(Holbrook and Dixon 1939) explored the subject measuring the voice characteristics of many talkers (as there is variation amongst talkers) to come up with an average characteristic.

Whilst in its day, obtaining instantaneous samples of voice was a challenge, it is trivial today and if you can’t believe the numbers given, try your own experiment (but realise it is for your own voice rather than the general population).

Many modern PC sound applications are capable of the measurement, I will demonstrate it with the feed Windows application Audacity with the stats.ny addin.

Above is a screenshot of a 6s recording of my voice made without stopping for breath. The statistics window shows a peak of -8.9dBFS and RMS of -27.4dBFS, giving a peak voltage to RMS voltage ratio of 18.5dB.

On repeated trials it is within tenths of a dB. If you try the experiment, keep your voice level constant, don’t stop for breath, don’t pause as you might in reading sentences as all these will result in an overestimate of instantaneous peak voltage to RMS voltage. Make sure the peak is well less than 0dBFS, otherwise you will underestimate instantaneous peak voltage to RMS voltage.

(Holbrook and Dixon 1939) gave the graph above which characterises the ratio of instantaneous peak to RMS voltage of voice telephony for different numbers of channels in a multiplex and different expectation of overload or clipping.

My measured instantaneous peak voltage to RMS voltage of 18.5dB reconciles well with (Holbrook and Dixon 1939) approximate operating limit (the dashed line) for n=1 channels.

Remember that PEP is 3dB less than the instantaneous peak voltage indicates, so in the measurement PEP/Pav=18.5-3.0=15.5dB. The chart suggests PEP/Pav=18.0-3.0=15dB.

If you have seen figures of Pav/PEP of 20% (-7dB) or PEP/Pav=5 (7dB) bandied around for uncompressed SSB telephony without experimental evidence or explanation, you might question the credibility of the source.

- B D Holbrook and J T Dixon. Oct 1939. Load Rating Theory for Multi-Channel Amplifiers” in Bell System Technical Journal, Vol. 18.

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 ICAS (Intermittent Amateur and Commercial Service) rating would be appropriate, we would rate it as 28.6/0.5=57.2W ICAS.

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 ICAS 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 ICAS 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 ICAS (Intermittent Amateur and Commercial Service) rating would be appropriate, we would rate it as 118/0.5=236W ICAS.

Lets calculate the SSB compressed telephony rating. we can calculate a SSB telephony (with compression) PEP ICAS 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).

]]>In estimating the power dissipated in components due to an SSB telephony waveform, a good estimate of the ratio of Average Power (Pav) to Peak Envelope Power (PEP) is very useful.

Long before hams had used SSB, the figure has been of interest to designers of FDM or carrier telephone systems to size amplifiers that must handle n channels of FDM multiplex without overload which would degrade S/N in other channels of the multiplex. The methods are applicable to SSB telephony, it uses the same modulation type and the overload challenges are the same.

(Holbrook and Dixon 1939) gave the graph above which characterises the ratio of instantaneous peak to RMS voltage of voice telephony for different numbers of channels in a multiplex and different expectation of overload or clipping. They recommend a very low probability of clipping at 0.1% to avoid significant intermodulation noise in adjacent channels.

We are interested in the single channel case, n=1, and we must subtract 3dB from the vertical axis readings and negate them to obtain the ratio of Pav/PEP.

We can see that for very low probability of clipping, say 0.1%, that the Pav/PEP ratio is about -15dB or 3%. A very low probability of clipping is essential to preventing transmitter output appearing in adjacent channels.

The effect of speech processing or speech clippers is to increase Pav/PEP, for example supplying 6dB higher input audio level (commonly spoken of as 6dB compression) will raise Pav, but by less than 6dB.

So, we can infer that for well adjusted transmitter and unprocessed speech, Pav is about 15dB lower than PEP, or about 3% of PEP, and for processed speech, Pav may be more like 10dB lower than PEP, or about 10% of PEP.

So, for the purpose of rating safe dissipation of components with relatively long thermal time constant that effectively average the power is to rate the Pav as 10dB lower than PEP so including a reasonable allowance for sensible compression.

- B D Holbrook and J T Dixon. Oct 1939. Load Rating Theory for Multi-Channel Amplifiers” in Bell System Technical Journal, Vol. 18.

This article documents its failure in June 2019 after five years service.

With the passage of time, the new PV array surface has degraded but on test, the PV array short circuit current is 90% of rating so it will be retained for a while yet. There is no doubt that inexpensive Chinese PV arrays do not survive direct exposure to weather, and it is doubtful that paying more money buys quality… Chinese Quality is a bit of an oxymoron.

The original 1000mAh 1S LiPo battery has failed almost 2000 shallow discharge / charge cycles, now giving less than 200mAh capacity so it will be replaced. Cell resistance @ 1kHz was 140mΩ, way too high (expected up to perhaps 50mΩ).

Above, a new protected battery was made from a 2500mAh LiIon cell and a 1S protection board and tails with JST RCY connector. This Turnigy cell cost around $5 as test showed is delivered its rated capacity.

The battery was served with heatshrink sleeve.

More damage to the ABS jiffy box as a result of ice expansion was repaired by plastic welding the affected screw well on the cover. These are clearly not a good option in climates where rain or condensation may freeze.

]]>This article documents its failure in June 2018 after three years service.

With the passage of time, the PV array surface has degraded until solar collection was insufficient to maintain the battery over several heavily overcast Winter days.

Above, a close up of the PV array surface. The pic is of about 8mm width, and one can barely see the silicon stripes which are about 2mm wide.

Two problems were identified:

- the UV activated adhesive securing the clear cap over the LDR had degraded and although still in place, it was pushed off with little effort; and
- the surface of the PV array was crazed and maximum current on full sun had degraded from 160mA to 17mA.

