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By Andrew Levido Power Electronics Part 8: AC to AC Converters Having covered DC-DC, DC-AC and AC-DC converters in the Power Electronics series published in the November 2025 through May 2026 issues (siliconchip.au/Series/452), I have finally been convinced to fill in the missing piece of the puzzle: AC-AC converters. I was not originally planning to include this topic in the series because they are not the sort of converters that readers of this magazine are likely to come across in practice, but since I was asked specifically, here we are! You won’t find an off-the-shelf chip or a ready-made development board to experiment with AC-AC converters, nor are you likely to be called on to repair one for a neighbour or family friend. Still, their operation is interesting enough to warrant a closer look. AC to AC converters, as the name suggests, convert power from one AC form to another. The inputs and outputs can be single-phase or threephase, and they can be configured to change the number of phases, the frequency and/or the voltage. They fall into two broad categories: those with an intermediate DC link and those without. The former is really a combination of an AC-DC converter and a DC-AC converter with a DC energy storage element in between. In this sense, they are not true AC-AC converters at all. We have already covered AC-DC and DC-AC converters in some detail, so I won’t provide any further details on such systems here. This article will focus instead on direct AC to AC converters, the oldest and most common of which is the cycloconverter. Naturally commutated cycloconverters (we’ll cover what this means in a moment) are used almost exclusively to drive very large induction or synchronous motors, typically in the 5-50 megawatt range. Their applications include marine propulsion, where turbogenerators provide the power and large electric motors are used to drive conventional propellers or Azipods. You will also find them driving very large industrial machines, such as rotary cement kilns. These are huge inclined cylindrical 64 Silicon Chip furnaces up to 6m in diameter and often over 200m long. Some of these kilns can process 10,000 tonnes of cement per day, so they require really big motors and drives to control their rotation! Another application that comes to mind is semi-autogenous grinding (SAG) mills used in mineral refining. SAG mills use hardened steel balls or cylinders to pulverise the ore, making it ready for further processing. They are huge steel drums, up to 12m in diameter and a similar length. This large diameter lets the falling balls or rods gain plenty of kinetic energy to hammer the ore into dust. A typical 12m diameter SAG mill can hold up to 175 tonnes of material, so it takes quite some torque to turn. Naturally commutated cycloconverters are used in these ultra-highpower applications because they are pretty much the only electronic drives able to deliver the high voltages and currents required. These motors typically require many thousands of amps per phase at a couple of kilovolts! Operating principles The circuit diagrams and waveforms associated with cycloconverters can get quite complicated, but we can understand what’s going on if we take it step by step. Fig.1 shows the simplest direct AC-AC converter I can think of. A set of four switches selects half-cycles of an AC source to put together a lower-frequency AC output waveform (in this case, one third of the input frequency). Switches S1 and S4 are closed during the first positive half-cycle of the source voltage, while switches S2 and S3 are closed in the first negative half-cycle, to provide the first two positive voltage pulses at the output. Switches S1 and S4 are closed again for the next full cycle of the input, to Australia's electronics magazine produce the third positive pulse and the first negative pulse of the output waveform. This process continues, with the switches selecting the appropriate half-cycles in turn. The output is certainly AC, but if we are interested in the fundamental component – and we almost always are – this is not a very effective circuit. The output is a kind of square wave with notches in it where the voltage falls to zero. You can imagine the harmonic content is pretty bad, especially the harmonics at twice the input frequency. We could do a lot better with a three-phase source and six switches because the resulting output would be much closer to a square wave. However, neither circuit allows us to control the amplitude of the AC output if the input voltage is fixed. You could think of this circuit as a kind of rectifier where we can control the polarity of the output at will. What we really need is a rectifier that can produce a positive or