# Handbook of Transformer Design and Applications

Eletrônica de Potência Transformer and Inductor Design Handbook

www.youronlinereviews.com/wp-content/lepibica/cagun-localizador-de.php Name of resource. Problem URL. Describe the connection issue. SearchWorks Catalog Stanford Libraries. Transformer and inductor design handbook. Responsibility Colonel WM. Edition 3rd ed. Imprint New York : Marcel Dekker, c Physical description 1 v. Series Electrical and computer engineering ; Online Available online. Full view. SAL3 off-campus storage. T7 M32 Available.

### Handbook of Transformer Design and Applications

Post Views: Move the magnet slowly, and the current will be less than if it is moved quickly. Contact Magnetics for more information. However, the absence of a comment should not be interpreted negatively - it may only show inadequate familiarity with the text. 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.

More options. Find it at other libraries via WorldCat Limited preview. Bibliography Includes bibliographical references and index. Contents Fundamentals of Magnetics. Magnetic Materials and Their Characteristics. Magnetic Cores, Iron Alloy and Ferrites. Window Utilization and Magnet Wire. Transformer-Inductor Design. Power Transformer Design. This is a ratio of , yet the turns ratio is only - what is going on?

The impedance ratio of a transformer is equal to the square of the turns ratio 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 VA transformer would need a core of at least 25 sq cm, assuming that the permeability of the core were about , 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. 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 VA transformer, it follows that you will need about turns for a V primary, although in practice it may be less than this.

The grain-oriented silicon steels used in better quality transformers will often tolerate 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 the transformer to be tested, wound over the existing windings. When powered from the correct nominal supply voltage, measure the voltage on the extra winding you created. Divide the number of turns 10 by the voltage measured to obtain the turns per volt figure 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 V 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 enamelled copper wire will provide 16V at the typical mA or so you will need. 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.

The magnetising current quoted or measured for any transformer is usually a combination of true magnetising current which is usually very low and saturation current, which can be up to half the calculated full load current for small transformers. Any transformer with a core silicon steel, ferrite, etc. This is covered in much greater detail in Section 2. Core saturation is reached when the peak input voltage is sufficient to cause the core to reach its maximum rated flux.

When the flux density is too high the core can no longer accept more, and it saturates. The saturation waveform is shown in Section 2, and although you may see the transformer's 'magnetising current' specified, this is almost always the no-load primary current, including saturation current. It is unrealistic to expect any mains transformer to remain well below saturation at all operating levels. This would require the core to be a great deal larger and more expensive than normal.

When the core flux density exceeds around 1. Once the core is fully saturated it effectively no longer exists, and current is limited only by the circuit resistance. This cannot be allowed, but partial saturation at idle is common, and this increases the apparent magnetising current. For transformers used in audio valve output transformers, microphone or 'line' transformers, etc. For power transformers, a small amount of saturation at no load is common.

While this increases the no-load current and temperature of the transformer, it also allows for slightly better regulation because fewer turns are used which reduces winding resistance. Saturation is a complex process and is not well understood by most hobbyists and even some professionals. The degree of allowable saturation depends on the intended usage, and how much distortion can be tolerated. As the frequency is reduced, a transformer will saturate more if the input voltage is kept the same.

For example, a power transformer designed for 60Hz operation will usually saturate heavily at 50Hz, even if the voltage is correct. As discussed above, the impedance ratio is the square of the turns ratio, but this is only one of many interesting things about transformers 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.

## Transformer and Inductor Design Handbook, Fourth Edition

This is counter-intuitive until you realise that an increase in the number of turns increases the inductance, and therefore reduces the current through the winding. 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 primary voltage due to the copper resistance , so flux at full load is lower than at no load. It's worth making a bit of noise about this, as it is widely misunderstood.

Although already pointed out at the beginning, it's so important that I'll state it again The flux density in a transformer is greatest at no load, and it decreases as load is increased. It's also important to understand another interesting fact about mains transformers. We tend to imagine that the inductance is important - after all, that's what stops a transformer from drawing 10A or more from the mains at idle.

In reality, inductance is not normally a design parameter, but is simply the result of getting the turns per volt figure right. Inductance is also a nebulous figure, and the value is not constant, but varies or at least appears to vary depending on conditions. When you have the right number of primary turns, the inductance pretty much looks after itself. A quick calculation will demonstrate what I mean. Let's assume a VA toroidal transformer, having a measured inductance of 52H at 50Hz. The formula for inductance tells us that the magnetising current will be However, when this transformer is tested see Part 2 - Magnetising Current , the magnetising current is actually measured at 42mA - 3 times higher than expected.

