Measuring matched line loss

Matched Line Loss (MLL) is the loss or attenuation of a transmission line terminated in its actual characteristic impedance, and usually give for some length, eg dB/100′, dB/100m, dB/m.

One method that occurs in ham radio articles is to measure the input resistance of a resonant s/c or o/c stub, and to calculate MLL as 8.686*Rin/Zo/length dB/unitlength. (This is not the only method, or even a good one, but it is commonly used.)

This formula is an approximation, and the bounds of its accuracy are not usually stated.

Autek Research recommend this method in their VA1 Instruction Manual (no authority given), calling it the Impedance (Z) method, they claim that

The Z method works well for any line impedance. Overall, we recommend the Z method for its greater accuracy.

The ARRL Antenna Handbook 21st edition gives the formula on page 27-30 without mention of the limits of its accuracy.

The formula has been given in QST, helping in its distribution, again without qualification of its accuracy.

Clip 127

Above is a comparison of the formula (blue squares) with the actual MLL of 49.466m length of Belden 8262 (RG58C/U) at its low impedance resonances from 1 to 99MHz. This is similar to common test configurations where some fixed length of line with o/c termination is measured at a range of odd quarter wave resonances (or s/c termination and even quarter wave resonances).

The example error exceeds 5% above 25MHz, and most of it is due to the approximation used.

The green squares are from a better approximation which I developed (though it may not be original), MLL=-10log|(Rin-Zo)/(Rin+Zo)|/length dB/m (log is to base 10). It is still subject to some error in assumptions about Zo, but as can be seen from the graph, error is small (<0.25% in this example), it is much better than the other method. It is subject to error where (actual)  Zo is assumed to be Ro (as are all methods that do the same). An advantage of this formula is that it also works for high impedance resonances, so twice as many data points are captured in a scan (provided they are within the accurate measuring range of the instrument).

See the online calculator at Calculate transmission line Matched Line Loss from Rin of o/c or s/c resonant section.