Quarter wave transformer.

Discussion in 'General Electronics Chat' started by alphacat, Aug 16, 2009.

1. alphacat Thread Starter Active Member

Jun 6, 2009
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Hey guys,

It is said that a quarter wave transformer (the transmission line between points A & B) is used in order to:
1. Deliver all power to the load.
2. Prevent from retreating waves to reach the generator.

Regarding the following example,
I understand well that in point A, the progressing wave (that comes from the generator) fully passes the border which separtes the two transmission lines, and since the Quarter Wave Transformer is a lossless line, then all power is delivered to the load.

But:
When the progressing wave finally hits the load, only some of it is absorbed by the load (since there's no impedance matching in point B, but only in point A), and the rest of it retreats towards the generator, isn't it?

Therefore:
1. Not all power is absorbed by the load.
2. There are retreating waves who reach the generator.

I just dont understand how a Quarter Wave Transformer helps after all.

Thanks alot.

Apr 5, 2008
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3. alphacat Thread Starter Active Member

Jun 6, 2009
186
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Hey Bertus,

I read the section about the Quarter Wave Transforemer, but it doesnt deal with the two difficulties i've raised here.

Apr 5, 2008
18,581
3,596
Hello,

Here I found a PDF with some analyses of the quarter wave transformer.

Greetings,
Bertus

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5. KL7AJ AAC Fanatic!

Nov 4, 2008
2,181
410
The Quarter wave transformer, or "Q section" is a special case that merits some attention (which you can confirm with the Smith Chart.

There is nothing magic about the Q section, except that it has the MAXIMUM impedance transformation possible for a transmission line.

When used as a matching device, the characteristic impedance will always be the GEOMETRIC MEAN between the source and load impedance. If the load impedance happens to equal the Z0 of the line, the Q section actually does NOTHING...you will have the same impedance everywhere...just as with any random length of line.

The geometric mean calculation, by the way, assumes the termination is PURELY RESISTIVE. If there is reactance as well, the calculations become very complicated, very quickly.

Q-sections are frequently used when matching 50 ohm transmission lines to voltage fed antennas, often using a Q-section of 450 ohm "ladder line". It's an ancient and effective little trick.

The "j-pole" vertical antenna also uses the lower section as a Q-section. You can find out a lot more about the Q-section from the ARRL handbook.

Eric

6. Tesla23 Senior Member

May 10, 2009
361
78
To understand it in terms of reflections, the reflected wave at A consists of two parts:
1. a reflection of the incident wave from the mismatch of Zo to Z1, and
2. the reflected wave from the load (from the mismatch Z1 to RL) that passes through A

The magic of the quarter wave transformer is that these exactly cancel, and so at A there is no net reflection, so the impedance seen at A is Zo.

If you try to work it out this way you need to account for the multiple reflections bouncing around between A and B. This accounts for how all the power finally ends up in the load despite it not being matched to Z1, it gets multiple chances!

7. KL7AJ AAC Fanatic!

Nov 4, 2008
2,181
410
Yes indeed. In fact, Walter Maxwell, W2DU wrote an excellent treatise on this multiple reflection business in his series of QST Articles "Another Look at Reflections" published in the 1970s. I understand his third printing "Reflections III" is coming out soon. I'll keep y'all posted. It's a fascinating topic.

Eric

8. alphacat Thread Starter Active Member

Jun 6, 2009
186
0
Tesla and Eric,
Lotsss of thanks!

I really appreciate it!