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 (\(B=\frac {-1} {2 \pi f L}\), \(Y= G + jB = \frac 1 R – \frac {j} {2 \pi f L}\)). 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 (\(B=2 \pi f C\), \(Y= G + jB = \frac 1 R + j 2 \pi f C\)). 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 enamelled 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 enamelled 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 loss cores, magnetic saturation is likely to be the significant limit on power handling.

Read widely, and analyse critically what you read.

]]>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 50/60Hz power transformers, Z1 and Z2 are mainly inductive and small (eg as would account for around 5% voltage sag under full load). Zm varies, it is large and mainly inductive for conservative designs using sufficient and good core material, and less so for designs that drive core magnetic flux into saturation.

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.

Keep in mind that if Zm is sufficiently high, Im is low, and even though Zm may contain a large Rm component, Im^2*Rm may be acceptably low.

There are scores of articles on this website about ferrites, many of which show how to measure or calculate Zm from datasheets.

Proponents of powdered iron will claim that large Im does not create much loss because Rm is small, but large Im destroys broadband nominal impedance transformation (ie Insertion VSWR). Powdered iron tends to be low µ which increases leakage impedance and also destroys broadband nominal impedance transformation.

An online expert on the unsuitability of #43 for HF UNUNs discussed the stuff that masquerades as science in the name of ham radio, and gives one example which questions the exptert’s opinion. Lets work through some examples, calculating and plotting two key metrics that should be considered right up front when designing an efficient broadband RF transformer with close to ideal impedance transformation (ie low InsertionVSWR).

The following analyses are of expected core loss due to the magnetising impedance of the primary winding when the transformer is loaded to present an input impedance of 50+j0Ω. The magnetising impedance can be measured with only that primary winding on the core, the presence of a secondary winding, even if disconnected, may disturb the results.

Note that there is a quite wide tolerance on ferrite materials, and measured results my differ from the predictions based on published datasheets. Designs based on measurements of a single core are exposed to risks of being atypical.

Graph Y axes are not identically scaled.

This configuration is very popular in ham radio. I am not sure who originated the design, PA3HHO’s web article is a commonly cited reference.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

Above is the Insertion VSWR caused by the magnetising impedance in shunt with 50+j0Ω. Note that this is not exactly the same configuration as for the previous chart.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

Above is the Insertion VSWR caused by the magnetising impedance in shunt with 50+j0Ω. Note that this is not exactly the same configuration as for the previous chart.

This is a small #43 core as used in Small efficient matching transformer for an EFHW.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

Above is the Insertion VSWR caused by the magnetising impedance in shunt with 50+j0Ω. Note that this is not exactly the same configuration as for the previous chart.

The Jaycar LO1238 is readily available in Australia, a medium size core of medium to high initial permeability (µi=1500) that seems overlooked by Australian hams in favor of harder to procure products.

Above is the percentage core loss when input impedance of the loaded transformer is 50+j0Ω.

It seems many hams have a “favorite mix”, and many spurn #43, nominating others (#31, #61 often for this application).

All are possibilities that for a given core geometry and mix will require a certain minimum number of turns on the nominal 50Ω primary to meet the designer’s loss and Insertion VSWR criteria. #61 is a lower loss material compared to #43, and it will require more turns to meet Insertion VSWR criteria at low frequencies, the length of the winding may limit the useful upper frequency.

- The context of the article is HF broadband transformers with close to ideal nominal impedance transformation, and does not necessarily apply to other contexts.
- Three of the examples use #43 material, two of those designs have core loss less than 10% at 3.5MHz and lower on higher bands demonstrating that it is possible to design a broadband RF transformer for HF using #43 material.
- The PA3HHO example shows that insufficient turns leads to appalling core loss.
- Traditional wisdom is that higher µ cores will be even worse than #43, but the LO1238 design shows that a low cost core readily available in Australia is a worthy candidate for Australian hams.
- There is more to designing a transformer than presented here, this article describes a first analysis to screen likely candidates and find minimum primary turns for a given core to meet the design loss and InsertionVSWR criteria.
- Successful designs are almost always a compromise to meet sometimes competing / conflicting design criteria.

Read widely, and analyse critically what you read.

]]>…The spec for type 43 makes it clear that it should never be used for HF unun construction. It is specifically engineered with a complex permeability that makes the core lossy on most HF frequencies. Since an unun is not a TLT (transmission line transformer) but rather an autotransformer, a low loss core is essential for efficient operation….

Now it contains the very common FUD (fear, uncertainty and doubt) that masquerades as science in ham radio, but without being specific enough to prove it categorically wrong. To a certain extent, the discussion goes to the meaning of efficient operation.

