[TowerTalk] dB Loss Equivilents for SWR Values

[Tom Rauch]

Pardon the lecture that follows, but I think you have been misled. 
This really is worth getting into!

> Whoa. Thanks for all of the fast responses. The most popular suggestion
> appeared to be looking in the ARRL Handbook. I checked out the handbook
> and with some consideration I figured out the following formula to get
> equivalent coax db loses from an SWR value:
> 
> ((SWR - 1) / (SWR + 1)) ^ 2 * 100% = % Lost
> 10log(100/(100 - % Lost)) = Loss In dB
> 
> So if your SWR's 3.0/1:
> 
> ((3 - 1) / (3 + 1)) ^ 2 * 100% = 25% Lost
> 10log(100/(100 - 25)) = 1.25db Loss

A 3:1 SWR does NOT cause a 25% power loss. It might cause an 
increase in loss, but that increase can be anything. SWR can even 
cause a DECREASE in line loss!

The ONLY case where that formula is correct is the special case 
where the source is a perfect resistive source without any 
shutdown circuits. The source Z must also match the line 
impedance exactly, and the line itself must be lossless. 

One example of where this formula "works" is with a signal 
generator feeding a high value 50 ohm attenuator pad, and that 
attenuator pad feeds a load that we "mismatch" to 3:1 VSWR from 
50 ohms j 0.

In that case, or a case where the line itself is so lossy it "looks 
like" the high value attenuator pad in the example above, the load 
power reduction caused by a 3:1 VSWR will indeed be an 
additional ~1.25dB.

In cases where the line is electrically short, and if we have a 
generator (transmitter) that has a matching circuit (antenna tuner) 
or a transmitter that "likes" a load above 50 ohms (many or most 
do)  a 3:1 SWR can cause a system loss REDUCTION when the 
mismatch is in a direction that reduces line current! 

That's right, the system can be more efficient with a mismatch in 
the line than without it!

So... unless you are talking about a source that is a perfect 
dissipative 50 ohm source without SWR shutdown or a very high 
matched loss line the answer you came up with is incorrect.

What most people want to know is the transmission line loss 
increase with SWR, and that is complex for short lines. For long 
lines, the Handbook gives formulas that work....but not the one you 
are using. Look in the Handbook under transmission lines, and at 
"additional losses caused by SWR".

I fought hard to have this formula (displayed on the screen) NOT 
included in the MFJ SWR analyzer because even engineers 
commonly misuse or misunderstand it. I didn't want to promote the 
misconception!
73, Tom W8JI
W8JI@contesting.com 

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