Share |

Elliott Sound Products Beginners' Guide to Transformers - Part 2 Transformers - The Basics (Section 2)

Copyright 2001 - Rod Elliott (ESP)Page Updated April 2015

Articles IndexMain Index

Contents - Section 2Section 1Introduction8. Windings in Series and Parallel

8.1 Series Connections8.2 Parallel Connections

9. Valve Output Transformer Example10. Compromises11. Losses

11.1 Iron Losses11.2 Copper Losses

11.2.1 Current Density11.2.2 Skin & Proximity Effect

11.3 Regulation11.4 Other Losses11.5 Temperature Classes11.6 Voltage & Frequency

12. Sample Measurements12.1 Magnetising Current Waveforms12.2 Inrush Current12.3 Inductance

13. Core Styles13.1 Air Gaps

14 Core Materials15 Distortion16 Reusing Transformers17 Current Transformers18 DC In Transformer Windings19 AutotransformersReferencesUnitsMagnetic TerminologySection 3

IntroductionFor 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 areprobably 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 areimperfect.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 tobe 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 orsecondary. Windings can be interconnected to do exciting and different things, but from a safety perspective it is imperative that primary and secondary windings arekept 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 ofthe shorted section of the winding. The current flow can be enormous, and with even one shorted turn, the transformer is no longer serviceable and must be discarded orrewound. No shield or other conductive material may be wrapped around the winding 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 (outside the core), and isnot 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 transistoramp 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. [See Note]1. A transformer wound for 50Hz operation can safely be used at 60Hz (with the correct or even slightly higher voltage).2. A 60Hz transformer will draw excessive magnetising current at 50Hz, and may fail due to overheating.3. Note: This is the practical case, assuming normal usage of the transformer. A theoretical 'ideal' transformer having zero winding resistance will have constant flux, regardlessof load - provided the input voltage is constant. Since the real world has real-world transformers, the flux decreases slightly with load due to the voltage lost across thetransformer's primary winding. This is explained in more detail below.

Before reusing any transformer - especially if designed for a different purpose, voltage or frequency - you need to check that it will not draw excessive magnetisingcurrent. Worst case is with no load, and the current should be measured and the temperature monitored for long enough to be certain that the transformer does not get sohot that it's uncomfortable to hold. If the idle temperature rise is more than about 25C the transformer should not be used. Bear in mind that some small transformers runrather hot all the time, so on occasion you may have to make a value judgement based on experience.

8. Windings in Series and ParallelMany 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. Forexample, 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.

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

1 of 20 29/04/2015 23:19

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 ParallelThere are some rules that apply to winding interconnections - if you break them, you may break your transformer as well. Note the dots on the windings - this is thetraditional way to identify the start of a winding, so that the phase may be determined.Autotransformers are covered in Section 19 below. These are a special case of windings in series, and are commonly used to obtain a reduced voltage with the highestpossible efficiency and lowest cost.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 antiphaseconnection 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 withoutsome form of protection for the transformer and house wiring!

8.1 Series ConnectionsWindings may be connected in series regardless of voltage. The maximum current available is the rating specified for the lowest current winding. Windings may beconnected 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 isnot 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 maytherefore be connected to provide any of the following ...

10V @ 5A - The 10V winding by itself50V @ 1A - The 50V winding by itself60V @ 1A - Both 50V and 10V windings, connected in series and in phase40V @ 1A - Both 50V and 10V windings, connected in series and out of phase

The above example was used purely for the sake of example (such a transformer would not be useful for most of us), but the principle applies for all voltages andcurrents. Series connections are sometimes used in the primaries as well, mainly for equipment destined for the world market. There are several common mains supplyvoltages, and primary windings are connected in various combinations of series and parallel to accommodate all the variants.

8.2 Parallel ConnectionsParallel 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 beconnected 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 totalwinding 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 unexpectedlyhot, 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 generallyto be preferred.The transformer manufacturer's specifications will indicate if parallel operation is permitted. If you are unsure, measure the voltages carefully, and avoid parallelconnection 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 predictwhat it will be. With toroidal transformers, the windings are often bifilar, meaning that the two windings are wound onto the transformer core simultaneously. The toleranceof such windings is normally very good, and should cause no problems.

9. Valve Output Transformer Example CalculationIn 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 inthe 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 inreal 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 impedanceaccordingly.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, andthe 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 2kVpeak 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 = 34.5VRMS = peak * 0.707 = 24VPower is therefore 24 / 8 = 72W

Notice 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 aconservative rating that is more likely to be met in practice.

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

2 of 20 29/04/2015 23:19

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 besubstituted. 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 - triodesbehave 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

VoltsPlateCurrent

ScreenVolts

ScreenCurrent

GridBias

LoadImpedance

PowerOutput

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 95365 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 252 x 91

400 2 x 3.02 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 652 x 71

- - -28V 5,000 (p-p) 16W Screen tied to plate, Cathode bias resistor 220 ohms, THD 3%Table 9.1 - Abbreviated Data For EL34 Power Pentode

* 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

As can be seen quite readily, the distortion of the S-E configurations is much worse than the push-pull versions. Not only that, but (to maintain relevance :-) thetransformers are larger and harder to design, and even then will be worse than their push-pull counterparts. In the maximum efficiency configuration, power output is100W, and distortion is still lower than for either of the single ended configurations. The losses across the output valve in this mode are about 58V, but are considerablyhigher for any of the cathode biased versions - as one might expect.This will be revisited in another article on the design of valve amplifiers.

