Above is the transformer with 100pF compensation capacitor across the input, and two resistors to make up a 3300Ω load in combination with the VNA port.

The transformer is an autotransformer of 16t tapped at 2t, so the nominal turns ratio is 1:8, or impedance 1:64.

Looking into the 2t tap with the transformer loaded with 3250+50=3300Ω, Luis measured s11, s21 parameters from 1-45MHz with a nanoVNA. (Nominally this should be a 3200Ω load, but the error is very small, VSWR equivalent of 1.03.)

Above is my analysis of this data for InsertionVSWR and ReturnLoss. It gets a bit shabby above 15MHz.

Above is a plot of InsertionLoss and Loss (or TransmissionLoss). See On Insertion Loss for explanation of the terms.

Compensation of the transformer with 100pF in shunt with the input improves the broadband response.

Above is InsertionVSWR and ReturnLoss. It is not too bad over all of HF (3-30MHz).

Above is a plot of InsertionLoss and Loss (or TransmissionLoss). See On Insertion Loss for explanation of the terms.

Almost all of the Loss is in core loss, and it gives us a good indicator of core heating. The worst case is at 30MHz where the Loss is 0.7dB, so about 15% of input power is converted to heat.

The tests here were using a dummy load on the transformer, and that did allow confirmation of the design.

Real end fed antennas operated harmonically do not present a constant impedance, not even in harmonically related bands. Note that the resonances do not necessarily line up harmonically, there is commonly some enharmonic effect.

Being a more efficient design that some, it might result is a wider VSWR excursion that those others as transformer loss can serve to mask the variations in the radiator itself.

Hats off to Luis, CT2FZI for his work in building and measuring the transformer, and to have the flexibility to consider more than FTxxx-43 cores.

]]>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.

]]>Above is the model topology. D1 is a daemon block which essentially, calculates key values for the other blocks based on exposed parameters and the named ferrite material complex permeability data file. The prototype used a Fair-rite 2643625002 (#43) core.

D1 code:

//Misc //Updates Tfmr, CoreLoss, and Cse. $data=file[]; // core mu aol; np; ratio; cse; cores; k; $u1=$data.R; $u2=$data.X; //u1=$u1; //u2=$u2; $ns=np*ratio; Ym=(2*Pi*G.MHz*1e6*(4*Pi*1e-7*$u1*aol*cores*1e9)*np^2*1e-9*(1j+$u2/$u1))^-1; Cse.F=cse; CoreLoss.ohms=1/Ym.R; $l1=1/(2*Pi*G.MHz*1e6*-Ym.I); $l2=$l1*(($ns-np)/np)^2; $lm=k*($l1*$l2)^0.5; Tfmr.L1_=$l1+$lm; Tfmr.L2_=$l2+$lm; Tfmr.L3_=-$lm;

L is the load block.

Cse models the self resonance of the transformer at lowish frequencies, Cse is an equivalent shunt capacitance.

Tfmr is a coupled coils model (above) of a (nearly) lossless autotransformer (core loss will come later). Wire loss is usually insignificant in these type of transformers and is ignored. (It seems that Simsmith will not simulate a pure inductance, in this cases the loss of the ‘lossless transformer is of the order of 5e-6dB, so satisfactory.) It is possible to simplify declaration of this component by using Simsmith’s coupled coils in a RUSE block, I have chosen to take full control and solve the mutual inductance effects explicitly.

(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.)

Coreloss brings the ferrite core loss to book.

Ccomp models a compensation capacitor used to improve broadband InsertionVSWR.

The G block provides the source and plot definitions.

Plots code:

//Plots //check lossless Tfmr behavior //tfmrloss_dB=10*Log10(Tfmr.P/(Tfmr.P-Tfmr.p)); //Plot("TfmrLoss",tfmrloss_dB,"LossdB",y1); coreloss_dB=10*Log10(CoreLoss.P/(CoreLoss.P-CoreLoss.p)); loss_dB=10*Log10(G.P/L.P); mismatchloss_dB=10*Log10(1/G.P); Plot("CoreLoss",coreloss_dB,"LossdB",y1); Plot("Loss",loss_dB,"LossdB",y1);;

The model was calibrated to measurement of the prototype, and the fit is quite good given tolerances on components.

The model allows convenient interactive sensitivity analysis where parameters can be dialed up and down with the mouse wheel and the response changes observed.

