Having recently published Graphic demonstration of loss under standing waves, I was interested in a thread running on QRZ.com which offered solutions to some mismatched scenarios. Continue reading Graphic demonstration of loss under standing waves #2

# Category: Transmission lines

## Exploiting your antenna analyser #8

## Finding resistance and reactance with some low end analysers

There are some analysers on the market that do not display reactance X or even magnitude of reactance |X| and possibly resistance, but do display VSWR and magnitude of impedance |Z|. Continue reading Exploiting your antenna analyser #8

## Walter Maxwell’s teachings on system wide conjugate matching

Walt Maxwell (W2DU) made much of conjugate matching in antenna systems, he wrote of his volume in the preface to (Maxwell 2001 24.5):

It explains in great detail how the antenna tuner at the input terminals of the feed line provides a conjugate match at the antenna terminals, and tunes a non-resonant antenna to resonance while also providing an impedance match for the output of the transceiver.

Walt Maxwell made much of conjugate matching, and wrote often of it as though at some optimal adjustment of an ATU there was a system wide state of conjugate match conferred, that at each and every point in an antenna system the impedance looking towards the source was the conjugate of the impedance looking towards the load.

This is popularly held to be some nirvana, a heavenly state where transmitters are “happy” and all is good. Happiness of transmitters is often given in online discussion by hams as the raison d’être for ATUs . Continue reading Walter Maxwell’s teachings on system wide conjugate matching

## Exploiting your antenna analyser #7

## Application to a loaded mobile HF whip

This article explores application of an antenna analyser to a helically loaded 7MHz mobile whip that has an adjustable length tip for tuning.

The task at hand is to ‘tune’ the antenna to a desired operating frequency.

The analyser used is a Rigexpert AA-600, but the article deals more generally with analyser features.

## Initial measurement and interpretation

Above is a plot of R, X, and |Z| measured at the cable connector that plugs onto the transmitter. Ignore |Z|, it is irrelevant and confusing but unfortunately a ‘feature’ of the Rigexpert software that cannot be disabled. Continue reading Exploiting your antenna analyser #7

## Graphic demonstration of loss under standing waves

Standing waves change the distribution of voltage and current on a transmission line, and that results in a change in attenuation from that published for a matched load (ie Zl=Zo).

There are many formulas given in various places for calculating the loss under mismatch, almost all of them depend on either ρ (the magnitude of the complex reflection coefficient Γ) or VSWR. Since these are simply related (VSWR=(1+ρ)/(1-ρ)), they have the same dependency. In fact, there is not enough information in ρ (or VSWR) to calculate loss exactly, so they are approximations with underlying assumptions that are rarely exposed.

This article compares the calculation using two common formulas which related loss under mismatch with Matched Line Loss (MLL) with the exact solution using lengths of RG58 terminated with two different VSWR=10 loads at a range of frequencies from 1-30MHz. Continue reading Graphic demonstration of loss under standing waves

## Exploiting your antenna analyser #6

## Shunt match

Now one of the methods that is often used to transform the impedance of an antenna to suit a 50Ω feed line is the shunt match.

Lets explore that with our test jig reconfigured.

Connect up the two line sections in cascade from the analyser, and terminate it with the two 50Ω loads on the tee piece. Don’t worry too much about what we have in terms of implementation, it provides a load to the analyser that presents a similar scenario to shunt matching a loaded short monopole.

So, measure the input impedance around 21MHz.

Above is a scan with the Rigexpert AA-600 from around 21MHz. Ignore the |Z| line, it is irrelevant and confusing but I cannot switch it off, a shortcoming of the software.

What we are exploring is that as we change frequency, the parallel equivalent resistance changes at 21.275MHz above, it equals 50Ω. The full parallel equivalent is 50Ω//-j77.3. So, if we were to make a small inductor of 77.3Ω reactance (L=X/(2*pi*f)=580nH) and connect it in shunt, the resulting impedance will be 50+j0Ω. Continue reading Exploiting your antenna analyser #6

## Exploiting your antenna analyser #5

## Measure MLL using the Rin where X=0

Another method of estimating Matched Line Loss (MLL) from measurement is using the input resistance of a section that is an odd or even number of quarter waves in electrical length.

I say estimate because this method depend on an assumption of the value of Zo, and using purely real nominal Zo introduces some error.

The required length can be approximated by fining a frequency where X passes through zero. Again, this method is an approximation.

## Simple formula

There is a simple formula published in many ham handbooks:

MLL≈8.686*Rin/Zo/length dB/unitlength

It is, a discussed at Measuring matched line loss, a crude approximation (and should be written with ≈ rather than =).

## Better formula

A better formula is one I developed though it may not be novel:

MLL=-10log|(Rin-Zo)/(Rin+Zo)|/length dB/m

It is exact, but there is error introduced in using nominal Zo.

## In practice

### Low Z measurement

Lets measure Zin of our 4m o/c line section, and find the lowest frequency where X passes through zero, and note the value of Rin.

Above is a wide sweep, the frequency we want to focus on is around 13MHz. Continue reading Exploiting your antenna analyser #5

## Exploiting your antenna analyser #4

## Measure MLL using the half ReturnLoss method

Again in the theme of measuring something known, let us determine the matched line loss (or normally quoted attenuation) of our cable at 3.5MHz.

To make the measurement, just connect the two test line sections used in the earlier articles in this series in cascade with a joiner, and one end on the instrument, other end open circuit, and measure ReturnLoss.

Most analyser manuals and lots of helpful articles in journals and handbooks will tell you that MLL=RL/(2*length) where RL is the ReturnLoss of an open circuit or short circuit line section (the only requirement is that the ρ=1 at the line end).

Wow, that is so low, and using the traditional formula:

MLL=0.02/(2*4)=0.0025dB/m.

Of course we are measuring way low in the instrument’s capability and there is some considerable uncertainty… but when we consult a good transmission line loss calculator, we expect around 0.029dB/m… that is 12 times what we measured. Continue reading Exploiting your antenna analyser #4

## Exploiting your antenna analyser #3

## The sign of reactance

At Exploiting your antenna analyser #2, the matter of determining sign of reactance was mentioned.

If you have an analyser that does not measure the sign of reactance, this information should be important to you.

Above is a Smith chart plot of measurements from 15MHz to 25MHz.

One can see that the locus of Zin on the Smith chart forms an arc, and the points on the arc rotate clockwise about the arc centre with increasing frequency. Continue reading Exploiting your antenna analyser #3

## Exploiting your antenna analyser #2

## Reconciling the single stub tuner results

So having found that the length of the RG58 lines sections are both 1.98m (approximately 2m), let’s try to reconcile measurement and prediction of Zin at 9MHz.

The examples discussed in this series of articles are designed for the test jig as described at Exploiting your antenna analyser #1 with a pair of nominally 2m length RG58 patch leads, a pair of 50Ω loads and some tee pieces and adapters to connect it all up. If you duplicate it, you will experience the same learning opportunities (the examples are structured). If you presume to redesign the experiment, your outcome will probably be different.

Before you read on, take a measurement of Zin at 20MHz and write down the impedance value. Do whatever you do to determine the sign of the reactance. If your instrument displays the sign properly, use it, otherwise use the method in your user manual or whatever wisdom you trust.

Done that? If so, read on… Continue reading Exploiting your antenna analyser #2