negative output at any arbitrary voltage level. You may recall from the article on AC-DC converters in the September 2025 issue that a full-wave, phase-­ controlled rectifier with an inductive load does exactly this. I have reproduced the schematic of such a rectifier in Fig.2. This converter has the special property of operating in two quadrants – the average output voltage ‹vx› can be positive or negative, depending on the thyristor firing angle, although the load current can only ever be positive. If the filter inductance is large enough, we can ignore the ripple current, so the load voltage Vload is equal to ‹vx›. The output voltage is Vload = (3Vll ÷ π)cos(φ), where Vll is the peak lineline voltage and φ is the thyristor firing angle. As we change the firing angle siliconchip.com.au from zero to π radians (0 to 180°), the load voltage changes from +(3Vll ÷ π) to -(3Vll ÷ π). When we are using this circuit as a rectifier, we fire the thyristors at a fixed phase angle to produce a fixed DC output, as shown in the upper chart. However, there is nothing preventing us from continually changing the firing angle to synthesise a rising or falling waveform, as shown in the lower chart. We could even produce a sinusoidal output with an arbitrary amplitude and frequency if we manipulate the firing angle appropriately. This is the principle on which all cycloconverters work – creating a lower-frequency AC output by ‘stealing’ appropriate sections of the input AC waveform. There are some limits on this, of course. The peak amplitude is limited to (3Vll ÷ π), as mentioned above, and the maximum output frequency is limited to some value well below the mains frequency. We will look into the frequency limit later on. Low-­ frequency output is not a problem for typical cycloconverter applications – 200m-long kilns don’t spin fast! If we want a sinusoidal output with an amplitude of Vo and a frequency of ωo, we have to control the firing angle according to the expression φ(t) = cos-1 (πVo ÷ 3Vll)sin(ωot). This looks messy, but the stuff in brackets after the inverse cosine operator (cos-1) is just a constant relating the input voltage to the desired output voltage, so the inverse cosine of this is also a constant (for a given input and output voltage). The firing angle therefore simply varies sinusoidally at the frequency of the output, just like the duty cycle for sinusoidally modulated PWM. That is obviously pretty easy to implement with a microcontroller and a few lines of code. Fig.1: the simplest conceivable AC-AC converter selects half-cycles of the input waveform to construct a crude AC output at a lower frequency. Fig.2: a phase-controlled rectifier with an inductive load can produce a positive or negative average output voltage. A cycloconverter is such a rectifier with the firing angle varied to produce a sinusoidal output. Fig.3: this six-pulse, four-quadrant, singlephase naturally commutated cycloconverter circuit is the building block for all sorts of multiphase naturally commutated cycloconverters. Naturally commutated cycloconverters If the firing angle is fixed, this circuit is a rectifier, but if we vary the firing angle as described above, this circuit is a six-pulse two-quadrant naturally commutated single-phase cycloconverter. Quite a mouthful for sure, but easy to break down: • Six-pulse because it is a threephase full-bridge arrangement that delivers six half-cycle pulses to the output per input cycle. siliconchip.com.au • Two-quadrant because the output voltage can be positive or negative, but the current must always be positive. • Naturally commutated because each thyristor is switched off when another is switched on, and the current commutates from one to another. • Single-phase because the output has a single phase. The applications mentioned above almost always require three-phase, Australia's electronics magazine four-quadrant operation. It is a simple matter to add a second set of ‘reverse’ thyristors, as shown in Fig.3. The original ‘forward’ thyristors are used when the output current is positive, while the ‘reverse’ thyristors are used when the output current is negative. This circuit is the basic building block for all sorts of naturally commutated cycloconverter configurations. To get three-phase output, we have August 2026  65 a couple of choices. The simplest arrangement is shown in Fig.4(a). You can look at this as three sets of the ‘top half’ of the single-phase building block circuit; one for each output phase. This is a relatively simple arrangement with only(!) 