- FT82-43 matching transformer for an EFHW
- Find |Z|,R,|X| from VSWR,|Z|,R,Ro
- A new impedance calculator for RF inductors on ferrite cores
- Calculate ferrite cored inductor (from Al)
- Calculate VSWR and Return Loss from Zload (or Yload) and Zo
- Duffy, O. 2015. A method for estimating the impedance of a ferrite cored toroidal inductor at RF. https://owenduffy.net/files/EstimateZFerriteToroidInductor.pdf.
- ———. 2006. A method for estimating the impedance of a ferrite cored toroidal inductor at RF. VK1OD.net (offline).

Having selected a candidate core, the main questions need to be answered:

- how many turns are sufficient for acceptable InsertionVSWR at low frequencies and core loss; and
- what value of shunt capacitance best compensates the effect of leakage inductance at high frequencies?

Lets look at a simplified equivalent circuit of such a transformer, and all components are referred to the 50Ω input side of the transformer.

Above is a simplified model that will illustrate the issues. For simplicity, the model is somewhat idealised in that the components are lossless.

- L1 represents the leakage inductance;
- L2 represents the magnetising inductance; and
- C1 is a compensation capacitor.

Since the magnetising inductance is assumed lossless, this article will not address design for core loss.

So, it is obvious that the InsertionVSWR curve is pretty poor at both high and low end.

Let’s look at a Smith chart presentation of the same information, it is so much more revealing.

Above is the Smith chart plot. Remember that the points go clockwise on the arc with increasing frequency, and that InsertionVSWR is a function of the distance from the centre to the point on the locus… we want to minimise that distance. Remember also that the circles that are tangential to the left had edge are conductance circles, they are the locus of constant G.

Now lets analyse the response.

Note that from 1 to 3MHz, the shape of the response tends to a circle tangential to the left hand edge, it a constant G circle. So, G is constant but susceptance B is frequency dependent and -ve. This the the response of a constant resistance R in parallel with a constant inductance (\(B=\frac {-1} {2 \pi f L}\), \(Y= G + \jmath B = \frac 1 R – \frac {\jmath} {2 \pi f L}\)). A part of that susceptance (shunt inductance) is due to the magnetising inductance L2 which contributes to the poor Insertion VSWR at low frequencies.

Note that from 12 to 15Hz, the shape of the response tends to a circle tangential to the left hand edge, it a constant G circle. So, G is constant but susceptance B is frequency dependent and +ve. This the the response of a constant resistance R in parallel with a constant capacitance (\(B=2 \pi f C\), \(Y= G + \jmath B = \frac 1 R + \jmath 2 \pi f C\)). A part of that susceptance (shunt capacitance) is due to the compensation capacitor C1 which contributes to the poor Insertion VSWR at high frequencies.

Lets adjust L2 and C1 for a better InsertionVSWR response.

Above is the response with L2=12µH and C1=80pF. Note that the distance to the centre is improved (and therefore InsertionVSWR is improved). The kink in the response is common, that is typically the mid region where InsertionVSWR is minimum.

It is still not a good response, the InsertionVSWR at the high end is too high, and compensation with C1 does not adequately address the leakage inductance. So, as a candidate design, this one has too much leakage inductance which might be addressed by improving winding geometry and increasing core permeability.

As mentioned, real tranformers using ferrite cores have permeability that is complex (ie includes loss) and dependent on frequency (ie inductance is constant).

Above, the magenta curve is measurement of a real transformer from 1-11MHz with nominal resistance load and three compensation options:

- cyan: 0pF, too little compensation;
- magenta: 80pF, optimal compensation; and
- blue: 250pF, to much compensation.

It should be no surprise that 80pF is close to optimal. Susceptance B at the cyan X is -0.00575S, and broadly, we want to cancel that with the compensation capacitor so we come so \(C=\frac{B}{2 \pi f}=\frac{0.00575}{2 \pi 11e6}=83pF\).

With optimal compensation (80pF in this case) The insertionVSWR at 3MHz is 1.8, probably acceptable for this type of transformer but it is still quite high (4.3) at 11MHz, which hints that leakage inductance needs to be addressed by improving winding geometry and possibly increasing permeability.

Keep in mind that measurements with a nominal resistive load are a guide, measurements with the real antenna wire are very important.

]]>This article builds an NEC model for an EFHW antenna at 3.6MHz incorporating a realistic model of the above transformer.

NEC provides for a NT card characterising a two port network using Y parameters.

The Y parameter model is based on measured input impedance with port 2 open circuit, and short circuit, and the observed turns ratio.

Impedance was measured with the transformer at 3.6MHz using an AA-600.

