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
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
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.
There is a simple formula published in many ham handbooks:
It is, a discussed at Measuring matched line loss, a crude approximation (and should be written with ≈ rather than =).
A better formula is one I developed though it may not be novel:
It is exact, but there is error introduced in using nominal Zo.
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
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 line sections 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:
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
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
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
I often see posts in online fora by people struggling to make sense of measurements made with their antenna analyser.
This article is about exploitation of a modern antenna analyser beyond its capability as a self excited VSWR meter. The latter is fine, and it is often not only all you need, but the best tool in optimising some antenna systems… but if you want to exploit the other capabilities of the instrument, read on.
Great benefit can be obtained by measuring some known loads, and reconciling the measurement with the known.
A quite simple set of equipment can be used to create a scenario rich with opportunity to prove your understanding of the basics of complex impedance, transmission lines, and measurement. Lets explore a simple example.
Above is a test jig. It is two equal lengths of identical coax connected to a tee piece on the analyser. The end of one piece of coax has a tee piece with two nominal 50+j0Ω loads as used on Ethernet 10base2 networks. The analyser is a Rigexpert AA-600. Continue reading Exploiting your antenna analyser #1
Voltage Standing Wave Ratio is the ratio of the voltage maximum (antinode) to the adjacent voltage minimum (node) on a transmission line. (This assumes a fully developed standing wave, that the maximum and minimum are not forced by end of line). Continue reading Expression of VSWR as a simple decimal real number
Another of those threads has broken out on eHam illustrating that lots of hams do not understand the complex nature of impedance and cannot see the consequences of the formula to calculate VSWR from load impedance and transmission line characteristic impedance.
Most methods of measuring VSWR are indirect, and they are based on an assumed Zo which is purely real (ie Xo=0Ω), and we speak loosely of that as the VSWR even though the standing wave that might exist on a practical transmission line is a little different as a consequence of that assumption being a little bit in error. Continue reading VSWR=1 and X≠0
This article describes an Aerial Under Test (AUT) that features in some of my experiments and write ups and is subject of some current experiments. It is a MobileOne M40-1 helically loaded vertical for 40m installed in the car roof. It is in the style of the popular US antenna, the Hamstick, but this is a little longer and the results are not directly applicable.
I hasten to add that this configuration is not suited to travelling, it is just a rather ideal mounting of a helically loaded whip without the questions that arise from the effects of roof racks, bumper mounts etc.
The M40-1 is fitted in the centre of the station wagon roof, the roof is 1.5m above ground and the antenna is 1.5m long including a 200mm unloaded tip (tip of the antenna is highlighted with a pink dot). (The setting is not the test site.) Continue reading AUT – MobileOne M40-1 40m helical