18 thyristors, but because we have chopped off the lower half of the six-pulse circuit, we only have three half-cycles available to construct our output. This is therefore 66 Silicon Chip a three-pulse, four-quadrant, threephase cycloconverter. To retain the six-pulse output, we have to connect three single-phase ‘building block’ cycloconverters in a star arrangement, as shown in Fig.4(b). This has 36 thyristors and is known as a six-pulse, four-quadrant, three-phase cycloconverter. Despite the apparent complexity, I am sure you can see that this is really Figs.4(a) & (b): typical three-phase cycloconverter circuits contain a lot of thyristors and can look very complex. Ultimately, you can break them all down to a series of phase-controlled rectifiers arranged in different ways. Australia's electronics magazine just a set of phase-controlled rectifiers that can synthesise a low-frequency sinusoidal output. 12-pulse cycloconverters At the upper end of the power spectrum, it is common to use 12-pulse cycloconverters, as shown in Fig.5(a) & (b). These consist of six of the sixpulse single-phase cycloconverter building blocks. The configuration on the left has two separate three-phase outputs because it is really two six-pulse three-phase cycloconverters (shaded yellow and blue respectively) feeding a motor that has two separate windings for each phase. Note that this is not a six-phase motor, as it has three pairs of windings, each electrically displaced by 120°. A true six-phase motor would have six windings, each displaced by 60°. The key to achieving 12-pulse operation is to shift the relative phase of the two converters by 60° so their pulses are effectively interleaved, with one converter providing the six odd-­ numbered pulses and the other providing the six even ones. This relative phase shift is obtained by wiring one of the transformer secondaries in star configuration and the other in delta. By the way, it is not a huge difficulty to use a special 2×3-phase motor in these circumstance, since the motor and transformers will almost certainly be custom designed and built for the application. You don’t get 20MW motors or transformers off the shelf! The circuit on the right is a 12-pulse cycloconverter with a standard threephase output. In this case, the star-fed and delta-fed six-pulse converters are connected in series, and the stacked pairs are star-connected, just like the six-pulse converter in Fig.4(b). Other arrangements are possible. Why would we go to the complexity of using a 12-pulse cycloconverter when a three-pulse or six-pulse one will do the job? The first reason is that the larger configurations spread the switching out over many more power devices, resulting in lower device stress. Remember that we are dealing with many megawatts; 10,000A per phase is not uncommon. Secondly, the higher the pulse number, the higher we can make the cycloconverter’s maximum output frequency, the lower the torque ripple, and the higher the efficiency. It all comes down to harmonics – a higher siliconchip.com.au Figs.5(a) & (b): these twelve-pulse cycloconverters like these can be used to drive AC motors in the 10-50MW range for applications like ship propulsion, rotary cement kilns and SAG mills. pulse number reduces the harmonics on both the input and the output of the converter. We already know that on the input side, higher harmonic content means a lower power factor, and this impacts the sizing of the switchgear and transformers in the supply network. On the load side, higher harmonics mean higher motor losses, as the motor is the output filter (or a very large part of it) – and only the fundamental current contributes to useful output torque at the motor shaft. The rest is dissipated as heat or unwanted torque ripple. Harmonics It is way beyond the scope of this article (and my abilities) to attempt to calculate the magnitude of the harmonics of a cycloconverter because they are extremely complex and highly dependent on the application. However, we can get a good feel for them by looking at which harmonics will be produced. We can assume that, in general, the amplitudes of the harmonics fall off as the harmonic number increases. The harmonics on the supply side are influenced by the pulse number siliconchip.com.au and the input frequency. For a p-pulse converter, the input harmonics will occur at frequencies (pn ± 1)fi, where n is an integer from 1 to infinity and fi is the input frequency. A three-pulse converter (p = 3) will have input harmonics at 2fi and 4fi for n = 1, at 5fi and 7fi for n = 2 and so on. A 12-pulse converter will have input harmonics at 11, 13, 23, 25... times fi. The lowest input harmonic present for the 12-pulse cycloconverter is the 11th, compared with the fifth for a sixpulse converter and the second for a three-pulse converter, so the difference is significant. The cycloconverter’s output will have harmonics related to the output frequency, plus those related to the input frequency, because these converters have no