Above, the calculated Y parameter model including a prototype NT card. This model captures the various loss components of the transformer, mainly magnetising loss, at 3.6MHz.

Note that the Y parameter model is frequency specific.

Above is a graphic showing the geometry of the NEC model. Essentially the feed point has about λ/10 ‘counterpoise’ at a height of 0.3m to the left of the feed point, and a wire slopping upwards at about 45° for the main antenna conductor.

Although the NT card is frequency specific to 3.6MHz, we get a fair idea of the VSWR response over a narrow frequency range. The minimum VSWR of 1.06 at 3.6MHz is correct.

Above is a summary of the NEC model. Network loss captures the loss in the transformer, and at 100W input the transformer loss is 9W. This is much better transformer efficiency than almost all of the published designs that I have reviewed.

Radiation efficiency is 39%, a combination of conductor loss, transformer loss and ground loss, mostly ground loss.

Above is the pattern, highest gain is at towards the zenith as can be expected of a low antenna. Maximum gain is about 1dBi.

Above, at lower elevation (30°) the pattern shows a little skew due to the sloping radiator.

If this looks like an improvised antenna that performs well, keep in mind that the top of the sloping wire is at 28m height.

This article builds an NEC model for an EFHW antenna at 3.6MHz incorporating a realistic model of the above transformer.

NEC provides for a NT card characterising a two port network using Y parameters.

The Y parameter model is based on measured input impedance with port 2 open circuit, and short circuit, and the observed turns ratio.

Impedance was measured with the uncompensated transformer at 3.6MHz using an AA-600, the compensation in the reference article has little effect at 3.6MHz.

Above, the calculated Y parameter model including a prototype NT card. This model captures the various loss components of the transformer, mainly magnetising loss, at 3.6MHz.

Note that the Y parameter model is frequency specific.

Above is a graphic showing the geometry of the NEC model. Essentially the feed point has about λ/10 ‘counterpoise’ at a height of 0.3m to the left of the feed point, and a wire slopping upwards at about 45° for the main antenna conductor.

Although the NT card is frequency specific to 3.6MHz, we get a fair idea of the VSWR response over a narrow frequency range. The minimum VSWR of 1.095 at 3.6MHz is correct.

Above is a summary of the NEC model. Network loss captures the loss in the transformer, and at 100W input the transformer loss is just under 10W. This is much better transformer efficiency than almost all of the published designs that I have reviewed.

Radiation efficiency is 38%, a combination of conductor loss, transformer loss and ground loss, mostly ground loss.

Above is the pattern, highest gain is at towards the zenith as can be expected of a low antenna. Maximum gain is about 1dBi.

Above, at lower elevation (30°) the pattern shows a little skew due to the sloping radiator.

Conductor loss is calculated at 1.6% for 2mm diameter copper. This is quite low but could easily exceed 10W for thin ‘stealth’ copper wire, and worse for steel or stainless steel conductors.

If this looks like an improvised antenna that performs well, keep in mind that the top of the sloping wire is at 28m height.

In a process of designing a transformer, we often start with an approximate low frequency equivalent circuit. “Low frequency” is a relative term, it means at frequencies where each winding current phase is uniform, and the effects of distributed capacitance are insignificant.

Above is a commonly used low frequency equivalent of a transformer. Z1 and Z2 represent leakage impedances (ie the effect of magnetic flux leakage) and winding conductor loss. Zm is the magnetising impedance and represents the self inductance of the primary winding and core losses (hysteresis and eddy current losses).

For broadband RF transformers, Z1 and Z2 need to be small as they tend to be quite inductive and since inductive reactance is proportional to frequency, they tend to spoil broadband performance.

Zm shunts the input, so it spoils nominal impedance transformation (Zin=Zload/n^2) if it is relatively low. For powdered iron cores Zm is mainly inductive; and for ferrite cores Zm is a combination of inductive reactance and resistance depending on frequency and ferrite type.

Where the transformer secondary turns and load (antenna) are adjusted for a near perfect 50Ω input match, we can estimate the approximate core efficiency as 1 minus 50 divided by Rmp (the parallel resistance equivalent component of Zm), 1-50/Rmp.

If we set a design criteria of at least 80% core efficiency, we can calculate a critical value for Rmp>50/(1-0.8)>250Ω.

We can measure Rmp with out trusty nanovna.

The measurement fixture has been OSL calibrated, and a two turn winding applied to an FT240-43 core and plugged into the fixture.

The sweep is controlled from nanoVNA MOD v3 and plotted.