10. CompromisesIt is very important that the core does not saturate (see below), since there will be no continuous sinusoidal variation of flux, greatly reduced back EMF, and excessivecurrent 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 giveacceptable 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 morecurrent, 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 primaryresistance, 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, andserves no function in the transformation process. It does cause the transformer to get hot (or hotter) than at no load. See the next section for more details on this.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 isat 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 littleconsequence if it fails in normal use due to overheating.For audio transformers, there are even more compromises.

11. LossesAs 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 (andconsequent mass) of the transformer core. High frequency losses are caused by eddy currents in the core (see below), and by leakage inductance and windingcapacitances.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 iscapable of doing the job required of it.

11.1 Iron (Core) LossesCore 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 LoopWhen the magnetomotive force is reversed in a magnetic material, the residual magnetism (remanence - also known as remnance in some cases) in the core tries toremain in its previous state until the applied flux is too great (coercivity). It will then reverse, and the same situation will occur twice for each cycle of applied AC. Thepower required to force the flux to change direction is the hysteresis loss, which although usually small, is still significant. I am not about to go into great detail on this, buta Web search will no doubt reveal more information than you will ever need.

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

3 of 20 29/04/2015 23:19

Figure 11.2 - B-H CurveAs can be seen from the two magnetic field drawings, the flux density (B) is dependent upon the applied magnetic field strength (H). For the example shown, the "knee" ofthe curve coincides with the point where permeability starts to fall. Above this, a progressively larger change in the magnetic field is required to increase the flux density.This is saturation, and most transformers will be designed to operate at or below the knee. Above the knee is dangerous, as a small increase in applied voltage will notproduce the required increase in back EMF, and the primary current will increase disproportionately to the rise in voltage. In other words, the transformer will be toosensitive to applied voltage, and will possibly self destruct if the mains voltage were even slightly higher than normal. If such a transformer is wound for 60Hz but used at50Hz, failure is inevitable.

Figure 11.3 - Cutaway View of a TransformerThe transformer shown is a "split bobbin" type, having separate sections on the former for the primary and secondary windings. This reduces the capacitance betweenwindings, and also provides a safety barrier between the primary and secondary. For some applications, this is the only winding method that meets safety standards. It isalso very simple to add an electrostatic shield between the windings - a flat plate of thin metal is cut so that it can be slipped over the bobbin, and the ends are insulatedso that it does not create a shorted turn. This is connected to earth, and prevents noise from being capacitively coupled between windings. The shield would logically beplaced on the secondary side of the bobbin divider for safety.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 thesecause 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. Eddycurrent 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 LaminationsThe eddy currents are shown for three lamination thicknesses. Although not shown (for the sake of clarity), the current loops are constantly overlapping, and areeffectively infinite in number. The thick laminations allow the loops to be larger, and therefore the lamination section is cut by more magnetic "lines" of force, so thecurrents (and losses) are larger. For high frequencies (above 10kHz), it is generally not possible to make laminations thin enough to prevent the losses from becomingexcessive, and ferrite materials are preferred. These effectively have a huge number of incredibly small magnetic particles, all insulated from each other, and eddy currentloops are very small indeed. Even so, ferrite materials are normally specified up to a few hundred kilo-Hertz for power applications before the losses become too greatagain.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 itsmaximum value for any given applied voltage / frequency combination. Power transformers are usually designed to operate below the knee of the saturation curve (this isessential 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. Whereone would hope for a nice sinusoidal current waveform with low distortion, significant current 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.For example, if the primary resistance is 5 ohms and the loaded primary current is 2A at 230V, 10V is lost across the winding resistance, so the effective primary voltageis reduced to 220V. This reduces the magnetising current, but the effect is not linear. It depends a lot on how close to saturation the core operates with no load, and thedifference may be anything from minimal to significant, depending on the design.

11.2 Copper LossesFollowing on from the previous point, the voltage lost to winding resistance is copper loss, and all such losses must be dissipated as heat. Consider the same transformeras above at idle, with 230V on the primary. The primary resistance may be in the order of 5 ohms (a transformer of around 300VA), and the idle current perhaps 20mA.

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

4 of 20 29/04/2015 23:19

The loss is determined by the normal power formula, and in this case is ...P = I * R = 0.02 * 5 = 2mWV = R * I = 5 * 0.02 = 100mV

For all intents and purposes, the full 230V is applied to the primary. When the transformer is loaded, this changes. Let's assume 2A primary current and look at the figuresagain ...

