> From: w8ji@w8ji.com
> The worse case SWR of a 50 ohm system with 75 ohm cable isn't 1.5:1 when
> normalized to 50 ohms. It is 2.25:1. 1.5*1.5 = 2.25
>
> A 50 ohm load with 1/4 wave of 75 ohm is 112.5 ohms, and that is 2.25:1.
> This is why the cable needs to be 1/2 wave long, so impedance is back around
> 50 ohms. If you are unlucky and pick an odd 1/4 wave, and the load is 50,
> the input SWR is 2.25 in the lossless cable case at the radio.
The SWR on the line is still 1.5:1. SWR= Zr/Zo or Zo/Zr, whichever case gives
a ratio greater than one. Zr is the load at the far end of the transmission
line, and Zo is the characteristic impedance of the line. In the above case,
Zr=50 ohms and Zo=75 ohms. Thus, SWR=75/50=1.5
The quarter-wave line (or odd multiple thereof) is a special case, in which the
line acts as a transformer. The impedance looking into the line, Zs = (Zo)^2/Zr
In the above case, Zs=(75)^2/50 = 5626/50 = 112.5 IOW, the transmitter "sees" a
112.5 ohm load looking into the line instead of a 50 ohm load, because the
quarter-wave line has "transformed" the impedance. Consequently, the tuning
network at the output of the transmitter would have to be tweaked in order for
the final amplifier to be properly matched to the load. A 50-ohm SWR meter
inserted between the transmitter and the transmission line would indeed read
2.25:1 - but this is only a virtual reading. The actual SWR along the feedline,
which by definition is the ratio of the maximum line voltage to the minimum
line voltage, would be 1.5:1
The longtime confusion between real and virtual SWR as read on a meter has led
to a popular misconception in the amateur community that trimming the length of
coax can reduce or eliminate standing waves.
With good quality coax up to a wavelength or so long, a SWR of less than 3:1
would be of little consequence, except that an impedance matching stage may be
needed between the final amplifier and the transmission line to properly load
the transmitter, which is not a bad idea to have available in any case.
> Also, on longer cables, the low SWR bandwidth is narrower. This is because
> the cable is multiple 1/4 wave sections in series. If there are ten of the
> 1/4 waves making up a 2.5 wave long cable, and if the frequency changes 5%,
> the total length error for all the sections is 50%. This narrows bandwidth,
> and reduces the depth of the magical low SWR point.
Again, you mean the magical low VIRTUAL SWR point, since the real SWR is a
function only of the load at the far end and the characteristic impedance of
the line, and does not significantly change with the total length of the
transmission line. However, your statement about the long transmission line is
very true, and explains why a TUNED feedline should be kept to less than 2 or 3
quarter wavelengths long if at all possible. The more quarter wavelengths
daisy-chained in series on a resonant feeder, the more critical the tuning and
the narrower the bandwidth for a given setting of the matching circuit. Not
only do feedline losses become significant, but the same tuning configuration
may not hold across the entire band. For example, at the bottom end of the band
series tuning may be optimum, but at the top end a match may be achieved only
by changing over to parallel tuning. And somewhere in between, one may end up
trying to feed near a midpoint between a voltage loop and a current loop, which
presents a highly reactive load difficult to match.
73,
Don k4kyv
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