# Reconciliation of Duffy CCS model with N7WS ladder line measurements

In developing and implementing A model of current distribution in copper clad steel conductors at RF reconciliation against some other published data was important.

(Stewart 1999) published a set of measurements of the popular Wireman windowed ladder line products. His measurements were in the range 50-150MHz. They form the basis for most calculators on quantitative analyses at HF, despite the fact that it is a dangerous extrapolation for CCS construction.

Nevertheless, the directly stated measurements at 50MHz are a useful calibration point for reconciliation.

Above is Table 1 from Stewart, it sets out measurements of four Wireman m.products and a plain copper line.

The table below compares Stewart’s measurements with the CCS model and with TLDetails results (where available).

The third case is a smooth round conductor of equivalent diameter to Wireman 553’s 19 strand bundle with cladding of the thickness expected on the individual strands. The CCS model is for conductor loss only of a single core conductor, measurement of the real line might reveal some additional loss due to current passing between strand contact points, and dielectric loss (though that should be very small). Importantly, approximate agreement validates the assumption that current in the 19 strand conductor will flow mainly in the circumferential copper of the bundle and current flow in internal copper will be insignificant.

 Line N7WS measurement (dB/m (dB/100′)) Duffy CCS model conductor loss (dB/m) TLDetails (dB/m) 1.291mm (#16) Copper @ 19.05mm (0.75″) 0.00984 (0.30) 0.009712 N/A 1.024mm (#18) CCS 67µm cladding (Wireman 551) 0.01083 (0.33) 0.011078 0.01403 1.024mm (#18) CCS 15.3µm cladding (similar to Wireman 553) 0.01247 (0.38) 0.012276 0.01983

Skin depth in copper at 50MHz is 9.225µm.

The CCS model quite closely agrees with Stewart’s measurements. TLDetails departs from both quite significantly.

## Conclusions

The CCS model is in close agreement with Stewart’s measurements of the three line types, and the agreement on the latter case validates the assumption that the 19 strand CVS conductor behaves much like a single core #18 conductor with cladding thickness equivalent to that of the individual strands.

## References

Stewart, W. (N7WS). Mar 1999. Balanced Transmission Lines in Current Amateur Practice.