P = I * R = 2.00 * 5 = 20WV = R * I = 5 * 1.00 = 10V

Now, the effective primary voltage is only 220V, because 10V is 'lost' due to winding resistance. Naturally, if the voltage is lower, the flux density must also be lower. Thepower lost in the primary must be dissipated as heat, so the transformer will start to get hot. Remember that there will be additional losses in the secondary that add to theheat that must be dissipated.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 thewinding, 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 theturns 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 towind a transformer based on the erroneous assumption that this would work, the finished 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 (provided saturation is avoided), there is virtually no loss, since the currents are low, but as secondary current increases, so too do thecopper losses.11.2.1 Current DensityThe 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 example2.565A/mm (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 hotterfor a given current. Side forces caused by the magnetic fields generated between each turn need to be considered in large power distribution transformers, especiallyunder short-circuit conditions where the forces can be destructive. There is no such thing as a "typical" current density, because different manufacturers use differentdesign criteria. In general, it's better to keep current density below 3.0A/mm and 2.5A/mm is even better. Naturally, a lower current density means that the transformer islarger 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 highefficiency is not needed, and the demand from normal music programme material has a rather low average value. As a result, transformers for power amplifiers (forexample) 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 basiswhen 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 iscomparatively low, averaging around 2.1A/ mm, while the secondaries all used a much higher current density - around 4.8A/ mm. This makes sense, because thesecondary 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, whichstands 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) haveworse regulation. A current density of up to 3.5A/ mm is typical of some smaller transformers. One reason for this is that it becomes extremely difficult to fit the number ofturns 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 withsmall 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 ahotter 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 burningout 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 notcovered 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 causethe 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 bemuch 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 pointwhere 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 thelarger 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 aproblem. 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 furtherbecause copper has a positive temperature coefficient of resistance. As the transformer gets hot, its resistance increases, increasing losses. This (naturally) leads togreater 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 anytransformer 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 lifeexpectancy of insulation (amongst other things) is halved for every 10C (some claim as low as 7C) temperature increase. When these two factors are combined, it isapparent that any transformer operated at a consistently high temperature will eventually fail due to insulation breakdown. The likelihood of this happening with a homesystem 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 arepowering, 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 beearthed, 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 oilcooled, 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 coolantleak or other major fault.11.2.2 Skin & Proximity EffectThe skin effect is well known (and exploited by snake-oil cable makers), but has little or no relevance for audio frequencies. With switchmode power supply transformers itis a real problem, and the most common way to minimise the influence is to use multiple small (insulated) wires in parallel - typically bundled and twisted into a singlerope-like strand. This is commonly referred to as Litz wire, and its use reduces skin effect losses because the wire bundle has a comparatively large surface (or 'skin')area.You don't normally hear much (if anything) of the so-called proximity effect, but it refers to the (often chaotic) disturbance of the current flow in a conductor when thatconductor is immersed in an intense magnetic field. For small transformers (below perhaps 2kVA), there is little evidence that it causes any problems, but in larger

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

5 of 20 29/04/2015 23:19

transformers it can cause localised heating because the current is forced to use far less of the wire's cross section than expected. Use of Litz wire again reduces theproximity effect, and may be crucial to prevent failure. Proximity effect may reduce current carrying ability far more dramatically than does skin effect, and at much lowerfrequencies.The proximity effect therefore has the potential to cause localised "hot spot" thermal problems, that degrade the insulation and cause eventual failure. It is especiallyproblematical when the transformer current is highly distorted, and this is invariably the case when a transformer is used with a bridge rectifier and filter capacitors.Despite the above, it's almost certain that there will be identifiable minor localised heating, but as noted it is unlikely to cause reduced life of any transformer used foraudio or other applications that are of interest to hobbyists or typical commercial products. Given the legendary reliability of transformers - most of which will outlast theproduct - the proximity effect never seems to have caused premature failure. Most transformer failures are the result of much more mundane abuse, such as consistentlong-term overload.However, the proximity effect does cause failures in large distribution transformers, and is also said to lead to motor failures. These failures are almost always attributableto a highly distorted mains current waveform, and may be localised to a single industrial installation. I suggest that the reader not stress about it - you didn't even knowabout it until now.

11.3 RegulationCopper 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, whichconsidering 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 beused 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 morevoltage 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 theregulation 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 hasan 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 articletwice :-)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 findout 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 knowwhat 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 windingresistances 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 todebate 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 weneed 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 at50V 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 voltageratio. 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 = 4.34:1ZR = TR = 4.34 = 18.83:1

Knowing this, we can determine the optimum winding resistance for each winding. Since half of the resistance is that reflected from the primary (Rp), the secondaryresistance (Rs) is 0.15 ohms, being half of the total. Primary resistance must be ...

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 theresistive (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 thewindings, 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 spaceallowed. 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, thereis good reason to keep primary losses lower than secondary losses, because the primary winding is trapped inside the secondary winding and heat can only escapethrough the outer layers. The toroidal core doesn't act as a heatsink either, because it's inside all the windings.

VA Reg % Rp - 230V Rp - 120V Diameter Height Mass (kg)15 18 195 - 228 53 - 62 60 31 0.3030 16 89 - 105 24 - 28 70 32 0.4650 14 48 - 57 13 - 15 80 33 0.6580 13 29 - 34 7.8 - 9.2 93 38 0.90120 10 15 - 18 4.3 - 5.0 98 46 1.20160 9 10 - 13 2.9 - 3.4 105 42 1.50225 8 6.9 - 8.1 1.9 - 2.2 112 47 1.90300 7 4.6 - 5.4 1.3 - 1.5 115 58 2.25500 6 2.4 - 2.8 0.65 - 0.77 136 60 3.50625 5 1.6 - 1.9 0.44 - 0.52 142 68 4.30800 5 1.3 - 1.5 0.35 - 0.41 162 60 5.101000 5 1.0 - 1.2 0.28 - 0.33 165 70 6.50