internal energy storage to decouple the two. The output is effectively modulated by the input, so the output harmonics contain the ‘beat’ (or sideband) frequencies that result from the two interacting. The expression for the output harmonic frequencies is pn fi ± mfo, where and fi is the input frequency, fo is the output frequency, and both m and n are integers with the condition that pn + m is odd. Australia's electronics magazine For a three-pulse cycloconverter, there will be output harmonics at the frequencies 3fi, 3fi ± 2fo, 3fi ± 4fo, 3fi ± 6fo… for n = 1, 6fi, 6fi ±fo, 6fi ± 3fo, 6fi ± 5fo… for n = 2 and so on. A 12-pulse has harmonics at frequencies 12fi, 12fi ± 2fo, 12fi ± 4fo, 12fi ± 6fo… for n = 1, 24fi, 24fi ± 1fo, 24fi ± 3fo, 24fi ± 5fo… for n = 2 and so on. Because of the sidebands, some harmonics may have a frequency below the input frequency, fi. These subharmonics cannot be filtered by the motor inductance and can result in potentially dangerous or damaging subharmonic oscillations in speed and torque. We want to avoid them if we can, or at least be sure their amplitude is very low. It is this phenomenon that dictates the maximum output frequency of cycloconverters in most cases. Isolated high-frequency cycloconverters There is another application of cycloconverters that is perhaps a bit more relatable, one sometimes used in grid-tied solar inverters. These typically use Mosfet switches that we can turn on and off at will, so we drop the ‘naturally commutated’ label. August 2026  67 A simplified example is shown in Fig.6. The circuit is fed with a high-­ frequency AC current source, usually derived from a resonant DC-AC converter. The input current passes through a high-frequency transformer to provide isolation from the power grid. A blocking capacitor, Cb, prevents the mains frequency from reaching the transformer. The load is the grid, shown here as a voltage source with a peak amplitude of Vg and a frequency of ωg. During the positive half-cycles of the grid voltage, Mosfets Q3 and Q4 are switched on as depicted in the top graph. Q1 and Q2 are switched complimentarily with a 50% duty cycle at the rate of the high-frequency source. When Q1 is on and Q2 off, the current sourced from the transformer is connected to the load. This current, io, flows into or out of the load and returns via Q4. When Q2 is on and Q1 off, the transformer secondary current circulates via Q2 and Q3. We can therefore control which parts of the sinusoidal secondary current we pass to the load. If Q1’s on-time coincides with a positive half-cycle of the high-frequency current, a positive half-cycle of current would be pushed towards the load. You can see this happening in the middle of the lower graph in Fig.6. If Q1’s on-time coincided with a negative half-cycle of the source current, a full negative half-cycle of current would be passed to the load. By controlling the phase of Q1 and Q2’s switching with respect to the high-­ frequency current, we can deliver partial cycles with any average value between the two extremes. In this example, we control the phase shift to ensure that the average current ‹io› is sinusoidal and in phase with the grid voltage, as shown in the lower chart in blue. The LC filter smooths this current to produce the grid current, ig, shown in green. During the negative grid voltage half-cycle, the whole process repeats, but this time Q1 and Q2 are always on, while Q3 and Q4 are switched complimentarily to shape the negative half-cycle current. The resulting current is sinusoidal and in-phase with the grid voltage, meaning a unity power factor at the grid interface. If the switching frequency is fairly high, the filter components can be quite small. This is a cycloconverter because it operates on the principle of ‘stealing’ bits of the high-frequency source to synthesise a lower-frequency AC waveform. The difference here is that we are doing it with current rather than voltage, and that we can turn switches off whenever we want. Matrix converters Earlier, we looked at cycloconverters Fig.6: the isolated highfrequency cycloconverter is sometimes used in grid-tied inverters to ensure the power factor at the grid interface is unity. Fig.7: the matrix converter uses bidirectional controllable switches and complex PWM switching strategies to implement direct AC-AC conversion. Practical implementations are rare because it is cheaper and better harmonically to use an AC-DC and DC-AC converter in series. Fig.8: the solid-state transformer (SST) is another AC-AC converter technology that has not really become practical. Mains-frequency transformers are cheaper and more reliable in power distribution applications. as phase-controlled rectifiers because this is the easiest way to understand their operation (at