conjugate impedance of the generator, but most systems that you will work with as an EE will have real impedances (with exceptions like electrically short antennas and AC Mains power consumers with low Power Factors that need corrective measures).

Yes, if you want to fix the large mismatch between the 50 Ohm TL and the 10k Ohm load, you would use a matching network that has 50 Ohm input impedance and 10k Ohm output impedance.

But this is obviously a bad thing to do, and the whole system should be re-engineered to make it work better without dissipating lots of un-needed power. Driving a 10k Ohm load with a transmission line would probably not be the way that you would handle that situation in real life. More likely you would use a low-power 50 Ohm TL with a separate low-power amplifier at the output to drive the high-Z load.

...And the "line resistance of 50ohms" plays here also then exactly the role
of "source impedance", right? (because the way how I understand the classical
impedance matching problem in usual/general setting
is reflected in the picture here: https://en.wikipedia.org/wiki/Impedance_matching
the source should "have" impedance, and the only paramater in Baluncore's
example coming into question for this "source impedance" ##Z_S## seems to be
this 50 ohm line.) In other words there are no some "additional" impedances on the source side given such that ##Z_S## arise as "total" impedance of these partial imps AND the line impedance of 50ohm? So this 50ohm line impedance is the only involved impedance contributing here to ##Z_S##, right? Or do I mixing here something up?

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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.

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.

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.

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.

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.