Transformers
Introduction
For those brave souls who have ploughed their way through the first section - I commend you! As you have discovered, transformers are not simple after all, but they are probably far more versatile than you ever imagined. They are, however, real world devices, and as such are prey to the failings of all real components - they are imperfect.
This section will concentrate a little more on the losses and calculations involved in transformer design, as well as explain in more detail where different core styles are to be preferred over others. Again, it is impossible to cover all the possibilities, but the information here will get you well on your way to a full understanding of the subject.
The first topic may seem obvious, but based on the e-mails I get, this is not the case. Transformers can have multiple windings, and these can be on the primary or secondary. Windings can be interconnected to do exciting and different things, but from a safety perspective it is imperative that primary and secondary windings are kept segregated.
There are several references to "shorted turns" within this article. If any two turns of a winding short to each other, the current flow is limited only by the DC resistance of the shorted section of the winding. The current flow is enormous, and with even one shorted turn, the transformer is no longer serviceable and must be discarded or rewound. No shield or other conductive material may be wrapped around a core and joined, as this creates a shorted turn capable of possibly hundreds of amperes. The exception to this is the magnetic shield sometimes used with E-I laminated transformers, but this is wrapped around the entire transformer, and is not considered as a "turn" as it is not in the winding window with the primary and secondary.
It is also worth noting that a transformer behaves quite differently depending upon whether it is driven from a voltage source (i.e. very low impedance, such as a transistor amp or the mains) or a current source or intermediate impedance. This will be covered in a little more detail further on in this article.
Three things that you need to keep in mind - always ...
- Core flux is at maximum when a transformer has no load.
- A transformer wound for 50Hz operation can safely be used at 60Hz (with the correct or even slightly higher voltage).
- A 60Hz transformer will draw excessive magnetising current at 50Hz, and may fail due to overheating.
8. Windings in Series and Parallel Many transformers are supplied with two (or more) secondaries. In many cases, the data sheet will indicate that the windings may be connected in parallel or series. For example, a toroidal transformer may be rated at 2 x 25V at 5A (250VA). With the windings in parallel, the available current is 10A, but only for a single voltage of 25V AC. Connect the windings in series, and you get 50V at 5A, or by referencing the centre tap to earth, the familiar 25-0-25 designation.
Figure 8.1 - Windings in Series and Parallel
Antiphase wiring will not harm a transformer when wired in series (although the zero volts output for equal windings is somewhat limited in usefulness). Parallel antiphase connection will destroy the transformer unless the fuse blows - which it will do mightily. Always use a fuse when testing, as a simple mistake can be rather costly without some form of protection for the transformer and house wiring!
8.1 Series Connections Windings may be connected in series regardless of voltage. The maximum current available is the rating specified for the lowest current winding. Windings may be connected so as to increase or decrease the final voltage. For example, dual 25V windings may be connected so as to produce 50V or zero volts - although the latter is not generally useful :-)
When windings are connected in phase the voltages add together, and if connected out of phase, they subtract. A 50V, 1 amp winding and a 10V 5 amp winding may therefore be connected to provide any of the following ...
- 10V @ 5A - The 10V winding by itself
- 50V @ 1A - The 50V winding by itself
- 60V @ 1A - Both 50V and 10V windings, connected in series and in phase
- 40V @ 1A - Both 50V and 10V windings, connected in series and out of phase
8.2 Parallel Connections Parallel connection of transformer windings is permitted in one case only - the windings must have exactly the same voltage output, and must be connected in phase. Different current capacities are not a problem, but it is rare to find a transformer with two windings of the same voltage but different current ratings.
Even a 1V difference between winding voltages will cause big problems. A typical winding resistance for a 5A winding might be 0.25 ohm. Should two such windings be connected in parallel, having a voltage difference of 1V, there will be a circulating current limited only by the resistances of the windings. For our example, the total winding resistance is 0.5 ohm, so a circulating current of 2A will flow between the windings, and this is completely wasted power. The transformer will get unexpectedly hot, and the maximum current available is reduced by the value of the circulating current.
Should the windings be connected out of phase, the circulating current will be possibly 100A or more, until the transformer melts or the fuse blows. The latter is generally to be preferred.
The transformer manufacturer's specifications will indicate if parallel operation is permitted. If you are unsure, measure the voltages carefully, and avoid parallel connection if the voltages differ by more than a couple of hundred millivolts. There will always be a difference, and only the manufacturer's winding tolerances can predict what it will be. With toroidal transformers, the windings are often bifilar, meaning that the two windings are wound onto the transformer core simultaneously. The tolerance of such windings is normally very good, and should cause no problems.
9. Valve Output Transformer Example Calculation In Section 1, I described a very basic push-pull valve output stage. Now it is time to examine this a little more closely. We shall use the same voltages as were obtained in the basic description of Section 1 - an RMS voltage of 707V. It must be said that the following is not intended to be an accurate representation of valves, as the losses in real life are somewhat higher than indicated here. This is for example only. We shall also take the (typical) losses as 10%, and adjust the secondary impedance accordingly.
A valve (tube) amplifier is required to drive an 8 ohm loudspeaker. The primary impedance (called the Plate-Plate impedance for a push-pull amplifier) is 6,000 Ohms, and the supply voltage is 600V. Allowing for losses of 100V across each valve, the maximum voltage swing on the plates (anodes) of the valves is 1kV p-p (or effectively 2kV peak to peak on the transformer primary). What is the output power?
Secondary impedance will be 7.2 ohms, based on the 10% loss ...
Zs = 8 / 1.1 = 7.2 ohmsThe impedance ratio is calculated first ...
