Beginners Guide to Transformer

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Beginners' Guide to Transformers

Copyright 2001 - Rod Elliott (ESP)Page Published & Updated 24 Mar 2001

Transformers - The BasicsSection 1

Contents - Section 1 Preface

Introduction

1. Magnetism and Inductors

2. Magnetic Core Terminology 3. How a Transformer Works

4. Interesting Things About Transformers

5. Examples of Transformer Uses

o 5.1 Push-Pull Valve Output Stage

o 5.2 Single Ended Triode (SET) Output

o 5.3 Line Level Applications

6. Safety

7. Noise

Section 2

References

Preface

One thing that obviously confuses many people is the idea of flux density within thetransformer core. While this is covered in more detail in Section 2, it is important thatthis section's information is remembered at every stage of your reading through thisarticle. For any power transformer, the maximum flux density in the core is obtainedwhen the transformer is idle. I will reiterate this, as it is very important ...

For any power transformer, the maximum flux density is obtained when thetransformer is idle.

The idea is counter-intuitive, it even verges on not making sense. Be that as it may, it'sa fact, and missing it will ruin your understanding of transformers. At idle, thetransformer back-EMF almost exactly cancels out the applied voltage. The small currentthat flows maintains the flux density at the maximum allowed value, and represents ironloss (see Section 2). As current is drawn from the secondary, the flux falls slightly, andallows more primary current to flow to provide the output current.

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It is not important that you understand the reasons for this right from the beginning, butit is important that you remember that for any power transformer, the maximum fluxdensity is obtained when the transformer is idle. Please don't forget this

Introduction

As you look through this article, you may be excused for exclaiming "This is forbeginners? - the man's mad. Mad, I tell you!" This is probably fair comment, buttransformers are not simple, and there is no simple way to provide all the informationyou need to understand them properly. There are sections here that probably go a littlebit 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 readall of it if you can. A full understanding to the extent where you can design your owntransformer is not the aim, but the majority of the information is at the very leastinteresting, and will further your general electronics knowledge.

For those who wish to delve deeper, Section 2 does just that. It is recommendedreading, 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 in1824, when Danish physicist Hans Oersted found that a current flowing through a wirewould deflect a compass needle. A few years after this, it was found that a movingmagnetic field induced a current into a wire. From this seemingly basic concept, the fieldof electromagnetism has grown to the point that society as we know it would not existwithout the many machines that make use of these discoveries.

Transformers are essential for all modern electronics equipment, and there are very fewdevices that do not use them. Each transformer type has a specific use, and it isuncommon that a transformer made for one application can be used for another (quitedifferent) purpose.

Before embarking on a description of the different types, the basic theory must beunderstood. All transformers use the same basic principle, and only the finer points everchange. A transformer works on the principle of magnetic coupling to transfer theenergy from one side (winding) to the other.

Transformers are bi-directional, and will work regardless of where the input isconnected. They may not work as well as they otherwise might, but basic functionality isunchanged. An ideal transformer imposes no load on the supply (feeding the primary)

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unless there is a load across the secondary - real life components have losses, so thisis 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 loadthat 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 thatthere is little or no real power in the load, but the transformer is still supplying a voltageand 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 willremain in a high permeability core with little leakage. The lower the permeability, thegreater is the flux leakage from the core (this is of course a gross simplification, butserves 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 500and upwards.

Powdered Iron - Steel magnetic particles formed into a core and held togetherwith a bonding agent, and fired at high temperature to create a ceramic-likematerial 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 (from50kHz to over 1MHz). An astonishing range of different formulations is availablefor 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 aregenerally unsuitable for low frequency operation, except at low levels. Ferrites are oftenused as signal transformers (such as isolation transformers for telecommunications orother 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 theirphysical properties (they are all hard to very hard), but is a reference to their ability toretain magnetism (remanence). Hard magnetic materials are used for magnets, and

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they have a very high remanence, which is to say they retain a very large proportion ofthe original magnetic field that was induced into them during manufacture.

All switchmode power supplies use ferrite transformers, since conventional laminationscannot 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 highflux density before saturation. Almost all other materials are inferior in this respect, oneof the main reasons this material is still so common.

