Don,
Tnx for your reply. I see exactly whar's happening. In fact I do the same
thing with my Delta Loop on 160. It's about 110 to 120 ohms at the
feedpoint, so I use a ¼ wavelength of 75 ohm Belden down to a ½ wavelength
of RG213. And that's it. The confusing point is there are two impedance
variations going on as you change frequency because of changing line Zo
values:
1) The impedance of the antenna is changing as you go up/down in frequency,
and
2) The impedance transformation of the ¼ wave matching section is changing
because it is getting shorter/ longer in electrical length as you go up/down
in frequency.
So now there are two variables that you can't really do anything about.
Therefore, the 2:1 bandwidth narrows the more frequency dependent variables
there are in the matching network. There is a paper which was written by
Fano which comes to the conclusion that about 4 matching elements is the
practical limit of wideband matching. Anyway please Google: "Fano" and I am
sure you will find a lot of info if you are interested.
This is not rocket science. I must apologise because I had never heard the
terms "apparent", "virtual" before. Everything Don has said is fine. It was
not clear until I drew it on the Smith Chart.
This Delta Loop has sure worked for me !!
73 Hardy N7RT
----- Original Message -----
From: "Donald Chester" <k4kyv@hotmail.com>
To: <topband@contesting.com>
Sent: Saturday, June 14, 2014 8:19 AM
Subject: Re: Topband: 50 ohm direct burial coax cable
From: n7rt@cox.net
Please explain virtual SWR. I never heard that in any college classroom I
have been in.
Hardy N7RT
That's a phrase I coined in response to the situation Tom described; maybe
another term would be used in the textbooks. A quarter wavelength 75 ohm
coax working into a 50 ohm load, transforms the 50 ohm load to 112.5 ohms,
non-reactive, as it appears at the end of the coax next to the
transmitter, as previously discussed. If we place a 50-ohm SWR meter at
the near end of the coax, between it and the rf source (the transmitter),
the meter will "see" 112.5 ohms, not 50 ohms nor 75 ohms. It will read
2.25:1 SWR. But the actual SWR on the coax line remains 1.5:1. If we add
another quarter-wave of coax to the line, making its total length a half
wavelength, the meter will now "see" a 50 ohm non-reactive load, and read
1:1 SWR. The SWR READING has changed from 1.25:1 to 1:1 as the length was
changed. But the actual SWR along the transmission line has not changed,
because Zo and Zr are still the same, and adjusting the length of the line
doesn't affect the standing wave generated by the 1.5:1 mismatch at the
far end. That meter reading is what I called 'virtual SWR'. Maybe a better
term would have been APPARENT SWR.
Don k4kyv
----------------------------------------
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.
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