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.

]]>There are two elements that are critical to efficient near ideal impedance transformation over a wide frequency range, low flux leakage and sufficiently high magnetising impedance. While low magnetising loss is essential for efficiency, it does not guarantee sufficiently high magnetising impedance for near ideal impedance transformation.

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.

Plugging the real part of Y into Estimate core loss for ferrite cored RF transformer we obtain the following.

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

Plugging the R,X pair into Estimate core loss for ferrite cored RF transformer we obtain the following. (You could also just enter just the R|| from this analyser value for Rpm.)

Above, the results from measurement are a little better than expected from the datasheets, I did mention that ferrites have quite wide tolerance.

Depending on your loss criteria, the 3t winding might be adequate from a loss perspective 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 consider the effect of magnetising impedance on impedance transformation.

]]>Some of us use a resistor as a load for testing a transmitter or other RF source. In this application they are often rated for quite high power and commonly called a dummy load. In that role, they usually do not need to be of highly accurate impedance, and commercial dummy loads will often be specified to have maximum VSWR in the range 1.1 to 1.5 (Return Loss (RL) from 26 to 14dB) over a specified frequency range.

We also use a known value resistor for measurement purposes, and often relatively low power rating but higher impedance accuracy. They are commonly caused terminations, and will often be specified to have maximum VSWR in the range 1.01 to 1.1 (RL from 46 to 26dB) over a specified frequency range.

It is more logical to discuss this subject in terms of Return Loss rather than VSWR.

Return Loss is defined as the ratio of incident to reflected power at a reference plane of a network. It is expressed in dB as 20*log(Vfwd/Vref).

Calibration of directional couplers often uses a termination of known value, and the accuracy of the termination naturally rolls into the accuracy of the calibration and the measurement results.

A simple example is that of a Return Loss Bridge (RLB) where a known reference termination is compared to an open circuit and then an unknown load to find the Return Loss (being the difference between them).

Let use look at three examples of RF load resistors at hand and consider their performance as a calibration reference. The discussion uses datasheet VSWR or RL figures which are the best one can rely upon unless high accuracy measurements of made of the device.

The MFJ-264N is a high power ‘dummy load’ with max VSWR specified as 1.3 to 650MHz, which is equivalent to RL>17.6dB. In a very good RLB, the directivity will approach the reference termination’s RL, so we can regard the RLB directivity in this case to be 18dB in round numbers.

We can calculate the uncertainty in measuring a given VSWR given the minimum directivity of the RLB.

Let’s say we wanted to measure VSWR down to 1.5, and we wish to know the uncertainty (error bounds).

Above is a calculation of the scenario. It can be seen that with a true VSWR=1.5 load, the RLB may indicate anywhere between VSWR 1.16 and 1.97.

The Bird 6150 is a high power ‘dummy load’ with max VSWR specified as 1.1 from 30 to 500MHz, which is equivalent to RL>26.4dB. In a very good RLB, the directivity will approach the reference termination’s RL, so we can regard the RLB directivity in this case to be 26dB in round numbers.

We can calculate the uncertainty in measuring a given VSWR given the minimum directivity of the RLB.

Let’s say we wanted to measure VSWR down to 1.5, and we wish to know the uncertainty (error bounds).

Above is a calculation of the scenario. It can be seen that with a true VSWR=1.5 load, the RLB may indicate anywhere between VSWR 1.35 and 1.67.

Definitely better than the MFJ-264N.

The KARN-50-18+ is a low power ‘termination’ with RL specified on the chart above. In a very good RLB, the directivity will approach the reference termination’s RL, so we can regard the RLB directivity in this case to be >46dB in round numbers up to 1000MHz.

We can calculate the uncertainty in measuring a given VSWR given the minimum directivity of the RLB.

Let’s say we wanted to measure VSWR down to 1.5, and we wish to know the uncertainty (error bounds).

Above is a calculation of the scenario. It can be seen that with a true VSWR=1.5 load, the RLB may indicate anywhere between VSWR 1.48 and 1.52.

