A correspondent suggested that with a ferrite core, flux leakage is insignificant. This article calculates the coupled coils scenario.
Above is the ‘schematic’ of the balun. Note the entire path from rig to dipole.
Let’s use the impedance measurement with short circuit termination to find the inductance of the two coupled windings in series opposed.
Above is a plot of the impedance, R+jX. X at 1MHz implies L=8.6µH. Remember that this is the inductance of two series opposed coils, so it includes the effect of mutual inductance.
We can estimate reasonably by calculation that the inductance of one coil L1 @ 1MHz is 114µH.
Measurement of a SC termination gave \(L=(L1-M)+(L2-M)=8.6µH \) and since L1=L2 we can calculate \(M=114e-6-\frac{8.6e-6}{2}=109.7\;µH\) and from that the flux coupling factor \(k=\frac{M}{\sqrt {L1L2}}=\frac{109.7}{114}=0.9623\).
So, k is very high, there is very little flux leakage, but not enough to ignore… it has a huge bearing on the outcome.
]]>Above is the ‘schematic’ of the balun. Note the entire path from rig to dipole.
Above is a plot of VSWR from 1 to 51MHz. It starts off at VSWR=2.8 @ 1MHz, not good, and increases with increasing frequency to VSWR=500 @ 30MHz. (The marker label is misleading, it is a significant software defect, the values are not s11 as stated on the chart but VSWR.)
VSWR @ 10MHz is 96.
You might ask how is this different to the case where the two wires were twisted together and 10 turns wound onto the core. They both seem like coupled inductors… and they are, but there is a significant difference is in the extent of coupling, the extent of flux leakage.
A simple measurement of the input impedance of the balun with a short circuit termination gives us a low frequency inductance of around 8.6µH for 0.6m of two wire transmission line, that is around 14µH/m. That is 25 times the inductance if they were wound as a close spaced pair. The capacitance of the wide space wires is lower than if they were wound as a close spaced pair, so both of these and increases loss drive characteristic impedance Zo up to something of the order of 1400Ω, and velocity factor VF down.
Measurement of the short circuit section shows first resonance (antiresonance actually) at 44MHz which allows calculation of VF as 35%.
The combination of extreme Zo and very low VF causes much greater impedance transformation of a 50Ω load than normally desirable, as can be seen from the VSWR plot above.
Let’s compare that simple model of the balun with a simulation
Above is the measured data presented as a Smith chart. For a low Insertion VSWR balun, we would expect the trace to be entirely very close to the prime centre of the chart. This doesn’t even start off there, and just gets worse with increasing frequency.
Though a very simple model, the series transmission line section of Zo=1400Ω ohms and VF=0.35 captures most of the measured behavior.
A more complete model would indicate higher transmission line loss due to the inclusion of the ferrite based inductance in the transmission line distributed inductance. There is little point in measuring the transmission loss as the balun is impractical due to the extreme Insertion VSWR.
There is a simple explanation for the very poor Insertion VSWR of the N6THN balun, it uses a loaded transmission line section with very high Zo and low VF.
If you want low Insertion VSWR in a Guanella 1:1 balun, ensure that Zo of the transmission line section is close to your load impedance.
]]>(Anaren 2005) explains a method of finding balun CMRR. Anaren gives a definition of CMRR:
Common Mode Rejection Ratio is defined and the ratio between the differential mode insertion loss/gain versus the common mode signal loss or gain.
Note that in a passive system, CMRR in dB will usually be positive, and the larger the better.
Anaren does not mention applying the CMRR statistic to antenna systems. I have commented elsewhere on the lack of utility of CMRR in analysing common antenna systems.
John, KN5L, has published his own solution to balun characterisation in some online forums.
Let’s look at his example with a 7t RG174 winding on a FT140-43 core in his recommended test fixture. He does not give a schematic of the test fixture, but it can be gleaned from his pic.
At the left is VNA Port 1 connection, the coax connects shield to the coax connector outer, and coax inner to connector inner. At the right hand end of the coax, the shield connects to the connector inner via a series 25Ω resistor, and the coax inner connects to the connector inner via another series 25Ω resistor, both coax connector outers are connected to the PCB copper plane, and the right hand coax connector connects to the VNA Port 2. He gives no explanation of why such a test fixture was chosen.
Above is his published VNA sweep. Analysing his published .s2p file reveals that the curves labelled “RG174 CMRR” is in fact |s21|… so he has implied his own meaning for CMRR, he does not give a clear definition other than this implication. The negative values of “RG174 CMRR” sound a warning.
John publishes a Simsmith model comparing a theoretical model of the balun in his test fixture with measurement. His Simsmith model of the balun in fixture is flawed, so I will use my own.
In this case, I have tweaked the number of turns a little to get a closer fit between model and measurement, ferrite has quite wide tolerance and the model is simple so we should not expect exact reconciliation.
Also calculated is the expected balun common mode impedance Zcm, in this case 1063+j617Ω @ 14MHz.
Above is my chart of his published measurement file. The curve “s21 dB” is simply |s21| from Port 1 to Port 2 through his test fixture, it is not in accord with Anaren’s definition of CMRR as he labels his plots.
The curves “t2s(s21) real Z” and “t2s(s21) real Z” mimic a calculation John gives on some other examples. The function t2s is documented in the VNWA help.
t2s is a VNWA built in function intended to solve the so-called s21 series through fixture for impedance measurement of two terminal Zx connected between Port 1 and Port 2.
