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.

]]>In this case, it is described in the referenced video as part of a half wave dipole antenna where you might expect the minimum feed point VSWR to be less than 2.

Apologies for the images, some are taken from the video and they are not good… but bear with me.

Above is the ‘schematic’ of the balun.Note the entire path from rig to dipole.

To the experienced eye, it immediately raises questions.

Above is the implementation.

Cursory analysis suggests this will have very poor Insertion VSWR. When used with a low VSWR(50) load like a half wave dipole, the VSWR looking into the balun will be very poor.

Let’s check it out with the ubiquitous nanoVNA.

Since Insertion VSWR is the initial concern, let’s measure Insertion VSWR from 1 to 51MHz. The original video used a #31 core, I have used a #43 as I have them on hand. Not exactly the same, but the same issue arises either way.

The balun was hooked up with an accurate 50Ω load (two tiny 1% 100Ω SM resistors at the left of the balun), and connected to the nanoVNA with a transformer to allow the balun balanced drive. The nanoVNA with the attached transformer is OSL calibrated at the terminal block on the transformer board, so we can measure the DUT with 50Ω termination.

Above is the test configuration.

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.)

Above is the same 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.

Above is a plot of the impedance, R+jX. For a low Insertion VSWR balun, we would expect that R would be very close to 50Ω over the whole range, and X would be very close to 0Ω over the whole range. This plot starts off with R=50Ω, X=55Ω @ 1MHz, and R just increases way off scale.

It is hard to find an adjective to describe how bad the Insertion VSWR is, it is clearly a total failure on that count alone.

Read widely, be critical of what you read on social media. In respect of balun designs, look for relevant measurements, think about them, analyse the offering.

]]>Take a look at the antenna with a VNA and sweep with the Phase function.

Let’s do that!

There are lots of competing firmwares for the nanoVNA, and having tried many and found them wanting, I use the latest firmware from ttrftech, the ‘originator’ of the nanoVNA. So, my comments are in the context of that firmware.

Let’s look at display of the magic phase quantity with a very good load on the nanoVNA, you might think of this load as the ultimate goal of an antenna system.

Above is a screenshot of my nanoVNA where I have selected the ONLY display format labelled phase, and it can be seen that the yellow trace appears to be quite random.

Above is a screenshot of nanoVNA Saver which seems the preferred PC client of the masses, again the same good load is attached. The upper left plot is the ONLY phase plot derived from s11, again it is quite random. Also show are plots of impedance (which is very good), VSWR (which is very good), and Return Loss (which is very good). Return Loss might look noisy, and it is, but it is always greater than 65dB… excellent! The only plot that has NO VALUE in this case is the phase plot!

In fact, when the magnitude of s11 becomes very small, the phase of s11 becomes dominated my measurement noise and it worthless. Yes, the closer you approach the Nirvana of VSWR=1 (ReturnLoss very high, |s11| very low), the less value in the phase of s11.

Let’s look at a sweep of a real antenna, a 5/8λ 144MHz vertical on my car, looking into 4m of RG58 feedline.

On this chart, the easiest curve to interpret for most hams is the VSWR curve (magenta). The markers show its minimum (1.09) and the VSWR=1.5 bandwidth (145.05-150.05MHz)… this is a good antenna from that point of view… but it could be improved by lengthening a little to move the frequency for minimum VSWR down to 147MHz (… but there is no adjustment left).

So, look at the Return Loss blue curve. Return Loss is related to VSWR and you could make exactly the same conclusions. We should accept Return Loss > 15dB.

Look at the s11 phase curve in red. It does not cross the zero phase line (the middle of the chart, in this sweep, it is 44° at minimum VSWR even though it is sometimes less at higher VSWR. Can you make any rational conclusion from the phase curve, and does the fact it is not zero condemn the antenna system?

Look at the R and X curves, green and black. Can you draw any conclusions from them directly? Can you see where the phase of R+jX would be zero? Hint: it is where X is zero… but hey, that doesn’t happen with this antenna system.

After all that information overload, the VSWR curve is the key performance indicator, and I could have used an ordinary VSWR meter to come to the same conclusions pretty much.

Yet another example where the focus on s11 phase is so misguided.

]]>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.

None of John’s test fixtures were equivalent to the circuit above required for valid t2s transformation.

What if we modify the Simsmith simulated circuit, does series through impedance measurement work?