Z = 6,000 / 7.2 = 833The turns ratio may now be determined
N = √833 = 28.8 (29:1)The voltage ratio is the same as the turns ratio, so the peak to peak voltage to the speaker is
Vs (p-p) = Vp / N = 2,000 / 29 = 69VTo convert this to RMS ...
Vp = 1/2 Vp-p = 34.5VNotice that at each calculation, the figures were rounded to the closest (or next lowest) whole number. This was for convenience, but the way I did it also gives a conservative rating that is more likely to be met in practice.
RMS = peak * 0.707 = 24V
Power is therefore 24² / 8 = 72W
Ouch! Sorry, that was a bit nasty for this time of day
.
A bit nasty or not, it is a reasonable representation of the reality of an output transformer design, but naturally real (as opposed to my "invented" figures) will be substituted. Typically the losses across the output valves will often be far greater than indicated here. but that depends on the valves used (and the topology - triodes behave very differently from pentodes or tetrodes).
Just to complete this section and to put the above into perspective, I have included a few figures (taken from the 1972 Miniwatt Technical Data manual) for the EL34/ 6CA7 power pentode - quite possibly the world's all-time favourite output valve.
| Class | Mode * | Plate Volts |
Plate Current | Screen Volts | Screen Current |
Grid Bias | Load Impedance | Power Output |
Comments |
| Class-A | S-E | 250 | 100 | 265 | 15 | -13V | 2,000 | 11W | Plate supply = 265V, THD** 10% |
| Class-AB | P-P | 375 | 2 x 75 ## 2 x 95 |
365 | 2 x 11.5 2 x 22.5 | -19V | 3,400 (p-p) # | 35W | Cathode bias resistor 130 ohms, common screen resistor, 470 ohms, THD 5% |
| Class-B | P-P | 775 | 2 x 25 2 x 91 |
400 | 2 x 3.0 2 x 19 | -39V | 11,000 (p-p) | 100W | Plate supply, 800V, THD 5% |
| Class-A (Triode) | S-E | 375 | 70 | - | - | -25V | 3,000 | 6W | Cathode bias resistor 370 ohms, Screen tied to plate, 400V plate supply, THD 8% |
| Class-AB (Triode) | P-P | 400 | 2 x 65 2 x 71 |
- | - | -28V | 5,000 (p-p) | 16W | Screen tied to plate, Cathode bias resistor 220 ohms, THD 3% |
* | S-E: Single Ended, P-P: Push-Pull |
| ** | THD - Total Harmonic Distortion (this is for the valves only, and does not include transformer distortion) |
| # | p-p: Plate to Plate impedance |
| ## | First figure is no load, second figure is full power |
This will be revisited in another article on the design of valve amplifiers.
10. Compromises It is very important that the core does not saturate (see below), since there will be no variation of flux, no back EMF, and excessive current will be drawn - especially at no load. The final design of any transformer is a huge compromise, and there is a fine line between a transformer that will give acceptable regulation and one that gets too hot to touch at no load.
Somewhat surprisingly, the flux density in the core actually decreases with increased load current drawn from the secondary. Even though the primary is drawing more current, this is transferred to the secondary and thence the load - it does not cause the flux density to increase. The flux density decreases largely due to primary resistance, which causes the effective primary voltage to decrease. Any voltage lost to resistance (remember Ohm's law?) is voltage that is "lost" to the transformer, and serves no function in the transformation process. It does cause the transformer to get hot (or hotter) than at no load.
Also, the normal variation of mains voltage must be allowed for. A transformer running at the very limit of saturation at nominal supply voltage will overheat if the mains is at the upper (normal) limit. A transformer that is designed to run at the limit will have superior regulation compared to a more conservative design, but this is of little consequence if it fails in normal use.
For audio transformers, there are even more compromises.
11. Losses As discussed earlier, a transformer is a real component, and therefore has losses. These are divided into two primary types, but there are other "hidden" losses as well. All losses reduce efficiency, and affect frequency response. The low frequency limit is determined by the primary inductance, and this is proportional to the area (and consequent mass) of the transformer core. High frequency losses are caused by eddy currents in the core (see below), and by leakage inductance and winding capacitances.
None of these can be eliminated, but by careful selection of core material, winding style and operational limits, they can be reduced to the point where the transformer is capable of doing the job required of it.
11.1 Iron (Core) Losses Core losses are partly the result of the magnetising current, which must keep forcing the magnetic field in the core to reverse in sympathy with the applied signal. Because the direction of flux is constantly changing, the transformer core is subject to a phenomenon called hysteresis, shown in Figure 11.1
Figure 11.1 - The Hysteresis Loop
Figure 11.2 - B-H Curve
Figure 11.3 - Cutaway View of a Transformer
In addition, there are so-called "eddy current" losses. These are small circulating currents within the magnetic core, as shown (exaggerated) in Figure 11.4, and these cause the core material itself to get hot. Each of these eddy current loops acts as a tiny shorted turn to the transformer, and to reduce the effect, the core is laminated - i.e. made from thin sheets of steel, insulated from each other. The thinner the laminations, the smaller are the eddy current losses, but they will never be eliminated. Eddy current losses increase with frequency, requiring different techniques for high frequency operation, and are the major contributor to the iron losses in any transformer.
Figure 11.4 - Eddy Currents in Laminations
Iron losses of both types are the primary source of losses in any transformer that is operating at no load or only light loading. At no load, the core flux density is at its maximum value for any given applied voltage / frequency combination. Power transformers are usually designed to operate below the knee of the saturation curve (this is essential with toroidal types), with sufficient safety margin to ensure that the core can never saturate.
Saturation involves a dramatic loss of permeability (and therefore inductance), and causes the primary current to rise disproportionately to an increase of voltage. Significant waveform distortion occurs once the core starts to saturate.
