Detailed explanation of the loss problem of magnetic components in transformers

Magnetic components generally refer to inductors and transformers. Here we discuss the transformer with primary-secondary isolation because this type of transformer is most widely used in switching power supplies.

The function of the transformer is to provide primary and secondary electrical isolation, so that the output voltage can be increased or decreased and energy can be transmitted. The quality of the transformer design is directly related to the safety, EMC, efficiency, temperature rise, output electrical performance parameters, life, reliability of the entire power system, and may even lead to system collapse.

I have done voltage boosting before, but I don't have much experience. I am just sharing my personal understanding, which may not be correct, but is for reference and discussion purposes only.

The difficulty of the step-up transformer has been pointed out by the above person. Because there are too many turns of the winding, it is difficult to have the best of both worlds for leakage inductance and distributed capacitance. At this time, I think we should start from the following aspects:

1. When choosing a transformer, if the structural dimensions allow, we try to choose a tall and long (vertical) or narrow and long (horizontal) type, because this type of transformer has a large number of single-layer winding coils, which can effectively reduce the number of winding layers, increase the coupling between the primary and secondary, and reduce the interlayer capacitance.

2. Optimize the winding sequence so that the coupling area between the primary and secondary can be increased or decreased. This winding method has been used before: 1/3 secondary--1/2 primary--1/3 secondary--1/2 primary--1/3 secondary. The results show that this winding method can reduce the leakage inductance a lot.

Of course, the winding process of this transformer is slightly complicated and the cost is slightly higher, but it is still acceptable.

3. As we all know, adding yellow tape between each layer can reduce the interlayer capacitance.

Of course, these measures are improvements made with safety regulations and EMC in mind. For boost power supplies, leakage inductance and interlayer capacitance can easily cause oscillations if not properly handled, making the power supply's EMC poor and the efficiency low, and sometimes causing the MOS tube to explode for no apparent reason (a situation I've actually encountered).

We know that transformer losses are divided into iron losses and copper losses. Let’s talk about iron losses first.

The iron loss of the transformer includes three aspects:

One is hysteresis loss. When AC current passes through the transformer, the direction and size of the magnetic lines of force passing through the transformer core change accordingly, causing the molecules inside the core to rub against each other, releasing heat energy, thereby wasting some electrical energy. This is hysteresis loss.

The second is eddy current loss. When the transformer is working, magnetic lines of force pass through the magnetic core, and an induced current will be generated on the plane perpendicular to the magnetic lines of force. Since this current forms a closed loop and forms a vortex, it is called eddy current. The existence of eddy current makes the magnetic core heat up and consumes energy. This loss is called eddy current loss.

The third is the residual loss. During the magnetization or demagnetization process of the core, the magnetization state does not change immediately with the change of magnetization intensity. There is a lag time. The lag effect is the cause of the residual loss.

From the definition of the three aspects of iron loss, the hysteresis loss can be reduced by controlling the size of the magnetic lines of force, and the eddy current loss can be reduced by reducing the area perpendicular to the magnetic core and the magnetic lines of force.

Teacher Zhao pointed out in the book "Magnetic Components in Switching Power Supplies":

From the above, it can be seen that when the core material, shape, volume, etc. are determined, the iron loss of the transformer is proportional to the operating frequency of the transformer and the magnetic induction intensity swing deltB.

Hysteresis can be ignored at low fields, and eddy current can also be ignored at low frequencies, leaving only residual losses. When the magnetic induction intensity is high or the operating frequency is high, the various losses affect each other and are difficult to separate. Therefore, when it comes to the magnitude of magnetic losses, the operating frequency f and the corresponding Bm value should be indicated. However, at low-frequency weak fields, it can be expressed by the algebraic sum of the three: tanδm= tanδh+tanδf+tanδr. Where tanδh tanδf tanδr are: hysteresis loss tangent, eddy current loss tangent, and residual loss tangent. The relationship between various losses and frequency is shown in the figure.

As can be seen from the figure, the residual loss has nothing to do with the size of B, but increases with the increase of frequency. The hysteresis loss increases with the increase of B, and the eddy current loss changes linearly with the frequency. Knowing this, we can know that: in the forward and bridge power supplies, the core loss focuses on the eddy current loss. In the flyback transformer and energy storage inductor, both eddy current loss and hysteresis loss must be considered, especially for the power supply working in DCM mode, hysteresis loss is the first. So it can be determined that the first point when making a power supply is to select the corresponding core material according to the operating frequency of the power supply.

Next, let's start discussing the copper loss of the transformer.

The copper loss of the transformer is the loss of the transformer winding, which includes DC loss and AC loss.

