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 Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2 

What does the tuner do?
Poll ended at Sun Jan 10, 2010 5:58 pm
It changes the antenna feedpoint impedance at Point A to 50 ohms 0%  0%  [ 0 ]
It changes the antenna feedpoint impedance at Point A to 300 ohms 0%  0%  [ 0 ]
It makes the VSWR on the ladderline 1:1 0%  0%  [ 0 ]
It creates a conjugate match at Point A 0%  0%  [ 0 ]
It changes the impedance at Point B to 300 ohms 0%  0%  [ 0 ]
It creates a conjugate match at Point B 0%  0%  [ 0 ]
It reduces the VSWR on the ladderline 0%  0%  [ 0 ]
It presents a 50+j0 Ohm load to the Transmitter 64%  64%  [ 7 ]
It creates a conjugate match at Point C 36%  36%  [ 4 ]
Total votes : 11

 Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2 
Silent Key

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Post Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2
Folks,

Now that we've learned a bit about conjugate matching, lets see how it works out in a practical antenna system:

Simon is considering the antenna system for 80m shown below:

Image

He realises that the doublet is not resonant and will have a complex feedpoint impedance. He also realises that the ladderline will transform that impedance into another complex value at the output of the tuner. But he knows that a good wide-range tuner should be able to match this impedance and present a 50 ohm load to the Transmitter. He asks a number of folk at his local club what function they think the tuner performs when it is adjusted for a reading of 1:1 on the SWR meter; by now you wont be surprised that he gets several answers


Which of the answers in the Poll is true? To keep things simple we'll assume that the ladderline and the tuner are loss-less, and that the SWR meter is "ideal" - i.e it reads accurately and doesn't affect the impedance seen by the Transmitter.

Enjoy,
Steve G3TXQ

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Thu Jan 07, 2010 5:58 pm
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 Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2 
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Post Re: Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2
1 to 7 are incorrect. as the "atu" only transforms any impedence between point B and C ( the input and output ) of the tuner . The values of Points A and B will be constant regardless of what the tuner does.

im going with number 8 as im still not 100% on conjugate (one for the to do list)

( im frying my head at the moment with the complexities of acid/ph and other chemicals in wine)

billy

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Thu Jan 07, 2010 7:52 pm
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 Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2 
Silent Key

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Post Re: Technical Puzzle #18
G7IGB wrote:
....... unless this is another play on words as the transceiver 'sees' a low SWR. :?


Rob,

No - there's no "play on words"! Whatever the load impedance is across the Transmitter output, that's what it "sees".

73,
Steve G3TXQ

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"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind;" (Lord Kelvin 1883)


Thu Jan 07, 2010 8:45 pm
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 Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2 
Silent Key

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Post Re: Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2
Folks,

I'll be posting the answer to this one tomorrow (Saturday) late afternoon/evening, so there's still plenty of time to have a go at the Poll - not many have dared so far, but remember it is anonymous :)

73,
Steve G3TXQ

_________________
"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind;" (Lord Kelvin 1883)


Fri Jan 08, 2010 5:56 pm
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 Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2 
Silent Key

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Post Re: Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2
Folks,

From the results of the Poll it looks like all of you are going to be very surprised by the answer, so I'd better try to explain it carefully and in some detail.

Let's look at the antenna system again, and this time we'll "open up" the various nodes A, B and C, and use an antenna analyser to see what are the impedances looking towards the antenna on 3.650MHz:

Image

Point A: We disconnect the ladderline from the antenna and connect our analyser across the doublet terminals. Because the doublet is well short of a half-wave long we will have a lowish Resistive component and a high Capacitive reactance - in fact we get an impedance of about 26-j420. Now reconnect the ladderline to the antenna.

Point B: We disconnect the tuner from the ladderline and connect the analyser across the ladderline terminals. We know the ladderline will transform the antenna impedance (26-j420) into something quite different - in fact we measure 8.8-j2.8 ohms.

Nothing the tuner does can alter these two impedances,; so Answers #1, #2, #3, #5 and #7 must be wrong. You all realised that!

Point C: We disconnect the SWR meter from the tuner and connect the analsyer across the tuner input. Assuming the tuner has been adjusted for a 1:1 VSWR, we will of course measure 50+j0, so Answer #8 is correct.

------------------------------------------------------------------------------------------------------------------------------------

All very straightforward so far, but here comes the really interesting bit!

Let's now replace our Transmitter with a 50 ohm resistor to represent its source impedance, and let's measure the various impedances again - this time "looking back" in the direction of the Transmitter instead of towards the Antenna; in other words we're looking at the source impedances at each point instead of the load impedances. Oh, and don't alter the tuner settings!!!

