Transformers - The Basics

Section 1
Preface
One thing that obviously confuses many people is the idea of flux density within the transformer core. While this is covered in more detail in Section 2, it is important that this section's information is remembered at every stage of your reading through this article. For any power transformer, the maximum flux density in the core is obtained when the transformer is idle. I will reiterate this, as it is very important ...
For any power transformer, the maximum flux density is obtained when the transformer is idle.
The idea is counter-intuitive, it even verges on not making sense. Be that as it may, it's a fact, and missing it will ruin your understanding of transformers. At idle, the transformer back-EMF almost exactly cancels out the applied voltage. The small current that flows maintains the flux density at the maximum allowed value, and represents iron loss (see Section 2). As current is drawn from the secondary, the flux falls slightly, and allows more primary current to flow to provide the output current.
It is not important that you understand the reasons for this right from the beginning, but it is important that you remember that for any power transformer, the maximum flux density is obtained when the transformer is idle.

Introduction
As you look through this article, you may be excused for exclaiming "This is for beginners? - the man's mad. Mad, I tell you!" This is probably fair comment, but transformers are not simple, and there is no simple way to provide all the information you need to understand them properly. There are sections here that probably go a little bit deeper than I originally intended, but were just too interesting to leave out.
There are parts of this article you may want to skip over, but I suggest that you do read all of it if you can. A full understanding to the extent where you can design your own transformer is not the aim, but the majority of the information is at the very least interesting, and will further your general electronics knowledge.
For those who wish to delve deeper, Section 2 does just that. It is recommended reading, even for beginners, as there is a great deal to be learned about transformers, despite their apparent simplicity.
The principles that allow us to make use of electro-magnetism were only discovered in 1824, when Danish physicist Hans Oersted found that a current flowing through a wire would deflect a compass needle. A few years after this, it was found that a moving magnetic field induced a current into a wire. From this seemingly basic concept, the field of electromagnetism has grown to the point that society as we know it would not exist without the many machines that make use of these discoveries.
Transformers are essential for all modern electronics equipment, and there are very few devices that do not use them. Each transformer type has a specific use, and it is uncommon that a transformer made for one application can be used for another (quite different) purpose.
Before embarking on a description of the different types, the basic theory must be understood. All transformers use the same basic principle, and only the finer points ever change. A transformer works on the principle of magnetic coupling to transfer the energy from one side (winding) to the other.
Transformers are bi-directional, and will work regardless of where the input is connected. They may not work as well as they otherwise might, but basic functionality is unchanged. An ideal transformer imposes no load on the supply (feeding the primary) unless there is a load across the secondary - real life components have losses, so this is not strictly true, but the assumption can be used as a basis of understanding.
Power transformers are rated in Volt-Amps (VA). Using Watts is of no use, since a load that is completely reactive dissipates no power, but there are still Volts and Amps. It is the product of "real" voltage and current that is important - a wattmeter may indicate that there is little or no real power in the load, but the transformer is still supplying a voltage and a current, and will get hot due to internal losses regardless of the power.
Transformer cores have a quoted permeability, which is a measure of how well they "conduct" a magnetic field. Magnetism will keep to the path of least resistance, and will remain in a high permeability core with little leakage. The lower the permeability, the greater is the flux leakage from the core (this is of course a gross simplification, but serves well enough to provide an initial explanation of the term).
A transformer may be made with various materials as the core (the magnetic path). These include ...
• Air - provides the least coupling, but is ideal for high frequencies (especially RF). Permeability is 1.
• Iron - A misnomer, since all "iron" cored transformers are steel, with various additives to improve the magnetic properties. Permeability is typically about 500 and upwards.
• Powdered Iron - Steel magnetic particles formed into a core and held together with a bonding agent, and fired at high temperature to create a ceramic-like material with very good properties at medium to high frequencies (over 1 MHz). Especially suited to applications where there is a significant DC component in the winding or for very high power. Permeability is typically 40-90.
• Ferrite - A magnetic ceramic, usually using exotic magnetic materials to obtain extremely high permeability and excellent high frequency performance (from 50kHz to over 1MHz). An astonishing range of different formulations is available for different applications. Permeability is from about 500 up to 9,000 or more.
Technically, powdered iron and ferrites are both classified as soft (see below) ferrites, but they have very different characteristics, even within the same "family". They are generally unsuitable for low frequency operation, except at low levels. Ferrites are often used as signal transformers (such as isolation transformers for telecommunications or other small signal applications), where the high permeability makes them an ideal choice for small size and high inductance.
Core materials are generally classified as "soft" - this has nothing to do with their physical properties (they are all hard to very hard), but is a reference to their ability to retain magnetism (remanence). Hard magnetic materials are used for magnets, and they have a very high remanence, which is to say they retain a very large proportion of the original magnetic field that was induced into them during manufacture.
All switchmode power supplies use ferrite transformers, since conventional laminations cannot be made thin enough to prevent huge losses in the core.
Many limitations exist in any core material. For low frequency power applications, grain-oriented silicon steel (about 4% silicon) is by far the most common, as it has a very high flux density before saturation. Almost all other materials are inferior in this respect, one of the main reasons this material is still so common.