As a load is drawn from the secondary, the primary must supply more current, and this means that the resistance of the primary winding becomes significant. Any voltage 'lost' to winding resistance is effectively no longer part of the applied voltage, so core flux is reduced.
11.2 Copper Losses Following on from the previous point, the voltage lost to winding resistance is copper loss, and all such losses must be dissipated as heat. Consider a transformer at idle, with 240V on the primary. The primary resistance may be in the order of 5 ohms, and the idle current perhaps 20mA. The loss is determined by the normal power formula, and in this case is ...
P = I² * R = 0.02² * 5 = 2mWFor all intents and purposes, the full 240V is applied to the primary. When the transformer is loaded, this changes. Let's assume 1A primary current and look at the figures again ...
V = R * I = 5 * 0.02 = 100mV
P = I² * R = 1.00² * 5 = 5WNow, the effective primary voltage is only 235V, because 5V is 'lost' due to winding resistance. Naturally, if the voltage is lower, the flux density must also be lower.
V = R * I = 5 * 1.00 = 5V
Minimising copper loss in both primary and secondary is essential, but there are limits to what can be achieved. These are imposed by the available space for the winding, and just how much copper the manufacturer can get into that space. Allowance must still be made for insulation and manufacturing tolerances.
You may see that in Figure 11.3 the windings are shown stacked directly on top of each other. Surely a more efficient winding can be made by making use of the "valleys", minimising the winding height and allowing heavier windings. Ah, if only life were that simple! The windings are traditionally made from left to right, then right to left, so the turns in each layer are at a slight angle relative to the layer below or above. It is therefore not possible to utilise the inter-turn winding valleys properly, and if you were to design a transformer based on the erroneous assumption that this would work, the winding would not fit into the window.
For the normal layered construction (i.e. primary closest to the core, and secondary over the top), we also have to allow for insulation between primary and secondary, and in some cases additional insulation is used between layers of larger transformers because of the large voltage difference between the outer limits of each winding. These are another set of compromises that must be made, all of which mean that the windings must be thinner than we might like, and thus the losses are increased.
Because any length of wire has resistance, there will always be winding resistance. The greater the resistance for a given current, the more power is dissipated as heat - this is a complete loss. At no load, there is virtually no loss, since the currents are low, but as secondary current increases, so too do the copper losses.
Current Density
The current density allowable for the copper windings is a somewhat variable figure. Current density refers to the current in Amps per unit of wire area, for example 2.565A/mm² (a reference standard used in Australia and presumably elsewhere as well). Increasing the current density has a major effect - it causes the wire to get hotter for a given current. Side forces caused by the magnetic fields generated between each turn need to be considered in large power distribution transformers, especially under short-circuit conditions where the forces can be destructive. There is no such thing as a "typical" current density, because different manufacturers use different design criteria. In general, it's better to keep current density below 3.0A/mm² and 2.5A/mm² is even better. Naturally, a lower current density means that the transformer is larger and heavier than one operated at a high density, and ultimately it's all a trade-off against temperature rise and cost.
For many transformers used in audio, the current density can often be expected to be somewhat higher than one might prefer. This is because exceptionally high efficiency is not needed, and the demands from normal music programme material has a rather low average value. As a result, transformers for power amplifiers (for example) are rarely operated at continuous full load - they are more likely to be run with short term overloads, but at perhaps 50% full load on a long-term average basis when operated at the onset of clipping with "typical" programme material.
I took a few measurements on transformers I have to hand, and found that with toroidals in particular, there is a common trend. The current density of the primary is comparatively low, averaging around 2.1A/ mm², while the secondaries all used a much higher current density - around 4.8A/ mm². This makes sense, because the secondary is on the outside and has the advantage of better cooling than the primary. The primary winding can only get rid of heat through the secondary winding, which stands between the winding and cooling air. This may be less of a problem with E-I cores, because the core itself acts as a heatsink (although not a very efficient one).
Small transformers are likely to be operated at higher current densities than larger ones, and this is reflected in that fact that they get hotter and (almost always) have worse regulation. A current density of up to 3.5A/ mm² is typical of some smaller transformers. One reason for this is that it becomes extremely difficult to fit the number of turns needed into the space allowed. The main reason is that the insulation requirements don't change, so insulation takes a larger percentage of the winding space with small transformers than with larger examples.
Guitar amplifiers (and any other that is regularly operated into heavy distortion) should have a transformer rated for at least double the nominal 10% THD output power. Thus a nominal 100W amp needs a 200VA transformer as the bare minimum. This is especially important for valve amplifiers, because they are already operating in a hotter than normal ambient due to the heat from the valves themselves. Regrettably, this is regularly ignored, with the result that some amps have a reputation for burning out mains transformers.
Note that skin effect can be ignored for mains frequency transformers (50/ 60Hz), but is a significant problem with high frequency switching transformers. These are not covered here - the information in this article is based almost exclusively on transformers used at low frequencies where skin effect has little or no impact.
Copper loss is the primary source of loss at any appreciable power from a transformer. Conventional rectifiers as used in semiconductor amplifier power supplies cause the resistance to be more significant than would otherwise be the case. See Linear Power Supply Design for more details on these losses, which cause regulation to be much worse than expected.
Ultimately, copper losses limit the power available from a transformer. Since all copper loss results in heat, this becomes a limiting factor, so once you reach the point where the temperature rise cannot be limited to a safe value, the size of the core must be increased. This allows the manufacturer to use fewer turns per Volt, and the larger core has more space for the windings. The wire size can therefore be increased, so copper losses are brought back to the point where overheating is no longer a problem. This process continues from the smallest transformers to the largest - each size is determined by the VA rating and allowable temperature rise.
