# Build own transformer - how to design a transformer - basics

_lazor_ 6585 34
This content has been translated » The original version can be found here
• 1. Magnetic field in matter

Prof. Roman Kurdziel „Podstawy elektrotechniki” wydanie II ca³kowicie zmienione. wrote:
The magnetic field in a vacuum depends only on the electrical circuits that produce it. In material environments there is also the influence of molecular currents in particles of matter. An electron moving around the nucleus with an angular velocity of omega_zero on an orbit with a radius r represents the elementary magnetic dipole. Magnetic dipoles are generally chaotic in matter, so that the body does not exhibit a magnetic state unless it is exposed to an external magnetic field, i.e. created by external causes, e.g. current in any electrical circuit.
The elementary magnetic dipole placed in the external magnetic field is affected by a mechanical moment, which puts the electron, regardless of orbital motion, in precession motion, similar to whirligig. The precession axis is the H field strength vector. This creates an additional magnetic field that weakens the external field slightly. This phenomenon is called diamagnetism.
For the reason given above, all bodies should have diamagnetism. However, in many bodies, placed in the external magnetic field, the reverse phenomenon is observed, i.e. some amplification of the external magnetic field. The phenomenon can easily be explained if it is assumed that the electron, in addition to orbital motion, performs a rotational movement around its axis, called an electron spin. The spin of the electron is accompanied regardless of the magnetic moment resulting from orbital motion, the spin magnetic moment p_s.
In individual atoms, some of the electrons spin in one direction, while the others in the opposite direction, which corresponds to the opposite return of the spin moment. If the numbers of electrons rotating back and forth are equal, the sum of spin magnetic moments is zero and the body exhibits diamagnetic properties resulting from the orbital motion of the electrons. However, if the number of electrons with a certain direction of rotation prevails, the sum of spin magnetic moments is different from zero and the atom exhibits a certain resultant spin moment, which in the external magnetic field tends to take a position consistent with the direction of field strength. The spin dipole field and the external magnetic field add up, i.e. the presence of this type of matter increases the magnetic field relative to the field that a given electrical circuit would produce in a vacuum. This phenomenon is called paramagnetism.
The impact of the environment on the magnetic field is therefore marked: in diamagnetic environments, a decrease, and in paramagnetic environments, an increase in magnetic inductance B in relation to the inductance B_o, which a given external field of H intensity would cause in a vacuum. The ratio of Resultant B induction to external field strength H is called the magnetic permeability of the environment
$$u = \frac{B}{H}$$
(...) At certain values of the ratio of the distance D between atoms to the diameter of the atom d, namely when 1.5 < D/d < 3.5, there are conditions favorable for the spontaneous parallel arrangement of the resultant spin moments of adjacent atoms. Clusters of atoms are formed, i.e. domains with the same orientation of spin magnetic moments, 10 ^ 14 to 10 ^ 16 atoms, and behave like correspondingly large magnetic dipoles. Such bodies were called ferromagnetic bodies because the above properties were first observed in iron.

(...) In ferromagnetic bodies, the relationship B = f (H) is non-linear.

The above introduction illustrates phenomena occurring in matter under the influence of a magnetic field. Is the above knowledge about the properties of the magnetic field in matter required to design a transformer? No, but it makes it easier to understand the phenomena occurring in the transformer. The topic of winding selection and estimation of the power that the core of the given material and cross-section can transfer, is repeated on the forum many times, which is why I decided to bring this topic closer. Especially, that from year to year, less and less used transformers working with 50/60Hz are used, and switching power supplies are increasingly used.
In the following text I will focus only on transformers that do not have a crack in the core.

2. Core material parameters

Transformer core materials are not linear elements. Core parameters strongly depend, among others, on:
- temperature
- magnetic field strength
- frequencies and changes in the magnetic flux amplitude
For this reason, material documentation on one chart often presents material behavior for e.g. 25 ° C and 100 ° C to illustrate a certain range of material work.