Table 11.1 - Typical Toroidal Transformer SpecificationsThe primary resistance for all of the examples in the above table was calculated using the method shown - this figure is rarely given by manufacturers. Resistance isshown for both 230V and 120V primary windings. Knowing the basics at this level is often very handy - you can determine the approximate VA rating of a transformer justby knowing its weight and primary resistance. The secondary resistance can be calculated from the primary resistance and the turns ratio. The result obtained by using

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

6 of 20 29/04/2015 23:19

nominal turns ratio (based on the stated primary and secondary voltages) is accurate enough for most purposes. As shown by the range provided, the primary windingresistance could be up to 15% lower than calculated to reduce the current density in the primary. (See Reusing Transformers for another table covering a wider range ofVA ratings.)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 = 2.3ZR = TR = 5.29

If the primary resistance is 2.8 ohms (from the table), then the secondary resistance must be approximately ...Rs = Rp / ZR = 2.8 / 5.29 = 0.53 Ohm

The 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 hereslightly. 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 appliedto 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 LossesSince 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 powertransformer, but become difficult to manage for transformers intended for wide bandwidth, such as microphone transformers and valve output transformers.The standard equivalent circuit does not include frequency dependent disruptions such as skin or proximity effect. Nor does it include any means to simulate thenon-linear magnetising current in a power transformer. As such, it is limited to general simulations of small signal transformers, valve amplifier output transformers (butonly at low levels and/or higher frequencies) and similar. While it can still be used with a power transformer, the results are generally not at all useful. Power transformersgenerally require measurements to confirm the overall performance, and we are only interested in low frequencies - 50Hz and 60Hz.

Figure 11.5 - Transformer Simplified Equivalent CircuitThe equivalent circuit shown in Figure 11.5 is greatly simplified, but serves to illustrate the points. Since the windings are usually layered, there must be capacitance (C1and C2) between each layer and indeed, each turn. This causes phase shifts at high frequencies, and at some frequency, the transformer will be "self resonant". This isnot a problem with power transformers, but does cause grief when a wide bandwidth audio transformer is needed.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 thetransformer. Although small, it tends to affect the high frequencies in particular, and is especially troublesome for audio output transformers. This is typically measuredwith 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 voltagesource, 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 issupplying 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 themusic. Toroidal transformers are very much worse than conventional (E-I) transformers in this respect, because of the large area of each winding. An electrostatic shieldwill all but eliminate such noises, but these are expensive and uncommon with toroids (pity).This problem always exists when the capacitance between primary and secondary is high - electrical noise on the primary is capacitively coupled from the primary to thesecondary. As noted above, this can lead to mains noise getting through the entire power supply and into the amplifier in extreme cases. The electrostatic shield is veryeffective, 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 drawa 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 completelyunnecessary and increases the primary-secondary capacitance dramatically.

Figure 11.6 - Interleaved Winding for Extended HF ResponseThe trick to winding transformers to minimise the winding leakage inductance and self capacitance is called "interleaving", but this results in much greater inter-windingcapacitance. The most common way an interleaved winding is done is to use a multi-segmented winding, as shown in the sectional drawing of Figure 11.6. This type ofwinding is (or was) quite common for high quality valve output transformers, and the extension of frequency on the top end of the audio spectrum is very noticeable.The capacitance between the primary and secondary can become troublesome with this technique, and although possible, an electrostatic shield (actually, a number ofelectrostatic 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 frequencypower transformers, and would lead to greatly reduced electrical safety because of the difficulty of insulating each section from the next. The same problem also existswith 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 ClassesAll the losses add together to increase the temperature of a transformer. Insulation materials (wire enamel, inter-layer insulation, formers and/or bobbins, tape overwinds,

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

7 of 20 29/04/2015 23:19

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 lowertemperature 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 ofgreater 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 universallyaccepted. 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

Table 11.2 - Insulation Temperature Classes* Class-C is not a globally recognised class, but 220C is accepted under several different world standards.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 lifeof the equipment. Unless stated otherwise, you can expect that nearly all commercial off-the-shelf transformers intended for DIY applications will be Class-A (105Cmaximum temperature). Higher temperatures are not recommended anyway, for the simple reason that having a transformer at (say) 100C will transfer its heat totransistors, electrolytic capacitors and all other components in the chassis. For this reason alone, specifying a larger than necessary transformer not only reducestemperatures, but improves regulation as well.