Keeping a transformer as cool as possible is always a good idea. At elevated temperatures the life of the insulation is reduced, and the resistance also increases further because copper has a positive temperature coefficient of resistance. As the transformer gets hot, its resistance increases, increasing losses. This (naturally) leads to greater losses that cause the transformer to get hotter. There is a real risk of drastically reduced operational life (or even localised "hot-spot" thermal runaway) if any transformer is pushed too far - especially if there is inadequate (or blocked) cooling.
It is generally accepted that any transformer will have one part of the winding that (for a variety of reasons) is hotter than the rest. It's also a rule of thumb that the life expectancy of insulation (amongst other things) is halved for every 10°C (some claim as low as 7°C). When these two factors are combined, it is apparent that any transformer operated at a consistently high temperature will eventually fail due to insulation breakdown. The likelihood of this happening with a home system is small, but it's a constant risk for power distribution transformers. Despite all this, mains frequency iron cored transformers typically outlast the product they are powering, and even recycled transformers can easily outlast their second or third incarnation. Once a transformer is over 50 years old I suggest that the chassis be earthed, as the insulation can no longer be trusted at that age.
Fan cooling can increase the effective VA rating of a transformer significantly, but does not improve regulation. Large power distribution transformers are almost always oil cooled, and they are now starting to use vegetable oils because they are less inclined to catch on fire, and pose minimal environmental impact should there be a coolant leak or other major fault.
11.3 Regulation Copper loss is responsible for a transformer's regulation - the ratio of voltage at no load versus full load. Regulation is almost always specified into a resistive load, which considering the way nearly everyone uses transformers, is virtually useless. It is rare that any transformer is operated into a purely resistive load - the vast majority will be used with a rectifier and filter capacitors, and the manufacturer's figure is worthless. Actually, it is worse than worthless, as it misleads the uninitiated to expect more voltage than they will obtain under load, and causes people grief as they try to work out why their amplifier (for example) gives less power than expected.
Naturally, there are some to whom any measurement is sacrilege, so none of this applies to them
The output voltage is (nearly) always specified at full load into a resistance. So a 50V, 5A transformer will give an output of 50V at a sinewave output current of 5A. If the regulation of this transformer were 4%, what is the no-load voltage?
The answer is 52V. Regulation is determined quite simply from the formula ...
Reg% = ( VN - VL) / VL * 100 / 1Where VN is no-load volts, and VL is loaded volts.
As determined earlier, this assumes a sinusoidal output current, and this just does not happen with a rectifier / filter load. It may be found that this same transformer has an apparent regulation of 8 to 10% when supplying such a load. See Linear Power Supply Design for more information on this topic (there is little point in doing the article twice :-)
The regulation with rectifier loads is a complex topic, but you will need to know the ramifications before you start construction of your latest masterpiece, rather than find out later that all your work has resulted in much lower output power than you expected. Not that you can change it for any given transformer, but at least you will know what to expect.
To gain a full understanding of regulation requires a lot more information than I can provide in a simple web page, but a crucial factor is getting the balance of winding resistances right. If you are making your own transformer you'll do this as a matter of course, but will a manufacturer (in the "far-East") go to the trouble? I'm not about to debate that point. If we determine from the specification that regulation is (say) 6% for a reasonable sized transformer (around 500VA), we can work out everything we need to know.
Knowing the regulation and voltage, we can calculate the effective winding resistance. A 50V transformer with 6% regulation will give us 53V at no load, and 500VA at 50V means 10A - all very straightforward. We lose 3V at full current, so the total effective winding resistance must be ...
Rw = V / I = 3 / 10 = 0.3 OhmsHalf of this resistance is in the secondary, and the other half is reflected from the primary, based on the impedance ratio. As you will recall, this is the square of the voltage ratio. If we assume a primary voltage of 230V, output voltage of 50V at 10A, we already know that the unloaded output voltage is 53V. The turns and impedance ratios (TR and ZR respectively) are therefore ...
TR = VIN / VOUT = 230 / 53 = 4.34:1Knowing this, we can determine the optimum winding resistance for each winding. Since half of the resistance is that reflected from the primary (Rp), the secondary resistance (Rs) is 0.15 ohms, being half of the total. Primary resistance must be ...
ZR = TR² = 4.34² = 18.83:1
Rp = Rs * ZR = 0.15 * 18.83 = 2.82 OhmsBased on all that, it is now possible for the designer to determine the appropriate wire gauge for the number of turns needed for the core size. The ideal case is that the resistive (copper) losses should be as close as possible to identical for both windings, and this is why we worked out the resistance. At full load, dissipation (copper loss) is 15W for each winding (almost exactly) at full load. Total dissipation is therefore 30W, and the transformer efficiency is 94.3% ...
Eff (%) = POut / Ptot * 100 / 1 = 500 / 530 * 100 / 1 = 94.34%It may not be immediately obvious, but there is a very good reason for keeping the primary and secondary copper losses equal. Any core only has a limited space for the windings, and this space must be used as efficiently as possible. It follows that if one winding is thicker than necessary, the other has to be thinner so it will fit in the space allowed. This invariably leads to total losses that are greater than would be the case if the resistance is optimised as described. In the case of toroidal transformers, there is good reason to keep primary losses lower than secondary losses, because the primary winding is trapped inside the secondary winding and heat can only escape through the outer layers. The toroidal core doesn't act as a heatsink either, because it's inside all the windings.
