This article discusses various measurements and models of Wireman 551 windowed ladder line, including adapting Simsmith’s bimetal line type to bear on the problem.

## Measurements

A starting point for characterising the matched line loss (MLL) of the very popular Wireman 551 (W551) windowed ladder line is the extrapolation of measurements by (Stewart 1999) to 1.8MHz. Since the measurements were made at and above 50MHz where the W551 has copper like performance, this is likely to underestimate actual MLL and such wide extrapolation introduces its own uncertainty. Nevertheless, the datapoint is MLL=0.00227dB/m.

Dan Maquire recently posted a chart summarising measurements of these lines.

For the purposes of this article, let’s tabulate the MLL at 1.8MHz in dB/m.

- KN5L WM551 MLL=0.148/30.48=0.00486dB/m
- G3TXQ WM551: MLL=0.117/30.48=0.00384dB/m

JSC 1318 is an OEM and their 1318 product has the same dimensions as W551, it should be very similar if not the same product.

VK2OMD JSC 1318: MLL=0.0028dB/m

So, there is quite a wide spread from 0.00227 to 0.0049dB/m.

## Models

TLDetails gives MLL=0.00824dB/m.

Above is a model in Simsmith using its characterisation of W551, and MLL=0.0083dB/m, nearly twice the highest of the three measurements given earlier. (I used v16.9av, the later version crashes on my machine.)

Simsmith has a new / experimental facility, the bimetal

line model. The model is designed for modelling coax, but lets see if we can use it for this two wire line.

A two wire line can be modelled as a single conductor against the neutral plane. Where the wires are spaced sufficiently that there is insignificant proximity effect (ie that current is uniformly distributed around the conductor), we can curl the neutral plane into a cylinder of diameter to obtain half Zo.

Above is a model of one wire of half of the W551 type line at 1.8MHz. It is modelled with air dielectric, it has little consequence in this case as the loss is dominated by the copper conductors which are sized as per the W551 specs. The shield is set to zero resistance. The in_cond parameter is the diameter of the conductor in inches, the documentation is wrong.

The calculated MLL is 0.00244dB/m.

Above is a current distribution plot from (Duffy 2017) for the same dimensions and the calculated MLL is 0.00240dB/m.

## Summary

Above is a summary in order of ascending MLL.

In the modern ham world where in the absence of much science, popularity is held to determine fact, one might accept the highest two as they are in close agreement… but they use the same model, so their agreement is just a tribute to implementation. In fact they are well above any of the measurements.

Let us consider the N7WS datapoint. This extrapolation is used by most line loss calculators and is likely to be an underestimate clouded with extrapolation uncertainty. An interesting point because of its common use more than anything.

The three measurements fall in the range 0.0028 to 0.0049dB/m, quite a spread but I should note that KN5L’s measurements may have been of JSC 1318 and his writeup of those measurements questions whether the line he had was in fact 30% IACS copper clad. If it was 21% as he writes, it should be discarded from the measurement set here. If that was done, we have two remaining measurements of 0.0028 and 0.0038dB/m.

That leaves two models, Simsmith’s bimetal and VK2OMD (Duffy 2017) which use different techniques to model the current distribution within the conductor and arrive at conductor loss.

Above is a chart of the current distribution in the VK2OMD model. Differently to a conductor with well developed skin effect where the phase of the bulk current lags the surface current by 45°, in this case it lags by just 30°.

My own view is that the VK2OMD and Simsmith bimetal models are probably pretty close to correct.

Note that the results here cannot simply be applied to the more popular stranded CCS types of line, they are significantly worse MLL due to the thinner copper that accompanies stranding.

## References

- Duffy, O. Apr 2017. A model of current distribution in copper clad steel conductors at RF.
- Harriman, E. May 2019. Modelling coax from first principles. Packaged in Simsmith v16.9av.
- Stewart, W. (N7WS). Mar 1999. Balanced Transmission Lines in Current Amateur Practice.