## Introduction

A recent article questioned the accuracy of measurement of Matched Line Loss (MLL) for a modified commercial transmission line. The published results were less than half the loss of an equivalent line in air using copper conductors and lossless dielectric, when in fact there would be good reason to expect that the line modification would probably increase loss.

How do you avoid the pitfalls of using analysers and VNAs to measure line loss?

Lets walk through a simple exercise that you can try at home with a good one port analyser (or VNA). Measuring something that is totally unknown does not provide an external reference point for judging the reasonableness of the results, so will use something that is known to a fair extent,

## Experiment

For this exercise, we will measure the Matched Line Loss (MLL) of a 6m length of uniform transmission line, RG58C/U cable, using an AIMUHF analyser. The AIM manual describes the method.

If you need to know the cable loss at other frequencies, enable the Return Loss display using the Setup menu and click Plot Parameters -> Return Loss and then do a regular scan of the cable over the desired frequency range with the far end of the cable open. Move the blue vertical cursor along the scan and the cable loss will be displayed on the right side of the graph for each frequency point

Note the one-way cable loss is numerically equal to one-half of the return loss. The return loss is the loss that the signal experiences in two passes, down and back along the open cable.

Our measurements will show that this is a naively simple explanation, and to take it literally as complete may lead to serious errors. Yes, it IS the equipment manual, but it is my experience that the designers of equipment, and writers of the manuals often show only a superficial knowledge of the relevant material.

## Datasheet

Above is an extract of the datasheet for Belden 8262 RG58C/U type cable, our test cable should have similar characteristics.

## Half Return Loss @ 1MHz

This measurement is literally that described in the AIM manual.

Above, the Return Loss Plot of 6m of RG58C/U with O/C termination. (The AIM Return Loss plot is upside down, Return Loss increasing downwards, just to be quirky.)

Note that Return Loss at 1MHz is almost zero, 0.02dB and implies MLL is 0.01dB for 6m, 0.166dB/100m which is grossly different to the datasheet's 1.3dB/100m.

How is it possible to have a similar cable with 13% of the specification MLL?

We can learn more from failures than successes, lets follow the opportunity.

Let's examine in detail two frequencies in the sweep range, 8.2MHz (the first resonance of the section) and 3.5MHz (a typical frequency for ham use).

## 8.2MHz

### O/C section

Looking at the screenshot above, the data at the right shows Return Loss as 8.2MHz is 0.61dB, and the calculated Cable Loss (meaning MLL) is 0.30dB.

The previous case should make us wary and test the accuracy of this result.

0.30dB/6m is equivalent to 5dB/100m, a little higher than the interpolation of the datasheet values, but believable.

Another method is to estimate loss from the input resistance of a resonant section.

From the screenshot, Rin is 1.75Ω. For the moment, lets assume that Zo is actually 50+j0Ω.

Using Calculate transmission line Matched Line Loss from Rin of o/c or s/c resonant section.

We obtain the result above, that MLL is 0.051dB/m, or 5.1dB/100m. This reconciles with the measurement, and is close to the datasheet interpolation.

On account of the fact that the datasheet, the O/C Half Return Loss and Rin of a resonant section values are very close, we conclude that both measurements are very likely to be valid.

### S/C section

Lets repeat that but with a scan of the same cable terminated with a S/C (though it is not mentioned in the AIM manual).

Above is the S/C sweep. Note the very different shape of the plot.

Nevertheless, at 8.2MHz, the Return Loss is almost identical, looking at the screenshot above, the data at the right shows Return Loss as 8.2MHz is 0.61dB, and the calculated Cable Loss (meaning MLL) is 0.31dB.

The previous case should make us wary and test the accuracy of this result.

0.30dB/6m is equivalent to 5dB/100m, a little higher than the interpolation of the datasheet values, but believable.

Another method is to estimate loss from the input resistance of a resonant section.

Maximum Rin around 8.2MHz is 1400Ω, so we will use that. For the moment, lets assume that Zo is actually 50+j0Ω.

Using Calculate transmission line Matched Line Loss from Rin of o/c or s/c resonant section.