Much better than either of the previous examples, but it is only rated for 2W so it unsuitable as a load for a high power device.

High power RF resistors tend to have poor RL, yet a high RL high power resistor is needed for checking or calibrating high power directional wattmeters.

A possible solution is to use a good RLB with good reference termination to ‘calibrate’ a high power load via an ATU, and use the latter for high power measurements. This typically is a single frequency technique, and there is unavoidable uncertainty introduce in this calibration process.

Another technique is to use an ATU + high power load on the directional coupler, adjusting the ATU for null reflection indication. Then move the cable from the directional coupler to a VNA or analyser and measure the impedance seen by the DUT. Again, being an indirect method, uncertainty flows from cascading measurements.

Resistor loads of lower RL lead to high uncertainty of measurements using them as a reference (directly or indirectly).

The uncertainty is worse as measured RL of the unknown approaches the RL of the reference used.

Depending on the accuracy needed of measurements, RL of the reference typically needs to be 10dB or more better than the intended measurement.

Watch the blog for continuing postings in the series Exploiting your antenna analyser. See also Exploiting your antenna analyser – contents.

]]>Above is a diagram of a Pawsey Balun used with a half wave dipole (ARRL).

Pawsey Balun on an asymmetric load reported model results in an asymetric dipole antenna, and showed very high common mode feed line current.

Pawsey Balun on an asymmetric load – bench load simulation showed that although the Pawsey balun is not of itself an effective voltage balun or current balun, it can be augmented to be one or the other.

So, you might ask what they do, what they are good for, and why they are used.

If you were to construct a quite symmetric half wave dipole and directly connected a coax transmission line to the centre, you would destroy the symmetry of the system as connection of the shield to one dipole leg only effectively connects the common mode conductor (the outer surface of the shield) to one leg of the dipole.

The Pawsey stub or balun is a narrowband device (ie tuned) that adapts the coaxial feed line to a pair of symmetric terminals for attachment to the antenna feed point.

In a perfectly symmetric system (source, feedline type and topology, antenna), current in the radiator will be symmetric and there will be negligible common mode current on the feed line.

Symmetry is easier to achieve with some types of VHF/UHF/SHF antennas than at HF.

Equivalent circuit of an antenna system gives measurements of a fairly symmetric G5RV Inverted V dipole + feed line and in that case, the Z1 and Z2 values are different on the two bands reported, more so on 80m.

On the other hand, a corner reflector with half wave dipole feed for 1296MHz can be constructed with very good symmetry, and fed from behind the reflector, a Pawsey balun should give the necessary feed symmetry to preserve system symmetry and have symmetric dipole currents and negligible common mode current on the feed assembly.

The question of why are they used is more difficult than the other questions. They do have application, but they are also used inappropriately and given that it is most unusual to seem validation of balun performance by measurement, such use highlights the bliss of ignorance.

]]>Pawsey Balun on an asymmetric load reported model results in an asymetric dipole antenna, and showed very high common mode feed line current.

This article looks at two test bench configurations modelled in NEC.

The configurations are of a horizontal Pawsey balun for 7MHz constructed 0.1m over a perfect ground plane. The ‘balanced’ terminals are attached to the ground plan by two short 0.1m vertical conductors which are loaded with 33 and 66Ω resistances. At the other end, the horizontal transmission line is extended by two different lengths and connected to the ground plane using a 0.1m vertical conductor. The two extension lengths are almost zero and a quarter wavelength.

The total horizontal length from the ‘balanced terminals’ to the grounded end of the transmission line is a quarter wavelength for the Pawsey balun and a further 20mm making approximately a quarter wavelength in total.

Above is a plot of current magnitude and phase from 4NEC2. The current on the two vertical conductors containing the 33 and 66Ω loads is quite different, and the product gives load voltages that are approximately equal in magnitude and opposite in phase.

