The article uses Rigexpert’s Antscope as the measurement / analysis application, the techniques will work with other good application software.
To demonstrate the technique for matching such an antenna, let’s use NEC-4.2 to create 80m feed point impedance data for a 12m high vertical with 8 buried radials (100mm) and centre loading coil resonating the antenna in the 80m band for simulation of measurement data.
An s1p file was exported from 4NEC2 for import into Antscope, to simulate measurement of an example real antenna.
Above is the VSWR curve displayed in Antscope. Note that the actual response is dependent on soil types, antenna length and loading etc, but this is a good example for discussion. It is not real bad, another example might be better or worse.
Above is a plot of the feed point impedance, ie the serial components of feedpoint impedance R and X. The possibility of a shunt match does not jump out, other that seeing that R<50.
Above is a Smith chart presentation, and this is more revealing. We can ‘see’ that the curve crosses the undrawn circle where G=1/50S. It is undrawn probably because the software author did not foresee the utility of G circles etc.
So, at the cursor, the admittance Y=1/49.5+j1/64.5S (the unit of admittance is Siemens), but they write it in a hammy way that Zpar=49.5-j64.5 ohms and it is quite flawed, algebraically it is wrong, they perhaps should have written Zpar=49.5||-j64.5 Ω to mean 49.5Ω in parallel with -j64.5Ω. A lot of people cannot handle admittance, and talk in the parallel impedances equivalent.
Talking in hammy parallel impedance, the capacitive element of Zpar can be ‘tuned out’ by an equal but opposite parallel reactance, leaving Zpar=49.5… pretty much right on target.
Above is a presentation of the parallel equivalent impedance components.
An important characteristic of this antenna is that at Rp passes through 50Ω, so it may be a good candidate for a shunt match at the frequency where Rp=50Ω. Rp does not pass through 50Ω, it is not candidate for a shunt match.
It can be seen that around the cursor, Rp is frequency sensitive, and at the cursor, Rp is almost exactly equal to 50Ω, so we just need to ‘tune out’ the parallel reactance with an appropriate inductor (one with X=64.5Ω).
You could then calculate the inductance of the shunt coil, make a coil and measure / adjust to minimum VSWR. In this case, \(L=\frac{X}{2 \pi f}=\frac{64.5}{2 \pi 3.538e6}=\text{2.9e-6}\), so we could design an inductor for 2.9µH.
This section shows simulation in Simsmith.
Above is a Simsmith model of the match. The s1p file is imported into the L element. The frequency is dialed to the point where the L element impedance crosses the G=0.02 circle, and the shunt inductor adjusted until the impedance at G is approximately 50+j0Ω.
In this case, a 2.9µH inductor could be prototyped as 10t of 2mm wire on a 38mm diameter form, stretched out to 33mm in length. (Design from Hamwaves RF Inductance Calculator.)
Above, the VSWR=2 bandwidth is about 130kHz.
Now the frequency at which we achieve this match might not be what we would prefer.
To do this, we go back to Step 2 and adjust the antenna (length; loading coil inductance, position; etc) to move the frequency where Rp≈50Ω.
Having done that, we calculate the inductance of the shunt coil, make a coil and measure / adjust to minimum VSWR at the preferred frequency.
The sweeps above were used to show what is happening in a wider context, but they are not essential. You do not need a scanning analyser… but scanning might well provide more confidence that the antenna is behaving as you assume.
You could simply set your analyser to display the parallel equivalent components at the frequency of interest, adjust the system to achieve Rp≈50Ω, note the required parallel opposite reactance, calculate the inductance of the shunt coil, make a coil and measure / adjust to minimum VSWR at the preferred frequency.
]]>This article documents measurement of the complex common mode impedance Zcm, and calibration of the predictive model.
Zcm is a most useful quantity, it can be used in NEC models of an antenna system.
Common mode impedance was measured using a nanoVNA.
The response is quite similar to previously modelled, but self resonant frequency (SRF) is a little lower, so the model needs calibration.
The model was calibrated by increasing Cs to 2.9pF to achieve SRF=9.4MHz.
The next step is to measure temperature rise (take thermographs) under measured common mode current.
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The diagram above from the video shows the topology of the series stub match.
Let’s work an example using 50Ω coax where the load is 10-j40Ω at 146MHz.
Above is a naive Simsmith model of the scenario with line lengths adjusted for a ‘perfect’ match. The inset VSWR curve looks great!
Why did I say naive?