Image

Point C: We disconnect the SWR meter from the tuner and connect our analyser across the SWR meter output terminals - "easy peasy", we will measure 50+j0 or 50-j0 - they're the same thing. Now reconnect the SWR meter to the tuner.

Point B: Disconnect the output of the tuner from the ladderline again, but this time connect the analyser across the tuner output terminals. Knowing the tuner component values which produced the 1:1 VSWR initially, we can work out how those components will change the 50 ohm resistance. For the simple L-network which I've assumed, the series L will be 1uH and the shunt C will be 1870pF. A few network calculations and we discover that these components will alter the 50 ohm resistance at the tuner input so that we measure 8.8+j2.8 ohms at the tuner output. Now reconnect the tuner output to the ladderline.

Point A: Finally, disconnect the ladderline from the antenna and connect the analyser across the ladderline terminals. The impedance we measured at the tuner output [8.8+j2.8] will have been transformed by the ladderline and we will measure an impedance of 26+j420

----------------------------------------------------------------------------------------------------------------------------------

Here's the "Eureka" moment! We've measured:

Point A: Source impedance = 26+j420, Load impedance = 26-j420
Point B: Source impedance = 8.8+j2.8, Load impedance = 8.8-j2.8
Point C: Source impedance = 50+j0, Load impedance = 50-j0

That should look familiar from the previous Puzzle! At every point - A,B, and C - there is a Conjugate Match between the source impedance and the load impedance !!!!!! So Answers #4, #6 and #9 are also correct!

Amazingly, adjustment of the tuner has created a conjugate match at every point in the system. At points between itself and the Antenna it hasn't been able to change the load impedances, but it has been able to change the source impedances to produce a conjugate match; at points between itself and the Transmitter it can't alter the source impedance but it can alter the load impedance to produce a conjugate match. And once it produces a conjugate match at one point, there will be a conjugate match at every point. Even if we broke the ladderline at some arbitrary point and measured the impedance looking towards the antenna and the impedance looking back towards the tuner, we would find they formed a conjugate match.

Call me odd, but it's discovering things like that which thrill me about engineering :)

Even without the maths, it's intuitive that this must be the case: the transmitter is "seeing" a 50 ohm load so it will deliver the maximum available power; the tuner and ladderline are lossless so there's only one place for the power to go - into the antenna. Therefore if we are extracting the maximum power available from the transmitter, and delivering it to the antenna, there must be a conjugate match everywhere in the system.

Another way of "getting your head" around this is to ask how we are going to easily transfer power into an antenna which has such a high capacitive reactance; the answer is that we need a source with the equivalent high inductive reactance. The action of the tuner and the ladderline is to transform the 50 ohm source resistance of the Transmitter into exactly the value of inductive reactance required to cancel the antenna's capacitive reactance and at the same time match its Resistive component.

So the next time someone tells you that a tuner doesn't alter the antenna's impedance, agree with them; but point out that it does alter the source impedance at that point so that maximum power gets transferred. Yes, the tuner really does affect the matching at the antenna feedpoint!

Please don't get confused - the 300 ohm ladderline is still mis-terminated at the antenna, and it still has a high VSWR on it - the tuner hasn't changed that; but it has created a system match at the antenna feedpoint - they are different things!

------------------------------------------------------------------------------------------------------------------------------

Don't worry - that's about as difficult a concept as we'll look at in these Puzzles :)

73,
Steve G3TXQ

_________________
"I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind;" (Lord Kelvin 1883)


Sat Jan 09, 2010 4:54 pm
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 Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2 
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Post Re: Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2
nice one steve, very good indeed and a great little read.. this is the stuff the forum should be about.. this is a great resource for new and old ops alike..

"Call me odd, but it's discovering things like that which thrill me about engineering"

not odd at all steve.. now if you were sat in a frock typing it that would be a little odd.. :lol:

billy

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Sat Jan 09, 2010 7:18 pm
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 Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2 
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Post Re: Technical Puzzle #18 - Matchmaker, matchmaker ...... Pt 2
Another belter, best poser and explaination to date.

This is what the hobby and guys like you are about. Self learning and spreading the knowledge. Pity there is not more contribution from other guys. But I am sure they are there on the sidelines and learning from this.

I didn't comment this time, as Billy and Rob had stated what I believed the answer to be, and went for the last two options. Although I did have a doubt where the point cojugate was, but didnt ever think in terms of all 3 points!

Looking forward to the next one.

C'MON you specators have a go even if it is anonymous. You might be surprised how much you know, but dont be surprised to find you don't, I have.... :roll:
G3TXQ wrote:
Folks,

From the results of the Poll it looks like all of you are going to be very surprised by the answer, so I'd better try to explain it carefully and in some detail.