A small sample of some transformers is shown above (not to scale). The toroidal and E-I transformers are the same power rating, and a small selection of little transformers and a plug-pack (wall transformer, wall-wart, etc) are shown as well.

Magnetism and Inductors
The transformer is essentially just two (or more) inductors, sharing a common magnetic path. Any two inductors placed reasonably close to each other will work as a transformer, and the more closely they are coupled magnetically, the more efficient they become.

When a changing magnetic field is in the vicinity of a coil of wire (an inductor), a voltage is induced into the coil which is in sympathy with the applied magnetic field. A static magnetic field has no effect, and generates no output. Many of the same principles apply to generators, alternators, electric motors and loudspeakers, although this would be a very long article indeed if I were to cover all the magnetic field devices that exist.

When an electric current is passed through a coil of wire, a magnetic field is created - this works with AC or DC, but with DC, the magnetic field is obviously static. For this reason, transformers cannot be used directly with DC, for although a magnetic field exists, it must be changing to induce a voltage into the other coil.

Try this experiment. Take a coil of wire (a loudspeaker crossover coil will do nicely for this), and a magnet. Connect a multimeter - preferably analogue) to the coil, and set the range to the most sensitive current range on the meter. As you move the magnet towards or away from the coil, you will see a current, shown by the deflection of the meter pointer. As the magnet is swung one way, the current will be positive, the other way - negative. The higher the coil's inductance and the stronger the magnet (and/ or the closer it is to the coil), the greater will be the induced current.

Move the magnet slowly, and the current will be less than if it is moved quickly. Leave it still, and there is no current at all, regardless of how close the magnet may be. This is the principle of magnetic induction, and it applies to all coils (indeed to all pieces of wire, although the coil makes the effect much greater).

If you now take a handful of nails and place them through the centre of the coil, you will see that the current is increased many times - the magnetic field is now more concentrated because the steel nails make a better magnetic path than air.

The ability of a substance to carry a magnetic field is called permeability, and different materials have differing permeabilities. Some are optimised in specific ways for a particular requirement - for example the cores used for a switching transformer are very different from those used for normal 50/60Hz mains transformers.

The permeability of transformer cores varies widely, depending on the material and any treatment that may be used. The permeability of air is 1, and most traditional cores have a much higher (i.e. > 1) permeability. A couple of notable exceptions are aluminium and brass, which are sometimes used to reduce the inductance of air cored coils in radio frequency (RF) work. This is much less common than a ferrite "slug" core, which increases the inductance and is used to tune some RF transformers.

As well as permeability, magnetic cores (with the exception of air) have a maximum magnetic flux they can handle without saturation. In this context, saturation means the same as in most others - when a towel is saturated, it can hold no more water, and when a magnetic core is saturated, it can carry no more magnetic flux. At this point, the magnetic field is no longer changing, so current is not induced into the winding.

You will be unable to saturate your nails with the magnet, as there is a very large air gap between the two pole pieces. This means that the core will always be able to support the magnetic flux, but the efficiency is also very much lower because the magnetic circuit is open. Nearly all the transformers you will see have a completely closed magnetic circuit, to ensure that as much of the magnetism induced into the core as possible will pass through the winding(s).

There are some cases where a tiny air gap will be left deliberately, and this is done routinely when a transformer or coil must sustain a significant DC component as well as the AC. This is covered briefly below, but there is more on this subject in the second section of the article.


Figure 1.1 - Essential Workings of a Transformer

Figure 1.1 shows the basics of all transformers. A coil (the primary) is connected to an AC voltage source - typically the mains for power transformers. The flux induced into the core is coupled through to the secondary, a voltage is induced into the winding, and a current is produced through the load.