DC loss is mainly caused by the copper enameled wire around the transformer, which has a certain impedance (Rdc) to the current passing through it. This current refers to the effective value of the current waveform of each winding. DC loss is proportional to the square of the current.

Relatively speaking, AC losses are much more complicated, including the skin effect of the winding, the loss caused by the proximity effect, and the loss caused by each harmonic.

Let's talk about DC impedance first. The reasons for its formation have been mentioned above. Now let's analyze how to reduce DC loss.

First, the DC loss calculation formula is given: Pdc=(Irms)^2*Rdc

It can be seen from the above formula that, when the effective value of the current is constant, the DC loss of the winding can be reduced by reducing the DC equivalent resistance of the winding.

We know that the resistance of the winding is related to the material, length, cross-sectional area and even temperature (very little relationship), so we can use the following methods to reduce the DC loss of the winding:

1. Use conductors with low resistivity to wind the transformer. Generally, copper enameled wire is used. Try not to use copper-clad aluminum enameled wire or aluminum enameled wire.

2. If the transformer window area allows, try to use enameled wire with a larger equivalent cross-sectional area (a single wire should not exceed the penetration depth, which will be analyzed later)

3. Appropriately reduce the number of turns of the winding (will increase iron loss), use with caution

Let’s first look at the definition of skin effect:

The skin effect, also known as the skin effect, refers to the phenomenon that when an alternating current passes through a conductor, there is a large current density at the edge and a small current density in the center of the conductor cross section.

The principle of skin effect is relatively complicated, and can be simply described as follows:

As shown in the figure above, let the current flowing through the conductor be i, and its direction is as shown in the figure. According to the right-hand rule, a mmf magnetic field will be generated, and it will be perpendicular to the current direction. The eight small circles in the figure are the magnetic lines of force entering and leaving the problem. According to Faraday electromagnetic induction, magnetic lines of force will generate eddy currents when passing through the conductor, and the direction is shown by the large circle around the eight small circles in the figure.

As can be seen from the figure, the direction of the eddy current strengthens the current at the edge of the conductor and offsets the current in the center of the conductor. This is the principle of the skin effect.

Regarding the skin effect, Mr. Zhao Xiuke has discussed it in detail in the book "Magnetic Components in Switching Power Supplies".

Here we introduce another term: penetration depth

Definition: When a high-frequency current flows through a conductor, the current flows through the conductor surface due to the skin effect. The thickness of this surface is called the penetration depth or skin depth, which is represented by "Δ".

It should be noted that the penetration depth refers to the radius of the conductor.

The penetration depth is related to the operating temperature, the resistivity of the conductor, the relative magnetic permeability of the conductor and the frequency.

The calculation formula is:

Δ=65.5/√f(mm) 20℃

Δ=76.5/√f(mm) 100℃

I will not derive the formula, if you are interested you can refer to the relevant information.

It is not difficult to see from the above formula that the higher the operating frequency, the lower the penetration depth of the wire. Therefore, when designing transformers, engineers must consider the effect of frequency on the penetration depth of the wire.

The current decreases, but the direction of the current remains unchanged, so the direction of the magnetic field generated remains unchanged.

Here we only explain the principle of skin effect, so we don't mention the influence of frequency. I understand it this way: the higher the frequency, the greater the rate of change of current, which means the stronger the magnetic field strength, that is to say, the greater the eddy current's obstruction to the current in the center, so there is a problem of penetration depth.

Next, let's look at the proximity effect

definition:

When currents in opposite directions flow through two adjacent conductors, a magnetomotive force is generated between them, and the magnetomotive force will generate eddy currents in the other conductor. This eddy current causes the current to increase where the conductors are close to each other and to decrease where the conductors are far away from each other.

As can be seen from the above figure, the proximity effect causes some parts of the conductor to have little or no current flowing through them, while other parts to have a lot of current flowing through them. This can cause a lot of heat loss, which is particularly obvious when the wire is thick.

Practice has shown that the proximity effect is closely related to the number of winding layers, and the proximity effect increases exponentially with the increase in the number of winding layers.

Regarding the principle of the proximity effect, Mr. Zhao Xiuke has a very detailed and wonderful analysis

There are too many uncertainties in the design of magnetic components. For example, for the same winding process requirements, different manufacturers may produce slightly different products. There are also differences in core materials because not every factory can afford TDK cores. Therefore, I believe that design requires rich experience and actual debugging to determine the final parameters.

I usually calculate the parameters roughly online, and then debug them in practice. The final parameters are mainly determined by the effect of debugging.