Let's analyze the parameters given in the 3C90 core documentation:

$$\matrix{u_i \text{ – It is the amplitude permeability of the magnetic core when the intensity}\\ \text{of the magnetic field is unboundedly close to “zero”. }\\ \\ u_a\text{ – It is the relative permeability acquired from the maximum value of the magnetic flux}\\ \text{density and the maximum value of the intensity of the magnetic field when there are}\\ \text{periodic changes in a magnetic core that is in a demagnetized state and a magnetic field}\\ \text{that makes the average value of the intensity “zero” is applied. }\\ \\ P_v\text{ – Losses in core under certain conditions } (\frac{kW}{m^3} = \frac{mW}{cm^3})\\ \text{ρ – Material resistivity }\\ T_c\text{ – Curie temperature}\\ \text{Density – Material density }}$$

After the above parameters we can learn a bit about the material, but they are of not very usefull when designing the transformer. They are used mainly to quickly estimate the material's capabilities. Much more important values are those contained in the charts:

Fig. 1 shows magnetic permeability as a complex number (u'_s and already '' _ s). The ratio of these two values (u '' _ s / u'_s) determines the material loss tangent (the ratio of the power stored in the magnetic field to the dissipated power in the form of heat).

Fig. 2 Initial permeability graph versus core temperature.

Fig. 3 Graph of magnetic hysteresis loop

Fig. 4 Graph of permeability values relative to the peak of the magnetic flux (for a sinusoidal wave).

Fig. 5 Magnetic permeability of a material by constant magnetic field (H_dc) magnetization at zero value of alternating magnetic field strength.

Fig. 6 Very important graph. It describes to us a very important B * f relationship to material losses. The B * f relationship directly determines in what conditions we can "squeeze" the most power from the material at specific losses in iron. Keep in mind that this is a graph given for a 100 degree Celsius core.

Fig. 7 The graph shows the effect of temperature on iron losses for several points of the previous graph.

3. Assumptions for transformers

We already know a bit about the parameters describing the materials from which the transformers are made, but what do we need to start physical winding of the transformer? Where to begin? From the converter topology and its assumptions. Some topologies (e.g. flyback or LLC) use transformers with gap. However, I will focus here on calculations for transformers without a gap, which can be found in such topologies as LCC, half / full bridge (including phase shift, PWM and other variations), push-pull and others.

3.1 Primary winding voltage, frequency and filling.

The voltage applied to the primary winding forces the magnetizing current to flow on the primary winding. The parameter that we should specify is the definite integral of the voltage on the primary winding in the angle 0 to PI (for a classic bridge with 50% filling). We obtain the voltage surface area in the time domain, i.e. voltoseconds [V * s] or Weber (wb), i.e. the unit of magnetic flux. For rectangular voltage it is child's play - amplitude * time, for sine it is not difficult to determine. Let the integrals finally be useful for you in something practical

3.2 Rms current (RMS current) of the primary and secondary windings

Quite an obvious parameter, the power supply supplies something, so we need to determine the square root mean current that will flow through the primary and secondary windings. This value consists of the current consumed by the load and the magnetizing current.

3.3 Secondary voltage

As above, there is nothing to dwell on this.

3.4 Current in the cable

If we have already assumed what current will flow through our windings, now it is worth considering what cross-section of the wires. Giving too small a cross-section of wires, we will have a voltage drop across the winding resistance and additional losses. When we give too large a section, we will have to use a core with a larger window and / or section.

3.5 Fill factor.

This is a relatively difficult to estimate factor. In a real transformer we are not able to use 100% of the core window and we need to determine to what extent we will use it. This factor will be influenced, among others, by: bobbin dimensions, winding varnish thickness, amount of insulation used, technique and winding winding quality.

3.6 Material, iron losses and Delta B

It is sometimes difficult to talk about the choice of material here, because the fewest ones (3C90, 3F3, F-827, F-867) are the easiest available and we need to adjust our parameters to the material. You have to consider here the losses in the core, the frequency of the converter and the delta B at which the core will work. Of course, all 3 parameters are interrelated - the higher the frequency and/or delta B, the greater the loss in the core.
Fortunately, the following chart can help us find optimal values:

What is Delta B anyway? This is the difference between the minimum and maximum magnetic induction with which the core works. It is worth remembering that for symmetrical systems such as the classic half bridge it is the value between the negative and positive value of the magnetic induction amplitude.
Bmax for which we can determine iron losses is not the same as delta B. This is the maximum amplitude from the average value (in the case of a symmetrical waveform from zero), so if we have delta B at 100mT, then we consider losses for Bmax 50mT, but there are exceptions - when the magnetic induction constant component appears. When does it appear? For example, during the first dozen or so cycles of starting the power supply.

