Above is the prototype transformer wound with 14t of 0.71mm ECW tapped at 2t. The mm rule gives some scale. The turns are close wound, touching on the inner diameter of the core.

Above is a screenshot of the model calibrated to measurement of the prototype.

Above is the measured InsertionVSWR (blue) and InsertionVSWR (magenta) and Loss chart from the model.

The model and its dependencies are attached.

In fact, the problem is the same as the one discussed in the article above, and the model is suited to application to the ferrite cored HF Ruthroff 1:4 balun case.

This analysis applies to a Fair-rite 2843009902 but may not apply to other manufacturer’s BN43-7051.

Above is a screenshot of the model calibrated against measurement. The magenta curve is the prediction and the blue curve is the measurement. Note that very small differences in measured value result in apparently large changes in InsertionVSWR, these two curves reconcile very well, especially considering the tolerances of ferrite material.

Above is a pic of the DUT and test fixture, the floating ground wire is bonded to the external threads of the SMA connector using the plastic clothes peg. All connecting wires are very short, the balun is wound with twisted pair stripped from a CAT5 LAN cable, it has Zo quite close to 100Ω which is ideal for this application.

In fact the uncompensated InsertionVSWR of this balun is well under 1.5 up to 100MHz.

Factors that contribute to very good broadband performance of this balun include:

- very short winding length (<200mm);
- very low leakage inductance (~15nH each side);
- Zo of the pair close to half the nominal load resistance; and
- very short connections in the test fixture.

Worst predicted loss is about 0.13dB @ 4MHz, about 3% if input power.

Above is an estimate of the power dissipation for 40° temperature rise in free air (conservatively based on the surface are of the four largest sides). So 2W loss at 3% of input power implies average input power of up to 2/.03=67W.

There are a plethora of designs using FT82-43 published on the ‘net, most of them have appalling loss.

Above is a Simsmith model and measurement of the transformer for reconciliation. The blue VSWR curve is the measurement and the magenta curve is the calibrated model, they agree well considering the tolerance of ferrite materials.

Above is a chart from the model, efficiency is worst at 3.5MHz, about 88% which should be acceptable to most users.

Above is a peak magnetic flux calculation for worst case (3.5MHz) @ 10W, it is way below the saturation flux (given as 0.3T, but best to stay below 0.1T). For other than pulse applications, maximum power (and flux) will usually be limited by heating rather than magnetic saturation.

We can estimate the temperature rise due to heat dissipation in free air from the surface area of the core.

40° rise on say 30° ambient is about as much as is compatible with many plastic insulation materials… but enough to burn skin. About 1.5W average power will achieve that rating.

So at frequencies where to efficiency is poorest at 88%, the transformer is suited to continuous or average power input of 12.4W (and for example, 12.4W continuous RTTY, 25W continuous A1 Morse Code).

If we take the average to peak ratio for SSB telephony to be -15dB (see Average power of SSB telephony), then this transformer should be capable of about 370W PEP of unprocessed speech (still below core saturation), perhaps more like 90W PEP of speech with 6dB processing. In practice, allowing for duty cycle and conversation style speed with pauses, these become conservative ratings.

The transformer as built and measured has performance that should be acceptable to most users, quite probably better efficiency than some QRP style ATUs.

The transformer is wound on a Jaycar LO1238 35x21x13mm toroid of L15 material (L15 appears to be a NiZn ferrite based on its very high resistivity), they sell at $7 for a pack of two.

The first test was of a 2:14 turn winding terminated in a 2450Ω load. The transformer is an autotransformer of 2+12t with 91pF compensation capacitor installed in shunt with the 2t winding.

As expected, |s11| is pretty poor at the low end, corresponding to an InsertionVSWR=1.7 @ 3.5MHz.

Design rejected due to high InsertionLoss, magnetising admittance too high.

The transformer is an autotransformer of 3+18t with 91pF compensation capacitor installed in shunt with the 3t winding.

Two winding configurations were explored, the very popular cross over style winding and the less common single layer close wound plain winding.

The winding configurations were made on two different cores from the same bag… so there is possibility of some variation… ferrites are like that.