At Small efficient matching transformer for an EFHW I described an ‘unun’ using #43 material, and gave design calcs and measured loss over HF.

I will concede that making loss measurements by that technique becomes less accurate at the high end of HF where the distributed inductance and capacitance of the combined load become significant… but good figures can be obtained below say 10MHz. In most cases, the core losses are greatest at the lowest operating frequencies, so that works well.

Back to the transformer, designs are typically a compromise of a lot of factors such as size, mass, loss, bandwidth etc. In the example case, it is a transformer intended for low power portable operation (eg SOTA) and efficiency is traded for size and mass to name a couple.

Nevertheless, the core efficiency is 90% at the lowest design frequency, 3.6MHz, and is higher at higher frequencies.

This example questions the impression that the online expert tries to leave in readers minds that #43… should never be used for HF unun construction.

Read widely, and analyse critically what you read.

]]>There are common some key properties that are relevant:

- where loss is high, core loss tends to dominate;
- the specific heat of ferrite is typically quite high;
- the capacity to dissipate heat is related to many factors.

Ferrite materials have loss at HF and above that warrants consideration.

Even though the effective RF resistance of conductors is much higher than their DC resistance, the wire lengths are short and conductor loss is usually not very high.

Core loss will commonly be much larger that conductor loss and so dominate.

The specific heat of ferrite is typically towards 800K/kgK, almost as high as aluminium so ferrite absorbs a lot of heat energy to raise its temperature.

When heated by a constant source of power, temperature will rise exponentially as a result of the combination of mass, specific heat, and loss of heat from the core as temperature increases. We can speak of a thermal time constant being the time to reach 63% of the final temperature change, and for large ferrite toroids (eg FT240) that may be over 2000s.

Factors include the temperature difference between the core and ambient and if you like, the thermal resistance between core and ambient. Ambient temperature may be high if the device is installed in a roof space. Incident heat from the sun increases the challenge.

Maximum core temperature depends on maximum operating temperature of the enclosure (PVC), wire insulation maximum temperature, fasteners (eg nylon screws or P clips), and Curie temperature all weigh in.

Thermal resistance is higher where the core is contained in a closed enclosure.

Lets say a EFHW transformer using a FT240-43 is housed in a small sealed PVC box mounted outside in fee air. The transformer uses a 2t primary winding as per a plethora of articles on the ‘net.

Above is a core loss profile for the transformer where the load is such that the impedance looking into the primary is 50+j0Ω. At 3.5MHz, core loss is 34%.

Lets say that the core can dissipate 10W continuously without damage or compromise. In that case, with core loss of 34%, the transformer could be rated for 10/0.35=28.6W continuous or average RF power input. One would confirm this continuous rating with a bench test measuring temperature until it stabilised. Thermographs are a good means of documenting the heat rise.

In applications where the transmitter was active only half the time, an IACS (Intermittent Amateur and Commercial Service) rating would be appropriate, we would rate it as 28.6/0.5=57.2W IACS.

Note that as we ‘increase’ the power rating, consideration must be given to voltage breakdown which is an instantaneous mechanism, there is no averaging like heat effects.

Now some modes have average power (ie heating effect) less than the PEP, so we could factor that in. Average power of SSB telephony develops a Pav/PEP factor for compressed SSB telephone of 10%, so we can calculate a SSB telephony (with compression) PEP IACS rating as 57.2/0.1=572W.

So this is a pretty ordinary ordinary transformer which we have been able to rate at 570W SSB IACS exploiting the low average power of such a waveform.

Above is a core loss profile for the transformer where the load is such that the impedance looking into the primary is 50+j0Ω. At 3.5MHz, core loss is 8.5%.

Lets say that the core can dissipate 10W continuously without damage or compromise. In that case, with core loss of 8.5%, the transformer could be rated for 10/0.085=118W continuous or average RF power input. Again, one would confirm this continuous rating with a bench test measuring temperature until it stabilised. Thermographs are a good means of documenting the heat rise.

In applications where the transmitter was active only half the time, an IACS (Intermittent Amateur and Commercial Service) rating would be appropriate, we would rate it as 118/0.5=236W IACS.

Lets calculate the SSB compressed telephony rating. we can calculate a SSB telephony (with compression) PEP IACS rating as 236/0.1=2360W.

Even more important at this power level is assessment of the voltage withstand.

So, when you see claims of power rating, read the details carefully to understand whether they are applicable to your scenairo. The last scenario about might be find for 1500W SSB compressed telephony, but not suitable for 500W of FT8.

An exercise for the reader: calculate the power rating for A1 Morse code (assume Pav/PEP=0.44).

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