You could be forgiven for thinking that the Pawsey stub itself is a good voltage balun, but in fact the voltage balun behaviour is due to the fact that the transmission line and Pawsey stub conductors in common mode are approximately a half wave electrical length, and being grounded at the far end, the common mode impedance looking into the ‘balanced’ terminals is very low… a hallmark of a good voltage balun.

The total horizontal length from the ‘balanced terminals’ to the grounded end of the transmission line is a quarter wavelength for the Pawsey balun and a further quarter wave making a half wavelength in total.

Above is a plot of current magnitude and phase from 4NEC2. The current on the two vertical conductors containing the 33 and 66Ω loads is approximately equal in magnitude and opposite in phase.

You could be forgiven for thinking that the Pawsey stub itself is a good current balun, but in fact the current balun behaviour is due to the fact that the transmission line and Pawsey stub conductors in common mode are approximately a quarter wave electrical length, and being grounded at the far end, the common mode impedance looking into the ‘balanced’ terminals is very high… a hallmark of a good current balun.

At intermediate lengths, the common mode impedance will range from one extreme to the other, and for the most part, it will be neither a good current balun nor a good voltage balun.

The Pawsey stub or balun is not of itself a good current balun or a good voltage balun, but can be used as part of a more complete solution to act as either a good current balun or a good voltage balun.

Creating that context may be impractical for many antenna topologies.

Without careful implementation of the context, the Pawsey balun or stub is anyone’s guess. Nevertheless they are written up this way in textbooks and find practical application, even though their performance is likely to be unpredictable and unmeasured.

]]>Above is a diagram of a Pawsey Balun used with a half wave dipole (ARRL).

Whilst these have been quite popular with VHF/UHF antennas, the question arises as to how they work, and whether they are effective in reducing common mode current IIcm) for a wide range of load scenarios.

To find an answer, and NEC model was constructed of an OCF half wave dipole a half wave above a perfect earth conductor, vertical feed line to ground, and the current magnitude and phase for all conductors evaluated.

Above is the current plot. Note that horizontal conductors are defined from low X to high X, and vertical conductors from low Z to high Z.

It can be seen that there is relatively high Icm at ground level, and when the currents in both Pawsey Balun conductors are added near the feed point, again relatively high Icm. Also of interest is that the currents in the dipole legs are flowing in opposite directions at the feed point.

This antenna acts more like a top loaded vertical monopole than a horizontal dipole.

Above, the radiation pattern reinforces the view that it is behaving as a top loaded vertical monopole.

In this scenario, the Pawsey Balun has not effectively suppressed common mode current (as would a good current balun), indeed it seems to facilitate it (as a good voltage balun would).

The Pawsey Balun as shown in the diagram is not of itself either a good current balun or a good voltage balun.

]]>These are often sold without specifications, but where specifications are given, VSWR is given as 1.5, though not stated as maximum so should perhaps be read as typical.

This article looks at 2m performance alone.

Above is a VSWR sweep around the 2m band.

VSWR at 146MHz if more than specification, but less than 2.0 below 147MHz.

Above is a VSWR sweep around the 2m band.

VSWR at 146MHz if way more than specification, but less than 3.5 over the whole 2m band.

The purchase price was refunded due to failure to meet specification.

Two antennas were purchased for $24 incl post.

Above is a VSWR sweep around the 2m band. Two antenna were tested with almost identical results.

VSWR at 146MHz if way more than specification, but less than 3.5 over the whole 2m band.

These antennas did show VSWR minimum around 1.5 at 165+MHz.

The purchase price was refunded due to failure to meet specification.

Above is a section through the loading coil unit. The centre conductor of the coax connector is connected to a steel spring (weakly magnetic, so probably austenitic stainless steel), then to the antenna element (which is 8 weakly magnetic wires wound in a helix).

The three antenna vintages tested above had different shaped coil enclosures and different markings, all claimed to be Nagoya genuine product by Revex of Taiwan.

Purchasing the Nagoya NA-771 on eBay is high risk, experience is that recently listed products are unlikely to meed specification at 2m and that is reason enough to reject them.

