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Old 29th Jul 2009, 12:04 pm   #61
G8HQP Dave
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Default Re: Impedance matching theory.

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Actually Dave, was maximum power transfer theorem more introduced with transmission line theory with the now obvious constraints
Transmission lines bring in extra complications because signals get reflected from discontinuities. For the sake of amusement I will raise a question: if a transmission line has a complex impedance should it be terminated by its impedance or the conjugate impedance? Transmission line theory says impedance (for no reflection), maximum power transfer says conjugate. Which is right? Can a little reflection sometimes be a good thing? (I think the right answer is that at the load end the impedance should match the transmission line, but at the source end the conjugate should be used.)

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The equal source/load impedance situation is also the point of lowest overall efficiency, in that half the power is lost in the source.
Well, it all depends! If you really have a voltage source with a series resistance then the lowest efficiency comes with a low (approx zero) load resistance, as all the power generated by the voltage source is dissipated in its own output resistance. The converse is true if you really have a current source with a parallel resistance. Remember that the Thevenin and Norton equivalent circuits are only equivalent as far as the rest of the circuit is concerned; internally they are different and can have different power loss.
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Old 29th Jul 2009, 2:18 pm   #62
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Default Re: Impedance matching theory.

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lowest efficiency comes with a low (approx zero) load resistance
Yes, obviously. (I must be getting old).

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if a transmission line has a complex impedance
... then it's not a transmision line, surely?? The whole point of a transmission line is that a chunk of it maps the rest of it to the impedance it first thought of. I can't see that working unless it's resistive.
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Old 29th Jul 2009, 2:33 pm   #63
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Default Re: Impedance matching theory.

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Originally Posted by GMB View Post
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lowest efficiency comes with a low (approx zero) load resistance
Yes, obviously. (I must be getting old).

Quote:
if a transmission line has a complex impedance
... then it's not a transmision line, surely?? The whole point of a transmission line is that a chunk of it maps the rest of it to the impedance it first thought of. I can't see that working unless it's resistive.
Totally agree, I have spent hours over smith charts .......... The best dummy load can be a very long piece of lossy cable

Mike
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Old 29th Jul 2009, 3:36 pm   #64
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Default Re: Impedance matching theory.

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... then it's not a transmision line, surely?? The whole point of a transmission line is that a chunk of it maps the rest of it to the impedance it first thought of. I can't see that working unless it's resistive.
Maybe I shouldn't have introduced this - I did say it was for amusement! You can have a transmission line with a complex impedance, but I think it will be lossy and dispersive so maybe not very useful. This is why the equations for transmission lines use Z rather than R and talk about characteristic impedance rather than characteristic resistance, even though Z is almost always then assumed to be a pure resistance. In real life, of course, all transmission lines have a complex impedance but the reactive part is small compared with the resistive part so is usually ignored.

Quote:
The best dummy load can be a very long piece of lossy cable
Yes, because almost any transmission line cable you buy will have a nearly pure resistive characteristic impedance, whereas most resistors have parasitic reactances. I think the original trunk telephone circuits had a complex impedance and were dispersive, and this was cured by adding lumped inductance - a counter-intuitive idea suggested by Oliver Heaviside and poo-pooed by the 'engineers' at the GPO, but tried and adopted in the US.

We seem to have come a long way from pentode audio output stage transformers!
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Old 29th Jul 2009, 3:48 pm   #65
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Arrow Re: Impedance matching theory.

Transmitter - transmission line - load; one of my pet subjects.


First of all, let's tidy up the use of the word 'impedance'. Although this word, by definition, includes reactance and resistance, in the context of transmission lines it gets mis-used. e.g. "this transmission line has an characteristic impedance of X ohms". Although I would agree that the line will have some reactance, for all intents & purposes, this reactance can be considered as insignificant - if it's a half-decent transmission line, that is! The load, on the other hand can be an impedance: resistive and reactive.

What seems to cause confusion to some people is when a transmitter O/P socket is labelled "X ohms". It does not have an O/P impedance of X ohms! The term means that it is designed to 'see' a resistive load of X ohms for perfect matching; the O/P impedance of the transmitter itself ideally will be very low - and almost certainly contain some reactance as well as a resistive component. Look at it this way: if the 'O/P impedance' was X ohms, only half the available power would go to the load of X ohms, where X is resistive only. (Assuming a transmission line with zero losses).

When the load contains a reactive element, some forward power is reflected back to the transmitter and since the transmitter does not have an O/P impedance of X ohms, a further reflection takes place and the wave travels back to the load - again - and so on. This last point is frequently not appreciated, in my experience.