The issue of the PV array is a serious one. It is low cost and comes from China, but there appears to be no way to buy produce with a known quality that includes UV resistance resin used to encapsulate the cells. It is a significant problem to solve.

Meanwhile, it was repaired like for like to buy time to evaluate other options. A new PV array from the same batch as the first was installed, and a new cap glued on with the same adhesive, battery charged and the thing reinstalled in the garden.

]]>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.

]]>Above is capture of the rectifier input current for a lab power supply set to 1A load current, the scale factor for the current probe is 1V/A.

It can be seen that the current flows for only a small part of each half cycle, peaking at 5A. The RMS value of the current is important as heating of the diodes is partly due to the RMS current flowing in the bulk resistance of the diode.

The RMS value of current shown was calculated and was 2.02A. The average of the absolute value of the samples is the DC current out of the rectifier, and it was calculated at 1.14A, so RMS is approximately 178% of the DC current. The heating effect on transformer windings and diode bulk resistance of the current is 1.78^2 or 3.2 times that of the DC current.

A conservative approach to selection of diodes is to choose them based on the RMS current flowing through them.

Datasheets specify the current rating of diodes in various ways and must be interpreted intelligently.

The datasheet for a 1n4004 states “Average Rectified Forward Current(single phase, resistive load,60 Hz, TA = 75°C)” to be 1A.

In a bridge rectifier, Iav of each diode is half the DC load current, so these diodes could be used at up to load current of 2A under the conditions stated (resistive load). The form factor for a half wave rectified sine wave is 1.11, so Irms into a resistive load etc is 1.11A, and therefore for the bridge rectifier, Irms is 2.22A. The 1n4004 is barely adequate for the example waveform which is 2.02Arms for 1.1A DC output.

The PA40 is a 15A rated bridge rectifier.

Above is a derating chart from the PA40 datasheet.

In the example waveform, Ipk/Iav=5/1.14=4.4, we will use the Ipk/Iav=5 curve. Following that curve, it can be seen that at 80° case temperature, the bridge is rated at 11A, derated due to waveform and case temperature.

Note that for discussion purposes, we have used the waveform for 1A load current. In designing a rectifier, you would use the waveform at maximum current, observed using the intended transformer and filter capacitors which all have a bearing on the waveshape.

The VKPowermate II design was published in Electronics Australia, a hobby magazine.

The design called for a bridge of 3A diodes and provision was made on the PCB for them. They were renowned for diode failure, followed by serious damage to regulator parts and PCB.

Given this history, I built mine with a PB40 (nominal 25A) bridge.

Above is the rectifier output current, 1A/V. The calculated RMS current for each diode is 4.8A, way too much for a nominal 3A diode (eg 1N5404) and probably near doubling the diode dissipation explaining observed high failure rate of the design.

As an aside, the diodes in the bridge appear to be mismatched with one half cycle contributing more current.

People are often surprised by the very high temperature of rectifier diodes in operation. Such high temperatures are often the result of failing to properly derate diodes for effects like peaky current waveform and temperature.

An example, the PB40 often appeared in 25A DC power supply projects, and with a capacitor input filter and case temperature of 100°, the current rating is more like 15A (depending on the other components that determine peak current).

Rectifier diode nominal current ratings may need derating for the higher heating effects of waveforms associated with capacitor input filters.

]]>The LTSPICE model was of a ‘test bench’ implementation of the balun which comprised an air cored solenoid of two wire transmission line, with a slightly asymmetric lumped load.

This article discusses limitations of SPICE in modelling practical baluns.

Guanella’s 1:1 balun and his explanation – Zcm gave the characteristics of a example ferrite cored balun.

Above is Zcm of a 11t balun wound on a FT240-43 toroid. The ferrite core acts on the common mode choke element and has negligible effect on the differential transmission line mode. The key characteristics are:

- TL Zo=100Ω and electrical length at 3.6MHz is 0.43°; and
- Zcm at 3.6MHz is 1007+j1862.

Let us create a model for a narrow band of frequencies around 3.6MHz where will will consider Zcm approximately constant.

Above is the LTSPICE schematic.

Above is the response. We will focus on the results at 3.6MHz (where Zcm is most accurate).

The cursor 2 value is total common mode current and cursor 1 is differential current. It can be seen that common mode current is very low, 35dB less than differential current so despite the asymmetric load, there is very little common mode current. The balun is effective is reducing common mode current (much more so than the air cored example given that reduce common mode current by less than 4dB at 3.6MHz).

The green plot is Zin, and it is quite close to 50Ω by virtue of the electrically short TL section at 3.6MHz.

The load formed by R2 and R3 could be replace by the frequency dependent three component model as discussed at Equivalent circuit of an antenna system, and the frequency specific balun Zcm used (as above), and a solution obtained for a single frequency.

Essentially, whilst it is possible to insert these single frequency values to drive the computation engine, it is not a good tool for the job when one really wants to capture the frequency dependent characteristic of the balun and the complexity of antenna and feed line coupled conductors, radiation etc.

To some extend, it suffers the problems discussed at Using Ohms law on antenna baluns.

SPICE is a quite capable modelling tool, however:

- SPICE does not really have convenient tools for modeling the frequency dependent complex impedance of ferrite cores often used in HF baluns; and
- SPICE does not really allow for entry of the coupled antenna and feed line conductors (ie modeling the antenna system).

- Duffy, O. Dec 2010. Baluns in antenna systems. https://owenduffy.net/balun/concept/cm/index.htm (accessed 31/05/19).
- ———. May 2011. Measuring common mode current. https://owenduffy.net/measurement/icm/index.htm (accessed 31/05/19).
- Guanella, G. Sep 1944. New methods of impedance matching in radio frequency circuits. The Brown Boveri Review.