Above is a plot of InsertionVSWR of the two configurations with a nominal 2450Ω load. The red trace is the cross over winding and the blue trace is the plain winding.

Above is the prototype transformer for measurement.

The transformer was measured with the 3t winding connected to Port 1 and the top end of the winding connected to Port 2 via a 2400Ω 1% 1210 SMD resistor.

Above is a plot of the loss components calculated from the .s2p file.

Above is a plot of the ReturnLoss and InsertionVSWR. It is OK but for the very high end were above 25MHz, InsertionVSWR increases rapidly.

Above is the prototype transformer in the test jig for measurement. The white material is 4mm thick PVC to isolate the transformer somewhat from the copper plane.

Above is a plot of the loss components calculated from the .s2p file.

Above is a plot of the ReturnLoss and InsertionVSWR. It is OK but for the very high end were above 25MHz, InsertionVSWR increases rapidly… but not as bad as the cross over configuration.

A Simsmith model was constructed and calibrated for the plain winding configuration.

Above is a screenshot of the model.

Above, the blue trace is measured InsertionVSWR and the solid magenta trace is model Insertion VSWR. After calibration (adjustment of Ll and cse), the two traces are very close.

The yellow and green traces are the model input R,X. the dashed red curve is the power in the load with 1W input. The dashed magenta curve is loss (or TransmissionLoss if you want to distinguish it), this is the quantity that gives rise to heating of the core, compensation capacitor, and wire.

At 100W impressed on the 50Ω primary, peak magnetic flux is way less than saturation (~0.3T). For other than pulse applications, maximum power (and flux) will usually be limited by heating rather than magnetic saturation.

We can estimate the temperature rise due to heat dissipation in free air from the surface area of the core.

40° rise on say 30° ambient is about as much as is compatible with many plastic insulation materials… but enough to burn skin. About 3W average power will achieve that rating.

So at frequencies where to efficiency is poorest at 90%, the transformer is suited to continuous or average power input of 30W (and for example, 30W continuous RTTY, 60W continuous A1 Morse Code).

If we take the average to peak ratio for SSB telephony to be -15dB (see Average power of SSB telephony), then this transformer should be capable of about 1000W PEP of unprocessed speech (still below core saturation), perhaps more like 250W PEP of speech with 6dB processing. In practice, allowing for duty cycle and conversation style speed with pauses, these become conservative ratings.

The transformer as built and measured has performance that should be acceptable to most users, quite probably better efficiency than some QRP style ATUs.

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Above is the equivalent circuit used to model the transformer. The transformer is replaced with an ideal 1:n transformer, and all secondary side values are referred to the primary side.

The model works quite well for low leakage inductance / low ratio transformers but falls down for the higher leakage inductance / higher ratio transformers.

The improved model is similar, but Cse in the model above is distributed to the outer sides of the lumped constant model.

Above is the equivalent circuit used to model the transformer. The transformer is replaced with an ideal 1:n transformer, and all secondary side values are referred to the primary side.

- Secondary side leakage inductance Lls is divided by n^2 to obtain the value primary referred leakage inductance in the circuit diagram.
- Cse is an equivalent shunt capacitance to partially model self resonance effects, it is distributed in the ratio 1:n^2 to both sides of the network.
- Bm is the magnetising susceptance (calculated from other parameters).
- Gm is the magnetising conductance (calculated from other parameters).
- Llp is the primary side leakage inductance.
- Ccomp is a compensation capacitance.

A Simsmith model was built to implement the transformer model above, and a prototype transformer measured.

Above is the prototype transformer, 2:14t on a Fair-rite 2643251002 core.

- Complex core permeability is captured from a permeability data file.
- np is the number of turns on the primary.
- ratio is the turns ratio.
- cores is the number of cores in a stack.
- cse is Cse per the circuit diagram.
- Ll is the value of Llp and Lls’ (which are assumed equal).

The chart above compares the model on the left with measured impedance from a .s1p file. The model is calibrated by adjusting Ll and cse for best fit of calculated VSWR to the measured VSWR.