The antennas can be purchased for as little at $3 each incl post, and there appears to be three kinds of packaging in item descriptions. They are probably all dysfunctional fake copies and worthless cheap Chines junk.

]]>A correspondent wrote of his project with a Guanella 4:1 balun where each pair was wound with a pair of insulated wires, and importantly the output terminals are free to float as the load demands. A Guanella 1:1 balun wound in the same way has the same characteristic.

To preserve balun choking impedance, it is best to preserve balun symmetry, and the use of a short open circuit coaxial stub across the output terminals for InsertionVSWR compensation introduces some asymmetry.

An alternative construction with coaxial cable that is more symmetric is shown above.

It is two pieces of RG58 with the shields fanned out and twisted into pigtails which will be the two terminals of the device. The inner conductors are connected across to the other cable’s shield. The cross connects are kept separated, as are the shield ends, and the space if filled with hot melt adhesive (which is electrically similar to polyethylene). Likewise, I have made sure the cut ends are clean of whiskers and used hot melt adhesive to insulate the parts from each other.

The prototype withstood 2.2kVp and the weak point was the open ends of the RG58. RG58 is strong internally, flashover occurs across the ends… so whilst the neatest smallest pigtails are good for RF, they are not conducive to high voltage withstand. By stripping the braid back 5mm and separating the braid ends similarly, it withstands 4.5kVp. Most ham ATUs cannot withstand even 2kVp, even though the capacitors may be rated for higher voltage, they tend flash over at coax connectors.

There are three open circuit transmission line stubs in parallel.

The first is formed by the outer surfaces of the two pieces of parallel RG58 with PVC jacket insulation. This turns out to have Zo close to 50Ω and VF around 0.6-0.7.

The second and third stubs are formed by the inner of each of the two pieces of RG58.

Because the three TL sections are close to Z0-6=50 and VF=0.66, we can treat them as a single stub with Zo=16.7 and VF=0.66. It is an approximation, but a good one considering the relative magnitude of error due to the pigtails when used on very short stubs as in this case.

In my correspondent’s case, his 70mm single RG58 stub could be replaced with the triple stub of length 20-25mm, enhancing symmetry by both the symmetric structure and smaller size.

Above is a measurement of the prototype. The observed capacitive reactance reconciles with 55mm of Zo=16.7 and VF=0.66 TL.

When the stub is very short electrically (<6°), its impedance is well approximated as the line’s capacitance per unit length of 1/(Co*vf*Ro). In this case, C=1/(299792458*0.66*16.7)=302pF/m, and the 55mm length should be about 302*0.055=16.6pF which reconciles with the chart above.

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Above is Fig 1, a diagram from the Rigexpert AA35Zoom manual showing at the left a link (to be connected the analyser) and the trap (here made with coaxial cable).

Above is the trap measured, the wires were connected as a bootstrap trap as in Fig 1. The coupling link is a 60mm diameter coil of 2mm copper directly mounted on the AA-600 connector, and it is located coaxially with the trap and about 10mm from the end of the trap.

Above is the ReturnLoss plot of the trap very loosely coupled to the AA-600.

Of course this technique will not work on a trap that is substantially enclosed in a shield that prevents magnetic coupling. Note also that many traps used in ham antennas are simply a coil wound on an insulating rod and each end connected to the adjacent tubing, possibly with an overall aluminium tube that may or may not be bonded to the element tube at one end. The latter really become part of the element and measurement separate to the element is not simply translated to in-situ.

The inductor has previously been carefully measured to be 3.4µH. We can calibrate a model of the coupled coils to the observed resonant frequency and ReturnLoss.

Above, the equivalent circuit. We can calculate the flux coupling factor k from the model, it is 2.3% so this is very loosely coupled to avoid pulling the resonant frequency high.

Above is the simulated ReturnLoss response over the same frequency range as measured.

It is practical to measure the resonant frequency of a trap by loosely inductively coupling an antenna analyser, depending on the structure of the trap and the capability of the analyser.

Practical measurements can be explained with a theoretical model of the measurement setup.

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