Toroidal E-I

Split Bobbin E-I Plug-Pack Conventional E-I

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 anda plug-pack (wall transformer, wall-wart, etc) are shown as well.

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1. Magnetism and Inductors

The transformer is essentially just two (or more) inductors, sharing a common magneticpath. Any two inductors placed reasonably close to each other will work as atransformer, 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 voltageis induced into the coil which is in sympathy with the applied magnetic field. A staticmagnetic field has no effect, and generates no output. Many of the same principlesapply to generators, alternators, electric motors and loudspeakers, although this wouldbe 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 thisreason, 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 forthis), and a magnet. Connect a multimeter - preferably analogue) to the coil, and set therange to the most sensitive current range on the meter. As you move the magnettowards or away from the coil, you will see a current, shown by the deflection of themeter pointer. As the magnet is swung one way, the current will be positive, the otherway - negative. The higher the coil's inductance and the stronger the magnet (and/ orthe 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 isthe 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 willsee that the current is increased many times - the magnetic field is now moreconcentrated 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 differentmaterials have differing permeabilities. Some are optimised in specific ways for aparticular 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 anytreatment that may be used. The permeability of air is 1, and most traditional cores havea much higher (i.e. > 1) permeability. A couple of notable exceptions are aluminium andbrass, which are sometimes used to reduce the inductance of air cored coils in radio

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frequency (RF) work. This is much less common than a ferrite "slug" core, whichincreases the inductance and is used to tune some RF transformers.

As well as permeability, magnetic cores (with the exception of air) have a maximummagnetic 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, andwhen a magnetic core is saturated, it can carry no more magnetic flux. At this point, themagnetic 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 airgap between the two pole pieces. This means that the core will always be able tosupport the magnetic flux, but the efficiency is also very much lower because themagnetic circuit is open. Nearly all the transformers you will see have a completelyclosed magnetic circuit, to ensure that as much of the magnetism induced into the coreas possible will pass through the winding(s).

There are some cases where a tiny air gap will be left deliberately, and this is doneroutinely when a transformer or coil must sustain a significant DC component as well asthe AC. This is covered briefly below, but there is more on this subject in the secondsection 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 anAC 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, anda 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 amagnetic field into the core in sympathy with the current produced by the applied ACvoltage. The magnetic field is concentrated by the core, and nearly all of it will passthrough the windings of the secondary as well, where a voltage is induced. The core in

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this case is typical of the construction of a "C-Core" transformer, where the primary andsecondary are separated. More common is the "traditional" EI (ee-eye) type, whichalthough somewhat out of favour these days is still used extensively. This is shownbelow.

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 calculatedby dividing the secondary turns by the primary turns ...

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

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

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

1.1.4 Is = Ip / NIf a current of 1A were drawn by the primary in the above example, then logically acurrent of 10A would be available at the secondary - the voltage is reduced, but currentis increased. This would be the case if the transformer were 100% efficient, but eventhis - the most efficient "machine" we have - will sadly never be perfect. With largetransformers 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 usedin power amplifiers can have efficiencies of up to 90% for larger sizes. The reasons forthe lost power will become clear (I hope) as we progress. For the time being, we shallconsider the transformer to be "ideal" (i.e. having no losses) for simplicity.

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Figure 1.2 - E-I Laminations

The conventional E-I lamination set is still extensively used, and a few pertinent pointsare 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 Eare the same width as (or sometimes slightly larger than) the outer legs. The windingwindow is where the copper windings live, and in a well designed transformer will bealmost completely full. This maximises the amount of copper and reduces resistivelosses 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 youaway. I have included the symbols and units of only three of the entries below, sincemost are of no real interest.

Coercivity -is the field strength which must be applied to reduce (orcoerce) theremanent flux to zero. Materials with high coercivity (e.g. those used for permanentmagnets) are called hard. Materials with low coercivity (those used for transformers) arecalled soft.

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

Effective length - of a core is the distance which the magnetic flux travels in making acomplete circuit. Usually this corresponds closely to the average of the physicaldimensions of the core, but because flux has a tendency to concentrate on the insidecorners 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 theeffective area of the magnetic circuit through which it flows.

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

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

Magnetic Field Strength - (symbol: H, unit; ampere metres (A m -1)) when current flowsin 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 thedistance from the conductor (hence the -1 superscript).