11.6 Voltage & FrequencyAll power transformers are rated for either a specific input voltage and frequency, or for a limited range. Often, dual primaries are used that allow the user to connect thewindings in series or parallel as shown in Figure 8.1, but on the primary instead of the secondary. The most common configuration is to have two windings, each rated for120V. For 120V mains, these are wired in parallel, and wired in series for 230/240V.Sometimes, the primary windings will be rated for 115V each. This has long been a problem in the US, with no-one quite certain for many years whether the voltage is110, 115, 117 or 120. According to US standards, the nominal mains voltage in the US and Canada is 120V, but like everywhere else it varies from one place to anotherand with time of day. All power transformers must be wound to take this inevitable variation into account. (Note that the US also uses a 'two-phase' system, providing240V at 60Hz - this is not the same as using two phases of a 3-phase connection, where the voltage is 208V at 60Hz.)While just two windings are common now, it used to be the case that transformers had multiple taps on the primary winding, or used several windings that could beconnected in often mysterious ways using a complex switching system. These still exist, but mainly as salvage items. The range of voltages offered was intended to coveranywhere in the world, but also could lead to a wrong assumption and blown fuses (or a burnt out transformer).Ultimately though, the claimed voltage of a transformer is the easiest to verify - the nameplate rating is always correct. I have never seen a transformer that claimed to be230V (or some other voltage) that didn't work properly at that voltage. Of more concern is the frequency rating. While usually stated, it is sometimes confusing to theuninitiated.A transformer rated for 50Hz can be used anywhere in the world - it will work perfectly at 60Hz. However, the converse is not true. A transformer designed specifically for60Hz will overheat at 50Hz, even if the voltage is correct! This is not well understood, and leads to an enormous amount of traffic on Usenet and in forum pageseverywhere. The answer is quite simple - 60Hz is 20% greater than 50Hz, so the core and turns per volt can both be reduced by up to 20% compared to a 50Hztransformer of the same rating.Therefore, a transformer that was designed for 60Hz at 220/230V (The Philippines, South Korea and a few others use this combination [Ref]) has a smaller core andfewer turns than an otherwise identically rated 50Hz transformer. As a result, it will most likely fail with 220V at 50Hz. Operating a 60Hz power transformer at 50Hz isexactly the same as operating the transformer at its rated frequency, but with a 20% voltage increase. If you absolutely must run a 60Hz transformer at 50Hz, you mustreduce the mains voltage from the rated value (say 230V) by 20% (184V). This is a large drop, and exceeds the normal mains variation allowances that are provided forin properly designed circuits.Failure to reduce the voltage will cause the transformer to be heavily into saturation, and it may easily consume half its rated VA (or more) at idle, due to excessivemagnetising current caused by core saturation. Needless to say, the secondary voltage will also be reduced by the same percentage. For evidence of the current increasedue to core saturation, see the next section (specifically Figure 12.1.1).Operating a 60Hz transformer at 50Hz is effectively the same as a 20% increase in mains voltage, but note that this does not mean that the secondary voltage isincreased. For a 230V transformer that's the same as running at 60Hz, but at a supply voltage of 276V. The core will be seriously saturated, and the magnetising currentwill be increased dramatically.Should the power transformer be for a valve amplifier, care is needed, because the valve heaters will be operating from a lower than normal voltage (6.3V will only be 5V)and may not reach the proper operating temperature. Output power is also reduced, and a 20% reduction of voltage will reduce the maximum power to fall from (say)100W to 64W, a drop of just under 2dB. It also means that all unregulated preamp supplies will be 20% lower. With regulated supplies, the drop might be enough to causethe regulator ICs to allow rectified mains buzz through to the signal circuits.For information about how you can reduce the supply voltage (in this case by 46V), see the article Bucking Transformers. While the methods described certainly do work,the other compromises you have to make will almost certainly mean that the transformer will have to be replaced to maintain original performance.Should you have a transformer rated for 240V at 50Hz and wish to use it at a lower voltage and/or 60Hz, then there is no problem. If used at 120V 60Hz, the transformerwill operate with an exceptionally low magnetising current, but the secondary voltages will obviously be halved. While the maximum current rating remains the same,regulation will be worse than a transformer wound for 120V mains because the winding resistance is higher.In short, you can operate a ...

50Hz transformer at 60Hz with no loss of performance, provided voltage is correct50Hz transformer at 60Hz at a supply voltage up to 20% higher than the nameplate ratingtransformer at any voltage below the nameplate rating. There is no limit other than that imposed by common sense60Hz transformer at 50Hz, provided the supply voltage is 20% lower than the rated voltage

Likewise, you cannot operate a ...60Hz transformer at 50Hz at full rated voltagetransformer at any voltage above the nameplate rating, unless rigorous testing shows that it will be safe (unlikely)

Note that I have simply assumed 20% in both directions (50Hz to 60Hz and 60Hz to 50Hz), although it is clear that a reduction from 60Hz to 50Hz is actually 17%. Feelfree to think of the extra 3% as a safety margin.

12. Sample MeasurementsI 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 suitablevariable 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 refersto 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 formore 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

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

8 of 20 29/04/2015 23:19

near) the design frequency of the transformer. The inductances shown are calculated, since the measured values with my meter were a long way off.Bear in mind that the inductance value shown is nominal, based on the magnetising current (which is actually distorted for most transformers), and is much lower than thereal value. It is included only as a guide - the actual value will be much higher, but only with a lower primary voltage that ensures that the core is nowhere near saturation.Manufacturers don't provide this figure, because it's meaningless in the real world.

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 5.0Toroidal 300VA 63 H 5R1 3 12mA 2.88W 20k ohms 2.7E-I 200VA 4.36 H 6R6 2 175mA 42W 1.37k ohms 3.2

Table 12.1 - Measured Characteristics of Some TransformersThe toroidals are clear winners in terms of core loss in particular, but it must be said that the E-I transformer tested is not really representative of the majority. This is oneof a few left that I had specially made to my design, and they were deliberately designed to push the saturation limits of the core. These transformers run quite hot at noload, but give much better regulation than a more conservative design - the vast majority of such transformers. They were actually designed to run just above the "knee"of the B-H curve for the laminations used, and although somewhat risky, none has failed (to my knowledge) since they were made about 20 years ago. I use a pair ofthem in my hi-fi system, which has been in daily use for 10 years now. I originally got the idea of designing transformers like this long ago, when I used to make my owntransformers for guitar and bass amps. I ran some tests at the time, and found that by pushing the core a little harder, I could make a transformer that had far betterregulation than anything I could buy from any of the existing manufacturers. I never had a transformer failure.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 weighin at about 5kg.