This happens because the core is partially saturated, not because the inductance is lower than measured or calculated. If operated at a much lower voltage where the magnetising current is undistorted meaning there is no core saturation at all , the magnetising current obeys the formula shown above. Without core saturation, the current is determined by the inductance, voltage and frequency, as with any inductor. However, most transformers are not inductors as such! This applies to transformers used in switchmode power supplies, or for audio transformers and others where low frequency response is critical.

It's only with mains frequency transformers 50 or 60Hz where we don't really care about the inductance, provided the magnetising current is sensible. There are no 'rules' here - if it works as required and according to the design specification , remains at an acceptable temperature and is reliable and safe, then that's all that matters.

That is why manufacturers rarely if ever specify the inductance of mains frequency transformers. Instead and if you're lucky , they might tell you the no load magnetising current at rated voltage and frequency. Most don't even bother to tell you that much. After all, there's nothing you can do about it anyway. In the preface, I mentioned that a transformer is not inductive when driving its rated load. If we imagine the same transformer described above 52H of inductance it will draw 14mA of inductive current at idle ignoring saturation.

However and this is important , the primary current is an almost perfect reproduction of the secondary current, and if the secondary current is non-linear, so too is the primary current. Rectifier and capacitor loads as used in nearly all linear power supplies have a poor power factor, but it's due to non-linearity , and not inductance. So, for normal mains transformers, inductance is not part of the specification and may be considered 'incidental'.

It has to exist to limit the no load current to a reasonably sensible value, but the greatest proportion of the magnetising current is due to partial saturation. Most mains transformers have to be tested at a voltage well below their specified mains input voltage to be able to measure the inductance. A typical V transformer will need to be measured at no more than around V to obtain the actual inductance. Having measured the primary inductance, you quickly discover that this data is useless - you can't do anything with it, and it doesn't help your understanding one iota.

This is partly due to the simple fact that it changes. As the flux density within the core is varied, so too is the measured inductance, so it really is a pointless parameter in the greater scheme of things. Transformers are designed to obtain the voltage and current desired at the secondary, and the design process is based on the number of primary turns needed to get a sensible no-load 'magnetising' current. It's largely a balancing act. For a given core size, a higher magnetising current is the result of using fewer turns on the primary, and that improves regulation because the wire can be larger.

However, if the no-load current is too high, the transformer will overheat because the core saturates, due to the high primary current. A transformer that is never operated at no load can be designed to be far smaller than otherwise. If we assume that a transformer for a particular application must provide good regulation and that it is only ever operated at full load, there is no reason to make the core as large as would otherwise be necessary.

We can also use fewer turns and reduce resistive losses. Modern microwave oven transformers fall into this category - if they are operated with no load, the magnetising current can be so high that the transformer would overheat and fail, but when run normally powering a magnetron , they are perfectly suited to the job. Most are also fan cooled, allowing them to be smaller still! When a transformer is only operated at full load, magnetising current is no longer a major consideration, and the number of turns needed is based on the effective voltage across the winding at full load.

A 1kW transformer might normally have a primary resistance of around 1. At 1kW, the primary current is 4. Rather than designing the transformer for a nice low magnetising current at V, it can be designed for a somewhat higher magnetising current at V - magnetising current alone might be as much as 1 or 2A - perhaps more. Attempting to measure the inductance of such a transformer is a waste of time.

You will be able to measure it, but the reading has no meaning. Even more conventional mains transformers are in the same boat - the inductance can perhaps - at a stretch be considered a 'figure of merit', but the only thing that really matters is the total magnetising current, including the effects of partial saturation. Don't imagine for one minute that normal mains transformers don't saturate - every transformer I have ever measured will draw between 2 to 5 times the current you'd expect based on the inductance alone. Of course, at normal operating voltages the two are inseparable. The inductance ratio of any transformer between primary and secondary is the square of the turns ratio.

A transformer designed for V mains with a measured output voltage of 23V at no load 20V full load has a turns ratio of If you measure the primary inductance at say 30H, the secondary inductance is mH. This isn't useful either, but it might come in handy if you wish to use the transformer in reverse, driven from an oscillator and power amplifier for example. One of the things that tends to cause confusion relates to how the transformer 'knows' that someone is trying to draw current from the secondary, so primary current can be increased in proportion.

This is due to the mutual inductance aka mutual coupling or just coupling factor between the windings. When two or more windings share the same magnetic circuit, the two are coupled by the flux. In an ideal transformer this coupling is unity, meaning that any perturbation on one winding is directly coupled to the other allowing for transformation ratio of course. If the coupling is unity, the windings act as one. The electrical separation insulation is of no consequence, so an attempt to draw current from the secondary is no different from drawing current from the primary - the two windings are linked together and are inseparable.

Of course, real transformers are not ideal, but perhaps surprisingly that only changes things slightly. This is the key to transformer operation, but despite its great importance it has little influence on the transformer design. It's also something that you can't change - the transformer is what it is, and parameters can only be changed at design time.