4. Calculation

Very accurate calculation of the transformer parameters requires the use of very complex formulas and not easy to use. In order to simplify the equations describing the transformer, a number of assumptions in the model have been introduced, which, unfortunately, have a large impact on the discrepancy between reality and calculations. Such simplifications include:
- uniform field strength in the core. At the same time, the winding is treated as a coil with a length of at least 20 times its radius.
- all magnetic flux passes through the core (no leakage flux).
- the core has no gap

4.1 Ap

Having the above assumptions, we can determine the power factor for our transformer:

$$A_p = \frac{\{V_1 * D_{on}\}*2*I_{1rms}}{f_s*ΔB*J*k}$$

As we would expect, increasing the transformer power (voltosecond * 2 * rms average current) increases the required transformer power factor. The denominator of this equation is much more interesting. We can conclude that by increasing the frequency, delta B, reducing the cross-section of the cable and improving the fill factor of the winding, we reduce the required value of the core power factor.
However, by increasing the value of the elements from the denominator, we increase the losses in iron and copper (in addition to the fill factor). The constructor and the requirements set for him are responsible for ensuring a proper balance between losses and core size.
Having the calculated power factor we can compare it to the real power factor of the core. If this parameter is not given, we can calculate it by the product of the cross-sectional area of the core and the window of this core.

4.2. Number of turns and magnetizing current.

$$n_1 = \frac{\{V_1*t_{on}\}}{ΔB*A_e}$$

The increase in the number of turns on the primary winding will have a higher value of magnetic flux induction (weber, voltosecond) and the decrease in the number of turns will be due to the higher value of delta B and the core cross-section.

To be sure, the magnitude of the magnetizing current can be calculated:

$$ΔI = \frac{\{V_1*t_{on}\}*l_e}{{N_1}^2 * A_e * µ_i * µ}$$

where:
$$\matrix{ l_e \text{ = average magnetic path }\\ A_e \text{ = effective core cross section }\\ µ_i \text{ = initial magnetic permeability of the material }\\ µ \text{ = magnetic permeability in a vacuum } }$$

It must be remembered that this is the difference between the maximum and minimum current amplitude. As the system works symmetrically, the maximum amplitude in one direction is half of this value. The exception is starting the transformer. Before the work is settled, the calculated difference will be asymmetrical and may lead to saturation of the core. Some controllers (eg L6699) have a "safe-start" algorithm protecting against such saturation of the core in the initial cycles of the power supply.
If we are satisfied with the magnetizing current, we can go about the physical design of the transformer.

5 Theory and reality

The calculated number of windings is often not the end of design. In fact, there are still many elements that affect the final appearance of the transformer. Among others:
- magnetic coupling factor
- leakage inductance
- inter-turn capacities
- EMI emission
- safety standards
- material selection for the insulator and spacing (creepage, clearance)
- heat dissipation from the core

and probably many more.

It must be remembered that the above formulas need to be modified for certain specific conditions. For example, if we use a core made of silicon metal sheets, it should be remembered that in this case the effective cross-section is slightly smaller than the measured cross-section due to ... insulation between individual sheets.
The gap in the core causes a decrease in the magnetic permeability value of the core, which increases the magnetizing current and energy stored in the magnetic field.

A very important parameter, which unfortunately is not calculated here, is the leakage inductance. Estimating this value is very difficult, because you have to count practically the magnetic flux for the entire space around the transformer ... Especially since the location of the primary and secondary windings relative to each other is very important.
Unfortunately, the most effective and fastest method of checking the leakage inductance is by measuring on an existing transformer ...

In the network you can find a lot of good studies on the determination of mutual inductance by the method of shifting and counter-winding winding, so I will not rewrite them. Unfortunately, calculating this value is theoretically not easy and you have to rely on Biot-Savart law.