Sample Simsmith model for download: EFHW-2643251002-43-2020-2-14-40-v103.7z. (Compressed with 7zip.)

]]>Another small efficient matching transformer for an EFHW – 2643251002 – #2 – prototype bench measurement continued the development of a transformer design.

This article analyses measurements at 7.1MHz reported by Mike, G8GYW of his build of a similar transformer.

Above is G8GYW’s build, that is a cm grid on the bench.

Above is G8GYW’s measurements using an NanoVNA of the transformer (it seems with a 100pF compensation capacitor in shunt with the 2t winding) with a 2400Ω resistor in series with Port 2 input pin. Assuming that the resistor is accurate and connections are very short, this puts approximately 2450+j0Ω on the transformer (its nominal load) and allows direct measurement of InsertionVSWR (shown above as s11 VSWR).

We can determine InsertionLoss from -|s21dB| by adjusting for the power division of the 2400 and 50Ω resistors: \(L=10 \log \frac{2400+50}{50}=16.9 \text{dB}\). So at the marker frequency 7.1MHz, \({InsertionLoss}=-|s21dB|-L=-(-17.22)-16.9=0.32 \text{dB}\).

It is very interesting to extract the simple Loss (or TransmissionLoss if you like) which is given by \(Loss=10 \log \frac{Power_{in}}{Power_{out}} \text{dB}\), as it can be used to calculate the heat dissipated in the transformer core and windings. This can be done from s11 and s21, a bit tedious but here is a handy little calculator that makes it a little easier.

The s11 and s21 values are obtained from the info panel on the NanoVNA-App screenshot above.

So, whilst the InsertionLoss is 0.32dB, the Loss is 0.26dB (rounded) and we can say that 6% of input power is lost as heat, so that with 50W average input power, dissipation is about 3W. This leads to efficiency \(\eta=\frac{Power_{out}}{Power_{in}}=94.29 \text{%}\).

Mike’s reported measurements at 7.1MHz are quite consistent with my earlier models and estimates.

]]>In the case of the Sontheimer coupler the winding with the higher number of turns appears in shunt with the nominal 50Ω load, and its effect on InsertionVSWR and the core loss can be predicted reasonably well and confirmed by measurements as in the referenced article.

In that instance, a 7t winding in shunt with the nominal 50Ω load causes excessive core heating, a 3t winding will be worse, and 2t worse again.

The case of an EFHW transformer is somewhat similar, the difference is now that the winding with less turns in approximately in shunt with the nominal 50Ω primary referred load. The same Simsmith model can be used to predict likely InsertionVSWR due to primary magnetising admittance, and the core loss.

Let’s try the 3t case first, with the experience of the referenced article we can expect it will have insufficient turns for good performance.

Above is the Simsmith model of a Fair-rite 5943000201 core (equivalent dimensions to FT37-43) with a 3t winding. Note this does not apply to Amidon #43 as their material is significantly different in characteristic.

So, the model scenario is of a 50Ω source that would deliver 5W into a matched load. With the magnetising admittance appearing in shunt, at 3.5MHz core loss is around 1.2W and power delivered to the transformed load is 3.4W. InsertionVSWR due to the magnetising admittance is 1.8.

So, will it work?

Well, anything ‘works’, it depends on your meaning of ‘works’.

There are two main questions:

- is the loss of power to the antenna a concern; and
- will the associated heat be an issue?

It seems that QRP aficionados are less concerned about loss of power to the antenna, QRP^2 if you like.

It is a personal matter.

Above, the predicted temperature rise for the core in free air of just 0.1W of dissipation is 22°, so on a hot day at 40° ambient, the core would reach 62° which is just enough to burn skin.

The good news is that the average power of uncompressed SSB telephony is around 5% of PEP, so this core scenario should withstand that mode at up to 2W PEP, less for compressed speech.

If your choice was FT8, the core would get dangerously hot, and even reach the Curie temperature (where the core loses its magnetic properties) in time.

If the transformer is enclosed, its power rating is reduced.