Let's look at the antenna system again, and this time we'll "open up" the various nodes A, B and C, and use an antenna analyser to see what are the impedances looking towards the antenna on 3.650MHz:

Image

Point A: We disconnect the ladderline from the antenna and connect our analyser across the doublet terminals. Because the doublet is well short of a half-wave long we will have a lowish Resistive component and a high Capacitive reactance - in fact we get an impedance of about 26-j420. Now reconnect the ladderline to the antenna.

Point B: We disconnect the tuner from the ladderline and connect the analyser across the ladderline terminals. We know the ladderline will transform the antenna impedance (26-j420) into something quite different - in fact we measure 8.8-j2.8 ohms.

Nothing the tuner does can alter these two impedances,; so Answers #1, #2, #3, #5 and #7 must be wrong. You all realised that!

Point C: We disconnect the SWR meter from the tuner and connect the analsyer across the tuner input. Assuming the tuner has been adjusted for a 1:1 VSWR, we will of course measure 50+j0, so Answer #8 is correct.

------------------------------------------------------------------------------------------------------------------------------------

All very straightforward so far, but here comes the really interesting bit!

Let's now replace our Transmitter with a 50 ohm resistor to represent its source impedance, and let's measure the various impedances again - this time "looking back" in the direction of the Transmitter instead of towards the Antenna; in other words we're looking at the source impedances at each point instead of the load impedances. Oh, and don't alter the tuner settings!!!

Image

Point C: We disconnect the SWR meter from the tuner and connect our analyser across the SWR meter output terminals - "easy peasy", we will measure 50+j0 or 50-j0 - they're the same thing. Now reconnect the SWR meter to the tuner.

Point B: Disconnect the output of the tuner from the ladderline again, but this time connect the analyser across the tuner output terminals. Knowing the tuner component values which produced the 1:1 VSWR initially, we can work out how those components will change the 50 ohm resistance. For the simple L-network which I've assumed, the series L will be 1uH and the shunt C will be 1870pF. A few network calculations and we discover that these components will alter the 50 ohm resistance at the tuner input so that we measure 8.8+j2.8 ohms at the tuner output. Now reconnect the tuner output to the ladderline.

Point A: Finally, disconnect the ladderline from the antenna and connect the analyser across the ladderline terminals. The impedance we measured at the tuner output [8.8+j2.8] will have been transformed by the ladderline and we will measure an impedance of 26+j420

----------------------------------------------------------------------------------------------------------------------------------

Here's the "Eureka" moment! We've measured:

Point A: Source impedance = 26+j420, Load impedance = 26-j420
Point B: Source impedance = 8.8+j2.8, Load impedance = 8.8-j2.8
Point C: Source impedance = 50+j0, Load impedance = 50-j0

That should look familiar from the previous Puzzle! At every point - A,B, and C - there is a Conjugate Match between the source impedance and the load impedance !!!!!! So Answers #4, #6 and #9 are also correct!

Amazingly, adjustment of the tuner has created a conjugate match at every point in the system. At points between itself and the Antenna it hasn't been able to change the load impedances, but it has been able to change the source impedances to produce a conjugate match; at points between itself and the Transmitter it can't alter the source impedance but it can alter the load impedance to produce a conjugate match. And once it produces a conjugate match at one point, there will be a conjugate match at every point. Even if we broke the ladderline at some arbitrary point and measured the impedance looking towards the antenna and the impedance looking back towards the tuner, we would find they formed a conjugate match.

Call me odd, but it's discovering things like that which thrill me about engineering :)

Even without the maths, it's intuitive that this must be the case: the transmitter is "seeing" a 50 ohm load so it will deliver the maximum available power; the tuner and ladderline are lossless so there's only one place for the power to go - into the antenna. Therefore if we are extracting the maximum power available from the transmitter, and delivering it to the antenna, there must be a conjugate match everywhere in the system.

Another way of "getting your head" around this is to ask how we are going to easily transfer power into an antenna which has such a high capacitive reactance; the answer is that we need a source with the equivalent high inductive reactance. The action of the tuner and the ladderline is to transform the 50 ohm source resistance of the Transmitter into exactly the value of inductive reactance required to cancel the antenna's capacitive reactance and at the same time match its Resistive component.

So the next time someone tells you that a tuner doesn't alter the antenna's impedance, agree with them; but point out that it does alter the source impedance at that point so that maximum power gets transferred. Yes, the tuner really does affect the matching at the antenna feedpoint!

Please don't get confused - the 300 ohm ladderline is still mis-terminated at the antenna, and it still has a high VSWR on it - the tuner hasn't changed that; but it has created a system match at the antenna feedpoint - they are different things!

------------------------------------------------------------------------------------------------------------------------------

Don't worry - that's about as difficult a concept as we'll look at in these Puzzles :)

73,
Steve G3TXQ

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Sun Jan 10, 2010 11:41 am
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