Figure 12.1 - Current vs. Voltage for the E-I TransformerTo take my measurements to the logical limit, I measured the magnetising current of my sample E-I transformer. Look closely at the graph in Figure 12.1, and you will seea typical BH curve (as shown in Figure 11.2 but with the axes reversed). As you can see, at 240V input, the transformer is operating at the knee of the curve, and is wellon the way to saturation. There was no point doing this for the toroidals, as they are operated well below saturation level and I would be unable to (conveniently) measurethem.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 thefully enclosed magnetic path, which has no air gaps at all. E-I laminated transformers have a small but significant gap where the 'E' and 'I' laminations meet. This isunavoidable in any practical transformer, but has little effect on performance in real life.

12.1 Magnetising Current WaveformsFor these measurements, I used a 300VA toroidal transformer, but not the same one as was used for the data in Table 12.1. There seems to be very little on the Net thatdiscusses or shows actual (as opposed to theoretical or imagined) magnetising current. The true value of this varies more or less linearly up to the point where the coreapproaches saturation, but it is very common that power transformers are designed so that they are already into the non-linear part of the BH curve for normal operation.While this region is usually well below true saturation, the current waveform is already quite distorted, because the mains voltage peaks cause the flux to rise to itsmaximum value, so additional current is drawn at the peak of the AC waveform, displaced by 90. This is shown below, for a 240V, 300VA toroidal transformer, operatedat four different voltages ... the first (A) is well below saturation at 120V, the second (B) at nominal input voltage (240V), the third (C) at a voltage that is somewhat greater(280V) and the last (D) at an excessive mains voltage (290V). The transformer was designed for nominal 240V operation.

Figure 12.1.1 - Magnetising Current Vs. Input VoltageThe magnetising current is a nice friendly 7.3mA at 120V input, and at 240V is showing signs of saturation, but the current is still only 42mA. When the voltage isincreased further, saturation is clearly well advanced - at 280V the transformer draws 443mA, but just a small further increase to 290V causes the current to soar to 1.6A -exceeding the transformer's continuous VA rating with no load. If you look carefully at Figure 12.1.1.A, you will notice that the waveform is slightly asymmetrical. Thisindicates that there is probably some remanent flux in the core from the last time the transformer was used.The volt-amps dissipated in the transformer primary winding is determined by VA = V * I, so at 240V the transformer draws only 10VA, climbing to 124VA at 280V and arather spectacular 464VA at 290V. Assuming the typical primary resistance of 4.7 ohms for a 300VA transformer, the power loss in the primary at each voltage (in turn) is250uW, 8.2mW, 0.9W and 12W at 290V.As you can see from the graphs (B, C & D), the current is highly non-linear, so cannot be corrected for power factor. While this is a common error made all over the

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

9 of 20 29/04/2015 23:19

Internet, there is no way that a non-linear waveform can be corrected for power factor by adding a capacitor. At best, you might be able to add a capacitor that creates afilter which reduces the peak current and improves the PF very marginally, but it will only be effective at one location and/or voltage. Any such filter will rely on the mainsimpedance, and is guaranteed overall to make matters worse, never better.Adding a power factor correction capacitor will only work if the cap is sized to draw a leading current of around 14mA (for this transformer). This is the only linear part ofthe magnetising current, being double the 'nice sinewave' current drawn at 120V. True magnetising current is a linear function of voltage, based on the reactance of thewinding. This would imply a capacitor of around about 180nF - unlikely to be useful (ok, it's completely pointless ).The actual magnetising current drawn (including that caused by core saturation) is a non-linear function, and is extremely difficult to simulate unless one has access to asimulator that handles iron cores properly. While such a thing may exist for transformer designers, I've not seen any simulation that comes even close to reality as shownabove. Note that these are actual captured waveforms from a real transformer connected to a high power Variac. As you can see, the saturation current waveformremains much the same once the core is thoroughly saturated, but the magnitude increases exponentially with voltage increase.With 290V applied, the peak current is about 5A (2A per division on the screen). You will see that the vertical resolution has been changed for each capture, and thecurrent monitor also has variable gain to maximise resolution. That is why the measured current may seem to be different from the oscilloscope display, but the reading involts has been converted into mA.When the transformer is loaded with a resistance, the voltage and current waveforms are in phase. Contrary to popular belief, a linearly loaded transformer (i.e. resistiveload) does not produce a lagging power factor, except for the small magnetising current's contribution. As we can see from the above, this is negligible. I tested the sametransformer with a 16 ohm load across one of the nominal 20V secondaries, and the input voltage and current waveform were perfectly in phase at any input - from lessthan 5V RMS up to the full rated primary voltage.

12.2 Inrush CurrentWhen powered on, many transformers draw a very high initial current. This phenomenon may not be noticeable with smaller transformers, but as the component getslarger (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 coresaturates 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 inrushcurrent is a combination of several factors ...

