Above is a plot of:
Looking at the higher frequencies first, the green curve does not track measurements, and the higher slope of ‘measured’ MLL suggests there is significant contribution from dielectric loss that is not captured by the \(MLL = k_1\sqrt f\) model. The other two models are quite good at the mid to higher frequencies.
At the lower frequencies, there are few data points and measurements on the nanoVNA were noisy, so the scatter of few points makes estimation challenging. To the eye, I fancy that the brown curve is probably an overestimate of the MLL. It is a more complicated model, it is harder to compute, yet it seems likely that it is an overestimate. It is difficult to choose between the green and blue curves at low frequencies given the data and noise.
Overall, only the blue curve seems a good estimator at low, mid and high frequencies. That is not to say that would be the case for other line types.
I might comment that the study has some underlying weaknesses:
At least one nanoVNA client application can do log sweeps of larger set of points, but on my inspection at the time, it had other defects that cause me to set it aside.
]]>So, let’s measure a sample of 14×0.14, 0.22mm^2, 0.5mm dia PVC insulated small speaker twin.
Above is the nanoVNA setup for measurement. Note that common mode current on the transmission line is likely to impact the measured Zin significantly at some frequencies, the transformer balun (A 1:1 RF transformer for measurements – based on noelec 1:9 balun assembly) is to minimise the risk of that. Nevertheless, it is wise to critically review the measured |s11| for signs of ‘antenna effect’ due to common mode current.
Above is a plot of the measured |s11| for SC and OC line sections.
Observe that there are no anomalous kinks or the like, but the OC section measurements become a little noise at the lower end.
Above is a plot of the calculated MLL (red dots) based on the s11 measurements, and a curve fit to the model \(MLL = k_1\sqrt f+k_2f \text{ dB/m}\).
Allowing for the scatter at the lower frequencies as we are measuring 1m of line with an inexpensive hobby grade VNA, \(MLL=\text{3.26e-5} \sqrt{f}+\text{1.39e-9}f \text{ dB/m}\) is a pretty good estimator.
]]>Starting with some basic magnetism…
The inductance of an inductor is given by \(L=N\frac{\phi}{I}\).
For a closed magnetic circuit of high permeability such as a ferrite cored toroid, the flux is almost entirely contained in the core and the relationship is \(\mathcal{F}=\phi \mathcal{R}\) where \(\mathcal{F}\) is the magnetomotive force, \(\phi\) is the flux, and \(\mathcal{R}\) is the magnetic reluctance. (Note the similarity to Ohm’s law.)
Rearranging that we have \(\phi=\frac{\mathcal{F}}{\mathcal{R}}\).
Permeance \(\mathcal{P}=\frac1{\mathcal{R}}\) we can rewrite the above as \(\phi=\mathcal{F} \mathcal{P}\). Permeances of parallel magnetic paths add, so if we stack two cores sharing the same winding, the total permeance is the sum of that of each core \(\mathcal{P}_t=\mathcal{P}_1+\mathcal{P}_2+…\).
So, returning to the inductance of the toroidal ferrite cored inductor, we can write that \(L=N \frac{\mathcal{F} \mathcal{P}}{I}\) and since \(\mathcal{F}=N I\), \(L=N \frac{N I \mathcal{P}}{I}\) which simplifies to \(L=N^2 \mathcal{P}\).
Now for a toroid \(\mathcal{P}=\mu\frac{A}{2 \pi r}\) and so \(L=N^2\mu\frac{A}{2 \pi r}\). Since A=f(r), we must integrate A over r. (Note that \(\mu=\mu_0 \mu_r=4e-7 \pi\mu_r\).)
Inductance of a toroidal ferrite cored inductor then is given by \(L=\mu N^2 \int \frac{A}{2 \pi r}dr\) (noting that µ is a complex quantity and frequency dependent). More properly, the ‘inductor’ is a resonator and as you approach its self resonant frequency, inductance alone is not an adequate model… nevertheless consideration of the simpler inductance calculation gives valuable insight.
If we stack two cores of the same physical size side by side, then µ is not uniform across the cross section, so we must capture µ in the integral \(L=N^2 \int \frac{\mu A}{2 \pi r}dr\).
In the simple case where we stack n1 cores of µ1 and n2 cores of µ2, then the expression can be simplified to \(L=(n_1 \mu_1 + n_2 \mu_2) N^2 \int \frac{A}{2 \pi r}dr\) where \(\frac{A}{2 \pi r}\) is the geometry of the consituent cores.
Readers will see that stacking one #61 mix core with one #43 mix core of the same sizes is roughly equivalent to a core of the combined cross section area with µ characteristic an average of the two mixes.
This is not equivalent to series connection of two separate inductors with each core type and same number of turns, the effects around self resonances will differ. Since to some extent, common mode chokes rely upon self resonance (albeit low Q) for their operation, this difference in response is quite relevant. Dissipation capacity is likely to be different.
In the light of that understanding, put your thinking cap on when you see magic properties ascribed to this configuration.
Note, this analysis does not address the behavior near or above the self resonant frequency.
]]>Pictured is a dual UnUn. I made this for experimenting. It’s both a 49 and 64 to 1 UnUn.
