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.

]]>

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.

]]>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.

]]>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.

Leakage inductance is the enemy of broadband performance, so it is important to minimise it.

Leakage inductance is affected by winding geometry. It is important to avoid opportunity for flux inside and around conductors that does not also ‘flow’ in the core, such flux does not ‘cut’ the other turns and is flux leakage. The winding should hug the core, so winding with wires with thick insulation, thick inflexible wires, and topologies like the Riesert cross over may compromise leakage inductance. High core permeability and high ΣA/l help to minimise wire length which helps in minimising flux leakage.

The transformer is configured as an autotransformer rather than separate primary and secondary windings to again minimise leakage inductance.

Above is a chart derived from s11 looking into the transformer primary with the 14t secondary short circuit showing the equivalent series inductance. The value will be taken as a total value of 236nH, or 118nH a side in the split model.

Note that the inductance at low frequencies is almost independent of frequency even though core permeability changes at these frequencies (see the #43 material data sheet), showing that, for the most part, leakage flux exists elsewhere than the core itself.

A simple model works quite well for predicting nominal load performance on low ratio transformers but less well for high ratio transformers, so best to proceed to measurement of the prototype with nominal load. A load was made from two small resistors in parallel having a combined DC resistance of 2480Ω, quite close to the nominal 2450Ω.

Measurement of the uncompensated transformer hinted that some 50-100pF was the likely optimum compensation capacitance. The transformer was measured with 47pF and it was under compensated, 100pF was perhaps more than needed but InsertionVSWR at the mid to high frequencies was not compromised so since there was a 100pF silver mica capacitor on hand, it was committed to the prototype.

Above is a plot of InsertionVSWR with 100pF silver mica compensation. InsertionVSWR is less than 2 from 1-30MHz. As this type of transformer goes, this is a very good result.

Note there is some contribution of the connecting wires to this response, it is just not possible to use zero length wires to connect the secondary load circuit… but then that applies to its application circuit as well.

Loss modelling ignores conductor loss. Even though the conductors are relatively small, the effective RF resistance referred to the primary side is very low and insignificant compared to core loss. Compensation capacitor loss is modelled, Q=1000 assumed for the silver mica capacitor, but his can be quite a deal lower and very significant for ceramic capacitors.

Above is a plot of the expected loss in dB, magenta on the left scale, and watts @ 50W continuous, red on the right scale. Maximum dissipation is less than 5W which should be accommodated within safe temperature rise for an unenclosed transformer.

Next step is to measure the transformer performance under power, capturing thermographs to confirm the predicted dissipation and power rating.

]]>I have also had lengthy discussions with Faraaz, VK4JJ, who is experimenting with a similar transformer.

This article describes my own design workup and measurements using a Fair-rite suppression core, 2643251002. The cores are not readily available locally, so I bought a bunch from Digi-key.

I really resist the tendency in ham radio to design around unobtainium, it is often quite misguided and always inconvenient. In this case, the motivation for these cores that use quite ordinary #43 material is the geometry of the core, they have ΣA/l=0.002995, a quite high and rivalling the better of binocular cores. High ΣA/l helps to minimise the number of turns which assists broadband performance. See Choosing a toroidal magnetic core – ID and OD for more discussion.

- EFHW;
- InsertionVSWR<2 3-22+MHz;
- nominal 49:1 transformation;
- compensated;
- autotransformer; and
- 50W average power handing.

Some key points often overlooked in published designs of EFHW transformers:

- Insufficient turns drives high core loss; and
- leakage inductance is the enemy of broadband performance, so the design tries to minimise leakage inductance.

Note that high number of turns drives high leakage inductance, so the design is to a large extent, a compromise between acceptable core loss and bandwidth.

From models, I expect that a turns ratio of 2:14 (ie 14t tapped at 2t) is likely to deliver the design criteria (with suitable compensation capacitor).

Above is a perhaps ambitious initial objective using a simple model of the transformer, dotted line is Loss and solid line is InsertionVSWR.

The first step is to measure a 2t winding alone on the core.

Above, the 2t winding measurement fixture. The wire is solid 0.5mm wire stripped from CAT5 LAN cable, the one end zip tied to the external threads of the SMA connector and the other end bent and inserted into the female part without damaging the connector.

Above, a plot or impedance. Note the resonance, the self resonant frequency (SRF) is 16MHz.

Above is a screenshot of a Simsmith model that will be used to develop the design.

It is initially configured to simply expose the impedance of the 2t winding using a simple model of the system as a resonator. The model estimates magnetising impedance from manufacturer’s complex permeability data and adds equivalent shunt capacitance cse as a first approximation of its first resonance. The model is calibrated by adjusting cse so that the model SRF coincides with the measurement.

In this case there is very good reconciliation between prediction and measurement, especially given the wide tolerance of ‘suppression’ ferrite components (see

Using complex permeability to design with Fair-rite suppression products).

The next step is to wind the 2:14 autotransformer winding and to make measurements of its SRF and leakage inductance to calibrate a predictive model.

]]>This article explains a little of the detail behind the graph.

The graph is based on a series of NEC-5.0 models of the loop in ground antenna. Key model parameters are:

- 3m a side;
- ‘average’ soil (σ=0.005, εr=13);
- depth=0.02m; and
- frequency 0.5 to 10MHz in 0.1MHz increments.

The models were scripted by a PERL script, and the output parsed with a Python script to extract feed point Z, structure efficiency, and average power gain (corrected to 4πsr).

The summarised NEC data was imported into a spreadsheet and an approximate model of the system built, comprising:

- Receiver input impedance 50+j0Ω;
- a length of transmission line (10m of Belden 8215 RG6/U);
- an ideal transformer (4:1);
- source impedance derived from the NEC data.

Calculation includes:

- transmission line loss and impedance transformation;
- transformer assumed ideal plus an allowance for transformer loss (1dB);
- mismatch loss; and
- average antenna gain.

Above is an extract of the spreadsheet.

Mismatch loss is an important element of the system behavior. A convenient place at which to calculate mismatch loss is the feed point of the loop in ground.

Above is a plot of the loop feed point impedance, the source impedance in the receive scenario.

Above is a plot of the loop load impedance, the receiver impedance transformed by transmission line and transformer. The varying impedance is a result of using 75Ω line.

The combination of these allows us to calculate mismatch loss.

Above is a plot of the calculated mismatch loss which must be added in to the system gain model.

From the system model, and an estimate of ambient noise from ITU-R P.372-14, we can calculate SND.

Above is a plot of SND.

Note that P.372-14 is based on a survey with short vertical monopole antennas, so it is likely to overestimate noise received by a horizontally polarised antenna (and therefore the SND estimate will be low).

Antenna performance is sensitive to soil parameters, especially those close to the surface and subject to variation with recent rainfall etc.

This is after all a feasibility study, and within acceptable uncertainty, the antenna system would seem to be feasible for low HF and even 160m receive.

]]>