The diagram also shows the various parts of a transformer. This is a simple transformer, with two windings. The primary (denoted as such during the design) will induce a magnetic field into the core in sympathy with the current produced by the applied AC voltage. The magnetic field is concentrated by the core, and nearly all of it will pass through the windings of the secondary as well, where a voltage is induced. The core in this case is typical of the construction of a "C-Core" transformer, where the primary and secondary are separated. More common is the "traditional" EI (ee-eye) type, which although somewhat out of favour these days is still used extensively. This is shown below.

The magnitude of the voltage in the secondary is determined by a very simple formula, which determines the "turns ratio" (N) of the component - this is traditionally calculated by dividing the secondary turns by the primary turns ...

1.1.1N = Ts / Tp
Tp is simply the number of turns of wire that make up the primary winding, and Ts is the number of turns of the secondary. A transformer with 500 turns on the primary and 50 turns on the secondary has a turns ratio of 1:10 (i.e. 1/10 or 0.1)

1.1.2Vs = Vp * N
Mostly, you will never know the number of turns, but of course we can simply reverse the formula so that the turns ratio can be deduced from the primary and secondary voltages ...

1.1.3N = Vs / Vp
If a voltage of 240V (AC, naturally) is applied to the primary, we would expect 24V on the secondary, and this is indeed what will be measured. The transformer has an additional useful function - not only is the voltage "transformed", but so is the current.

1.1.4Is = Ip / N
If a current of 1A were drawn by the primary in the above example, then logically a current of 10A would be available at the secondary - the voltage is reduced, but current is increased. This would be the case if the transformer were 100% efficient, but even this - the most efficient "machine" we have - will sadly never be perfect. With large transformers used for the national supply grid, the efficiency of the transformers will generally exceed 95%, and some will be as high as 98% (or even more).

Smaller transformers will always have a lower efficiency, but the units commonly used in power amplifiers can have efficiencies of up to 90% for larger sizes. The reasons for the lost power will become clear (I hope) as we progress. For the time being, we shall consider the transformer to be "ideal" (i.e. having no losses) for simplicity.


Figure 1.2 - E-I Laminations

The conventional E-I lamination set is still extensively used, and a few pertinent points are worth mentioning. The centre leg is always double the width of the outer legs to maintain the cross-sectional area. Likewise, the "I" lamination and the "back" of the E are the same width as (or sometimes slightly larger than) the outer legs. The winding window is where the copper windings live, and in a well designed transformer will be almost completely full. This maximises the amount of copper and reduces resistive losses because the windings are as thick as they possibly can be.

2. Magnetic Core Terminology
This list is far from complete, but will be sufficient to either get you started or scare you away. I have included the symbols and units of only three of the entries below, since most are of no real interest.

Coercivity - is the field strength which must be applied to reduce (or coerce) the remanent flux to zero. Materials with high coercivity (e.g. those used for permanent magnets) are called hard. Materials with low coercivity (those used for transformers) are called soft.

Effective Area - of a core is the cross sectional area of the centre limb for E-I laminations, or the total area for a toroid. Usually this corresponds to the physical dimensions of the core but because flux may not be distributed evenly the manufacturer may specify a value which reflects this.

Effective length - of a core is the distance which the magnetic flux travels in making a complete circuit. Usually this corresponds closely to the average of the physical dimensions of the core, but because flux has a tendency to concentrate on the inside corners of the path the manufacturer may specify a value for the effective length.

Flux Density - (symbol; B, unit; Teslas (T)) is simply the total flux divided by the effective area of the magnetic circuit through which it flows.

Flux linkage - in an ideal inductor the flux generated by one turn would be contained within all the other turns. Real coils come close to this ideal when the other dimensions of the coil are small compared with its diameter, or if a suitable core guides the flux through the windings.

Magnetomotive Force - MMF can be thought of as the magnetic equivalent of electromotive force. It is the product of the current flowing in a coil and the number of turns that make up the coil.

Magnetic Field Strength - (symbol: H, unit; ampere metres (A m-1)) when current flows in a conductor, it is always accompanied by a magnetic field. The strength, or intensity, of this field is proportional to the amount of current and inversely proportional to the distance from the conductor (hence the -1 superscript).

Magnetic Flux - (symbol: ; unit: Webers (Wb)) we refer to magnetism in terms of lines of force or flux, which is a measure of the total amount of magnetism.

Permeability - (symbol; µ, units: henrys per metre (Hm-1) is defined as the ratio of flux density to field strength, and is determined by the type of material within the magnetic field - i.e. the core material itself. Most references to permeability are actually to "relative permeability", as the permeability of nearly all materials changes depending upon field strength (and in most cases with temperature as well).

Remanence - (or remnance) is the flux density which remains in a magnetic material when the externally applied field is removed. Transformers require the lowest possible remanence, while permanent magnets need a high value of remanence.