Designing transformers is not a simple thing, but I hope that the above article will help many beginners to enter this world more smoothly. When designing a transformer, you need to have an overview of the entire power supply (and often what it will supply), and not just focus on it as one element.

source:

_lazor_
Moderator Design
Offline
_lazor_ wrote 1823 posts with rating 354, helped 161 times. Live in city Wroc³aw. Been with us since 2016 year.
• SylwekK
Level 30
I wound up my first network hit (and the next few) in primary school. My father subscribed to a young technician in which all necessary calculations were described. These transformers are still working today, and some time has already passed
• And!
In general, the topic is beyond me, so after reading I did not speak, but since the topic of network transformers was raised,
then I will ask for one detail, maybe I can find the answer to such a question:

Why do some transformers on a core made of metal EI plates (e.g. in a microwave) have a "welded core" in one place so that there is a "short circuit" between the core plates?

I found some illustrative photos:
https://www.alibaba.com/product-detail/220v-1...ve-power-voltage-transformer_60475738378.html
https://www.indiamart.com/proddetail/microwave-oven-transformer-20222540248.html
https://www.kitchenwareonline.com/samsung-high-voltage-transformer-c2x14483870

PS
I wonder if it could be "drawn" material from pdf
to the post in case the pdf disappears.
• _lazor_
Moderator Design
I'm not an expert on network transformers, but they probably weld to minimize costs. After all, everything must fit tightly so that it does not buzz too much and the use of screws and flat bars would probably be more expensive and less convenient to install than weld. These are my suppositions.

As for pdf I will transfer the charts to the post.
• And!
It can really be an optimization of production costs, but whether such welding does not increase the loss in the core and more specifically eddy current.
• ArturAVS
Moderator - At Weso³a HydePark
And! wrote:
does such welding increase the losses in the core and more specifically eddy currents?

It increases, it also causes a large no-load current. Note, however, that such luck works casual.
• User removed account
Level 1
• ArturAVS
Moderator - At Weso³a HydePark
There is a simple way not to count complicated designs. When the mains transformer is called, count the turns when unwinding the secondary winding. By dividing the number of turns by voltage, we get the number of turns per volt. It remains to count the number of windings for the new voltage and select the wire according to the required current. The maximum power cannot be exceeded because the wire will not fit on the wireframe.

Yeah, and who will want to count those unwound rolls?

Simple and proven pattern:
Quote:
Core cross section (Qr) - for classic EI cores - cross section area of the middle column of the core. The core cross-section, operating frequency and maximum induction determine the number of winding turns according to the formula:

n = (U * 10 ^ 8) / (4.44 * f * Bm * Qr) where:
n - number of turns
U - voltage [V]
f - frequency [Hz]
Bm - maximum induction [Gs]
Qr - core cross section

As you can easily calculate, for induction maximum 10,000 Gs (== 1T), frequency 50 Hz, core cross section 1 cm ^ 2 and voltage 1V we need 45 turns.
After analyzing and transforming the pattern, we can derive a fairly practical formula for the number of turns per volt for a classic 50 Hz mains transformer:

n = 45 / Qr [zw / V, cm ^ 2]

As I remember, this pattern has two characters differing in number 45 vs 44, one for continuous work and the other for occasional work. A dozen or so dozens of transformers according to this and all of them worked approx.
• _lazor_
Moderator Design
SylwekK wrote:

My father subscribed to a young technician in which all necessary calculations were described.

There is a simple way not to count complicated designs. When the mains transformer is called, count the turns when unwinding the secondary winding. By dividing the number of turns by voltage, we get the number of turns per volt. It remains to count the number of windings for the new voltage and select the wire according to the required current. The maximum power cannot be exceeded because the wire will not fit on the wireframe.

