[Amps] Mismatch loss

[Larry Benko]

I have started a new topic.

Jim Brown said:

Both.  See the family of curves in the ARRL Handbook for excess
attenuation due to mismatch, which has been in every edition of the
handbook since I've been buying it (the 50s), and which I've confirmed
by cranking the equations. The curve for a 2:1 SWR shows an excess
attenuation of 0.1 dB if the matched loss is 0.4dB, 0.2dB if the matched
loss is 1dB, 0.4dB if the matched loss is 10dB. And remember, the
connector is quite small as a fraction of a wavelengh at HF, which is
what this discussion is about, and not much more in the lower half of
the VHF spectrum.  If you've measured more than that, I suspect you are
simply seeing the standing waves at the point of the measurement.

My response follows.

There are two different topics going on with this question:
1.) Mismatch loss
2.) Additional attenuation in a transmission which is operated with an 
SWR different than 1.0:1.

Topic #1: Mismatch loss

There are many texts and websites showing that a 2:1 SWR is a mismatched 
loss of 0.512dB (my original posting was for a 2.1:1 SWR which is a 
mismatched loss of 0.584dB).
See:
http://www.microwaves101.com/encyclopedia/mismatchloss.cfm
http://chemandy.com/calculators/return-loss-and-mismatch-calculator.htm

 From textbooks Mismatch loss = 1 - Gamma^2  where Gamma is the 
reflection coefficient.  Reflection coefficient = (SWR-1)/(SWR+1) so a 
2:1 SWR has a reflection coefficient of 1/3 and a mismatch loss of 1 - 
(1/3)^2 = .8888 and 10*log10(.8888) = 0.512dB.

A simulation can easily be done in LTSpice which gives exactly the same 
answer.  This all assumes a signal source with an output impedance the 
same as the load.  However the transmitters we use may not follow this 
mismatch rule due to non 50 ohm output impedance, peak voltage swing 
allowed, peak current, protection circuits etc.

See: http://www.w0qe.com/IC7000_vs_IC706_mobile_pwr.html
for power output measurements I made with NO TRANSMISSION LINE for 2 
radios with 4 different 2:1 SWRs (25+j0, 100+j0, 40+j30, 40-j30).

Topic#2: Transmission line loss

The tables in the ARRL handbook refer to additional loss in a 
transmission line operating at an SWR other than 1.0:1 and not mismatch 
loss.  The tables and formulas in the Handbook are correct for long 
transmission line lengths but not for short lengths.   However the 
program TLW (included in every ARRL Antenna Handbook) does the 
calculation correctly.  At HF, transmission line loss is primarily 
proportional to the integral of the current that is flowing along the 
line.  Try TLW with 10' of LMR-400 with load impedances of both 2.5+j0 
and 2500+j0 (both 20:1 SWRs).  With a 2.5+j0 load the additional loss in 
the 10' of cable is .391dB but with a 2500+j0 load the additional loss 
is only .005dB.  This is a big difference.  Change the length to 100' 
and the 2 results are closer.

Let's see how well I did explaining a topic that I didn't understand for 
many years even though I have BSEE and MSEE degrees. :)

73,
Larry, W0QE