[Elecraft] [K3] SWR - Numerical Indication

[Wes Stewart]

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