# Measuring coaxial cable loss by reflection with a directional wattmeter

At Measuring coaxial cable loss by reflection with a VNA I discussed measuring terminated coax cable loss by reflection with an VNA, and you might ask the question can it be done with a scalar network analyser, return loss bridge, or directional wattmeter, all of which provide a measure of the amplitude of reflection wrt some reference impedance.

This article explores using a Bird 43 directional wattmeter to measure line loss in a similar scenario. We will use 6m of Belden 8359 (RG58A/U) @ 3.6MHz.

## Expectation

A short digression, what is the specification Matched Line Loss (MLL) at 3.6MHz? Using TLLC we get 0.171dB, that is our expectation.

## Return Loss of SC section

(Bird 2004) gives the following advice.

Line loss using open circuit calibration: The high directivity of elements can be exploited in line loss measurements, because of the equality of forward and reflected power with the load connector open or short circuited. In this state the forward and reflected waves have equal power, so that φ = 100% and ρ = ∞.
Open circuit testing is preferred to short circuit, because a high quality open circuit is easier to create than a high quality short. To measure insertion loss, use a high quality open circuit to check forward and reverse power equality, then connect an open-circuited, unknown line to the wattmeter. The measured φ is the attenuation for two passes along the line (down and back). The attenuation can then be compared with published data for line type and length (remember to halve Ndb or double the line length to account for the measurement technique).

This also contains the hoary old chestnut that a good OC termination is hard to achieve, but this author’s experience of measurement with modern VNAs is not consistent with Bird’s assertion.

So lets do a theoretical simulation of the Bird 43 applied to this problem.

Lets say we connect a source to the line section with a short circuit (SC) termination, and that the Bird 43 reads Pfwd=90W, and we read Pref=78W, we can calculate return loss $$RL=10 \cdot log_{10}\frac{P_{fwd}}{P_{ref}}=0.65dB$$, so RL/2=0.65/2=0.325dB.

Hmmm, that is nearly double the expected 0.171dB, time to chuck it?

No not yet, let’s do an open circuit sweep.

## Return Loss of OC section

Now we connect a source to the line section with a open circuit (OC) termination, and that the Bird 43 reads Pfwd=75W, and we read Pref=72W, we can calculate return loss $$RL=10 \cdot log_{10}\frac{P_{fwd}}{P_{ref}}=0.177dB$$, so RL/2=0.177/2=0.088dB.

Hmmm, that is less than half the expected 0.171dB, a quarter of the SC measurement, what is going on?

## The problem

The problem is that the Bird 43 is calibrated using a 50+j0Ω load, and its reference impedance is now 50+j0Ω meaning that directional power measurements and therefore RL is wrt 50+j0Ω, and since Zo is more like 51.42-j1.33Ω there is error in the two results that should theoretically agree with each other.

## An approximate solution

A good approximation when the departure of actual Zo from the reference impedance is small is that $$MLL\approx\frac{RL_{sc}+RL_{oc}}4dB$$.

So $$MLL\approx\frac{0.65+0.177}4=0.206dB$$, not a lot worse than spec at 0.171dB, and given measurement uncertainties, we could not say if fails spec.

This is discussed in more detail at On Witt’s calculation of Matched Line Loss from Return Loss .

A problem in applying the Bird 43 to this example is that we cannot read the meter to sufficient resolution or accuracy, though it might be quite suitable for a higher loss section.

Nevertheless, the measurements do expose the fact that the measured Return Loss wrt 50+j0Ω may be quite different for a SC section to a OC section, and it is not explained by the traditional mumbo jumbo about the quality of an OC termination. It IS true that an OC has associated with it some fringe capacitance which for a N type OC calibration piece amounts to some tens of fF (femtoFarads are thousands of a pF) so work out the effect at HF, and even VHF is very small. A N type plug with nothing connection is a little worse, but inconsequential at HF. For this scenario 50fF fringing capacitance is roughly equivalent to the cable appearing to be 0.5mm longer than you measured.

Other instruments mentioned earlier may be capable of higher resolution and accuracy than the Bird 43 and may be more practical for low loss scenarios.