Above is a minimum change to the simulation circuit to comply with the series through test fixture requirement. The two 25Ω resistors are made 0Ω, and at the other end of the transmission line, both wires are connected together. More on the now redundant elements later.

The figure above is from (Agilent 2009) and it shows the expression for calculation of s21 in the series through configuration. A rearrangement gives \(Z_x=\frac{100}{s_{21}}-100\), which is used in the Simsmith model below.

Above is the simulation showing the calculations used for key values. In element A, Zcm is calculated as 1.413K+j1.04K, and in the G element Plots, Zx is calculated using the algorithm.

Not surprisingly, Zx reconciles with Zcm when the correct test fixture is used.

The simulation circuit above with minimal modification to comply with the series through test requirement now contains redundanct components.

Above, the simulation circuit with the redundant parts removed. It produces exactly the same results, and demonstrates that balun common mode impedance can be measured by connecting the transmission line wires at each end and measuring between the ends. If the transmission line is coax, it is sufficient to measure between the shield ends with the inner conductors left disconnected.

KISS!

The same is true of the simpler s11 reflection method for impedance measurement.

- Agilent. Feb 2009. Impedance Measurement 5989-9887EN.
- Agilent. Jul 2001. Advanced impedance measurement capability of the RF I-V method compared to the network analysis method 5988-0728EN.
- Anaren. May 2005. Measurement Techniques for Baluns.
- Skelton, R. Nov 2010. Measuring HF balun performance in QEX Nov 2010.

Above is the subject balun in fixture.

John’s schematic shows the balun as coupled coils, but that does not capture the transmission line transformation that occurs in the actual device. Again the test fixture is used without explanation.

To implement a transmission line model of the balun, we need to capture both its transmission line behavior to differential currents, and its choke behavior to common mode current. To do that, two pairs of coupled coils are added at each end of the transmission line to divert the common mode current via the choke elements.

So, now we can reasonably accurately model the transmission line effect and the choke effects.

Above is the revised Simsmith model that implements the schematic above, and compares the model with measured for that balun configuration and test fixture. Again the value of n was tweaked to calibrate the model, and Cse adjusted for good high end tracking.

Above is my reinterpretation of his measurement data.

Looking at the marker values on my chart, they indicate Zx=5640+j4321Ω @ 14MHz, much higher than the expected common mode impedance of the choke. They are of course nonsense, the t2s function is not a valid transformation for John’s test fixture.

The test fixture used seems inspired by the theme ‘more complicated is naturally better’. KN5L’s model is flawed.

- Agilent. Feb 2009. Impedance Measurement 5989-9887EN.
- Agilent. Jul 2001. Advanced impedance measurement capability of the RF I-V method compared to the network analysis method 5988-0728EN.
- Anaren. May 2005. Measurement Techniques for Baluns.
- Skelton, R. Nov 2010. Measuring HF balun performance in QEX Nov 2010.

(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’.

- Agilent. Feb 2009. Impedance Measurement 5989-9887EN.
- Agilent. Jul 2001. Advanced impedance measurement capability of the RF I-V method compared to the network analysis method 5988-0728EN.
- Anaren. May 2005. Measurement Techniques for Baluns.
- Skelton, R. Nov 2010. Measuring HF balun performance in QEX Nov 2010.

Firstly two quarter wavelengths OC stubs were tuned to 14.2MHz by iterative cut and measure. The coax was 20mm longer than prediction, I am not convinced that the transmission line models in Simsmith are better than that. Then the tees were made up and the connecting section and tuned by cut and measure for minimum |s11| at 7.1MHz.

Above is the VNA sweep for the completed filter. Rejection around 14.2MHz exceeds 50dB with bandwidth of over 0.6MHz.

Above is calculation of the loss at the marker frequency at 7.1MHz.

Above is a plot of the loss components on an expanded scale to see those around 7MHz. The is very little Mismatch Loss in the 7MHz band.

Above is the Return Loss plot around 7MHZ, the match is better than most practical antennas will be, and Return Loss with an ideal load is greater than 20dB.

A reminder that the models and calculations in the reference article assume that linear circuit theory applies, that the source is well represented by a Thevenin equivalent circuit with Zth=50+j0Ω. Most ham transmitters are not well represented by such a circuit, and the calculated results may not apply exactly.

The results given here were measured with a VNA and do reconcile well with calculation.