I mention these here for the sake of completeness, but their real importance is not discussed further in Section 1. Section 2 of this article will revisit the terms, and their importance is somewhat enhanced in context.

3. How a Transformer Works
At no load, an ideal transformer draws virtually no current from the mains, since it is simply a large inductance. The whole principle of operation is based on induced magnetic flux, which not only creates a voltage (and current) in the secondary, but the primary as well! It is this characteristic that allows any inductor to function as expected, and the voltage generated in the primary is called a "back EMF" (electromotive force). The magnitude of this voltage is such that it almost equals (and is effectively in the same phase as) the applied EMF.

Although a simple calculation can be made to determine the internally generated voltage, doing so is pointless since it can't be changed. As described in Part 1 of this series, for a sinusoidal waveform, the current through an inductor lags the voltage by 90 degrees. Since the induced current is lagging by 90 degrees, the internally generated voltage is shifted back again by 90° so is in phase with the input voltage. For the sake of simplicity, imagine an inductor or transformer (no load) with an applied voltage of 230V. For the effective back EMF to resist the full applied AC voltage (as it must), the actual magnitude of the induced voltage (back EMF) is just under 230V. The output voltage of a transformer is always in phase with the applied voltage (within a few thousandths of a degree).

For example ... a transformer primary operating at 230V input draws 150mA from the mains at idle and has a DC resistance of 2 ohms. The back EMF must be sufficient to limit the current through the 2 ohm resistance to 150mA, so will be close enough to 229.7V (0.3V at 2 ohms is 150mA). In real transformers there are additional complications (iron loss in particular), but the principle isn't changed much.

If this is all to confusing, don't worry about it. Unless you intend to devote your career to transformer design, the information is actually of little use to you, since you are restrained by the "real world" characteristics of the components you buy - the internals are of little consequence. Even if you do devote your life to the design of transformers, this info is still merely a curiosity for the most part, since there is little you can do about it.

When you apply a load to the output (secondary) winding, a current is drawn by the load, and this is reflected through the transformer to the primary. As a result, the primary must now draw more current from the mains. Somewhat intriguingly perhaps, the more current that is drawn from the secondary, the original 90 degree phase shift becomes less and less as the transformer approaches full power. The power factor of an unloaded transformer is very low, meaning that although there are volts and amps, there is relatively little power. The power factor improves as loading increases, and at full load will be close to unity (the ideal).

Now, another interesting fact about transformers can now be examined.

We will use the same example as above. A 240V primary draws 1A, and the 24V secondary supplies 10A to the load. Using Ohm's law, the load resistance (impedance) is therefore 24/10 = 2.4 Ohms. The primary impedance must be 240/1 = 240 Ohms. This is a ratio of 100:1, yet the turns ratio is only 10:1 - what is going on?

The impedance ratio of a transformer is equal to the square of the turns ratio ...

3.1.1Z = N²
Transformers are usually designed based on the power required, and this determines the core size for a given core material. From this, the required "turns per volt" figure can be determined, based on the maximum flux density that the core material can support. Again, this varies widely with core materials.

A rule of thumb can be applied, that states that the core area for "standard" (if indeed there is such a thing) steel laminations (in square centimetres) is equal to the square root of the power. Thus a 625VA transformer would need a core of (at least) 25 sq cm, assuming that the permeability of the core were about 500, which is fairly typical of standard transformer laminations. This also assumes that the core material will not saturate with the flux density required to obtain this power.

The next step is to calculate the number of turns per volt for the primary winding. This varies with frequency, but for a 50Hz transformer, the turns per volt is (approximately) 45 divided by the core area (in square centimetres). Fewer turns are needed for a 60Hz transformer, and the turns per volt will be about 38 / core area. Higher performance core materials may permit higher flux densities, so fewer turns per volt might be possible, thus increasing the overall efficiency and regulation. These calculations must be made with care, or the transformer will overheat at no load.

For a 625VA transformer, it follows that you will need about 432 turns for a 240V primary, although in practice it may be less than this. The grain-oriented silicon steels used in better quality transformers will often tolerate much higher total flux per unit area, and fewer turns will be needed.

You can determine the turns per volt of any transformer (for reasons that will become clearer as we progress) by adding exactly 10 turns of thin "bell wire" or similar insulated wire to an existing transformer, wound over the existing windings. When powered from the correct nominal supply voltage, measure the voltage on the extra winding you created, and divide by 10 to obtain the turns per volt rating for that transformer.