## ISBN 13: 9780070212916

Leakage inductance reduces the mutual inductance, preventing unity coupling. However, this doesn't actually change anything much in mains frequency transformers. Even 'conventional' E-I lamination transformers have comparatively low leakage inductance compared to primary inductance , and toroidal types have very low leakage inductance.

Any flux that 'leaks' from the core is unable to pass through the two windings equally, thus reducing the effective flux in the secondary and reducing the coupling between them.

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The coupling is such that if you were to drive a mains transformer from a low impedance signal generator, anything on the secondary is reflected back to the primary. If the load is a capacitor, the primary will appear to be capacitive leading power factor. When the load is a resistor, the primary appears to be resistive. The primary will be inductive only if the load is an inductor. To run this test which is not difficult to do , the current drawn from the secondary has to be at least 10 times and preferably times greater than the magnetising current the no load current due to the transformer's primary inductance.

You need to draw at least 39mA from the secondary, and that's enough to cause the primary voltage and current to be within less than one degree of each other. If you now connect a capacitor that draws the same current this needs to be calculated based on the voltage and frequency the primary appears to be entirely capacitive. This is an aspect of mutual coupling that is rarely explained, but understanding this simple concept means that you can avoid a whole bunch of rather tedious maths that won't actually help you to understand the principles involved.

As regular readers know, I won't provide extensive formulae if they don't help anyone to figure out how something works. This is a case in point. Throwing a formula at this will reveal almost nothing, but if you run the test for yourself, you will understand how it works. A transformer does not have a defined impedance. You can be excused for thinking otherwise, but that's because some transformers are designed for valve amplifier output stages or for nominal ohm signal lines for example. In this role, the inductance of the primary winding is important, because it needs to be high enough to ensure good coupling between the valves and speakers at the lowest frequency of interest.

This is covered briefly in this section, and is examined in more detail in Section 2. While the inductance is important, it's even more important to ensure that the core remains well away from even partial saturation at the lowest frequencies. This is why good output transformers are so large and expensive. It also works with higher source impedances, but then the inductance may not be great enough to ensure good bass response.

The required inductance is determined by the source impedance and the lowest frequency of interest - typically 40Hz for many valve amps. So, using the example given, the inductance and -3dB frequency can be determined As should be apparent, as the source impedance is increased, more inductance is required for the same -3dB frequency. This also requires that the core flux is kept well below saturation.

Even a small amount of saturation causes gross distortion. There are some claims that this distortion is not as objectionable as might be imagined, because it falls off with increasing frequency. However, if a low and high frequency are passed simultaneously, the higher frequency will be distorted as well - once the core starts to saturate, all frequencies present at the time are distorted, not just the frequency that causes saturation.

This is only a brief discussion of the many uses of transformers.

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Handbook of Transformer Design and Applications [William M. Flanagan] on ykoketomel.ml *FREE* shipping on qualifying offers. Library of Congress Cataloging-in-Publication Data. Flanagan, William M. Handbook of transformer design and applications / William M. Flanagan. — 2nd ed.

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 Apart from the obvious uses in power supplies, transformers are used in other areas as well. Valve vacuum tube 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. 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 V, 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 in reality, 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 net steady state magnetic flux 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, volts.

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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. 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, 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 one 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,V. When V1 is turned on completely, it has zero volts for our example only at the plate, and V2 has a plate voltage of 1,V. V1 and V2 have exactly the same voltage peaks, but they are degrees out of phase. The total voltage across the transformer is therefore the sum of the two voltages.

The RMS voltage assuming a sinewave and ignoring losses is easily calculated from the standard formula 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.

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 direction, 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.

Transformer And Inductor Design Handbook, Fourth Edition by Colonel Wm. T. McLyman PDF

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.

This is one area where the transformer actually is an inductor, and circuit operation relies on the stored 'charge' of the inductor. The secondary winding simply couples the voltages to the load. 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 V - a significant drop in primary AC voltage again ignoring losses, it's exactly half.

This means that the valve loading is higher for the same speaker impedance because the transformation ratio is smaller, so we get less power again. Regular readers will be aware that I consider the 'SET' to be an abomination. The claimed advantages are mostly in the eye or ear of the beholder, and don't stand up to the slightest scrutiny. 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. 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.

## Transformer and inductor design handbook in SearchWorks catalog

There may be in excess of 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. 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 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.

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. Note that many subscriber circuits are now operated via purpose-built ICs that eliminate the transformer.

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. Today, there are tens hundreds? 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. Once the thermal fuse opens, the transformer must be discarded, as it is usually not possible to gain access to the fuse for replacement.

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This is not as silly as it may sound, since the thermal degradation of the overheated 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 'inherently 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. Note that any transformer classified as 'inherently safe' must usually meet very strict approval conditions in most countries. Figure 6. 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.