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:

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.

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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!!!

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

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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!

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

73,

Steve G3TXQ