**Inductance** of a conductor is the property that a change in current in a conductor causes a electro motive force (emf or voltage) to be induced in a conductor.

We can speak of **self inductance** where the voltage is induced in the same conductor as the changing current, or **mutual inductance** where the changing current in one conductor induces a voltage in another conductor.

At low frequencies, the current is distributed uniformly inside the conductor, and its self inductance can be calculated readily (formula is in most good text books). For example, the self inductance of a 2mm diameter round copper conductor is about 1370nH/m. Note that this includes the effect of flux within the copper conductor, **internal inductance**, it contributes 50nH/m.

At low frequencies, the current is distributed uniformly inside the conductor, and its self inductance can be calculated readily (formula is in most good text books). For example, the self inductance of a 10mm diameter thin round copper conductor is about 998nH/m. There is no magnetic flux inside the tube as there is no current flowing there to create flux.

If we locate a round conductor concentrically or coaxially within a hollow tubular conductor (shield), there is not only the self inductance L1 and L2 of each conductor respectively at play, but the mutual inductances M12 and M21. M12 and M21 are equal to each other, and by virtue of the fact that all of the flux of L2 is shared with L1, M12 and M21 are equal to L2.

If we consider the series path of current flowing in the inner conductor and returning via the outer conductor, we have L=L1-M21+L2-M12 and given M12=M21=L2, we can write L=L1-L2 which tells us that the inductance is due to the flux inside the shield, there is no flux outside the the shield.

If the example 2mm and 8mm conductors were arranged coaxially, the return circuit inductance would be L1-L2=1370-998=372nH.

The effect of self inductance is to cause current to concentrate in the area where self inductance is least. This effect is more pronounced as frequency increases and because tends to flow mainly near the surface it is commonly known as skin effect. We can think of the current density as decaying exponentially with increase depth, and although it is more complicated than that, this is an adequate model for this discussion. We speak of the skin depth δ as the depth that carries 63% of the total current and often make the assumption that the total current is carried in a depth of 3δ, it that there is insignificant current at greater depth.

Skin effect implies that at sufficiently high frequency, the current on the inner conductor flows mainly near the outer surface. A consequence is that the internal inductance approaches zero.

Skin effect implies that at sufficiently high frequency, the current on the outer conductor flows mainly near the inner surface.

With well developed skin effect, the outer conductor behaves almost like two independent / isolated tubes being the inner and outer surfaces with negligible current flowing in the region between those ‘layers’.

Coaxial cable is usually used in TEM (Transferse Electro Magnetic) mode, magnetic flux is circular within the coax, and radial electric field exists between the outside surface of the inner conductor and inside surface of the outer conductor (there is no magnetic flux due to inside currents outside the coax). Other modes are possible at some frequencies, but they cause higher loss and are usually discouraged.

In TEM mode in the presence of well developed skin effect, a current I flowing at a point along the coax on the outer surface of the inner conductor is accompanied by an equal current flowing in the opposite direction on the inner surface of the outer conductor. This is a really important attribute to consider when analysing a system.

In the presence of well developed skin effect, the combination of self inductance and mutual inductance of each of the outer surface of the inner conductor and inner surface of the outer conductor result in no external magnetic or electric fields, and the constraint that a current I flowing at a point along the coax on the outer surface of the inner conductor is accompanied by an equal current flowing in the opposite direction on the inner surface of the outer conductor.

These if you like define what is going on inside the coax as a private scope that is affected only by the transmission line characteristics, load impedance and source. Calculators such as RF Transmission Line Loss Calculator provide solutions to this problem.

In the presence of well developed skin effect, the outside surface of the outer conductor can carry currents independent of what his happening inside the coax. The fields due to these currents are entirely external to the outside surface of the outer conductor, and the outer conductor is free to interact with other sources of magnetic and electric fields.

In the presence of well developed skin effect, the inner and outer surfaces of the outer conductor are effectively isolated, but they connect to each other at the ends of the coaxial structure.

One can analyse the configuration by considering that there is a node formed at the shield end, and connected to that node are the inner and outer surfaces of the shield and any other external conductors. At the node, Kirchoff’s Current Law applies.

Two scenarios will be analysed to demonstrate an approach to the problems.

An ideal resistor for this discussion is one that is electrically so small that we can ignore distributed capacitance and inductance and phase change of current through the resistor.

If a ideal resistor is attached to the cut of of a coax cable and excited from the other end, the current flowing from the inner conductor to the resistor flows entirely to the inner surface of the outer conductor, there is no residual to flow to the outer surface of the outer conductor. This is independent of whether there are standing waves on the inside of the coax (ie whether the load resistor equals Zo).

Nothing above prevents current flowing on the outer surface of the outer conductor due to other excitation, but none will flow into the inner of the coax.

The configuration is a coaxial cable directly attached to the centre of a practical half wave dipole. For the purpose of discussion, the dipole is not perfectly symmetric and the current flowing into one leg is not exactly equal to that from from the other leg.

Lets call the current from the centre conductor to one dipole leg I1, and the current from the other leg I2. I2 flows into the node formed by the connection of the inner surface of the other conductor, other surface of the outer conductor and the dipole leg. By Kirchoff’s Current law, the current flowing into the outer surface of the outer conductor at the node is I2-I1, and that current (often termed common mode current) gives rise to external fields (including radiation).

Likewise, voltage induced into the outer surface of the outer conductor by external source will flow into the same node and divide between the attached dipole leg and inner surface of the outer conductor. The current flowing to the dipole leg causes a current in the other dipole leg providing the complementary differential current in the interior of the coax, eventually delivering energy to the remote load.

]]>Above, the completed adapter. DIP-28 are located carefully so that the pins 10-18 are in the socket, the same connections are used for both chip sizes for STC15F104E and STC15F204E.

Above, the copper side of the adapter.

The 6 pin female header accepts a USB-RS232 adapter (break out board style or cable) with the common Arduino pinout. The USB-RS232 adapter powers the chip being programmed, and it needs to be a 5V adapter.

Alternatively one of the little MAX232 adapter boards could be used with a physical RS232 port, but power will be required.

To use it, load a chip and set the STC software up for the operation. Press the operation button then quickly press and hold the switch on the adapter until the software notifies the download is complete.

]]>(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.

This is a measurement at source of my voice and the recorded data shows that no clipping took place.

Different voices may produce different results.

Lower Peak/Average is almost always a sign of non-linearity (eg peak clipping, compression etc) and warrants further tests of system linearity.

- 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.

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