| VA | Reg % | RpΩ - 230V | RpΩ - 120V | Diameter | Height | Mass (kg) |
| 15 | 18 | 195 - 228 | 53 - 62 | 60 | 31 | 0.30 |
| 30 | 16 | 89 - 105 | 24 - 28 | 70 | 32 | 0.46 |
| 50 | 14 | 48 - 57 | 13 - 15 | 80 | 33 | 0.65 |
| 80 | 13 | 29 - 34 | 7.8 - 9.2 | 93 | 38 | 0.90 |
| 120 | 10 | 15 - 18 | 4.3 - 5.0 | 98 | 46 | 1.20 |
| 160 | 9 | 10 - 13 | 2.9 - 3.4 | 105 | 42 | 1.50 |
| 225 | 8 | 6.9 - 8.1 | 1.9 - 2.2 | 112 | 47 | 1.90 |
| 300 | 7 | 4.6 - 5.4 | 1.3 - 1.5 | 115 | 58 | 2.25 |
| 500 | 6 | 2.4 - 2.8 | 0.65 - 0.77 | 136 | 60 | 3.50 |
| 625 | 5 | 1.6 - 1.9 | 0.44 - 0.52 | 142 | 68 | 4.30 |
| 800 | 5 | 1.3 - 1.5 | 0.35 - 0.41 | 162 | 60 | 5.10 |
| 1000 | 5 | 1.0 - 1.2 | 0.28 - 0.33 | 165 | 70 | 6.50 |
Taking the 500VA example again, and assuming a 230V primary and a dual 50V secondary winding (100V total), the total secondary resistance is ...
TR = Vp / Vs = 230 / 100 = 2.3If the primary resistance is 2.8 ohms (from the table), then the secondary resistance must be approximately ...
ZR = TR² = 5.29
Rs = Rp / ZR = 2.8 / 5.29 = 0.53 OhmThe resistance of each half of the secondary winding is naturally half of the total.
Note: Because of the common practice of using different current densities for the inner (primary) and outer (secondary) wire, this will skew the figures shown here slightly. The figures determined above are based on a theoretical "ideal" case, but this will rarely translate into reality due to the inevitable "fudge factors" that are applied to real world parts. Basic tests I've run indicate that the above figures are more than satisfactory for a quick check of the expected resistances. As a very basic rule, expect the primary resistance to be a little less than calculated, and the secondary resistance will be a little higher.
11.4 Other Losses Since the transformer is not an ideal device, it has unwanted properties apart from the losses described so far. The other losses are relatively insignificant for a power transformer, but become difficult to manage for transformers intended for wide bandwidth, such as microphone transformers and valve output transformers.
Figure 11.5 - Transformer Simplified Equivalent Circuit
In addition, there is some amount of the magnetic field that fails to remain in the core itself. This creates a "leakage" inductance (LL) that is effectively in series with the transformer. Although small, it tends to affect the high frequencies in particular, and is especially troublesome for audio output transformers. This is typically measured with an inductance meter, with the output winding short circuited. Any inductance that appears is the direct result of leakage flux.
Lp is the primary inductance, and as you can see, there is a resistor in parallel (Rp). This represents the actual impedance (at no load) presented to the input voltage source, and simulates the iron losses. The series resistance (Rw) is simply the winding resistance, and is representative of the copper losses as described above.
Cp-s is the inter-winding capacitance, and for power transformers can be a major contributor to noise at the output. This is especially irksome when the transformer is supplying a hi-fi system, and mains borne noise gets through and makes horrid clicks, electronic "farts", electric motor whine, and various other undesirable noises in the music. Toroidal transformers are very much worse than conventional (E-I) transformers in this respect, because of the large area of each winding. An electrostatic shield will all but eliminate such noises, but these are expensive and uncommon with toroids (pity).
Another problem exists when the capacitance between primary and secondary is high - electrical noise on the primary is coupled through the capacitance to the secondary. This can lead to mains noise getting through the entire power supply and into the amplifier in extreme cases. To combat this problem, an electrostatic shield is sometimes used, and this is connected to earth. Note that the shield cannot be joined in a complete circle around the winding, as this would create a shorted turn that would draw a tremendous current and burn out the transformer.
There is a technique that is used for valve output transformers, shown in Figure 11.6 - you will not find this method used in power transformers, as it is completely unnecessary.
Figure 11.6 - Interleaved Winding for Extended HF Response
The capacitance between the primary and secondary can become troublesome with this technique, and although possible, an electrostatic shield (actually, a number of electrostatic shields may be needed) adds considerably to the cost, but creates a minimal overall benefit. This winding method is not used (or needed) with low frequency power transformers, and would lead to greatly reduced electrical safety because of the difficulty of insulating each section from the next. This problem also exists with an output transformer, but is easier to control because one side of the secondary is earthed and the internal DC is already isolated from the mains.
11.5 Temperature Classes All the losses add together to increase the temperature of a transformer. Insulation materials (wire enamel, inter-layer insulation, formers and/or bobbins, tape overwinds, etc.) all have limits to the maximum safe temperature. It should come as no surprise that the high temperature materials are considerably more expensive than lower temperature grades, and as always there is a trade-off (compromise) between minimising losses for cool running or reducing the size and weight at the expense of greater losses and higher temperature operation.
There are several internationally recognised temperature grades, as well as one that is recognised by the authorities, but the class designation is not universally accepted. Temperature is specified as either an absolute maximum figure, temperature rise, or both. The standard classes are ...
| Class | Max. Temp. | Temp Rise |
| A | 105 °C | 60 °C |
| E | 120 °C | 75 °C |
| B | 130 °C | 80 °C |
| F | 155 °C | 100 °C |
| H | 180 - 200 °C | 125 °C |
| C (not global *) | 220 °C | 160 °C |
It's inevitable that transformers in use will get hot, and it is up to the equipment designer to ensure that the insulation class is adequate for reliable operation over the life of the equipment. Unless stated otherwise, you can expect that nearly all commercial off-the-shelf transformers intended for DIY applications will be Class-A (105°C maximum temperature). Higher temperatures are not recommended anyway, for the simple reason that having a transformer at (say) 100°C will transfer its heat to transistors, electrolytic capacitors and all other components in the chassis. For this reason alone, specifying a larger than necessary transformer not only reduces temperatures, but improves regulation as well.