Now, what earthly use is this to you? Well, you might be surprised at what you can do with this knowledge. Assume for a moment that you have a transformer for a fair sized power amplifier. The secondary voltage is 35-0-35V which is much too high to power the preamp circuit or even its power supply - but you will be able to do that with a single 16V winding. Another transformer would normally be used, but you can also add the extra winding yourself. This is almost too easy with toroidal transformers, but with others it may not be possible at all. If the transformer uses (say) 2 turns per volt, a mere 32 extra turns of bell wire (or similar) will provide 16V at the typical 100mA or so you will need. Add a 10% margin, and you still have only 36 turns to add, and this can be done in a few minutes. Make sure that the extra winding is securely taped down with a good quality tape (Kapton is highly recommended if you can get it). Do not use ordinary electricians' tape - it is not designed for the temperature that transformers may operate at under consistent load.

NOTE: Ensure that there is no possibility whatsoever of the added winding shorting between turns - this will cause the smoke to escape from the insulation in a spectacular fashion, and you may ruin the transformer itself.

4.Interesting Things About Transformers
As discussed above, the impedance ratio is the square of the turns ratio, but this is only one of many interesting things about transformers ... (well, I happen to think they are interesting, anyway ).

For example, one would think that increasing the number of turns would increase the flux density, since there are more turns contributing to the magnetic field. In fact, the opposite is true, and for the same input voltage, an increase in the number of turns will decrease the flux density and vice versa. This is counter-intuitive until you realise that an increase in the number of turns increases the inductance, and therefore reduces the current through each coil.

I have already mentioned that the power factor (and phase shift) varies according to load, and this (although mildly interesting) is not of any real consequence to most of us.

A very interesting phenomenon exists when we draw current from the secondary. Since the primary current increases to supply the load, we would expect that the magnetic flux in the core would also increase (more amps, same number of turns, more flux). In fact, the flux density decreases! In a perfect transformer with no copper loss, the flux would remain the same - the extra current supplies the secondary only. In a real transformer, as the current is increased, the losses increase proportionally, and there is slightly less flux at full power than at no load.

5. Examples of Transformer Uses
This is only a brief discussion of the many uses of transformers. I have avoided switchmode supplies in this section, and will only present the most common linear applications. Power supply applications are covered more fully in Section 2, and also in the article on Linear Power Supply Design.

It would be impossible to cover all aspects of transformers and their uses, since they are so diverse and are used in so many different things. Computer network interface cards, modems, through to power amplifiers and microwave ovens, car and marine ignition systems, Tesla coils and moving coil phono preamps, power distribution from the power station to your home ... this is a very small sampling of the diversity of the humble transformer (well, maybe it is not so humble after all.

5.1 - Push-Pull Valve Output Stage
Apart from the obvious uses in power supplies, transformers are used in other areas as well. Valve power amplifiers nearly all use a transformer for the output stage, and this converts the high impedance of the anodes to the loudspeaker impedance, as well as providing the voltage feed to the output valves. No biasing or other support components have been shown here - for more information on this, have a look at How Amplifiers Work. Another reference for valve stages is in the Valves section.


Figure 5.1 - Push-Pull Valve Output Stage

Figure 5.1 shows how this works. The primary winding acts in a manner that may surprise you at first, but it is quite in accordance with all the theory. The supply voltage shown is 500V, and we will assume that the valve can turn on hard enough to reduce this to zero alternately at each end of the winding. This is never the case, because valves do not have a low enough internal impedance, but it makes the explanation simpler .

Neither valve will draw appreciable current with no signal, and the amount drawn does not magnetise the core. The reason is simple - an equal amount of current is drawn through each section of the primary winding, but effectively in opposite directions. The magnetic field created by one half of the winding is cancelled by that from the second half, leaving a nett steady state magnetic field of zero.

When valve V1 turns on completely, the voltage at its end of the winding is reduced to zero, and the voltage at the anode of V2 is 1,000 volts. This must be the case, or the transformer theory is in tatters. The primary is operating as an "auto-transformer". Likewise, when V1 turns off and V2 turns on, the situation is reversed. You may well ask why 2 valves are needed at all? The voltage from one valve is quite capable of swinging the voltage from one extreme to the other, it would seem.