I would not rely upon the coax lengths calculated in Simsmith to cut the coax, I would cut them a little longer and ‘tune’ to required electrical length using a VNA (as Bruce did) or a good antenna analyser. With knowledge and experience, the filter could be adjusted using a good VSWR meter, a noise bridge, or a Return Loss Bridge for example, a good antenna analyser (meaning a one port VNA) or a VNA is a higher productivity tool.

The design concept of the two stub filter for a 7.1MHz pass and 14.2MHz reject is sound, the built filter has high rejection at 14.2MHz and very low Insertion VSWR at 7.1MHz

The only feedback from Bruce was that the cut lengths were very slightly longer than I predicted using Simsmith. Even so, the Return Loss plot reveals that the filter is tuned very slightly high on 7MHz.

The filter is designed to match a 50+j0Ω load, and it does that very well. When used on practical antennas that depart from that, the filter Return Loss and input VSWR will also depart.

The measurements reported were for RG214, results depend on line loss and may be quite poorer for lossier line.

]]>A shunt OC stub of 90° electrical length was proposed to start thinking. My thoughts were that online experts often propose such as a cheap and effective solution… but I suspect they had read about it rather than speaking from actual experience.

The models and calculations assume that linear circuit theory applies, that the source is well represented by a Thevenin equivalent circuit with Zth=50+j0Ω. Most ham transmitters are not well represented by such a circuit, and the calculated results may not apply exactly. The calculated results should be observed when measuring with a good VNA.

Above is a Simsmith model of a shunt stub in a linear matched 50Ω system. The stub achieves a reduction of more than 20dB over about 900kHz, and a maximum reduction of around 35dB at 14.2MHz.

But, it ruins the VSWR seen at G at 7.1MHz, VSWR is 2.6.

Expected InsertionLoss is 1.0dB.

This is why this is a pretty naive approach in a system that requires low InsertionVSWR for a transmitter.

This VSWR could be fixed with an ATU at the transmitter. So in this case, the length of the stub determines the notch frequency, and an ATU restores the load to suit the transmitter (as needed).

An option that has low insertion VSWR and better harmonic reduction uses two stubs.

Above is a Simsmith model of the two stub harmonic filter. It has better harmonic reduction at 14.2MHz, and input VSWR(50) is low.

The length of T1 and T3 set the notch frequency, and the length of T2 is chosen of best input VSWR.

Expected InsertionLoss is 0.2dB.

Third harmonic more commonly a greater problem that second harmonic.

Above is a design for 7MHz pass and 21MHz reject.

Expected InsertionLoss is 0.1dB.

Above is a design for 7MHz pass and 21MHz reject.

Above is the full schematic.

Expected InsertionLoss is 0.4dB.

A follow up article will describe the implementation.

]]>## Relationship between angle of reflection coefficient and angle of impedance

It was stated above that the angle (or phase) of s11 or Γ is not the same as the angle (or phase) of Z.

Given Zo and Γ, we can find θ, the angle of Z.

\(

Z=Z_0\frac{1+\Gamma}{1-\Gamma}\)Zo and Γ are complex values, so we will separate them into the modulus and angle.

\(

\left | Z \right | \angle \theta =\left | Z_0 \right | \angle \psi \frac{1+\left| \Gamma \right | \angle \phi}{1-\left| \Gamma \right | \angle \phi} \\

\theta =arg \left ( \left | Z_0 \right | \angle \psi \frac{1+\left| \Gamma \right | \angle \phi}{1-\left| \Gamma \right | \angle \phi} \right )\)We can see that the θ, the angle of Z, is not simply equal to φ, the angle of Γ, but is a function of four variables: \(\left | Z_0 \right |, \psi , \left| \Gamma \right |, \& \: \phi\) .

It is true that if ψ=0 and φ=0 that θ=0, but that does not imply a wider simple equality. This particular combination is sometimes convenient, particularly when ψ=0 as if often the case with a VNA.

This article offers a simulation of a load similar to a 7MHz half wave dipole.

The load comprises L, L1, and C1 and the phase of s11 (or Γ) and phase of Z (seen at the source G) are plotted, along with VSWR.

Firstly, note that the two phase plots are very different, but in this case they cross over at phase=0 at 7.077MHz.

Secondly, note that even thought both phases are zero at 7.077MHz, the VSWR is 1.20. Neither phase demonstrates the best conditions for least feed line loss, minimum VSWR is slightly lower at 7.099MHz.

Maximum power in the load coincides with minimum VSWR at 7.099MHz.

Beware of claims that phase (of something) is the optimisation target, the author probably doesn’t really understand this stuff.

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