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.

]]>I took a baseline measurement with an AA-600 after some refurbishment work in Jan 2018, and was able to compare a current sweep to that baseline.

Above, a wide Return Loss sweep of the Diamond X-50N with feed line compared to the baseline (the thin blue line).

By and large they are almost identical, save small departure around 435MHz.

Above is a comparison of the Return Loss at low values. Antscope does not display mathematically correct plots when the data goes off scale (as in this case), this plot is mathematically correct and allows better comparison of the important out of band Return Loss.

It is worth remembering that the AA-600 operates on second harmonic above 200MHz, and third harmonic above 400MHz, so the measurements become a little noisier.

Importantly, the out of band Return Loss is almost identical and this would not be so if feed line loss had degraded (eg due to water ingress), so there is no evidence to suggest that the feed line had degraded.

Above is a narrower sweep around the normal operating frequencies. There is a small degradation in Return Loss which is probably attributable to temperature differences of more than 20° between measurements.

So, the comparison with the archived baseline gives no cause of concern, the antenna system is probably unchanged.

Well, in fact I have done just that at 80 frequencies over a wide range, in-band and out-of-band, if you like. That captures much more information than VSWR measurement at one or a few frequencies.

The traditional ham approach is the measure VSWR at the operating frequency and focus on that, but that is unlikely to be very sensitive to some types of transmission line degradation (eg increased loss).

Analysis of the derived Return Loss figures in-band and especially out-of-band gives much more insight.

I have a clear window that shows if water has leaked down the cable. It should not leak down the inside because it is closed cell foam, but it should indicate if the birds pick a hole in the jacket… and possibly the copper.

]]>Note that the measurements are of a particular implementation and should not be taken to imply generally to 5/8λ verticals, but the solution method can be applied more generally. Lets assume that the measurement is not affected by common mode current.

The answer to the last question first is that a series inductor will not bring the VSWR much below 3. It is a common belief that a 5/8λ vertical can be matched simply with a series inductor.

There are many ways to match the measured antenna, and there are articles on this site describing some of them, but a simple and effective method in this case is the single stub tuner.

Above is a graphical solution using Simsmith. The section of line nearest the measurement load is -ve length, it is to back out the effect of the line section into which measurements were made (antenna feed point is at the cursor, 139-j191Ω). The next line section is the series section, followed by the S/C stub. In this case the series section and stub use RG213 to reduce loss. Total matching system loss is a little under 0.3dB, and the stub can easily be weatherproofed with hot glue and heat shrink tube.

One could use RG58, an exercise for the reader is to assess the loss of that option.

Obviously the length of the measurement section plays into the solution, and using its length to the mm in the model gives a more accurate result.

]]>A coax trap (before cross connection).

The whole subject of trapped antennas elicits a lot of online discussion that is often more about semantics than understanding.

Some key points:

- It is impossible to wind a coil that does not exhibit self resonance at some frequency, and the assertion that it is adequately characterised as an ideal inductance in series with some resistance is quite wrong at frequency higher than say 10% of its self resonance frequency (SRF). So the distinction between a coil and a parallel resonant circuit is often misguided.
- A simplistic explanation of a trap is that it is designed to be resonant at the higher desired band of operation, and at that frequency it acts like an open switch disconnecting the outboard wire sections. You can make a trap that way but it has some significant disadvantages.
- The coax trap is a little more complicated that a fixed inductor tuned by a fixed capacitor.

A trapped dipole for 80m and 40m using bootstrap coax traps used a coax trap that is resonant at about 6.5MHz.

Zooming in a little, we can see that the traps have a modest inductive reactance at 80m (400 – 500Ω) and a largish -ve reactance around 40m (-4000 – -3000Ω). In concert with the wire length and configuration, this results in VSWR minima in the 80m and 40m band, fairly low structure loss, and a pattern largely like an Inverted V dipole of half wave length.

You could fret about the series resistance component of trap Z, but at the end of the day, what is important is how much power is lost in the structures (dipole wire, traps) and in this case dipole + trap loss is less than 0.5dB at 40m, comparable to the coax feed line loss. The situation is a little worse on 80m where it is a shortened loaded dipole, but loss is still quite low (<1dB in antenna structure).

This design was built and tested, and worked pretty much to the model predictions. It demonstrates that a lot of notions about trapped dipoles are flawed.

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.

]]>Above is a low frequency equivalent circuit of a transformer. Although most accurate at low frequencies, it is still useful for RF transformers but realise that it does not include the effects of distributed capacitance which have greater effect with increasing frequency.

The elements r1,x1 and r2,x2 model winding resistance and flux leakage as an equivalent impedance. Whilst for low loss cores at power frequencies, flux leakage is thought of as an equivalent inductance, purely reactive and proportional to frequency, the case of lossy ferrite cores at RF is more complicated. Winding resistance with well developed skin effect increases proportional to the square of frequency, but with lossy ferrite cores will often be dwarfed by the loss element of leakage impedance.