12. Some Measurements I measured the characteristics of a small selection of transformers to give some comparative data. I excluded regulation from this, as it is difficult to make a suitable variable load, and loads tend to get rather hot even with short usage. Most manufacturers will provide this information in their specifications, but be warned that this refers to a resistive load, and regulation will be much worse when supplying a conventional rectifier and filter capacitor (see above, and the Power Supply Design article for more details). It is also worth noting that an inductance meter is often of little use with large iron cored transformers, unless it operates with a sinusoidal waveform at (or near) the design frequency of the transformer. The inductances shown are calculated, since the measured values with my meter were a long way off.
| Type | Rating | Inductance | Resistance | Turns/Volt | Magnetising | Core Loss | Reactance | Mass (kg) |
| Toroidal | 500VA | 34.7 H | 2R4 | 2 | 22mA | 5.28W | 10.91k ohms | 5.0 |
| Toroidal | 300VA | 63 H | 5R1 | 3 | 12mA | 2.88W | 20k ohms | 2.7 |
| E-I | 200VA | 4.36 H | 6R6 | 2 | 175mA | 42W | 1.37k ohms | 3.2 |
It is also worth noting that the mass is lower than for a more "traditional" transformer design - a conventional design of the same power rating would be expected to weigh in at about 5kg.
Figure 12.1 - Current vs. Voltage for the E-I Transformer
Toroids usually have a more pronounced knee, and a correspondingly steeper rise in current once the saturation limit has been reached. This is primarily because of the fully enclosed magnetic path, which has no air gaps at all (E-I laminated transformers have a small but significant gap where the laminations are joined. This is unavoidable in any practical transformer, but has little effect on performance in real life.
12.1 Inrush Current When powered on, many transformers draw a very high initial current. This phenomenon may not be noticeable with smaller transformers, but as the component gets larger (above ~300VA) it tends to occur most of the time. You may see lights dim momentarily when a large transformer is switched on, and now you know why. The core saturates when power is applied, so very high current is drawn until normal operation is established (after around 20 complete mains cycles). The magnitude of the inrush current is a combination of several factors ...
- What was the polarity and magnitude of the mains at switch off
- What is the polarity and magnitude of the mains at switch on
- To what extent has the core de-magnetised itself between events
- Transformer type (toroidals have greater inrush than E-I cores)
- The resistance of the transformer primary and the mains - right back to the sub-station
Figure 12.2 - Transformer Inrush Current
As you can see, the inrush current is one polarity (it could be positive or negative), so superimposes a transient 'DC' event onto the mains. Other transformers that are already powered may also saturate (and often growl) during the inrush period. This is often known as 'sympathetic interaction'. To minimise the effects of inrush current and flow-on effects with other equipment, any toroidal transformer over 300VA should use a soft-start circuit such as that described in Project 39.
13. Core Styles There is a huge array of different core shapes, and each has its own advantages and disadvantages. The two most common for commercial and DIY audio equipment are the E-I "shell" core and the toroidal core, but there are many others.
Ferrites in particular are moulded, and therefore have many specialised shapes to suit various applications, as well as the more traditional shapes shown below.
Toroidal cores are made from a continuous strip grain oriented silicon steel, and are bonded to prevent vibration and maximise the "packing density". It is important that there are no gaps between the individual layers, which will lower the performance of the core. The sharp corners are rounded off, and they are usually coated with a suitable insulating material to prevent the primary (which is always wound on first) from contacting the core itself.
I don't propose to even attempt them all, but one iron core that warrants special mention is the "C" core. These were once very popular, but have lost favour since suitable winding machines became available for toroids. They are still a very good core design, and are especially suited where an intrinsically safe transformer is required (i.e. where the primary and secondary windings are physically separated), and this technique also ensures that the inter-winding capacitance is minimal. C-cores are made by rolling a continuous strip into the desired shape, and after bonding, it is cut in half. To ensure the best possible magnetic coupling (i.e. no air gap), the cut ends are machined and polished as a pair - it is very important to ensure that the two are properly mated or unacceptable losses will occur. The core halves are commonly held together with steel banding, similar to that used for large transport boxes.
Figure 13.1 - C-Core Transformer
C-cores are not as efficient as toroidal cores, but are easier to wind with conventional coil winding machines. The overall efficiency lies between the E-I core and the toroidal.
Figure 13.1A - Double C-Core Transformer
Figure 13.2 - Some Ferrite Core Styles
For maximum transformer efficiency, the stack should be square if possible. A square stack is one where the height of the lamination stack is the same as the width of the centre leg (the tongue), so the centre looks like a square from end-on. This gives the best possible wire resistance for the core size. Thicker and thinner stacks are commonly used, but this is for expedience (or to minimise inventory) rather than to improve performance.
Figure 13.3 - E-I Lamination Stacking
"Yes, but what good is that? The laminations are insulated from each other anyway." The inter-lamination insulation is sufficient to prevent eddy currents, but cannot withstand the mains voltage, so in case of electrical breakdown, the core may become "live" if not earthed.
In order to reduce the radiated flux from an E-I transformer core, you will sometimes see a copper or brass band* wrapped around the winding and the outside of the core, as shown in Figure 13.4. This acts as a shorted turn to the leakage flux only, and greatly reduces magnetic interference to adjacent equipment. Such measures are not needed with toroidal transformers, as leakage flux is very much lower, and the core is completely enclosed by the windings.