What was the polarity and magnitude of the mains at switch offWhat is the polarity and magnitude of the mains at switch onTo what extent has the core de-magnetised itself between eventsTransformer type (toroidals have greater inrush than E-I cores)The resistance of the transformer primary and the mains - right back to the sub-station

The longer a transformer is left unpowered, the lower the remanent flux, and the less likelihood there is of an excessively high inrush current. This is a nice theory, but inreality it makes no practical difference. Of far more importance is the point on the mains waveform where the power is actually applied. If the mains is applied when at itspeak value, inrush current is at its lowest. Conversely, if the mains is applied at the zero crossing point, inrush current will be maximum - this is exactly the reverse of whatyou might expect, and is shown below. The inrush current lasts for several cycles, and is made much worse with a rectifier and filter capacitor on the output. The capacitoris a short circuit when discharged, and large capacitors will take longer to charge. The inrush current due to capacitors charging is not asymmetrical - that privilege isreserved for core saturation at power-on.

Figure 12.2 - Transformer Inrush CurrentThe above is an oscilloscope capture of the current in a 200 VA E-Core transformer, when power is applied at the zero crossing of the mains waveform. This is the worstcase, and can result in an initial current spike that is limited only by the winding and mains wiring resistance. For a large toroidal, peak currents can easily exceed 150A. Ifthe mains is applied at the peak of the AC waveform (325V in 230V AC countries, 170V in the US), the peak inrush current for the same transformer is typically reducedto less than 1/4 of the worst case value ... 4.4A (both can be measured with good repeatability for the transformer tested).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 arealready powered may also saturate (and often growl) during the inrush period. This is often known as 'sympathetic interaction'. To minimise the effects of inrush currentand flow-on effects with other equipment, any toroidal transformer over 300VA should use a soft-start circuit such as that described in Project 39.

12.3 InductanceThe inductance of a transformer is not normally part of its specifications, unless it's designed for a switchmode power supply. For normal mains frequency applications,the figure we are interested in is the magnetising current. As shown above in Figure 12.1.1, the magnetising current is non-linear, so if you do need to know theinductance you must take the measurement at a voltage that's well below the nominal primary voltage. If you have a way to monitor the current waveform, you can verifythat there is no evidence of saturation at the test voltage (see Project 39 or Project 39A for suitable current monitors).Once you know the voltage and current you can calculate the impedance, and from that you can work out the inductance ...

XL = V / I (where V is applied RMS voltage and I is RMS current)L = XL / ( 2 * * f ) (where f is the applied frequency)

For example, the transformer I used to produce the oscilloscope captures in Figure 12.1.1 draws 7.31mA with a mains voltage of 120V at 50Hz.XL = 120 / 7.31 = 16.41 kL = 16.41 k / ( 6.283 * 50 ) = 52.25 Henrys

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

10 of 20 29/04/2015 23:19

This is an interesting 'figure of merit', but is not actually useful for anything. Of course, if you have a need for a 52H inductor you can use the primary winding to get it, butremember that it will start to saturate at not much more than 10mA. If you tried to use it for audio, the distortion will be quite high at even lower currents, especially as thefrequency is reduced below 50Hz. In addition, the inductance will probably be non-linear, because the core may not magnetise properly at very low current. The testtransformer's inductance fell to 42H with a voltage of 35.2V and a current of 2.64mA.As noted above, inductance is part of the specification for switchmode power supply transformers. That's because they are operated in a somewhat different way fromlinear transformers. One area of commonality is that saturation must be avoided, and like linear transformers saturation is worse with no load. For the same power output,a switchmode transformer will be a great deal smaller than a conventional transformer operating at 50 or 60Hz. Typical operating frequencies range from a few kHz up to100kHz or more. As a rough guide, the necessary size of a transformer will halve for each doubling of frequency (and vice versa of course), but there are many otherinfluences that must also be considered. A complete discussion of this is way outside the intent of this article.

13. Core StylesThere 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 arethe standard E-I core and the toroidal core, but there are many others. Occasionally you will see C-cores, double-C-cores and R-cores, but these are not as common asthe two most popular types.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 thatthere 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 asuitable 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 suitablewinding 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 byrolling 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 aremachined 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 heldtogether with steel banding, similar to that used for large transport boxes.

Figure 13.1 - C-Core TransformerThe main disadvantage of the single c-core arrangement shown above is that its leakage inductance is rather high. Although both windings could be placed onto a singlebobbin with a pair of cores, it is more common to use four 'C' sections as shown below. This provides more iron (twice as much) and allows fewer turns for a givenvoltage. Naturally, the double c-core as shown below is not intrinsically safe, because both windings are wound together in the same way as for an equivalent E-Itransformer. While not intrinsically safe, as with any bobbin-wound windings it's still fairly easy to build one that complies with all double insulation standards.C-cores are not quite 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 thetoroidal. Note that toroidal transformers are very difficult to build so they comply with double insulation standards. I've never seen a double insulated toroidal transformer,except for those that are used in electronic transformers intended for halogen downlights. These have a plastic case that fully encloses the primary.

Figure 13.1A - Double C-Core TransformerA sample of ferrite cores is shown in Figure 13.2 - this is but a small indication of the selections available, and most styles are also available in many different grades tosuit specific applications.