However, times are changing and network transformers are less and less used. Instead they are switched-mode power supplies, which are highly optimized and often you can forget about rewinding. However, the cost of the set (carcass, cores, hairpins, winding wire, insulation) comes out relatively cheap these days, so it's worth just designing the optimal transformer for your own needs. And since the formulas used for network transformers are not optimal for calculating pulse transformers, I decided to present more optimal calculations.

arturavs wrote:

Simple and proven pattern:
Quote:
Core cross section (Qr) - for classic EI cores - cross section area of the middle column of the core. The core cross-section, operating frequency and maximum induction determine the number of winding turns according to the formula:

n = (U * 10 ^ 8) / (4.44 * f * Bm * Qr) where:
n - number of turns
U - voltage [V]
f - frequency [Hz]
Bm - maximum induction [Gs]
Qr - core cross section

As you can easily calculate, for induction maximum 10,000 Gs (== 1T), frequency 50 Hz, core cross section 1 cm ^ 2 and voltage 1V we need 45 turns.
After analyzing and transforming the pattern, we can derive a fairly practical formula for the number of turns per volt for a classic 50 Hz mains transformer:

n = 45 / Qr [zw / V, cm ^ 2]

As I remember, this pattern has two characters differing in number 45 vs 44, one for continuous work and the other for occasional work. A dozen or so dozens of transformers according to this and all of them worked approx.

The patterns given in the article are simply more general and can be used for various waveforms and importantly fillings. In the above case, constants such as 4.44 make them optimal only for transformers powered by sinusoidal voltage.
Instead, the constant 10 ^ 8 reminded me that I had to complete the formulas with units.
• SylwekK
Level 30
There is a simple way not to count complicated designs. When the mains transformer is called, count the turns when unwinding the secondary winding. By dividing the number of turns by voltage, we get the number of turns per volt. It remains to count the number of windings for the new voltage and select the wire according to the required current. The maximum power cannot be exceeded because the wire will not fit on the wireframe.

I also used this obvious method. My father rewound the engines, I had access to virtually any size of DNE, and the winder that counted the unwound turns helped me count the turns. Unfortunately, it wasn't rosy with everyone. Some of them were simply melted to the ankle and even the carcass had to be made from scratch with only (or as much as ...) a core.
• ArturAVS
Moderator - At Weso³a HydePark
_lazor_ wrote:
The patterns given in the article are simply more general and can be used for various waveforms and importantly fillings. In the above case, constants such as 4.44 make them optimal only for transformers powered by sinusoidal voltage.

By all means I meant mains transformers, where we have sinusoidal voltage.
• User removed account
Level 1
• Renegat_pol
Level 20
[Quote = "SylwekK"]
... Some of them were simply melted to the ankle and even the carcass had to be made from scratch with only (or as much as ...) a core.

The reality of the 1980s. There was nothing to do with the carcass. In the factory where I had apprenticeships, the bobbins were made of ... fiberboard.
• RitterX
Level 37
With microwave welding from a microwave it seems a simple matter. It is about magnetostriction and acoustic experience that would accompany this size of a fully loaded transformer. Welding the sheet metal along the edges causes some slight deterioration of the core loss, but there is no drama. Eddy current loss is a spatial phenomenon from the point of view of the magnetic field in the core. It is better to increase core losses as losses due to returned microwaves because they are more and more buzzing . Let's make an appointment, it will no longer be better packaged than when you leave the factory.
• rysieklew
Level 2
Hello, I used to use the article from the Young Technician for calculations, then the Excel spreadsheet. Now it is the low and medium power power supplies that are replaced by switching power supplies. Maybe someone will need this Excel sheet.
• Mark II
Level 21
Modern low power industrial on classic EI shapes are also welded. I suppose that in this case the reduction of production costs is of particular importance.
• ^ToM^
Level 36
arturavs wrote:

n = 45 / Qr [zw / V, cm ^ 2]
As I remember, this pattern has two characters differing in number 45 vs 44, one for continuous work and the other for occasional work. A dozen or so dozens of transformers according to this and all of them worked approx.