least in my opinion). However, if you look at the three-pulse cycloconverter circuit in Fig.4(a), you might be able to see it in another light. The circuit consists of nine pairs of back-to-back thyristors, one pair connected between each input phase and each output phase. We can think of this as a kind of switch matrix. Building on this idea, if we could use some kind of bidirectional fully controllable switch in place of each thyristor pair, we could connect any input phase to any output phase at any point in time (subject to not shorting the input or output phases together) to synthesise the output of our choosing. This is known as a matrix converter (Fig.7) and was proposed in the 1980s. The switches can be controlled using high-frequency PWM to generate a variable three-phase output without some of the limitations of cycloconverters. For example, we can improve the harmonics by using higher frequency switching and economical filters, although we won’t escape the beat-frequency problems because there is no DC link storage element to decouple the input and output. It is a complex device to implement because we do not have bidirectional fully controllable semiconductor switches. We would have to use nine pairs of Mosfet or IGBT switching elements and associated floating gate drivers to implement the circuit. A power-factor-corrected threephase rectifier and a three-phase bridge can do exactly the same job while being less complex and having better harmonic performance, so you just don’t see practical matrix converters. They are nonetheless beloved by academics, so they appear in all the textbooks and they seem to have inspired plenty of research papers describing novel switching algorithms. It is an interesting rabbit-hole to explore if you are so inclined. Solid-state transformers The solid-state transformer (SST) was first proposed and patented by William McMurray (a truly famous name in power electronics) in the 1960s. This circuit, shown in Fig.8, modulates the incoming AC waveform at a high frequency and demodulates it on the other side of a high-frequency transformer to reconstruct the original waveform. I have drawn the circuit as McMurray described it, with a centre-tapped transformer and two switches on either side, but you could equally use a transformer with single windings and a full bridge on either side. McMurray envisioned SSTs taking over from conventional transformers in power distribution systems due to their reduced size, but unfortunately, it was not to be. They require bidirectional switches, which means eight devices with isolated drive circuits (or 16 if you use a full bridge on either side) so they are just not as cost-effective or reliable as a conventional passive mains-frequency transformer. Low cost and high reliability are close to the top of the wish list for power distribution systems, so the idea never took off. Conclusion That’s it for AC-AC converters. At the very top end of the power range, the cycloconverter is hard to beat, but in most other applications, combining AC-DC and DC-AC converters is a far SC better option. Back Issues The UK ’s Circui t Pr Electractical onics fT sTa r TE r premier electron ics so and Underst Surgery using anding and gyrato rs Make computin g ma ker ma Mrom Finishin h Mic E Th g gazine light con the PicoMite ite E ‘sP La troller T’ aT Audio softwar smart e Designi Out sw iTc h- on discreteng a practic ! al audio op am a Mi p GPS-Sy Analog nchronise ue Cloc d k it wit Ta 6- d Ec WIN M mTo ICRO A CH u Dev ch AR IP elo 10 adE pm 00 LLionPico r Es Kit ent PrEc MisE VaLU ite smis Ta n c Es Tolight E b ox finECont art YoUr TUnErolle dEsiG r ns WIN! Microch ip Inte grat Graphic ed sE s and Touch M CuriTE osity sT – Pa luation bUEva iLd Kit an rT 3 d Us siL ic E oU on ch r ULTiM Ec kE aT E r Jump start Mini LE Driver D Egg Tim er – eg to pe gcellen rfectio t brea n! kf ast, tim Compl PLUS! APRIL 13 Cover.in dd 1 ractica lelec practic ed etin g WideTechno range the Tal inter Cool Bea k – My tru face, Ohmmet th, you ne r truth techn Net Wo ns – Arduin er and AI o tal t work, cir o Boo rk – Rou k, pic ters, pow tcamp: new n’ mix cuit Surg www.e bo er sup Sep 202 ery, re lectron plies, TEM ards update 3 £5.9 adout, publish 9 ! U and ing.co 09 more m 9 7726 <at>p 32 5730 30 alelec APRIL 201 3 £4.40 tronics Practical Electronics is the UK’s premier electronics, computing & maker magazine. Each month has a wide variety of electronics projects suiting beginners and experts alike. It also includes many different features on topics like audio, radio, computers and more. 14/02/2 013 10:33:4 7 24 YEAR COLLECTION OF PRACTICAL ELECTRONICS Every issue of Practical Electronics published from January 2000 to December 2023. 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