Well, when we look at the series stub more completely, along with the differential mode behaviour that is captured in the Simsmith model above, we have the outside surface of the outer conductor of the stub connected to the main line inner conductor on the source side of the stub and it is capable of carrying current.
This stub outer surface current may give rise to radiation and impresses a load impedance across the main line coax in shunt with the perfectly transformed 10-j40Ω load. The value of this unintended impedance depends on the stub physics.
In this case, the stub is just under a quarter of a wavelength, and modelled as a monopole over a ground plane would present a driving impedance of around 15-j80Ω.
Above is the Simsmith model with the addition of the estimated impedance of the stub outer as a radiator in shunt with the main line. The matching result is degraded by the stub exterior’s ‘antenna effect’ and that unintended radiation / pickup may be undesirable.
The VSWR curve is not so good now when the ‘antenna effect’ of the stub is brought to book. The match could be tweaked some, but it does not remove the radiation / pickup behavior of the stub.
Matchers using series or shunt stub tuners are nearly ideal in waveguide and can be quite good / practical in two wire lines; but while shunt tuners are nearly ideal in coax, series tuners in coax may not be so good and tend to be avoided.
]]>Above is the prototype 2631540002×2 wound with 3.5t of RG316.
Above is the plot of R and X components of Zcm from 1-30MHz. Self resonant frequency SRF is 5.4MHz.
|Zcm| is very high from 2-14.5MHz and high from 1-26MHz, and this should make an effective choke for most reasonable scenarios.
Having measured the SRF, we can calibrate the predictive model.
Above, the calibrated model is quite close in form to the measured, allowing for the rather wide tolerance of ferrite.
A follow up article will report thermal tests on the prototype balun.
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Above is the prototype 2843009902 binocular wound with 3.5t of RG316.
Above is the plot of R and X components of Zcm from 1-30MHz. Self resonant frequency SRF is 8.75MHz.
|Zcm| is very high from 3-22MHz and high from 1.8-30MHz, and this should make an effective choke for most reasonable scenarios.
Having measured the SRF, we can calibrate the predictive model.
Above, the calibrated model is quite close in form to the measured, allowing for the rather wide tolerance of ferrite.
A follow up article will report thermal tests on the prototype balun.
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This article presents the workup of a balun with similar design objectives using a low cost Fair-rite 2843009902 binocular core (BN43-7051).
Above, a pic of the core.
The design is a variation on (Duffy 2007) which used RG174 coax for the choke to give low Insertion VSWR.
For low Insertion VSWR, the choke uses 50Ω coax wound around a pair of ferrite tubes. The coax is a miniature PTFE insulated cable, RG316 with silver plated copper centre conductor (be careful, some RG316 uses silver plated steel and it is less suitable for HF).
Matched line loss in the 350mm length of coax is 1.2% @ 30MHz, 0.4% @ 3.5MHz, and could be higher or lower with standing waves.
PTFE coax is used for high voltage withstand and tolerance of high operating temperature.
Above, an insulation test of the RG316. It withstood 7kV peak (5kV RMS) from inner to outer, and the jacket also withstood 7kV peak at a knife edge. Voltage breakdown is more likely to occur somewhere else in the balun.
For this design, the cores need to be large enough to accommodate 4 passes of RG-316 coax, but no larger.
Above, the cores will accommodate four round conductors of diameter 2.6mm, so they will comfortable accommodate the four passes of the RG-316 coax (2.45mm each). (For the mathematically minded, the minimum enclosing circle diameter for four equal circles is 1+√2 times the diameter of the smaller circles.)
Al (10kHz) is about 9µH.
The main contribution to loss and heating will be the ferrite core losses, and they are dependent on common mode current.
Above is a first estimate of common mode impedance of 3.5t (4 in one hole, 3 in the other – an approximation) assuming an equivalent shunt capacitance of 2pF. The latter is an experienced guess, and will be adjusted upon measurement of a prototype.
Implementation will be described in a follow up article.
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This article presents the workup of a balun with similar design objectives using a pair of low cost Fair-rite 2631540002 cores (FB-31-5621) which are similar in size to the LF1260 and have higher µi (1500 vs 1000).
Above, a pic of the cores from Amidon’s catalogue.
The design is a variation on (Duffy 2007) which used RG174 coax for the choke to give low Insertion VSWR.
For low Insertion VSWR, the choke uses 50Ω coax wound around a pair of ferrite tubes. The coax is a miniature PTFE insulated cable, RG316 with silver plated copper centre conductor (be careful, some RG316 uses silver plated steel and it is unsuitable for HF).