Above is the measurement from 1-31MHz, and it can be seen that Rmp falls below 250Ω from 1.6-11.5MHz. Two turns is not sufficient for more than 80% core efficiency from 1.6-11.5MHz.

At 3.5MHz, Rmp=171Ω and so core efficiency is 1-50/171=71%, or -1.5dB.

An exercise for the reader is to try three turns, and to try smaller cores such as the popular FT114-43.

]]>The original transformer above comprised a 32t of 0.65mm enameled copper winding on a FT240-43 ferrite core, tapped at 4t to be used as an autotransformer to step down a load impedance of around 3300Ω to around 50Ω.

The FT114 core has a quite low ΣA/l value (0.000505), essentially a poor magnetic geometry.

A better choice for his enclosure is the locally available LO1238 core from Jaycar (2 for $5) with ΣA/l=0.0009756/m which is comparable with the FT240 form (though smaller in size) and nearly double that of the FT114. The LO1238 is a toroid of size 35x21x13 mm, and medium µ (L15 material).

A more detailed analysis of a 3t primary winding of the effects of magnetising impedance on InsertionVSWR and system loss when it is in shunt with a 50Ω load was performed.

Above is the expected core loss.

Above is the expected InsertionVSWR.

These both look encouraging, and the next step would be to build and measure some prototypes.

Above, VK4MQ’s prototype in development. (I do not recommend the pink tape.)

]]>The original transformer above comprised a 32t of 0.65mm enameled copper winding on a FT240-43 ferrite core, tapped at 4t to be used as an autotransformer to step down a load impedance of around 3300Ω to around 50Ω.

A very rough approximation would be that with two stacked cores, the number of turns would be around the inverse of square root of two, so 70% of the original.

A more detailed analysis of the effects of magnetising impedance on InsertionVSWR and system loss when it is in shunt with a 50Ω load was performed.

Above is the expected core loss.

Above is the expected InsertionVSWR.

These both look encouraging, and the next step would be to build and measure some prototypes.

To the original question, would half the turns be enough? No. Notwithstanding that, you are likely to find such being used, being sold.

]]>Lets work through an example of a FT50-61 core with 10t primary at 3.5MHz.

Magnetic saturation is one limit on power handling capacity of such a transformer, and likely the most significant one for very low loss cores (#61 material losses are very low at 3.5MHz).

Let’s calculate the expected magnetising impedance @ 3.5MHz.

Above is the manufacturers B/H curve for #61 material. Lets take the saturation magnetising force conservatively as 2Oe=2*1000/(4*pi)=159A/m (or At/m for a multi turn coil).

The ID of a FT50 core is 7.15mm, so magnetic path length l=0.00715*pi=0.0225m.

So, we take saturation current as Is=Hs*l/t=159*0.0225/10=0.358A.

Saturation voltage magnitude at 3.5MHz=Is*|Zm|=0.358*144=51.6Vpk. This corresponds to about 25W in a 50Ω system.

Increasing the number of turns decreases Is for a given Hs, and increases Zm which reduces I for a given applied voltage. For example in this example, a 12t primary has |Z|=207, Is=0.298A, Vs=61.7Vpk which corresponds to a 43% 50Ω power increase.

Lets work through an example of a 2643625002 core with 3t primary at 3.6MHz (Small efficient matching transformer for an EFHW).

Magnetic saturation is one limit on power handling capacity of such a transformer. For lossier materials, heat dissipation is likely to be the practical limit in all but low duty cycle applications, but lets calculate the saturation limit.

Let’s calculate the expected magnetising impedance @ 3.6MHz.

Zm=94.1+j197Ω, |Zm|=218Ω.

Above is the manufacturers B/H curve for #43 material. Lets take the saturation magnetising force conservatively as 1Oe=1*1000/(4*pi)=79.6A/m (or At/m for a multi turn coil).

The ID of a 2643625002 core is 7.29mm, so magnetic path length l=0.00729*pi=0.0229m.

So, we take saturation current as Is=Hs*l/t=79.6*0.0229/3=0.607A.

Saturation voltage magnitude at 3.5MHz=Is*|Zm|=0.607*218=132Vpk. This corresponds to about 175W in a 50Ω system. This transformer would not withstand such high power continuously, but pulses or bursts to that level would remain in the substantially linear range of the material characteristic.

- Magnetic saturation is one limit on power handling capacity of ferrite inductors and transformers.
- For very low loss cores, magnetic saturation is likely to be the significant limit on power handling.

Read widely, and analyse critically what you read.

]]>