We obtain the result above, that MLL is 0.052dB/m, or 5.2dB/100m. This reconciles with the measurement, and is close to the datasheet interpolation, and to the previous measurements.

We have stronger reason to conclude that all measurements are very likely to be valid.

## 3.5MHz

### O/C section

Lets move the cursor on the O/C scan down to 3.5MHz.

Looking at the screenshot above, the data at the right shows Return Loss as 3.5MHz is 0.09dB, and the calculated Cable Loss (meaning MLL) is 0.04dB.

0.04dB/6m is equivalent to 0.67dB/100m, a lot higher than the interpolation of the datasheet values, unbelievable.

This is not a resonant section, so we cannot use the Rin method directly, but since MLL is almost entirely due to conductor loss for this type of cable at this frequency, we can interpolate from the datasheet MLL=(3.5/10)*4.59=2.71dB, or extrapolate from our own Rin based MLL at 8.2MHz MLL=(3.5/8.2)*5.1=3.3dB. Neither of these support the measurement of 0.67dB/100m… so it is probably wrong.

### S/C section

Lets move the cursor on the O/C scan down to 3.5MHz.

Looking at the screenshot above, the data at the right shows Return Loss as 3.5MHz is 0.59dB, and the calculated Cable Loss (meaning MLL) is 0.29dB.

0.29dB/6m is equivalent to 4.83dB/100m, a lot higher than the interpolation of the datasheet values, unbelievable.

This is not a resonant section, so we cannot use the Rin method directly, but since MLL is almost entirely due to conductor loss for this type of cable at this frequency, we can interpolate from the datasheet MLL=(3.5/10)*4.59=2.71dB, or extrapolate from our own Rin based MLL at 8.2MHz MLL=(3.5/8.2)*5.1=3.3dB. Neither of these support the measurement of 4.83dB/100m… so it is probably wrong.

### But wait…

The average of the O/C and S/C Return Loss is (0.09+0.59)/2=0.340, MLL=0.170/6m or 2.83dB/100m. This falls in the range between our datasheet interpolation and extrapolation from our 8.2MHz Rin based MLL.

## More about Zo

Stated earlier was an assumption that Zo=50+j0Ω, and we often assume that Zo equals the nominal Zo for convenience… but:

- are results sensitive to Zo; and
- is the convenience safe?

For this example, I have measured complex input Z of the O/C and S/C sections at 3.5MHz. Zo can be calculated Zo=(Zoc*Zsc)^0.5.

Here is the calculation in Python

>>> zo=cmath.sqrt((0.616-61.496j)*(2.779+39.865j)) >>> zo (49.55229895635798-1.4766271906868134j)

So, Zo=49.55-j1.48Ω. (Of course this value is subject to measurement error, but it is quite within the range of expectations for this cable type at this frequency… but quantifying Zo is a larger subject in its own right.) This value of Zo is not a defect, this is a natural consequence of mainly conductor based loss at this frequency. It is this departure from nominal Zo (50+j0Ω) that gives rise to the difference between Return Loss of the O/C and S/C sections at 3.5MHz.

As explained at On Witt's calculation of Matched Line Loss from Return Loss, taking half of the average of Return Loss for O/C and S/C sections gives a reasonably good approximation of MLL provided the error in assumed Zo is small.

## Learning from failure

If you were to make a single measurement at 3.5MHz following the method given in the AIM manual, you would obtain MLL of about 25% of the correct value, a gross error in anyone's terms.

By comparing that value with expectation based on the datasheet, and measurements at other frequencies including using other techniques, we challenged the validity of the measurement, and ultimately the AIM manual advice,

By questioning the validity of the first measurement, we learned that:

- the Half Return Loss method is sensitive to accuracy of Zo;
- the AIM method is naively incomplete;
- Zo in the example was sufficiently different from assumed nominal Zo to cause large error in calculated MLL at 3.5MHz using the AIM method;
- estimating MLL as half the average of Return Loss for O/C and S/C sections gave a reasonably good approximation of MLL provided the error in assumed Zo was small.