Quote:
Originally Posted by stvcmty
Would a ¾ wavelength section of 450 ohm lead perform the same impedance transformation as a ¼ wavelength section?
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Quote:
Originally Posted by GroundUrMast
No. I believe you would effectively be inserting three step up transformations in series.
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Both seem correct.
That is, a 3/4 wavelength could transform similar to a 1/4 wavelength section. And yes, 3 transformations is one way of looking at it.
Roughly,
First 1/4 wave transforms up or down depending on whether the line impedance (Z) is above or below the input impedance. Then, the 2nd 1/4 wave transforms back to original input impedance.
Two, 1/4 wavelength lines in series equals one 1/2 wavelength line.
Recall, 1/2 wavelength provides no transformation regardless of Z of the transmission line.
The 3rd 1/4 wavelength starts over again.
There is a bit more:
A 1/4 wavelength line is only 1/4 wavelength at one frequency. The transformation becomes more complex when the frequency is above or below 1/4 wavelength frequency. Also, if the in/out impedance is not purely resistive, the transformation is not as straightforward.
The preceding constraints give rise to this:
Three 1/4 lines in series have a bandwidth that is less than a single 1/4 line.
Bandwidth continues to shrink if the line is lengthened further (5/4 wavelength etc.).