An approximate equivalent circuit can be obtained by referring secondary components to the primary side (adjusted by 1/n^2) with an ideal 1:1 transformer which can then be deleted.

For broadband ferrite cored transformers with good InsertionVSWR at low frequencies, it is leakage impedance that tends to degrade InsertionVSWR at higher frequencies. Leakage impedance will tend to dominate, and so a simplified approximate equivalent circuit becomes leakage impedance in series with the transformed load (50Ω or other value as appropriate).

Flux leakage (and leakage impedance) is higher with lower permeability cores, it is worse with spread out windings (as so commonly shown) and worsened by the Reisert cross over winding configuration (again used without obvious reason). Popular designs of high ratio transformers (eg n>3) typically tightly twist for the first primary and secondary turns for reduced flux leakage, but again without evidence that it is an improvement and in my experience an autotransformer configuration has lower flux leakage and is simpler to wind.

The transformer above is wound as an autotransformer, 3+21 turns, ie 1:8 turns ratio, and the winding is not spread to occupy the full core, it is close wound (touching on the inner parts of the wind).

The effects of the series leakage impedance can often be offset to some extent by a small capacitor in shunt with the input, and due to the complexity of the characteristic of leakage impedance and distributed capacitance, is often best found by substitution on a prototype transformer.

Above is a sweep of the uncompensated nominal n=8:1 prototype ferrite cored transformer with a 3220+50Ω load.

A 100pF silvered mica was connected in shunt with the transformer primary. This is not an optimal value, benefit may be obtained by exploring small changes to that value.

Above is a sweep of the roughly compensated transformer. The capacitor makes very little difference to the low frequency behavior, but it reduces the input VSWR significantly at the high end. VSWR<1.8 over all of HF. Compensation is not usually adjusted for response at a single frequency, but for an acceptable broadband response (as in this case).

Note that the compensation capacitor needs to be high Q for good efficiency, and it should be rated to withstand the applied voltage with a safety margin adequate to the application.

Whilst this example shows the compensation evaluated on a bench load, compensation on a typical antenna system is more relevant to those applications.

]]>This article considers the effect of magnetising impedance on VSWR.

For medium to high µ cored RF transformers, flux leakage should be fairly low and the transformer can be considered to be an ideal transformer of nominal turns ratio shunted at the input by the magnetising impedance observed at that input winding.

A good indication of the nominal impedance transformation of the combination is to find the VSWR of the magnetising impedance in shunt with the nominal load (eg 50+j0Ω in many cases), and to express this as InsertionVSWR when the transformer is loaded with a resistance equal to n^2*that nominal load (eg 50+j0Ω in many cases). This model is better for low values of n than higher, but it can still provide useful indication for n as high as 8 if flux leakage is low.

Magnetising impedance can be estimated using one of the following calculators, but keep in mind that there are quite wide tolerances on ferrite cores.

- Inductance of RF cored inductors and transformers
- Calculate ferrite cored inductor – rectangular cross section
- Calculate ferrite cored inductor – circular cross section
- Calculate ferrite cored inductor (from Al)
- Calculate ferrite cored inductor – ΣA/l or Σl/A
- Ferrite permeability interpolations

Magnetising impedance can be measured (eg with an analyser), but it should be measured with only the measured winding on the core. Did I mention the wide tolerance of ferrites?

You might ask the question is 3t sufficient for the primary of an EFHW transformer that delivers a 50+j0Ω load to a transmitter.

Estimating with a calculator, we get the following.

Let’s work with admittance, it is easier for shunt circuits.

We will take the magnetising admittance above and add the admittance of the load transformed to 50+j0Ω (G=1/50=0.02S). (Use another value for G if it is more appropriate.) So we want to calculate the VSWR of a load with Y=0.02305-j0.0064S.

Above, InsertionVSWR=1.39. Not apalling, but not wonderful, up to the designer whether it is acceptable.

Measuring a core with a 3t winding using very short wires to the AA-600 coax socket, the following results were obtained.

Let’s work with admittance, it is easier for shunt circuits.

We will take the magnetising R|| and X|| above, convert each component to admittance (1/397.4+1/j234.9=0.002516-j0.004257S) and add the admittance of the load transformed to 50+j0Ω (Y=1/50=0.02S). So we want to calculate the VSWR of a load with Y=0.022516-j0.004257S.

Depending on your InsertionVSWR criteria, the 3t winding might be adequate on 3.6MHz. On the other hand you might be tempted to test 4t, but there is a limit as more turns tends to compromise the higher frequency performance, especially on a large core.

A follow up article will look at first pass compensation of InsetionVSWR for optimised broadband response.

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