(* While I am sure that many people would love to see their local brass band wrapped around a transformer, this is not what I had in mind. It does create an interesting mental picture though
.)
Figure 13.4 - Flux Banded Transformer
Figure 13.5 - Assembled Laminations and Punching Dimensions
13.1 Air Gaps DC flows in the windings for any transformer that is used for "flyback" switching supplies or SET power amplifiers, to name but two. The effect is that the DC creates a magnetomotive force that is unidirectional, and this reduces the maximum AC signal that can be carried before saturation in one direction. Indeed, the DC component may cause saturation by itself, so the transformer would be rendered useless as a means of passing the AC signal without severe degradation. Even the use of a half wave rectifier will introduce an effective DC component into the windings, and these should be avoided at any significant power level (i.e. more than a few milliamps).
To combat this, transformers that are subject to DC in the windings use an air gap in the core, so it is no longer a complete magnetic circuit, but is broken by the gap. This lowers the inductance, and means that a larger core must be used because of the reduced permeability of the core material due to the gap. An air gap also increases leakage inductance because of the flux "fringing" around the gap, and resistive (copper) losses are increased as well, because more turns will be needed.
It is beyond the scope of this article to cover this in great detail, but it does impose some severe restrictions on the design of transformers where DC is present. This is (IMO) one of the biggest disadvantages of the SET amplifier so popular with audiophiles, as it almost invariably leads to unacceptable compromises and equally unacceptable distortion (both harmonic and frequency).
In some designs, it is possible to eliminate the DC component by using a tertiary winding that carries ... DC. If the additional winding can be made to induce a flux that is equal and opposite that of the bias current, then the quiescent flux in the transformer can be reduced to zero (where it belongs). The disadvantage with this is that it requires an extra winding, and that takes up valuable winding space on the core. It is also a difficult technique to get right, and is not often seen these days. It was a popular technique in telecommunications equipment at one time, and meant that smaller transformers could be used for the same (or better) performance.
E-I transformers all have a minuscule "air gap" because of the way the laminations are assembled. With care, this can be almost be considered negligible, but it cannot be eliminated. C-cores will have their cut ends machined to minimise the effect, but again, it cannot be eliminated entirely. The toroidal core has no air gap at all, and is therefore more efficient (magnetically speaking) - they are utterly intolerant of DC in the windings. With large toroidal transformers the primary resistance is very low, and even tiny DC voltages on the mains will cause partial saturation.
This is commonly heard as a growling noise from the transformer, and if bad enough you'll hear it just before the fuse or circuit breaker opens. It's easy to get several times the normal full load current to flow in the primary with asymmetrical mains waveforms that have an effective DC component. See Blocking Mains DC Offset for more information on the problem and how to fix it.
14. Materials There is an enormous range of core materials, even within the same basic class, so I will mention only a few of the most common. All materials have some basic requirements if they are to be used with AC (for transformers, rather than solenoids or relays, which can operate with DC). The core cannot be solid and electrically conductive, or excessive eddy current will flow, heating the core and causing very high losses. Therefore, all cores use either thin metal laminations, each electrically insulated from the next, or powdered magnetic material in an insulating filler. The list below is far from exhaustive - there are a great many variations of alloys, and I have mentioned only a few of those that are in common use.
GOSS
Commonly thought to be an acronym for 'Grain Oriented Silicon Steel', it's actually the name of the man who invented it - Norman P. Goss (US Patent 1965559). See Wikipedia for a bit more.
Silicon Steel (General Information)
Typically, soft (i.e. low remanence) magnetic steel will contain about 4% to 4.5% silicon, which lowers the remanence of the steel and reduces hysteresis losses. Normal mild steel, carbon steel or pure iron has quite a high remanence, and this is easily demonstrated by stroking a nail (or screwdriver) with a magnet. The nail will become magnetised, and will retain enough magnetism to enable it to pick up other nails. The addition of silicon reduces this effect, and it is very difficult to magnetise a transformer lamination strongly enough so it can pick things up.
This is not to say that the remanence is zero - far from it. When a transformer is turned off, there will often be residual magnetism in the core, and when next powered on, it is common for the transformer to make noise - both toroids and E-I transformers can sometimes make a noise (sometimes rather loud) when power is applied. This is due to core saturation and inrush current - see Section 12.1 above for a more complete description.
Silicon steel and other metal (as opposed to ferrite) materials are normally annealed by heating and then cooling slowly after stamping and forming. This removes most of the internal mechanical stresses caused by the stamping or rolling operation(s) - these stresses reduce the magnetic properties of the material, sometimes very dramatically.
CRGO - Cold Rolled Grain Oriented Silicon Steel
Like many steels, this version is cold-rolled to obtain the required thickness and flatness needed for a transformer core. The magnetic "grain" of the steel is aligned in one direction, allowing a higher permeability than would otherwise be possible. This material is ideal for toroids and C-cores, since the grain can be aligned in the direction of magnetic flux (i.e. in a circular pattern around the core). It is less suited to E-I laminations, because the flux must travel across the "grain" at the ends of the lamination, reducing permeability.
CRNGO - Cold Rolled Non Grain Oriented Silicon Steel
Generally more suited to E-I laminations, this is essentially the same process as the CRGO, but the magnetic grain is left random, with no alignment of the magnetic domains. Although this reduces overall permeability, the effective permeability may be better with stamped laminations (as opposed to rolled, as with toroids and C-cores).
Powdered Iron
A soft ferrite ceramic material, used where there is significant DC in the winding. Powdered iron cores have relatively low permeability (about 90, maximum), and are designed for high frequency operation. These cores are most commonly used with no air-gap, and will not saturate easily. Typically used as filter chokes in switching power supplies, and as EMI (Electro-Magnetic Interference) filters - the toroid is the most common shape.