Figure 13.2 - Some Ferrite Core StylesThe diagram in Figure 13.3 shows the correct way to stack an E-I transformer. Sometimes manufacturers will use 2 or 3 laminations in the same direction, then the samein the other. This cuts costs, but the transformer performance will never be as good. Alternate laminations minimise the air gap created between the E and I sections dueto imperfect mating of the two. It is essential that the laminations are packed as tightly as possible so that the effects of the air gaps are minimal.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 thecentre 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 arecommonly used, but this is for expedience (or to minimise inventory) rather than to improve performance.

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

11 of 20 29/04/2015 23:19

Figure 13.3 - E-I Lamination StackingWhen a transformer using E-I laminations is bolted together, it is important that the bolts are insulated from the core. If not, this would allow large eddy currents tocirculate through the end laminations and the bolts, reducing performance dramatically. For safety, the core should always be bonded to mains earth unless thetransformer is rated as "double insulated"."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 cannotwithstand 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 thecore, 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. The band must besoldered where it overlaps to ensure a very low resistance. Such measures are usually not needed with toroidal transformers, as leakage flux is very much lower, and thecore is completely enclosed by the windings.However, in critical applications a flux band can still be used. For a toroidal, the band is simply wrapped around the outside of the winding and soldered to give a lowresistance connection. The band must not be allowed to touch other metal parts that are connected to the mounting bolt in such a way as to form a shorted turn. This willcause a huge circulating current - the fuse will blow if properly sized, or the transformer will burn out if not. It is alright to earth the flux band though, and this will minimiseradiation of any HF noise (rectifier noise for example).

(* 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 aninteresting mental picture though .)

Figure 13.4 - Flux Banded TransformerJust in case you were wondering, the dimensions of E-I laminations are worked out so that the laminations can be created with no material waste (other than the holes).The relative dimensions are shown below, and are just a ratio of the real dimensions, which will naturally be in millimetres or inches. This arrangement is known as a'scrapless' lamination because there is an absolute minimum of waste material.

Figure 13.5 - Assembled Laminations and Punching DimensionsThe magnetic path length is the average for the dual path shown in the assembled lamination drawing, and is generally assumed to be 12 (units). This may be thought alittle pessimistic, but is the commonly accepted figure. The winding window size is restricted by the punching dimensions, and it is critical that the maximum usage ismade of the limited area available. Should the winding wire be too thin, there will be plenty of room, but copper losses will be excessive. Make the winding wire too thick,and the completed winding will not fit into the available space. Additional space must be allowed for the winding bobbin, and for inter-winding insulation and the finalinsulation layer.

13.1 Air GapsDC 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 amagnetomotive force that is unidirectional, and this reduces the maximum AC signal that can be carried before saturation in one direction. Indeed, the DC componentmay 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 halfwave 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. Thislowers 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 increasesleakage 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 equallyunacceptable 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 isequal 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 itrequires 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 apopular technique in telecommunications equipment at one time, and meant that smaller transformers could be used for the same performance.

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

12 of 20 29/04/2015 23:19

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 beeliminated. 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 istherefore more efficient (magnetically speaking) - they are utterly intolerant of DC in the windings. With large toroidal transformers the primary resistance is very low, andeven 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 severaltimes 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 moreinformation on the problem and how to fix it.

14. MaterialsThere 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 basicrequirements 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 electricallyconductive, or excessive eddy current will flow, heating the core and causing very high losses. Therefore, all cores use either thin metal laminations, each electricallyinsulated 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 havementioned only a few of those that are in common use.GOSSCommonly 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). SeeWikipedia 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. Normalmild 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 becomemagnetised, 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 atransformer 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 isdue 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 ofthe internal mechanical stresses caused by the stamping or rolling operation(s) - these stresses reduce the magnetic properties of the material, sometimes verydramatically.CRGO - Cold Rolled Grain Oriented Silicon SteelLike 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 onedirection, 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 ofmagnetic 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 SteelGenerally 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 magneticdomains. Although this reduces overall permeability, the effective permeability may be better with stamped laminations (as opposed to rolled, as with toroids andC-cores).Powdered IronA soft ferrite ceramic material, used where there is significant DC in the winding. Powdered iron cores have relatively low permeability (about 90, maximum), and aredesigned 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 switchingpower supplies, and as EMI (Electro-Magnetic Interference) filters - the toroid is the most common shape.FerriteSoft 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 switchingtransformers. 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 isrequired.MuMetalNamed 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 usedas magnetic shielding for cathode ray tubes in high quality oscilloscopes, screening cans for microphone transformers, and as laminations for low level transformers. Themaximum 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 DistortionAn 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 very littledistortion. The winding resistance of the transformer itself is effectively in series with the 'ideal' winding, so to get a true 'zero resistance' source you need a negativeimpedance driver. If the negative impedance is made to be the same magnitude as the winding resistance (a positive resistance/ impedance), the two cancel. This is nottrivial, but it can be done, and there is some information about the technique in the Audio Transformers article.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/ oroperating 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 mainspower transformers, but is very important for valve output and line level coupling/ isolation 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 ofdetermining 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 TransformersTransformers 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 withsome 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 foundin 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 ismuch 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 thevoltage 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

Transformers Part 2 - Beginners' Guide to Electronics http://sound.westhost.com/xfmr2.htm

13 of 20 29/04/2015 23:19

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 verylong. 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 increasehum 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 ispossible 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 meansthat 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. Justbecause 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 differentindeed.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 thevoltage 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 itwas 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 bemessing with transformers in the first place.

VA Resistance ()