Matched line loss in the 350mm length of coax is 1.2% @ 30MHz, 0.4% @ 3.5MHz, and could be higher or lower with standing waves.
PTFE coax is used for high voltage withstand and tolerance of high operating temperature.
Above, an insulation test of the RG316. It withstood 7kV peak (5kV RMS) from inner to outer, and the jacket also withstood 7kV peak at a knife edge. Voltage breakdown is more likely to occur somewhere else in the balun.
For this design, the cores need to be large enough to accommodate 4 passes of RG-316 coax, but no larger.
Above, the cores will accommodate four round conductors of diameter 2.6mm, so they will comfortable accommodate the four passes of the RG-316 coax (2.45mm each). (For the mathematically minded, the minimum enclosing circle diameter for four equal circles is 1+√2 times the diameter of the smaller circles.)
The main contribution to loss and heating will be the ferrite core losses, and they are dependent on common mode current.
Above is a first estimate of common mode impedance of 3.5t (4 in one core, 3 in the other) assuming an equivalent shunt capacitance of 2pF. The latter is an experienced guess, and will be adjusted upon measurement of a prototype.
Implementation will be described in a follow up article.
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Should we have expected this outcome?
Let us solve a very similar problem analytically where measurement errors do not contribute to the outcome.
Taking the load impedance to be the same 10.1+j0.2Ω, and calculating for a T match similar to the MFJ-949E (assuming L=26µH, QL=200, and ideal capacitors) with Simsmith we can find a near perfect match.
The capacitors are 177.2 and 92.9pF for the match.
Also calculated is the impedance looking back from the load to the source shown here as L_revZ. The impedance looking back towards the 50Ω load is 17.28-j0.6216Ω, which is quite close to the value obtained by measurement, 18.0-j0.8Ω (which is dependent on the actual Q of the ATU elements).
Is there some smoke and mirrors in calculation of L_revZ? Lets turn the network around.
Now turning the network around by swapping the capacitors and changing the load to 50+j0Ω.
Above, the impedance looking back towards the 50Ω load is 17.28-j0.62Ω, which consistent with the L_revZ calculation and is quite close to the value obtained by measurement, 18.0-j0.8Ω (which is dependent on the actual Q of the ATU elements).
So, in answer to the question Should we have expected this outcome?
, the answer is yes, it is not surprising and quite similar to what we might expect from a network of this type.
Walt Maxwell’s Conjugate Mirror (Maxwell 2001 24.5) which imbues a magic system wide conjugate match with certain benefits, a utopia, which does not apply to systems that include any loss, it does not apply to real world systems. Maxwell does not state that limitation of his proposition.
Is a ham transmitter conjugate matched to its load? Watch for a follow up post.
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The MDF is located where the underground cable enters the building. From here it rises vertically and travels some 25m across the ceiling to the VDSL modem.
The choke can be seen in the pic, it is 7 turns of CAT5 data pair wound around a LF1260 ferrite sleeve.
Above is the measured common mode impedance R,X of the choke. It is designed to peak between 3.5 and 7MHz to afford some moderately high impedance at both frequencies.
Measurements were made with a nanoVNA-H and the graphic made in Python scikit-rf from a saved .s1p file.
On test, the choke is effective on 40m.
]]>An SWR shifting Tillustrates the pitfalls in naive design and implementation of transmission line matching systems. I say naive because the article does not address the matter of loss, yet QST publishes it as an example.
K2PO outlines an issue that looking into the end of the feed line at 3.58MHz he measures Z=135-j90Ω, and his solution using a single stub tuner of RG-8X right on the back of the power amplifier.
Let’s model that in Simsmith (though I must declare I have issues with Simsmith’s transmission line modeling).
The model above implements a near perfect match, and the source is set to supply 1500W. If we are to accept Simsmith’s loss model, the calculated power values as the signal flows right to left (huh!), 35W is dissipated in the open circuit stub, and 269W is dissipated in the 20m long series section. In all 20% of the 1500W transmitter output is converted to heat in the matching system.
Above is a pic of the series section that dissipates 269W, fairly tightly coiled foam dielectric coax may get quite hot risking migration of the centre conductor.
Of course this is less a problem for low power or low duty cycle modes that high duty cycle modes like RTTY or even CW.
By contrast, a good ATU should provide the same impedance transformation at perhaps a quarter of the power lost.
A purpose specific L match does even better.
Above, a model of an L match with a good capacitor and mediocre inductor yields a loss of less than a tenth of the power of the single stub tuner solution described.
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