A reader has asked the question in a transmission line context after reading Walter Maxwell’s teachings on system wide conjugate matching.
In the real world, transmission lines have loss and almost always, the nature of that loss will mean that Zo is not purely real.
The answer to the question depends on whether or not there are standing waves on the transmission line.
Nothing in this article is to imply that a transmitter is well represented by a Thevenin equivalent source. Continue reading Is maximum power transfer and conjugate matching simultaneously possible
Measuring an RF inductor
This article walks through practical measurement of a ferrite toroidal inductor using an antenna analyser.
To be relevant practically, lets use an example from N4SPP’s end fed wire antenna on 3.6MHz. His coupling transformer uses a two turn winding on an FT240-43 core for the nominal 50Ω connection to the antenna system.
We could calculate the impedance of this winding using one of the plethora of online and desktop inductance calculators, but lets first fetch the data from the manufacturer.
A simple statistic that is widely used is Al, and above, Fair-rite gives Al=1075nH +/-20%. Note that although they give a tolerance of +/-20%, it is not uncommon that manufactured product has greater error, they may have optimistically quoted the standard deviation and it is easy to fall outside that (37% chance). Continue reading Exploiting your antenna analyser #10
Disturbing the thing you are measuring
In all measurements, we need to be careful that the measurement does not disturb the thing being measured.
This article explores an example where the instrument measurements appear wrong.
The story starts with a mobile antenna that the transceiver indicates has very high VSWR over the 40m band, though starts to decrease towards 7.350MHz.
To assist in problem identification / tuning, the antenna connector is disconnected from the radio and connected to the AA-600 analyser and a sweep taken.
Above is the sweep, but it is quite inconsistent with the transceiver’s VSWR meter readings. The plot above looks good, a little adjustment of the tip would get it down to 7.060… but the transceiver does not see it that way. Continue reading Exploiting your antenna analyser #9
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
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
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
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
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