Looking at the marker values on my chart, they indicate Zx=5554+j4366Ω @ 14MHz. Is that the true common mode impedance? Hhe seems to be saying that:
ALL previous NEC Balun CM current models using a single inductor to
simulate two flux coupled inductors, of the same value, are flawed.
Well, applying the t2s function to data from a different test fixture circuit is invalid, the results are invalid, conclusions drawn from it are invalid.
NEC is quite capable of modelling the common mode current path separately to a TL element (which models only the differential mode), the appropriate value to load the common mode conductor path with is the calculated Zcm (which is frequency dependent).
The test fixture used seems inspired by the theme ‘more complicated is naturally better’.
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 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.)
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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The transformer of interest is the one to the left, and if you follow the tracks, the multiturn winding is connected between ground and a track that routes across to the through line. The transformer primary appears in shunt with the through line.
The transformer appears to comprise a 24t primary on a 2646665802 #46 toroid. Note that #46 is a MgZn ferrite, where other designs tend to use either powdered iron or NiZn ferrite.
For the purpose of this article, flux leakage is ignored as it will have very little effect on the calculated ReturnLoss due to this component alone.
Above is the calculated ReturnLoss due to the magnetising admittance of the voltage transformer that is in shunt with the through line based on the published permeability characteristics and assuming 3.5pF of equivalent shunt capacitance to model self resonance. ReturnLoss is presented here as InsertionVSWR is very very small, VSWR=1.02 equates to ReturnLoss=40dB.
ReturnLoss at the lowest specified frequency, 1.8MHz, is 47dB.
Now this is not the only source of mismatch that would drive low ReturnLoss, but in most ham designs, this single component is responsible for ReturnLoss less than 20dB at their specified lower frequency limits.
There is little point having an instrument that indicates VSWR down to say 1.1 when it invisibly causes VSWR=1.3 looking into it (eg
Grebenkember’s original Tandem match).
Measurement of VK4MQ’s wattmeter using one of these couplers showed ReturnLoss (-|s11|) jack to jack at 1.8MHz to be 46dB, and it remains above 30dB to 30MHz, 25dB at 50MHz.
I purchased one of the couplers for use with a DIY digital display, and although I have had it longer, it isn’t yet realised!
A common failing of almost all hammy Sammy designs is appalling InsertionVSWR at the lower end of the specified frequency range. This coupler is specified for 1.8-54MHz, and differently to most, has meaningful published characteristics.
In this implementation, 60mm lengths of solder soaked braid coax similar to Succoform 141 were used between the PCB and box N connectors. The expected matched line loss of both of these is about 0.01dB @ 50MHz.
The measurements here were made by VK4MQ using an Agilent E5061A ENA, data analysis by myself.
Above are the raw s parameter measurements plotted. It is a full 2 port measurement, and it can be observed that the device is not perfectly symmetric, quite adequate, and quite good compared to other ham designs that I have measured.
ReturnLoss is -|s11|, it is simply stunning, a huge departure from most ham designs. Some that I have measured were less than 20dB at their specified lower frequency limit.
An interesting perspective is to disaggregate InsertionLoss (-|s21|) into Mismatch Loss and (Transmission) Loss.
As we expect from the |s11| plot, MismatchLoss is very low, InsertionLoss is dominated by Loss. Loss tells us how much of the actual input power is converted to heat.
Above is a plot of the expected dissipation due to Loss. Most of it is likely to be in the ferrite cores, mainly in the voltage sampler with a 50Ω load.
Difficulties were encountered in adapting Kiciak’s design to the unmodified coupler. Kiciak didn’t deal with intercept and gain calibration entirely in the coupler or the display electronics, it is spread between them.
The VK3AMP coupler would have been much easier to use if it incorporated pots for intercept and gain calibration in each channel. This will not be an issue in my digital meter project as each channel (fwd, rev) will have slope and intercept calibration in the firmware.
Custom meter scales were designed to suit two available taut band meters.
Above, the forward power meter scaled in dBm (Bruce’s preference). The sharp mind will recognise 56dBm is 400W.
Above, the return loss meter scaled in dB.
Above is the interior of VK4MQ’s build.
Above is the inside of the front panel. The electronics is built dead bug style on the PCB that is visible, the two meter movements are in the lower part.
Above is the front panel with the rescaled meters recovered from some e-waste. The meter does not overhang the edge, it is a perspective issue with the pic.
This article compares the results for the FT240-43 example at 3.5MHz with calculation using tools on this web site.
Above is a very simple approximation of an ideal 1:1 transformer where the effects of flux leakage and conductor loss are ignored. A 1:n transformer can be modelled the same way, as if flux leakage and conductor loss are ignored, the now ideally transformed secondary load becomes 50Ω.
First step is to find the complex permeability of the core material.
Next, calculate the RF impedance and admittance at 3.5MHz of a 4t winding.
The real part of Y is the magnetising conductance Gm (the inverse of the equivalent parallel resistance).
We can calculate core magnetising loss as \(Loss_m=10 log \left(1 + \frac{Gm }{0.02}\right)=10 log \left(1 + \frac{0.00168}{0.02}\right)=0.35 \; dB\).
We can calculate InsertionVSWR using Ym+0.02 S as the load admittance.
Above, InsertsionVSWR is 1.21.
Measured | Predicted | |
Loss (dB) | 0.32 | 0.35 |
InsertionVSWR | 1.15 | 1.21 |
Given the tolerance of ferrite cores, the reconciliation is very good.
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