Al. / Skywave.
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Old 29th Jul 2009, 3:52 pm   #66
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Wink Re: Impedance matching theory.

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Originally Posted by G8HQP Dave View Post

Maybe I shouldn't have introduced this - I did say it was for amusement!

We seem to have come a long way from pentode audio output stage transformers!
Yes - but since the title of the Thread is "Impedance Matching Theory" - it is On Topic.

Al.
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Old 29th Jul 2009, 4:26 pm   #67
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Default Re: Impedance matching theory.

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Originally Posted by Skywave View Post
Transmitter - transmission line - load; one of my pet subjects.




When the load contains a reactive element, some forward power is reflected back to the transmitter and since the transmitter does not have an O/P impedance of X ohms, a further reflection takes place and the wave travels back to the load - again - and so on. This last point is frequently not appreciated, in my experience.

Al. / Skywave.
Well put Al , exactly what happens and then you get a nice standing wave develop.

Mike
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Old 29th Jul 2009, 5:12 pm   #68
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Default Re: Impedance matching theory.

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First of all, let's tidy up the use of the word 'impedance'. Although this word, by definition, includes reactance and resistance, in the context of transmission lines it gets mis-used. e.g. "this transmission line has an characteristic impedance of X ohms". Although I would agree that the line will have some reactance, for all intents & purposes, this reactance can be considered as insignificant - if it's a half-decent transmission line, that is!
No, this is not a mis-use of the term. It is a recognition that, in general, a transmission line does not have to have a resistive characteristic impedance. However, it is likely that any useful
Quote:
half-decent
line will be resistive.

Quote:
What seems to cause confusion to some people is when a transmitter O/P socket is labelled "X ohms". It does not have an O/P impedance of X ohms! The term means that it is designed to 'see' a resistive load of X ohms for perfect matching; the O/P impedance of the transmitter itself ideally will be very low - and almost certainly contain some reactance as well as a resistive component. Look at it this way: if the 'O/P impedance' was X ohms, only half the available power would go to the load of X ohms, where X is resistive only. (Assuming a transmission line with zero losses).

When the load contains a reactive element, some forward power is reflected back to the transmitter and since the transmitter does not have an O/P impedance of X ohms, a further reflection takes place and the wave travels back to the load - again - and so on. This last point is frequently not appreciated, in my experience.
I agree. I think my comment about conjugate matching at the source end was a bit daft! The typically huge mismatch at the source end is the reason why low SWR is not quite as important as some people seem to think.

The maximum power transfer theorem does have a relevance to receivers - the match between the antenna and the input (mediated via the transmission line, if present). You do get best power transfer by conjugate matching the impedances, and the power lost in the source resistance is real: it is re-radiated by the antenna (I only realised this a few years ago). So a well-matched receive antenna will radiate half the power it absorbs from the incoming signal, and send the other half to the receiver.
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Old 29th Jul 2009, 5:22 pm   #69
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Default Re: Impedance matching theory.

If the source impedance is complex, then maximum power transfer does occur if the load impedance is the conjugate of the source impedance. Having a transmission line between them complicate things, because the impedance you see at your source end is not in general the same as at the load end. But, reflections, mismatches, or not, at a given frequency, it can always be represented as a real and imaginary part.

As has been said, decent transmission lines have a resistive characteristic impedance anyway.

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Originally Posted by G8HQP Dave View Post
So a well-matched receive antenna will radiate half the power it absorbs from the incoming signal, and send the other half to the receiver.
I can see this is going to be true, but it is something I had not thought of. Thanks very much Dave! What a great thread!
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Old 29th Jul 2009, 6:00 pm   #70
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Arrow Re: Impedance matching theory.

Quote; Al. / Skywave:
First of all, let's tidy up the use of the word 'impedance'. Although this word, by definition, includes reactance and resistance, in the context of transmission lines it gets mis-used. . . . .

Quote; Dave, G8HQP:
No, this is not a mis-use of the term. It is a recognition that, in general, a transmission line does not have to have a resistive characteristic impedance.

Point taken. I should have written "gets mis-understood".

Al.
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Old 29th Jul 2009, 6:26 pm   #71
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Default Re: Impedance matching theory.

Yes, Kalee20, after that post I did the maths and decided that a constant current source with parallel Ri did indeed loook like a constant source voltage with Ri as the series impedance. I guess a triode might have been a better example of a non-linear source.

Of course what all that ignores is the power consumed by the valve in generating the constant current. Being a class A output, the HT power consumed is a constant so arguably the maximum power transfer does indeed occur with an 8 ohm load rather than the 64 ohms.

it's been a fun thread but we seem to have got to the point where we all agree so I guess there's no entertainment value left.
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Old 29th Jul 2009, 9:00 pm   #72
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Question Re: Impedance matching theory.