Ferrite
Soft ferrites are the mainstay of switching power supplies, and low level high speed transformers (such as might be used for network interface cards and small switching transformers. Ferrites are available with outstanding permeability, which allows small cores with very high power capability. Flyback (a type of switchmode operation) transformers in particular are usually gapped because of the DC component in the primary current.
High permeability ferrites are also very common in telecommunications and for other small audio frequency transformers where very high inductance and small size is required.
MuMetal
Named after the symbol for permeability, as one might expect, this material has an extraordinarily high permeability - typically in the order of 30,000. It is commonly used as magnetic shielding for cathode ray tubes in high quality oscilloscopes, screening cans for microphone transformers, and as laminations for low level transformers. The maximum flux density is quite low compared to other metallic materials. Apart from being relatively soft, if dropped, the magnetic properties may be adversely affected (MuMetal requires careful annealing to ensure that its magnetic properties are optimised).
15. Transformer Distortion An ideal transformer has zero distortion, but there are zero ideal transformers. Therefore, it can be deduced that transformers do have distortion, but how much?
The answer depends entirely on how the transformer is used. When supplied from a voltage source of zero ohms impedance, the real life transformer has no distortion, but again, there is no such thing as zero ohms (actually, it can be done, but yields little real benefit).
Any transformer operating at low flux density, and with a low impedance source, will contribute very little distortion to the signal. As frequency decreases, and/ or operating level increases, the limits of saturation will eventually be reached in any transformer, and distortion will become a problem. This is not really an issue with mains power transformers, but is very important for valve output transformers, particularly at low frequencies.
The distortion characteristics of transformers used as valve output devices is a complex subject, and will not be covered here. Suffice to say that the normal methods of determining the turns per volt, based on the bare minimum lowest frequency response will give unacceptably high distortion levels at low frequencies.
There is a discussion of valve audio output transformers in the valves section. See the Valves Index for a listing of the articles available. The 'Design Considerations' articles in particular look at transformer behaviour and requirements.
16. Reusing Transformers Transformers can often be reused, with the new usage completely different from what was intended. Great care needs to be taken though, as there are a few traps with some transformers used in consumer equipment. In general, a transformer taken from an old amplifier will be fine to use in a new amplifier, but not all transformers found in consumer goods are usable for anything unless you know exactly what you are doing.
A question that was raised on the ESP forum some time ago related to the use of old microwave oven transformers (MOT for brevity). While the secondary voltage is much too high (typically around 1.1 to 1.5kV RMS), it was suggested that the high tension winding could simply be removed and a new secondary wound to give the voltage needed. While this will work, beware of current (cost cutting) manufacturing trends!
It is very common that an MOT taken from an oven that is less than 15 years old will be wound such that the transformer is well into saturation at no load. In one unit I tested, the unloaded current was 1.2A (yes, 1.2A - not a misprint). The core started to saturate at only 150V, and by 240V was very heavily saturated. In its intended use, this will not cause a problem - remember that core flux decreases when the transformer is loaded, and a microwave oven also has a fan, and normally never runs for very long. The transformer is never operated unloaded unless the magnetron supply circuit is faulty or the magnetron itself is dead.
An amplifier normally applies very light loading most of the time. Operating a transformer such as the one I tested in an amp would result in the transformer overheating (288VA of no-load heat), as well as unacceptable overall efficiency for the amp itself. In addition, a MOT is not designed for low leakage flux, so will dramatically increase hum levels because of induced currents in the wiring and chassis. To add insult to injury, the transformer was also quite noisy (mechanical noise due to magnetostriction), and that alone would make it unsuitable for use in a hi-fi system (assuming that it was electrically suitable).
As you can see from the above, the transformer is completely unsuitable for continuous duty at light loading - in fact, it is not designed for continuous duty at all. While it is possible to add more turns to the primary, a great many additional turns would be needed to reduce the flux to below saturation. In addition, adding primary turns means that the insulation must be perfect to prevent potentially fatal mishaps.
All transformers that you intend for reuse should be examined on their merits, and tested in a controlled environment to ensure that they will survive in their new role. Just because a transformer was used in one piece of equipment does not mean that it can be used in any other equipment, as the design criteria are often very different indeed.
If you are satisfied that a transformer is suitable for the new task you are about to set it towards, then turns can be removed from or added to the secondary to get the voltage you need. Do not tamper with the primary unless you understand the insulation requirements, and can ensure that the final transformer is at least as safe as it was when you found it. This article will not even try to cover the task of rewiring the secondary - if you don't know how, and can't work it out, then you shouldn't be messing with transformers in the first place.
| VA | Resistance (Ω) | Regulation | VA | Resistance | Regulation |
| 4 | 1100 | 30% | 225VA | 8 | 8% |
| 6 | 700 | 25% | 300 | 4.7 | 6% |
| 10 | 400 | 20% | 500 | 2.3 | 4% |
| 15 | 250 | 18% | 625 | 1.6 | 4% |
| 20 | 180 | 15% | 800 | 1.4 | 4% |
| 30 | 140 | 15% | 1000 | 1.1 | 4% |
| 50 | 60 | 13% | 1500 | 0.8 | 4% |
| 80 | 34 | 12% | 2000 | 0.6 | 4% |
| 120 | 22 | 10% | 3000 | 0.4 | 4% |
| 160 | 12 | 8% |
|
Regulation is often misunderstood, and the values shown are (again) approximate. Transformer manufacturers almost always quote regulation based on a resistive load, which is the best case. In real applications, regulation will be (often considerably) worse than the value quoted or shown above. See 11.3 for a detailed explanation.
My thanks to Phil Allison for the data in the above table.
