# What are the disadvantages of the leakage flux

## Coupled inductors and their applications

This technical article starts a series on coupled inductors. At the beginning it will be clarified how these components basically work, what advantages and disadvantages they have and how they are used in principle.

Two inductors coupled together can be defined as separate components that share part of their magnetic flux lines. Due to the common coupling, a voltage is induced in the other winding by one winding: this is called mutual coupling.

What is the difference between a transformer or transmitter and a coupled inductor?

Unfortunately, the terms “transformer” and “transformer” can no longer be differentiated in terms of their specific application. The transformer, actually intended as a component for the "transmission" and impedance adjustment of signals, is nowadays also used for the transmission of energy, ie voltage and current, in the "transformative" sense, which is why only the term "transformer" is used in the following. used.

The two components - coupled inductance and transformer - are, on the surface, very similar. Their parameters, however, are optimized differently. Due to the different naming - coupled inductance and transformer - the different purposes are to be clarified.

Of course, in the end only the data sheets tell you which parameters the components have and where they can be used. A transformer is specifically designed to transfer power from one winding to the other. The coupling between the two windings must be as good as possible and the leakage inductance should approach zero. The absolute inductance of the individual winding is often of minor importance for this type of application.

A transformer transfers the energy directly from the primary winding to the secondary winding without storing the energy in the magnetic circuit. To do this, the current flows in both windings at the same time, their magnetic fluxes are polarized in opposite directions and cancel each other out. Standard transformers are usually designed with a fixed coupling, which can assume values of over 99%.

Typically, transformers are used for power transmission, where a reduction in coupling leads to losses and poor efficiency. Coupled inductances are available in different strengths of coupling, from very low coupling, typically only 5% to 10% up to over 90%.

In the case of a transformer, an alternating voltage is normally applied to the primary winding in order to generate a voltage on the secondary side; the current is transmitted immediately here. Any piece of energy that is stored is usually seen as a problem because it causes losses. Most transformers are wound on cores with low magnetic resistance (reluctance). The cores have magnetization and leakage inductances, but these result from parasitic effects.

An ideal transformer does not have these parasitic properties; an ideal transformer does not store energy. A coupled inductance can store energy depending on the embodiment. The inductor is then designed to store a significant amount of energy in the core flux.

For this reason the core has a gap, either a discrete gap or a distributed one, as in a core made of iron powder, in which this energy is stored as a magnetic field. In addition, ferrite material and winding structures are adapted to the respective type of coupled inductance.

In the case of coupled inductances, each winding is still used alone as the actual inductance, although of course the "certain mutual coupling" also plays a role in the circuit, otherwise there would be two separate inductances. In general, with coupled inductors, leakage inductance is less of a problem.

In fact, it can be useful to have some guaranteed, low, uncoupled inductance or leakage inductance for each winding. The absolute inductance of each winding with the secondary winding open is an important parameter here that is precisely defined. Most of these coupled inductors have the same number of turns - that is, a transformation ratio of 1: 1, but some special designs have a higher transformation ratio of 1:50 and more.

The mutual coupling of the magnetic circuits in a coupled inductance is interesting insofar as the magnetic fluxes generated by the windings have the same polarity and thus an addition, which means that the magnetic flux has a value that cannot be neglected and magnetic energy is stored in the core. In a transformer, the coupling is different in that the fluxes counteract and thus cancel each other out, leaving a negligible net flux in the magnetic circuit.

Coupled inductor applications typically include circuits that primarily use separate inductors, but where some coupling between the two inductive circuits will benefit function in one or more circuit parameters. For example, a coupled inductor can be used in a flyback converter, where it stores the energy while the switching transistor (MOSFET) is on, and then releasing the energy to the output when the switching transistor (MOSFET) is off.

Coupled inductances allow a number of other advantages, such as a significantly reduced current ripple, voltage transformation, changing the impedance of a circuit and galvanic isolation. The application in switched-mode power supplies, for example, includes SEPIC converters, converters with galvanic isolation, multi-phase converters and special converter circuits that weaken the negative properties of hard switching.

However, the coupled inductance also has disadvantages and these lead to the fact that the inductance works with somewhat higher losses, for example in flyback converters, and cannot cause ideal, e.g. rounded, instead of triangular signal shapes, which must be taken into account in terms of circuitry. Also, the current specifications for a coupled inductor will vary depending on whether its windings are in series or in parallel.

For example, if the windings are connected in series, the equivalent inductance will be more than twice the nominal inductance due to mutual inductance. The saturation and rms current ratings must be applied to the current flowing through both windings at the same time, unless otherwise specified in the data sheet. A clear understanding of the functionality and specifications of coupled inductors is therefore essential in order to be able to use these components optimally.

### Negative coupling and coupling factor

A single inductor is only "coupled to itself," that is, it has an input and an output (**Image 1**), with voltage and current according to the relationship **Equation 1** consequences:

The coupled inductance consists of two windings or coils that share a common core. The inductance of a winding depends on the core material, the geometry of the core material, the winding turns and the type of windings. Since the two windings are inductively coupled, they influence each other. The mutual inductance between the two windings can be expressed with

where M is the mutual inductance, with the unit H, and L_{1} and L_{2} are the inductances of the primary or secondary winding.

#### Negative coupling and coupling factor, Figures 1-4

Show all pictures (4)

However, this assumes that there is perfect coupling between the windings without leakage flux. In reality, there is always some leakage flux, even though some designs are extremely tightly coupled. A number for expressing the coupling between the windings is the coupling coefficient k. It is represented by a number between zero and one, where k = 0 means that there is no coupling and k = 1 means that there is a perfect coupling. This coefficient can be used to calculate the **Equation 2** to modify, thus results **Equation 3**.

In coupled inductors there are two windings that share a single core and are thus coupled together. This principle is known from the transformer and **picture 2** clarifies the connections. In **picture 2** causes a current i_{1} in inductance L._{1} a voltage u via the magnetic flux Φ_{2} in inductance L._{2} on the secondary side of the transformer. This effect is known as mutual inductance and can be caused by the **Equation 4** to be discribed:

A transformer therefore consists of two magnetically coupled inductances, the self-induction voltage and the mutual induction voltage. The voltages at the inductances can be described with:

and

In **picture 3** the corresponding circuit diagram is shown.

The two points on the inductance symbols in the circuit diagram indicate the winding direction. The ideal inductance has no losses and no stray field. Neither losses in the copper wire, nor in the ferrite core and in the insulating material. The wire resistance is 0 Ω and the magnetic resistance of the ferrite core is 0 (μ_{r} -> ∞). In this case the following applies:

The following relationship therefore applies to the ideal transformer or the coupled inductance:

The corresponding circuit diagram of the ideal transformer or the ideal coupled inductance shows**Picture 4**.

1.

**Coupled inductors and their applications**

2. Parasitic components

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