No, the higher value was for small transformers and the smaller for larger ones made of better transformer sheet. The counter ranged from 43 to even 48. It all depends on which core and transformer the equation applied to. Nevertheless, the model is the most correct and practical.
• _lazor_
Moderator Design
All in all, you don't need to include insulation between packet sheets in your formulas and add a column fill factor?
• OldSkull
Level 27
It is a pity that the assumption in the calculations is the lack of a gap. In practice, the gap is very important, because although it reduces inductance, it protects against saturation of the core. Unfortunately, sometimes detailed information is missing in the catalog notes.
In practice, there are a lot of things that need to be measured on a finished transformer and iterate the next change of design. For example, the very presence of other windings has an effect on inductance (but this is the effect of affecting other transformer parameters). In practice, no prototype or movement. It is good that the impulse transformers are demountable (if someone does not flood them), because you can easily play with cores and moderately with windings.
Usually it looks like this, we get to know what the transformer working conditions are and we calculate what the windings and core should be based on.

Also remember that the transformer is an induction coil (only multiple) and the same rules apply to it as the coils.

I have an additional question:
Well, the epidermal effect is important for choosing the face that we wind the transformer. But there is one more effect that affects: the currents flowing through the individual threads of the weave of the face affect each other ("proximity effect"), causing uneven distribution of currents in the face. In short: the current is more likely to flow through the outer surface of the face, even reducing the depth of penetration of the current into the face. The result is that you would have to take smaller veins of the face than it results from epidermis. I met with a study on this subject, but it was too academic and came out for practical cases, quite impractical small cross-sections. Do you know anything about this? Did you meet something like that?
• _lazor_
Moderator Design
Generally, the slit causes many unwanted effects like:
- increasing the number of turns
- the stream in the crevice likes to run sideways, which can cause problems with EMI
- energy accumulation in a transformer, if it is not a topology based on it, it is undesirable
- saturation is fought differently, e.g. the mentioned safe-start algorithm or DC component cut-off capacitors.

I have heard about the proximity effect but I haven't really explored it so much, so unfortunately I won't write more about it at the moment.
• ^ToM^
Level 36
OldSkull wrote:

I have an additional question:
Well, the epidermal effect is important for choosing the face that we wind the transformer.

After all, I don't know if you are talking about transformers with an iron core powered from a 50 Hz network or pulsed on powder cores. Because these are two different fairy tales basically. The former are usually not used with the classic DNE face. The epidermal effect should be considered, but usually not at 50 Hz.

In addition, many network transformers do not have a traditional air gap when the core packet is alternately assembled.

In my opinion it's getting a mess. There should be two themes, run in parallel. How to design a network transformer and another How to design a transformer for a pulse converter.
• _lazor_
Moderator Design
The article is about the use of ferrite cores, not powder cores. Powder cores are cores with a dispersed gap and are not the same as ferrite, where the joining points are ground and adhere to minimize the gap, which is undesirable.

In total, network transformers are closer to this topic than transformers with a slot for converters such as flyback.
• OldSkull
Level 27
^ToM^ wrote:
The epidermal effect should be considered, but usually not at 50 Hz.

The article is based on the example of a pulse transformer.
^ToM^ wrote:
In my opinion it's getting a mess. There should be two themes, run in parallel. How to design a network transformer and another How to design a transformer for a pulse converter.

All in all a good idea because the approaches are different. For network, e.g., toroid winding is very important. At pulses due to the small number of turns, they even take a toroid, the problem is not great.

_lazor_ wrote:
Generally, the slit causes many unwanted effects like:
- increasing the number of turns
- the stream in the crevice likes to run sideways, which can cause problems with EMI
- energy accumulation in a transformer, if it is not a topology based on it, it is undesirable
- saturation is fought differently, e.g. the mentioned safe-start algorithm or DC component cut-off capacitors.

When generating high voltage, it is generally difficult to bite the subject without a gap.
By contrast, increasing the number of turns: it's not always bad. Sometimes, although a small gap helps a lot not to operate on the level of the number of turns, e.g. 2-3 (if the relatively low inductance value is important but high currents may be), because then the repeatability of the conductors in the transformer is of great importance.
In other words: wherever there are relatively high currents or high voltages, the gap is very useful. E.g. when we have a large gear ratio.
• _lazor_
Moderator Design
OldSkull wrote:
_lazor_ wrote:
Generally, the slit causes many unwanted effects like:
- increasing the number of turns
- the stream in the crevice likes to run sideways, which can cause problems with EMI
- energy accumulation in a transformer, if it is not a topology based on it, it is undesirable
- saturation is fought differently, e.g. the mentioned safe-start algorithm or DC component cut-off capacitors.