This is not the case. Since the valve can only turn on, it will only be able to supply current for 1/2 of the waveform. A Class-A push-pull design will normally have each valve carrying 1/2 of the maximum peak current required at idle, and the full peak current when turned on to the maximum before distortion (the other valve is turned off). In the case of a push-pull design, there is no core saturation because of the DC current (which cancels out as before), so although two valves are needed, the transformer will be smaller and will have very much better performance. Single-ended Class-A amps require a very large core with an air-gap to prevent saturation. This reduces the performance of the transformer dramatically, and increases distortion and gives a poorer low frequency response because of the lower inductance. High frequencies can also be adversely affected, because the air-gap causes some of the magnetic flux to "leak" out of the core. This is the cause of leakage inductance (covered in more detail in Section 2).

It is worth noting that the effective peak to peak swing across the entire transformer primary is 2,000V. When V1 is turned on completely, it has zero volts (for our example only) at the plate, and V2 turns on it has a plate voltage of 1,000V. V2 has exactly the same voltage peaks, but they are 180 degrees out of phase. The total voltage across the transformer is therefore the sum of the two voltages. From an AC perspective, the B+ supply line can be considered the same as zero volts (remember it will be bypassed with a large capacitance).

The RMS voltage is easily calculated from the standard formula ...

5.1.1Vp = Vp-p / 2
To obtain the peak value from peak to peak, then ...

5.1.2Vrms = Vp / √2
To find the RMS value.

In this case, the peak to peak voltage is 2,000V, so peak is 1000V. The RMS value is 707V.

5.2 Single Ended Triode (SET) Output
Figure 5.2 shows the basic arrangement of a SET amplifier output stage. The full DC current must flow through the transformer primary, and as discussed above, an air-gap must be introduced into the core to prevent saturation. Because an air gap reduces the efficacy of the magnetic path, the core needs to be considerably larger than would otherwise be the case.


Figure 5.2 - Single Ended Triode Output Stage

The core operates with only one polarity of flux, which varies with the signal. One might think that this alone would reduce distortion, since the flux never crosses the zero point, but this is not the case. It is still necessary for the flux to change, and the characteristics of magnetic materials indicate that the resistance to change (rather than the absolute polarity of the magnetic field) is the dominant factor. The valve (and transformer primary) must now carry a current equal to the peak AC current demanded by the load - subject to the transformation ratio, of course. Maximum negative swing (valve turned on) will double this current, and it will be reduced to nearly zero as the valve turns off (positive swing). As the current is reduced below the average standing (quiescent) current, the voltage across the transformer increases in the opposite polarity - hence the fact that the plate voltage exceeds the supply voltage.

For the same power output, the valve in a single ended circuit must be considerably larger than that required for a push-pull circuit, because of the higher dissipation needed for the extra current. There are also many other issues with this arrangement - in particular high distortion and comparatively high output impedance..

Not the least of the issues is that the advantage of the additional voltage swing when using a centre tapped transformer is now gone, so the maximum RMS voltage that can be developed is 353V - a significant drop in primary AC voltage. This means that the valve loading is higher for the same speaker impedance (the transformation ratio is smaller) so we get less power again.

5.3 Line Level Applications
Transformers are also used for "line-level" low power applications, typically balanced microphone inputs and line output stages. A transformer is unsurpassed for real-world balanced circuits, as the input or output is truly floating, and requires no connection to earth. This means that common mode signals (i.e. any signal that is common to both signal leads) are almost completely rejected.
Figure 5.3 shows a transformer balanced input, converting to unbalanced. The signal is amplified, and sent to the output transformer for distribution as a balanced signal again. The "amplifier" will typically be a mixing console, and will take mic or line level signals as the input (having run from the stage to the mixing area), and the final mixed output is sent back to the stage for the main (Front of House) public address amplifiers and speakers. There may be in excess of 100 metres of cable from the microphone to the mixer and back to the main amps, and barely any noise will be picked up in the process.


Figure 5.3 - Balanced Microphone and Line Outputs
The telephone system used to be completely dependent on transformers to feed the signal from the exchange (or Central Office in the US) to the customer premises equipment (CPE). The phone switch used in offices, (PABX - Private Automatic Branch Exchange, or PBX for the US) equipment still uses transformers for nearly all incoming circuits whether analogue or digital. The principle is exactly the same as for the audio application shown above, except that for telephone circuits there is usually a DC voltage present to power the CPE (in the case of a home telephone) and to provide some basic signalling. All modern PABX circuits use ferrite cored transformers, with DC isolation circuitry to ensure that no DC flows in the transformer windings, as this degrades the performance in the same way as with the output transformer for a SET power amplifier.

Audio applications for transformers in balanced circuits came from the telecommunications industry where the concepts were first thought of. A telephone line may be 4km or more in length, and is not shielded, so a method of eliminating hum and noise was essential.

6.Safety
Safety is a major consideration for any power transformer (and in the case of telecommunications, the isolating transformers), and electrical contact between primary and secondary must not be allowed under any realistic fault condition. All countries have safety standards that apply to transformers where electrical isolation is important, and if in any doubt about the safety of a transformer for a particular purpose, make sure that you verify that the transformer complies with the relevant standard(s). It is well beyond the scope of this article to cover all the possibilities of standards and compliance issues, so I shall leave that to you - and your supplier.

Many power transformers are fitted with an internal "once only" thermal fuse that will become open circuit in the event that a preset temperature is exceeded. This temperature is chosen to be the maximum safe temperature of the windings before the insulation melts or breaks down, so in the event of a fault, the thermal fuse will open before the insulation is damaged and the component becomes potentially dangerous. It also helps to prevent the risk of fire (and no, this is not intended to be humorous - a friend of mine had his house burned to the ground because of a faulty power transformer in a video recorder - as determined by the fire investigators. True story!). See Figure 6.1 (below) as an example of how bad things can get if the transformer is not protected.

Once the thermal fuse opens, the transformer must be discarded, as it is usually not possible to gain access to the fuse for replacement. This is not as silly as it may sound, since the thermal effects on the insulation cannot be predicted, and the transformer may be unsafe if it were still able to be used.

There are transformers that are designed to be "intrinsically safe", and these usually have the windings on separate sections of the core, not in physical contact with each other. If the core is connected to the electrical safety earth (which is usually a requirement), no method of failure (including a complete meltdown) in the primary will allow mains voltage to appear at the secondary. Side by side windings are the next safest, and although primary and secondary are on the same bobbin, the material used is selected to withstand high temperatures and will maintain separation of the windings. Toroidal cores and other concentrically wound transformers are the least safe, since the only separation between primary and secondary is a rather thin layer of insulation. This is one of the reasons that thermal fuses are often used with toroids.

Figure 6.1 - Transformer Meltdown
Figure 6.1 shows a transformer I removed from a repair job. It is a complete meltdown, and the remains of the plastic bobbin can be seen quite clearly. In any circuit, it is extremely important to protect the user from coming into contact with the mains should this happen. In this case, the bobbin had melted away from the windings, dribbled on the base of the equipment, and generally made a big mess. Despite all this, there was no electrical connection between primary and secondary or the laminations. This was a well made transformer (it failed due to gross continuous overload, not any failure in the transformer itself).

Proper safety earthing is the only real way to ensure that a transformer that fails catastrophically (such as that shown) does not cause the chassis to become live - not all transformers are created equal when safety is concerned. Correct fusing will ensure that the fuse blows - hopefully before the electrical safety is compromised. A thermal fuse would have prevented the situation from becoming as bad as shown, but the transformer would have been just as dead.

7.Noise
Transformers make noise. This is not only the electrical noise that is created by the nasty current waveform through the windings, diodes and into the filter capacitors, but actual audible noise. One source is winding vibration, due to the wire moving because of the magnetic field and the current flowing through the conductors. This is to be avoided at all costs, since constant vibration will eventually wear away the insulation, the windings will short circuit, and the transformer is ruined. Fortunately, this is rather unusual, but it can (and does) happen on occasion.

Most of the noise is from the laminations or other core material, which contract when subjected to an intense magnetic field. This is called magnetostriction, and happens to a greater or lesser degree with all magnetic materials. A stethoscope will verify the source of the noise, and there is little or nothing that will stop it. A resilient mounting will stop most of the noise from being acoustically amplified by the chassis, and generally the noise will be worse at no load. In some cases, a transformer may have been designed for 60Hz, but is used at 50Hz. In this case, the flux density will probably exceed the maximum allowable for the core, and the transformer will get much hotter than it should, and will almost certainly be a lot noisier as well. Toroidal transformers will generally be much quieter than EI laminated (i.e. conventional) types.

Most (all?) transformers designed specifically for 60Hz will eventually fail with 50Hz mains, due to overheating. The reverse is not true, and 50Hz transformers can be operated quite safely on 60Hz.

Another problem with E-I laminations is that they may not have been fastened together well enough, and this allows the outer laminations in particular to vibrate. Better quality conventional transformers will commonly be impregnated with varnish (sometimes under vacuum) and baked in a moderate oven until tender .... oops, I mean until the varnish is completely dry. This binds the laminations and windings together, preventing noise, and also making the transformer more resistant to damage by water or other contaminants, and/ or under conditions of high humidity (such as in the tropics)

Section 2

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.
Before reusing any transformer - especially if designed for a different purpose, voltage or frequency - you need to check that it will not draw excessive magnetising current. 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 so hot that it's uncomfortable to hold. If the idle temperature rise is more than about 25°C the transformer should not be used. Bear in mind that some small transformers run rather hot all the time, so on occasion you may have to make a value judgement based on experience.