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

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

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

I mention these here for the sake of completeness, but their real importance is notdiscussed further in Section 1. Section 2 of this article will revisit the terms, and theirimportance 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 issimply a large inductance. The whole principle of operation is based on inducedmagnetic flux, which not only creates a voltage (and current) in the secondary, but theprimary 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 thesame phase as) the applied EMF.

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No simple calculation can be made to determine the internally generated voltage. Asdescribed in Part 1 of this series, for a sinusoidal waveform, the current through aninductor lags the voltage by 90 degrees. Since the induced current is lagging by 90degrees, so too is the induced voltage (back EMF). For the sake of simplicity, imaginean inductor or transformer (no load) with an applied voltage of 100V. For the effective

back EMF to equal the applied AC voltage (as it must), the actual magnitude of theinduced voltage (back EMF) is 141V. If this is all to confusing, don't worry about it.Unless you intend to devote your career to transformer design, the information isactually of little use to you, since you are restrained by the "real world" characteristics ofthe components you buy - the internals are of little consequence. Even if you do devoteyour life to the design of transformers, this info is still merely a curiosity for the mostpart, since there is little you can do about it.

When you apply a load to the output (secondary) winding, a current is drawn by theload, and this is reflected through the transformer to the primary. As a result, theprimary 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 shiftbecomes less and less as the transformer approaches full power. The power factor ofan 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 atfull 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 24Vsecondary 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 ...

3.1.1 Z = NTransformers are usually designed based on the power required, and this determinesthe core size for a given core material. From this, the required "turns per volt" figure canbe 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 squareroot 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 ofstandard transformer laminations. This also assumes that the core material will notsaturate with the flux density required to obtain this power.

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The next step is to calculate the number of turns per volt for the primary winding. Thisvaries 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 60Hztransformer, and the turns per volt will be about 38 / core area. Higher performance corematerials may permit higher flux densities, so fewer turns per volt might be possible,

thus increasing the overall efficiency and regulation. These calculations must be madewith care, or the transformer will overheat at no load.

For a 625VA transformer, it follows that you will need about 432 turns for a 240Vprimary, although in practice it may be less than this. The grain-oriented silicon steelsused 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 becomeclearer as we progress) by adding exactly 10 turns of thin "bell wire" or similar insulatedwire to an existing transformer, wound over the existing windings. When powered from

the correct nominal supply voltage, measure the voltage on the extra winding youcreated, 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 dowith this knowledge. Assume for a moment that you have a transformer for a fair sizedpower amplifier. The secondary voltage is 35-0-35V which is much too high to powerthe preamp circuit or even its power supply - but you will be able to do that with a single16V winding. Another transformer would normally be used, but you can also add theextra winding yourself. This is almost too easy with toroidal transformers, but with othersit may not be possible at all. If the transformer uses (say) 2 turns per volt, a mere 32extra 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 donein a few minutes. Make sure that the extra winding is securely taped down with a goodquality tape (Kapton is highly recommended if you can get it). Do notuse ordinaryelectricians' tape - it is not designed for the temperature that transformers may operateat under consistent load.

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

4. Interesting Things About Transformers

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As discussed above, the impedance ratio is the square of the turns ratio, but this is onlyone of many interesting things about transformers (well, Ithink 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, theopposite is true, and for the same input voltage, an increase in the number of turns willdecrease the flux density and vice versa. This is counter-intuitive until you realise thatan increase in the number of turns increases the inductance, and therefore reduces thecurrent through each coil.

I have already mentioned that the power factor (and phase shift) varies according toload, 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. Sincethe 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 wouldremain 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 lessflux 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 avoidedswitchmode supplies in this section, and will only present the most common linearapplications. 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 theyare so diverse and are used in so many different things. Computer network interfacecards, modems, through to power amplifiers and microwave ovens, car and marineignition systems, Tesla coils and moving coil phono preamps are a very small samplingof the diversity of the humble transformer (well, maybe it is not so humble after all :-)

5.1 - Push-Pull Valve Output StageApart from the obvious uses in power supplies, transformers are used in other areas aswell. 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 asproviding the voltage feed to the output valves. No biasing or other support componentshave been shown here - for more information on this, have a look at How AmplifiersWork.

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