When generating high voltage, it is generally difficult to bite the subject without a gap.
By contrast, increasing the number of turns: it's not always bad. Sometimes, although a small gap helps a lot not to operate on the level of the number of turns, e.g. 2-3 (if the relatively low inductance value is important but high currents may be), because then the repeatability of the conductors in the transformer is of great importance.
In other words: wherever there are relatively high currents or high voltages, the gap is very useful. E.g. when we have a large gear ratio.

The article is a result of the fact that it designs a 230 / 15kV system in SR topology (series resonance with parallel load to C). There, the most fissure is something undesirable.
• ^ToM^
Level 36
_lazor_ wrote:
The article is about use ferrite cores, not powder cores.

The powder core is the general name for cores made by sintering or pressing particles instead of silicon iron sheets.

Basically, powder cores can be divided into two groups:

- powder cores made of Iron powder core,
- powder cores made of alloys (Alloy powder core).

Thus, the IPC core are ferrite cores.
• _lazor_
Moderator Design
https://pl.wikipedia.org/wiki/Ferryt

3C90 material is not included in the IPC. If you do not agree, please provide some evidence or do not litter the thread.
• ^ToM^
Level 36
_lazor_ wrote:
https://pl.wikipedia.org/wiki/Ferryt

3C90 material is not included in the IPC. If you do not agree, please provide some evidence or do not litter the thread.

I gave general information. The subject is, after all, general, while the core is given as an example, for which the example was considered. It is hard to believe that the topic was to apply only to the core of 3C90 material.

https://pl.wikipedia.org/wiki/Ferryty

Ferrites are usually made by sintering powdered metal oxides in the right proportions.

https://de.wikipedia.org/wiki/Ferrite

The starting materials for the production of soft magnetic ferrites are finely ground iron-oxygen compounds, such as iron (III) oxide or hematite. ..... These powder materials are mixed as evenly as possible or as evenly as possible in a water bath. Then the mixture is subjected to a chemical process, calcining at a temperature of about 1000 ° C.

All pressed cores are made of powders. Both ferrite and all the rest. 3C90 material and successors are made of ferrite powders. I don't know what the dispute is. It's a matter of precision in naming to distinguish it from silicon metal cores and other transformer metal sheets.
• jack63
Level 42
_lazor_ wrote:
3. Assumptions for transformers

I suggest you change it, because it looks a bit strange in Polish.
Like a trifle, but why spoil a job well done.
_lazor_ wrote:
Fig. 1 shows magnetic permeability as a complex number (u'_s and already '' _ s). The ratio of these two values (u '' _ s / u'_s) determines the material loss tangent (the ratio of the power stored in the magnetic field to the dissipated power in the form of heat).

It should be noted that this makes sense for a sinusoidal waveform, i.e. practically only network transformer.

I think that you should clearly separate the calculations for transformers or chokes powered by sinusoidal and impulse voltage (current).
The phenomena that you describe as the start of the network transformer are the basis for the work of transformers in impulse systems.
In fact, the latter work only in consecutive transient states. There is no phase shift between voltage and current. Effective values etc. must not be used.
One more remark:
Computational selection of magnetizing current is quite arbitrary. That is, two transformers wound on the same core with identical assumptions regarding voltage and power may have different numbers of turns! Both will work and only one can have more losses and more heat.
Various crafters, such as manufacturers of "space" welders, use it.
• _lazor_
Moderator Design
In general, the rectangular waveform is considered as a Fourier series and the data determined for the sine (as a sum) can be used as much as possible.

In general, switched-mode power supplies can work in sine, for example, resonant power supplies. Anyway, the above formulas can be used for different waveforms, because we operate with the integral of voltage and not constants determining the shape of voltage on the primary winding.

Switching power supplies can have their current and voltage phase shifts determined as much as possible. Look at such topology as phase shift full bridge.
For example, I once built something like this on stm32f334 in half bridge topology: