I would be surprised if two garden variety instruments, even placed at the same
point, would agree. The directional bridges/couplers in most "(V)SWR" meters
that hams routinely use externally or which are built into our radios are not
precision instruments. There are a number of error sources in reflection
measurements; source match, diode non-linearity, coupler tracking errors and
often the most significant, directivity error.
In an ideal coupler, (i.e signal separation device) one port measures the
forward (incident signal) and another measures the reverse (reflected) signal
and there is no coupling between ports in the unwanted direction(s). In other
words there is no signal at the reverse port due to the forward signal. In a
real world coupler there is some leakage signal appearing at the reverse port
due to the forward signal, absent any reflected signal. The "goodness" of a
directional coupler in this instance is called "directivity" and the error
signal is directivity error. Directivity is usually specified in dB. Really
good couplers might have directivities in the 40 dB neighborhood. Really really
good directional bridges can be 50 dB, but so-so units might be 25-30 dB. Not
ready for prime time units are lower than this.
Now I have no way of knowing what the directivities are of the couplers built
into K3s, KPA500s, KAT500s, etc. but considering that they have to work over
about 5 octaves, I'm going out on a limb and saying that 25 to 30 dB is a fair
estimate. If I'm wrong, I'm sure I'll hear about it. For sake of discussion
I'm going to use 26.5 dB. What this means is that if I terminate the output
spigot of one of these radios with a perfect 50+j0 load, I'm going to measure a
leakage signal (directivity error) that is 26.5 dB below the incident value.
I'll introduce the concept of return loss here.
We hams usually speak in terms of SWR. SWR = (1 + p) / (1 - p) where p is the
reflection coefficient. Here the p = the voltage measured at the reflected port
and the constant 1 represents the incident signal. In reality both of these
quantities are complex numbers, they have both magnitude and phase but SWR
measurements are scalar, we throw away the phase (since it's difficult to
measure) and just use the magnitude. (In fact the symbol "p", which is really
the Greek letter rho, indicates the magnitude of the reflection coefficient in
normal usage) We can also express this ratio as return loss, which is -20 *
log10(p). So return loss, SWR and reflection coefficient are just different
ways to express the same thing; the ratio of incident to reflected signal.
Let's return to our example; the coupler with 26.5 dB directivity, which
indicates a return loss (RL) of 26.5 dB even with a perfect termination. Doing
the math and converting RL = 26.5 dB to SWR we get 1.1:1. Our perfect load
measures 1.1:1 with our imperfect instrument. And this assumes that there are
no other errors, which there always are. But it gets worse.
Let's say that the load we want to measure really is 1.1:1. We now have two
(apparent) reflections, 1) the real one and 2) the directivity error and they
both have the same magnitude. In our simple detector, they sum together. Now I
said earlier that we don't measure phase, only magnitude, but just because we
don't, or can't measure the relative phases doesn't mean they aren't there. We
will examine two cases to determine the limits of error. Case 1) both
reflections are in phase, they add up to p + p or 2p, RL = 20.5 and SWR
~1.21:1. Case 2) they are exactly out of phase, they sum to zero. p = 0, RL is
infinite and SWR = 1:1. The possible RL error is then -6 to +infinity dB!
In other words, an actual SWR of 1.1:1 can be measured anywhere between 1.0:1
and 1.2:1. Is it any wonder that we often read about concerns that one device
measures one thing, while another located at the same, or close location
measures something different. Of course all of this is predicated on a
directional coupler with 26.5 dB directivity and no other error sources. It's
entirely possible that the Elecraft couplers are better than this. They are
certainly no better than 40 dB since the internal reference resistors are 51
instead of 50 ohm. Plus the "Tandem Match" configuration is in itself not a
great match to the transmitter output.(1) Furthermore, the coupler, at least in
a K3 is driven by a LPF, which isn't a great 50 ohm source. Plus the coupler
output port isn't connected directly to the coax connector..... and so on and so
forth (2). All of this creates "uncertainty."
In a metrology lab heroic efforts are made to reduce uncertainty but do we, or
should we, really care in this situation? In my opinion, no, but everyone is
free to differ.
Wes N7WS
(1) See "An HF In-Line Return Loss And Power Meter" by Paul Kiciak, N2PK.
http://n2pk.com/#TP3
(2) See "Gauge the Accuracy of SNA Measurements"
http://www.testmart.com/webdata/appnote/763.PDF
On 7/27/2018 1:08 PM, Bob McGraw K4TAX wrote:
Yes, the K3S SWR display can show a 1.0:1 value. But in my case, it does not
exactly agree with another instrument in the feed line system. As to why
you are showing two different values, as minute as they are I might add, you
are measuring 2 different places in the feed line. In my thinking, it is
physically impossible to put two SWR bridges in the same place electrically.
In theory the SWR on a given line should be the same at all places, but maybe
not since there is loss of some minute value in the line. Since you are
measuring on antennas, common mode current, may be the contributing cause.
Difference in measurement calibration, may be a factor as well.
VSWR bridges are calibrated with some specific value of load. Ideally, it is
50 ohm non-reactive, but it could be 49 ohms or 51 ohms or some other value.
Just because a load says "50 ohms" on the label is no real indication that is
actually fact. To that end, I have 3 dummy loads which are "50 ohm" loads
according to the label but none are not true 50 ohm loads. I do have a
Celwave load that says 50.5 ohms on the label and measures 50.5 ohms per my
General Radio bridge. The others are +/- something, but good enough to
evaluate a ham transmitter or amplifier.
Frankly, a difference between 1.1:1 and 1.0:1 won't make any realistic
difference in any form or fashion other than to appease the operator.
73
Bob, K4TAX
On 7/27/2018 9:58 AM, Dick Dickinson wrote:
I've noticed that I'm not showing a reading of less than 1.1:1 SWR on my
antennas per K3 SWR Numerical Readout. K3EZ will record 1.0:1 SWR in band
sweeps.
Can the K3(S) Numerical Display show 1.0:1 SWR? If so, is there a likely
reason why K3EZ will show 1.0:1 while my K3 will only go as far down as
1.1:1?
Dick - KA5KKT
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