The devil is in the detail – real world transmission lines and loss under standing waves

We are traditionally taught transmission line theory starting with the concept of complex propagation constant γ, and that loss in a section of line is \(Loss=20log_{10}( l |\gamma|) dB\) where l is length. That is the ‘one way’ loss in a travelling wave, also the the matched line loss (MLL) (as there is no reflected wave).

There are some popular formulas and charts that purport to properly estimate the loss under standing waves or mismatch conditions, usually in the form of a function of VSWR and MLL, more on this later.

Let’s explore theoretical calculations of loss for a very short section of common RG58 at 3.6MHz with two different load scenarios.

The scenarios are:

  • Zload=5+j0Ω (VSWR(50)=10); and
  • Zload=500+j0Ω (VSWR(50)=10).

Above is the RF Transmission Line Loss Calculator (TLLC) input form. A similar case was run for Zload=500Ω.

Now lets compare the outputs side by side. Items of interest are highlighted.

Note that the input Zload figure is different, 5+j0Ω at left and 500+j0Ω at right, both have VSWR(50)=10. Note also that the loss under mismatch in the 500Ω case is less than the MLL, there is less loss under standing waves in this scenario.

The calculated loss is different in both cases, 0.272 vs 0.0139, one is 20 times the other. Note that in both cases, VSWR(50)=10, yet the loss under standing waves is very different so it is not simply a function of VSWR as popularly held.

For the same reason that the loss under mismatch of these two line sections with similar VSWR are so different, the loss along a line under mismatch of that cable type is not uniform. In fact, more generally, loss under mismatch is not uniform for lines that are not distortionless lines, ie for most practical lines.