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
There 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 the traditional way to identify the start of a winding, so that the phase may be determined.

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
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 and currents. Series connections are sometimes used in the primaries as well, mainly for equipment destined for the world market. There are several common mains supply voltages, and primary windings are connected in various combinations of series and parallel to accommodate all the variants.

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 ohms
The impedance ratio is calculated first ...
Z = 6,000 / 7.2 = 833
The 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 = 69V
To convert this to RMS ...
Vp = 1/2 Vp-p = 34.5V
RMS = peak * 0.707 = 24V
Power is therefore 24² / 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 a conservative rating that is more likely to be met in practice.

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.


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 :-) the transformers are larger and harder to design, and even then will be worse than their push-pull counterparts. In the maximum efficiency configuration, power output is 100W, 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 considerably higher 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. 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

When the magnetomotive force is reversed in a magnetic material, the residual magnetism (remanence - also known as remnance) in the core tries to remain 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. The power 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, but a Web search will no doubt reveal more information than you will ever need.


Figure 11.2 - B-H Curve

As 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" of the 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 not produce 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 too sensitive 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 at 50Hz, failure is inevitable.


Figure 11.3 - Cutaway View of a Transformer

The transformer shown is a "split bobbin" type, having separate sections on the former for the primary and secondary windings. This reduces the capacitance between windings, 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 is also 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 insulated so 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 be placed 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 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

The eddy currents are shown for three lamination thicknesses. Although not shown (for the sake of clarity), the current loops are constantly overlapping, and are effectively 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 the currents (and losses) are larger. For high frequencies (above 10kHz), it is generally not possible to make laminations thin enough to prevent the losses from becoming excessive, and ferrite materials are preferred. These effectively have a huge number of incredibly small magnetic particles, all insulated from each other, and eddy current loops 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 great again.

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 = 2mW
V = R * I = 5 * 0.02 = 100mV
For 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 ...

P = I² * R = 1.00² * 5 = 5W
V = R * I = 5 * 1.00 = 5V
Now, 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.

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 / 1
Where 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 Ohms
Half 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 = 4.34:1
ZR = TR² = 4.34² = 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 secondary resistance (Rs) is 0.15 ohms, being half of the total. Primary resistance must be ...

Rp = Rs * ZR = 0.15 * 18.83 = 2.82 Ohms
Based 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.



The 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 is shown 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 just by 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 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 winding resistance could be up to 15% lower than calculated to reduce the current density in the primary.

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 = 2.3
ZR = TR² = 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 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
The 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 (C1 and 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 is not 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 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 trick to winding transformers to minimise the winding leakage inductance and self capacitance is called "interleaving", but this results in much greater inter-winding capacitance (between primary and secondary). The most common way this is done is to use a multi-segmented winding, as shown in the sectional drawing of Figure 11.6. This type of winding 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 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-C is not a globally recognised class, but 220°C 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 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.


The 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 one of 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 no load, 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 of them 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 own transformers 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 better regulation 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 weigh in at about 5kg.



To 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 see a 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 well on 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) measure them.

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 affect on performance in real life.

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
The 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 single bobbin 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 given voltage. 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-I 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

A 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 to suit specific applications.

Figure 13.2 - Some Ferrite Core Styles

The 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 same in 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 due to 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 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

When 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 to circulate through the end laminations and the bolts, reducing performance dramatically. For safety, the core should always be bonded to mains earth unless the transformer 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 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

Just 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.


Figure 13.5 - Assembled Laminations and Punching Dimensions

The 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 a little 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 is made 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 final insulation layer.

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.

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 "boing" noise when power is applied. That this phenomenon is intermittent 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
The longer a transformer is left unpowered, the lower the remanent flux, and the less likelihood there is of an excessively high inrush current. If the mains is applied when at it's peak value, inrush current is at it's lowest. Conversely, if the mains is applied at the zero crossing point, inrush current will be maximum - this is exactly the reverse of what you would logically expect. The inrush current lasts for several cycles, and is made much worse with a rectifier and filter capacitor on the output. The capacitor is a short circuit when discharged, and large capacitors will take longer to charge.

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.

References
1. http://sound.westhost.com/xfmr.htm#s1.0-magind
2. http://sound.westhost.com/xfmr2.htm