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Originally Posted by G8HQP Dave View Post
I agree. I think my comment about conjugate matching at the source end was a bit daft! The typically huge mismatch at the source end is the reason why low SWR is not quite as important as some people seem to think.
Not necessarily; for serious powers at UHF & up isn't this need met by the use of a circulator, a 3-port device where forward power in at port 1 is fed to the load on port 2 and reverse power from the load arriving back at port 2 is sent to port 3 only and thus dumped into an idling load?

Aside: I phrase this as a Q. since it's not something I've actually had practical experience with, only read about.

Al. / Skywave.
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Old 29th Jul 2009, 10:18 pm   #73
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Default Re: Impedance matching theory.

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Not necessarily; for serious powers at UHF & up isn't this need met by the use of a circulator, a 3-port device where forward power in at port 1 is fed to the load on port 2 and reverse power from the load arriving back at port 2 is sent to port 3 only and thus dumped into an idling load?
Yes, with that arrangement any power reflected from the antenna would be dumped as you say. Likewise, I have no experience of this sort of thing.
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Old 29th Jul 2009, 11:12 pm   #74
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Default Re: Impedance matching theory.

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So a well-matched receive antenna will radiate half the power it absorbs from the incoming signal, and send the other half to the receiver.
Excuse my ignorance but I do not understand this statement.

Assuming a perfectly matched antenna surely there is no reflected power back to the source.

My limited understanding of antennas is that it may aborb the power but how well it raditaes that power is entirely dependent upon the antenna. You make the statement that half the power is radiated and half is relected back to source with a matched antenna.

There are antenna designs which use terminating resistors etc ( folded dipole with the ends terminated with a resistor as an example) which give a good broadband low SWr across a very broad frequency range however very little power is radiated because they are poor radiators broadband but good absorbers of power.

Mike
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Old 29th Jul 2009, 11:38 pm   #75
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Default Re: Impedance matching theory.

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Originally Posted by Skywave View Post
...for serious powers at UHF & up isn't this need met by the use of a circulator, a 3-port device where forward power in at port 1 is fed to the load on port 2 and reverse power from the load arriving back at port 2 is sent to port 3 only and thus dumped into an idling load?...
Depends on what you mean by 'serious' power. I've never personally met any circulator in use at, say, Band IV/V frequencies that operated at a power of much more than 50watts or so. Bear in mind that the insertion loss of a circulator is going to be of the order of 0.5 to 1.0dB in the forward direction, and in the reverse direction only of the order 20 to 25dB. This forward power loss is, in the context of 'serious' power levels (and I'm talking kilowatts here, not watts) quite unacceptable, and circulators are not used at these high power levels: in turn, this means that the antenna match is a problem that has to be seriously addressed if the main problem of reflected power (delayed images in the case of vision signals) is to be avoided (additionally, feeder systems are often quite highly stressed, and running at or near their peak power/voltage ratings: any significant standing waves therefore cannot be tolerated).

For lower power levels, there are alternative configurations that can be used to 'mop up' reflected power that don't incur quite the high loss levels (or the expense) of a circulator - the 'Engelbrecht' configuration of using two parallel amplifiers combined with a 3dB hybrid being a good example.
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Old 30th Jul 2009, 9:18 am   #76
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Default Re: Impedance matching theory.

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What seems to cause confusion to some people is when a transmitter O/P socket is labelled "X ohms". It does not have an O/P impedance of X ohms! The term means that it is designed to 'see' a resistive load of X ohms for perfect matching; the O/P impedance of the transmitter itself ideally will be very low
I have wondered about this, but now I disagree.

Anyone who doesn't have a button marked "tune" will know that there is a definite setting of the output matching that gives highest power output. This is characteristic of the maximum power theorem situation.

But I have a transmitter (Syncal 30) that, if any is going to have a low impedance output, this will be it. Designed to drive short aerials and with an internal tuner that can only correct for reactance, surely this will be one with a low output impedance?

But on high power it has a 50 ohm impedance. I just measured it. (On low power it seems to be a little higher, but that may just be a calibration issue.)

So I think it likely that RF systems do indeed match their outputs as suggested by the documentation. If you disagree then find a transmitter that actually does have a low output impedance while maximising it's output into 50 ohm load, i.e. not just a consequence of it's output matching being set that way.
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Old 30th Jul 2009, 9:40 am   #77
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Default Re: Impedance matching theory.

