Line loss under standing waves – recommendation of dodgy tool on eHam

In a discussion about using a 40m centre fed half wave dipole on 80m, the matter of feed line loss came up and online expert KM1H offered:

Use this to help make up your mind. Add it to the normal coax loss. http://www.csgnetwork.com/vswrlosscalc.html

This is to suggest that the feed line loss under standing waves can be calculated with that calculator.

He then berates and demeans a participant for commenting on his recommendation, bluster is par for the course in these venues.

Calculator analysis

The calculator in question states this calculator is designed to give the efficiency loss of a given antenna, based on the input of VSWR (voltage standing wave ratio) and other subsequent factors.

This is a bit wishy washy, efficiency loss is not very clear. The usual meaning of efficiency is PowerOut/PowerIn, and the usual meaning of loss is PowerIn/PowerOut, both can be expresssed in dB: LossdB=10*log(Loss) and EfficiencydB=10*log(Efficiency).

A sample calculation with VSWR=5 gives Loss in %=44.44% and Loss in dB= 2.553dB. Note that converting 44.44% to dB gives 3.5dB so that is inconsistent, an error.

How did it calculate Loss in %?

A little exploration of the code shows the following:

LOSSPCT=100*Math.pow(((vswr-1)/(vswr+1)),2)

At the heart of this is that loss is the square of the reflection coefficient ρ, and so the value is the ratio of PowerRef/PowerFwd, 0.4444 in the test case of VSWR=5, and this value is the inverse of the well known quantity ReturnLoss (2.25 in the test case, or 3.5dB).

So where does it get Loss in dB?

LOSSDB=-10*log10(1-(LOSSPCT()/100))

What it calculates here is (PowerFwd-PowerRef)/PowerFwd in dB, and that is the well known quantity MismatchLoss, 2.55dB for VSWR=5.

So, on both counts, the calculator entitles quantities calculated with well known quantities, but gives them different meanings… in other words it calculates well known quantities incorrectly.

Hams are won’t to appropriate industry’s well known quantities, and apply their own meaning to suit themselves. This is work in that style.

So, the calculator calculates wrong results, but is that the end of the problem?

There are two problems:

  1. the calculator does not attempt to calculate the change in feed line loss under standing waves; and
  2. use of MismatchLoss is not relevant to the discussion scenario.

Line loss under standing waves

In most practical transmission lines at HF, conductor loss dominates, and so under standing waves, loss per unit length is greatest in the region of current maxima, and least the region of current minima.

Most calculators that attempt to calculate the loss under standing waves are based on a formula that has a bunch of underlying assumptions which are not usually disclosed. The unstated assumptions are relevant to accuracy, and if they are non complied with, the results are not reliable.

The subject calculator does not claim to calculate line loss under mismatch, nor does it attempt to do so, which questions the poster’s understanding of the subject.

Misuse of MismatchLoss

It is a common ham practice to quantify the reduction of power output from a transmitter with mismatched load of know VSWR using MismatchLoss calculated from that VSWR.

The problem in application to a transmitter is that it may not be well represented as a Thevenin equivalent source with source impedance equal to the reference impedance used to determine VSWR, and the basis for MismatchLoss collapses.

It is widely held in ham radio that transmitters are well represented by a Thevenin equivalent source impedance equal to 50+j0Ω, thanks in no small part to the teachings of Walt Maxwell; and in ham radio, popularity is commonly taken to determine fact.

Jonathon Swift wrote:

Reasoning will never make a Man correct an ill Opinion, which by Reasoning he never acquired.\

In any event, the relevant source impedance in the discussion context is that looking back into the ATU… and it isn’t a Thevenin source of 50+j0Ω.

Conclusions

The recommended calculator is seriously flawed in what it purports to do, and it neither purports to, nor calculates line loss under standing waves.

Don’t take tools for recommendations on face value, there is no substitute for understanding the topic and validating the tools.

The transmission line topic is not well understood in ham radio, little wonder at the smoke and mirrors used to support individual beliefs.

To many if not most practitioners, modern ham radio is an antiscience, more about beliefs and talking the talk rather than walking the walk.