At Where is the best place to measure feed point VSWR I discussed location of the VSWR meter and projection of its reading to another point on a known transmission line.

One of the conclusions drawn in that article is:

Feed point VSWR can be estimated from measurements made at another place if the transmission line parameters are known. It, like all measurements, is subject to error but it may be a manageable error and indeed possibly better overall than direct measurement.

This article discusses some issues that may arise in referring measurements from one place to another (eg near transmitter to antenna feed point).

## Characteristics of transmission line categories

Let's consider two categories of transmission lines in terms of characteristic impedance Z0 and propagation constant γ:

- Lossless line; and
- practical line.

A lot of theoretical analysis uses lossless line for simple explanations, and whilst for a lot of purposes, approximation of practical line as lossless line serves well, at other times the error may be significant.

### Lossless Line

A Lossless Line has imaginary part of Z0 equal to zero and the real part of γ equal to zero.

### Practical line

A practical line has non-zero imaginary part of Z0 and non-zero real part of γ, and these are frequency dependent.

Under standing waves, attenuation along a practical line is not uniform, in most practical applications conductor loss/m is higher than dielectric loss so loss is higher near current maxima than near current minima.

For the purpose of this article, it is the frequency dependence of Z0, particularly the non-zero imaginary part that is significant.

## A model

A model of a load similar to a 7MHz half wave dipole fed with 10m of RG58A/U was created in Simsmith to provide a basis for discussion. Whilst the model is subject to some errors computation, it is much less than comparing two field measurements at both ends of a transmission line.

## VSWR at each end of the transmission line

Let's look at the ACTUAL VSWR. Actual means that if you were to observe the standing waves on the line (eg with a voltage probe), this is the VSWR you would expect to observe.

Firstly, observe that the source end VSWR (orange) is a little lower than the load end VSWR. This is by virtue of the attenuation on the line. The difference between the two can be calculated, but it is moderately complicated.

As mentioned, Z0 of a practical line is frequency dependent and not a pure real number. In the example, at 7MHz, Z0=50.98-j0.9091Ω.

Now let's add VSWR wrt Z0=50+j0 (as would be indicated by a 50Ω VSWR meter). Load end is blue and source end is magenta. Note that while this can be measured, the measurement does not indicate the actual VSWR because the calibration impedance does not match the line.

Above, VSWR calculated wrt Z0=50+j0 is different to the actual VSWR, and assuming they are the same can lead to significant error.

This departure of actual Z0 from nominal is more likely:

- in lossier transmission lines; and
- at lower frequencies (say less than 10MHZ for low loss lines).

## ReturnLoss at each end of the transmission line

Let's now look at ACTUAL ReturnLoss. Blue is load end, magenta is source end.

ReturnLoss could be calculated from VSWR measured directly with a voltage probe as mentioned above.

Note that the vertical distance is fairly uniform and is twice the matched line loss (MLL). MLL is frequency dependent, though for the narrow frequency range shown in the plot, it is almost constant.

Now let's add ReturnLoss calculated wrt Z0=50+j0 (as would be indicated by a 50Ω VSWR meter). Load end is orange and source end is green. Note that while this can be measured with a 50Ω directional coupler, the measurement does not indicate the actual VSWR because the calibration impedance does not match the line.

Above, the two sets of ReturnLoss plots are different, not a lot in this case, but they are different. Let's focus on the second set. Load end is orange and source end is green.

Above, it can be seen that these curves cross over. No longer is the calculated ReturnLoss always higher at the source end… which might seem at first to discredit the explanation given earlier… but the cause is that calculated value is INVALID, it is based on an incorrect value for Z0.

## Other errors in Z0

There are of course manufacturing tolerances that give rise to error in the assumed value of Z0.

Additionally, Z0 can be affected by poor installation, termination, and faults (including water ingress and corrosion, dielectric contamination to name a couple).

## Error in transmission line parameters and calculation model

There are several broad methods used to solve these types of transmission line problem, and none of them is without its problems (errors). The most popular method used in the ham world is one that I avoid having been unable to reconcile measurement with prediction in some case studies.

## Conclusions

- Feed point VSWR can be estimated from measurements made at another place if the transmission line parameters are known. It, like all measurements, is subject to error but it may be a manageable error and indeed possibly better overall than direct measurement.
- Uncertainty (error) in the transmission line parameters or transmission line model / calculations is likely to contribute error to the referred results.
- Z0 error is more likely to be observed in lossier transmission lines; and at lower frequencies (say less than 10MHZ for low loss lines).