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...So I think it likely that RF systems do indeed match their outputs as suggested by the documentation. If you disagree then find a transmitter that actually does have a low output impedance while maximising it's output into 50 ohm load, i.e. not just a consequence of it's output matching being set that way.
Just stop and think about this for a moment. If you have, say, a transmitter generating 50kW with an output impedance of 50 ohms feeding a 50 ohm load, then 25kW will be dissipated in the load, and 25kW in the output stage of the transmitter. There is no way that transmitter engineers are going to throw away this amount of hard-won power, quite apart from the problem of where you safely dissipate 25kW of RF power inside the transmitter. The truth of the matter is that a TX labelled '50 kW, 50 ohm' will be designed to safely drive its 50kW into an external 50 ohm load, and there is no supposition that the output impedance of the TX (ie, that impedance seen looking backwards into the TX output socket) is actually 50 ohms. The output impedance of the TX will actually be as low as can be achieved (and which is what causes all of the problems with reflected signals from a badly-matched aerial system), and one of the first things that TX engineers are taught is that the Maximum Power Transfer theorem has no part in their everyday lives, and should ideally be taken outside and burnt.

(I'll just give you some typical figures for a 25kW vision TX. RF output power from TX = 25kW, measured. DC power input to final amplifier, 42kW, measured. Overall efficiency thus about 60%. But if the TX had an output impedance of 50 ohms, there'd also be 25kW being dissipated in the TX: total RF power, 50kW, but input DC power still 42kW. Efficiency, 120%. maybe we're onto something in the perpetual motion line, here...)

Last edited by Ray Cooper; 30th Jul 2009 at 9:46 am.
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Old 30th Jul 2009, 9:56 am   #78
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Default Re: Impedance matching theory.

You are assuming that a thing that varies it's output voltage as if it has an internal resistance actually does contain a resistor and hence dissipates the undelivered power.

It doesn't have to be that way and I suspect that most transmitters do manage to dissipate less power than you would expect from the matching.
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Old 30th Jul 2009, 10:28 am   #79
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Default Re: Impedance matching theory.

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...Anyone who doesn't have a button marked "tune" will know that there is a definite setting of the output matching that gives highest power output. This is characteristic of the maximum power theorem situation...
But it's also characteristic of any matching system that converts an optimum working load (from the TX active device) into a wanted load (the aerial). There's no need to invoke the MPT theorem at all.

Quote:
...But I have a transmitter (Syncal 30) that, if any is going to have a low impedance output, this will be it. Designed to drive short aerials and with an internal tuner that can only correct for reactance, surely this will be one with a low output impedance?

But on high power it has a 50 ohm impedance. I just measured it. ...
It may only need to have a low output impedance in comparison to the rather high load impedance presented by a short wire aerial. It may well be about 50 ohms, in this particular case. But in the case of a TX designed to drive a 50 ohm load, the output impedance would be much lower.

Quote:
...You are assuming that a thing that varies it's output voltage as if it has an internal resistance actually does contain a resistor and hence dissipates the undelivered power...
I'm sorry, you'll have to re-phrase that statement in a form that a person of my limited brain can understand...

Of course there's an internal resistance. It may not be a physical component with wire ends and '50 ohms', or whatever, written upon it, but a source resistance is present in equivalent form in some manner, whether copper losses in tuning circuits, AC load lines of active components or whatever. And that equivalent resistance will dissipate power. If you're maintaining that there is no internal resistance, then of course the thing must have a zero output impedance (let's leave reactive components aside for the moment) annd would dissipate no power at all. Which seems a far cry from your claimed 50 ohms output impedance...
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Old 30th Jul 2009, 12:01 pm   #80
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Default Re: Impedance matching theory.

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It may only need to have a low output impedance in comparison to the rather high load impedance presented by a short wire aerial.
Once the reactance is cancelled out a short aerial has a very low resistance, hence the expectation of a low transmitter output impedance to drive it.

Quote:
I'm sorry, you'll have to re-phrase that statement
I'm not good at expressing myself, especially as I don't have enough time to think about this interesting subject...

What I am saying is that I think it is possible to have a system that appears to have a source impedance, in that as you load it up the voltage goes down, but there are (almost) no losses. This situation occurs when there is some energy limited transfer going on, e.g. like in a switched mode power supply (or class C output stage?). But I would add that the impedance will not appear to be a simple constant in this situation, and (rather usefully) it seems to mirror the load, which is perhaps not so surprising.

Having said that I calculate that the example of 42KW in to get 25KW into 50 ohms could have a simple output impedance of 34 ohms - so not really that low at all.
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