The 49 to 1 tap uses the SS eye bolt for the feed through electrical connection and the SS machine screw on the top is the 64 to 1 connection. If I want to use the 49 to 1 ratio, there’s a jumper on the eye bolt that connects to the top machine screw where the antenna wire is attached. The jumper shorts out the last two turns of the UnUn. Disconnect the jumper from the top connection and now you have a 64 to 1 ratio.
The advice to short the section of the winding (the white wire in the pic) is really bad advice.
Tapping an air cored solenoid can be effective and with low loss… can be… but not unconditionally. Tapping a ferrite cored inductor almost always has quite high Insertion Loss, it is akin to shorted turns in an iron cored transformer, … so if you try it, measure it to see if the outcome is acceptable.
Keep in mind that flux leakage degrades broadband performance, so conductors wound loosely around the core (as in the pic) and wide spaced single layer windings (as in the core) tend to have higher flux leakage and poorer broadband performance. Measure what you make to verify that it did what you think.
An S parameter file from a two port sweep over HF would be informative.
I offer this analysis without measurement evidence to prove the case, but sometimes an understanding of basic circuit analysis allows one to avoid wasting time on poor designs.
]]>One of the first questions to mind is whether it is likely to deliver the rated power, so let’s review the MOSFET output circuit design from that perspective.
Sellers mostly seem to need to obscure the MOSFET type in their pics, so essentially you buy this with no assurance as to what is supplied, no comeback if the supplied MOSFET is not up to the task. Online experts suggest the MOSFET is probably a MRF9120 (or 2x IRF640 in a 70W build). The amplifier claims 100W from 12-16V DC supply.
Note that this module does not include the necessary output filter which will lose 5-10% of the power from this module.
In this case Carlos, VK1EA, connected a sample output transformer (T2) core from a recently purchased MiniPa100 kit to a EU1KY antenna analyser. The fixture is critically important, it is at my specification.
We also need to know the geometry parameter ΣA/l.
Above, from the measured dimensions of a sample core, ΣA/l=0.003415/m.
The saved S parameter file was processed as described at nanoVNA-H – measure ferrite core permeability described a method for characterising an unknown ferrite material and a complex permeability curve produced.
Above, the results are fairly good and fairly much as expected, but let’s remove the noise by digitising the plots.
Above, the points sampled for the digitised output. Though there is a lot less data in the result, when points are obtained by interpolation, noise is greatly reduced.
The above pic from an eBay advertisement of the 2020 version of the PA would suggest very strongly that there are three turns on the secondary of the output transformer, and a half turn on each drain. Interestingly the 70W versions also appear to use three turns, alarm bells ring!
From all this, we can produce an approximation in Simsmith that captures most of the expected behavior of a practical transformer, including core loss.
Above is the RUSE block schematic used for Core which models the frequency dependent magnetising admittance of the transformer and sets the frequency dependent inductances of the Tfmr element.
(The model assumes that k is independent of frequency which is not strictly correct, but for medium to high µ cores, measurement suggests it is a fairly good assumption.)
More to come…
]]>Essentially, my analysis was that it comprises two 12t winds of two wire transmission line in parallel on the ferrite ring. The potential benefit was that the characteristic impedance Zo of each transmission line is probably close to 100Ω, and the parallel combination is probably close to 50Ω.
Online experts following fashion are opining that a low Insertion VSWR balun is better made with two wire line(s) than winding a single 50Ω coax line. They make these claims without evidence, I am not convinced.
In that vein, here is a variation on the TrxBench balun above.
The designer describes it:
Wound with 18 AWG PTFE, Solid Silver Plated Copper wire. By using that specific gauge wire with PTFE insulation tightly coupled in pairs results in a 100-Ohm transmission line. Two in parallel = 50-Ohms. The advantage using the wire over coax is it flattens and widens the bandwidth. I stress it is extremely important to pay attention to the small details. The spacing, twisting, orientation, neatness, and symmetry are extremely important.
He is quite correct regarding his last point.
His claim that the each pair of wires wound on the core has Zo of around 100Ω without supporting evidence, but it is believable based on my own experience of making and measuring similar line sections
The ‘tails’ are not just two continuations of the 100Ω transmission lines (as wrapped on the core) paralleled at the connector and load resistor, they are two line sections of some other geometry and again without evidence of their Zo. I cannot call upon experience to inform me about likely Zo, I suspect it may be significantly higher than 100Ω.
Whilst the designer explained that the picture was of a test setup for measurement with a VNA, he did not give the results of such a measurement, an InsertionVSWR plot would be informative.
I wrote a series of articles that showed how a very small length of pigtails impacted InsertionVSWR of a balun:
So, we return to claims along the lines of If I recall correctly, that was also K9YC’s conclusion. His updated ‘cookbook’ moved away from coax to wire
which of course is fallacious if it attributes someone’s personal opinion to a well known author.
Where is the evidence of the InsertionVSWR of this ‘superior’ design? It is great to see thinking and experimentation, but a bit of scientific method would make it so much more valuable… if the claims are supported.
]]>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.
]]>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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