I have had enquiries from hams about similar transformers on small #43 cores, FT82-43 matching transformer for an EFHW discusses one of the popular designs. It seems everyone is a designer, and adapting an often poor design by changing the core size is seen and an obvious path to success.

The promotion of these ‘designs’ speaks to the credibility of the ‘designer’.

There are several designs on this web site, start with Small efficient matching transformer for an EFHW.

Search the net for published designs that include exposition of the magnetic design, prediction of core loss, measurement of a prototype, and thermographs to validate the design performance.

This 3t primary on a Fair-rite 5943000201 (FT37-43) is not a good choice for 80m, it has high InsertionVSWR and high core loss.

- RF transformer design with ferrite cores – initial steps
- Duffy, O. 2015. A method for estimating the impedance of a ferrite cored toroidal inductor at RF. https://owenduffy.net/files/EstimateZFerriteToroidInductor.pdf.
- Grebenkemper, L. Jan 1987. The tandem match – an accurate directional wattmeter In QST.
- Sontheimer,C & Frederick,RE. Apr 1966. Broadband directional coupler. US Patent 3,426,298.

Above, the EFHW transformer prototype.

Above is a Simsmith model of the 6t balun common mode impedance Zcm on a 2543251002 core, and measured (squares) impedance, the model is calibrated to the measured self resonant frequency.

The core is quite suited to both the EFHW transformer and a common mode choke. 6t of RG316 would be ok on the common mode choke for modest power, 0.6mm ECW on the EFHW transformer.

]]>Another small efficient matching transformer for an EFHW – 2643251002 – #2 – prototype bench measurement continued the development of a transformer design. This article presents thermal measurements.

Losses were predicted from a model as follows.

Loss in watts is in red against the right hand axis. Loss is greatest at around 3.6MHz, so it will be measured there. Expected loss is about 4.3W @ 3.6MHz running 50W through power.

Above, temperature rise is estimated to be about 36° under those conditions.

Above is a thermograph of the inductor in free air showing 43.7-12.2=31.5° rise over ambient, fairly stabilised after 8m of continuous 3.5MHz 50W carrier through signal.

]]>End Fed Half Wave matching transformer – 80-20m described a EFHW transformer design with taps for nominal 1:36, 49, and 64 impedance ratios.

Keep in mind that this is a desk design of a transformer to come close to ideal broadband performance on a nominal 2400Ω load with low loss. Real antennas don’t offer an idealised load, but this is the first step in designing and applying a practical transformer.

The transformer comprises a 32t of 0.65mm enamelled copper winding on a Fair-rite 5943003801 core (FT240-43) ferrite core (the information is not applicable to an Amidon core), to be used as an autotransformer to step down a EFHW load impedance to around 50Ω. The winding layout is unconventional, most articles describing a similar transformer seem to have their root in a single flawed design, and they are usually published without meaningful credible measurement.

This article presents a model of the transformer using the 1:49 taps, and measurements used to calibrate the model.

See also On ferrite cored RF broadband transformers and leakage inductance.

Above is a pic of the prototype being measured with a 2400+j0Ω load in a 4t:28t connection. Sweeps of the transformer with OC and SC terminations were also made, and all three used to calibrate the Simsmith model.

Above is the calibrated Simsmith model with 65pF compensation capacitor added. The blue curves are the uncompensated VSWR and losses, and the magenta are with compensation. Note that the compensation capacitor is a high quality capacitor, eg silvered mica.

Optimal compensation capacitance on a real antenna may be a little different, pre prepared to measure and trim.

So, InsertionVSWR on a nominal 2400Ω load is less than 2.3 from 80m to 20m.

Core loss is highest at 20m, 0.36dB, which equates to 8.6W of core loss at 100W input.

Above, worst expected core temperature rise in free air is at 14MHz, about 51°.

Above, at 3.6MHz, expected core temperature rise in free air is a little lower at about 37°.

The core measured showed 35° in free air @ 100W through @ 3.6MHz suggesting it is probably best rated for no more than 300W continuous, perhaps less depending on the enclosure. These results are consistent with the measured impedance of the prototype, but it is wiser to use the model prediction of expected average characteristic of the cores.

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