What is the advantage of calculating the inductance coefficient of the inductor?

Jun 27, 2024 Leave a message

This has to start with the hidden inductance of the transformer. The transformer has to be regarded as an inductor, because as we said, both the inductor and the transformer are in the form of a coil around a magnetic core.
The inductance of the transformer is a name based on the electromagnetic principle, not a name for actual use.
The name of the transformer is based on the purpose of its design, because it transmits energy and changes the output voltage.
However, one thing that cannot be ignored is that the coil is wound around the magnetic core (here we are talking about the inductor with a magnetic core, of course, there is also an air-core inductor), which is the most common inductor in our power supply. Since the transformer windings share the magnetic core, the magnetic circuit le, magnetic flux cross section Ae, and magnetic permeability μ of the primary Np and secondary Ns coil inductances Lp and Ls are the same, which means that the magnetic resistance Rm of the magnetic lines is the same, because the magnetic resistance describes the characteristics of the magnetic core.
Let's first understand the expression of magnetic resistance of our regular magnetic field or magnetic circuit. Later we will know that it is also derived from a basis:
The reciprocal of magnetic resistance is magnetic permeability G. This parameter is also the inductance coefficient AL that we often see. This must be clear
In the above formula, μ is the material magnetic permeability, which is the absolute magnetic permeability, le is the equivalent magnetic circuit, and Ae is the equivalent cross-sectional area of ​​the magnetic core
Since the inductance coefficient or magnetic permeability G is the same for the same magnetic core, the relationship between the number of turns and the inductance is naturally the following expression. This is our very common method of calculating the number of turns using the measured inductance (cracking the transformer of other designers).
Tip: Remember, it is the secondary connected load that takes current through the transformer, not the transformer actively giving current to the load. The transformer passively transmits energy, so this distinguishes the difference between the transformer and the inductor. The inductor releases energy to the load and actively releases energy to the load. For easy understanding, you can say that the transformer is a passive device and the inductor is an active device. Of course, don't understand it as the concept of "passive device" and "active device" of semiconductor devices.
Principle, when the secondary of the transformer is connected to the load, due to the load factor, the secondary voltage us is added to the load R to generate the current is (here we regard the load as an equivalent resistor R, and the current flows out from the same end), and the current is generates the magnetic motive force Fs=is*Ns (the principle of electromotive force in the circuit) in the secondary coil Ns, and the magnetic flux generated is φ22=φs.
Remember Ohm's law in the magnetic circuit? The quotient of the magnetic motive force (NI, the product of the number of turns and the current) and the magnetic resistance is the magnetic flux. The derivation of this formula is also very simple. The basic principle is the Ampere circuit theorem (the connection between current and magnetic field). In the formula, Rm is the magnetic resistance and G is the magnetic permeance. This is a constant in the same magnetic core.
The magnetic flux φ22 caused by the load is opposite to the magnetic flux φ11 generated by the primary coil caused by the load current. This is what Lenz's law tells us. In essence, the magnetic flux generated by the secondary coil must be balanced with the primary coil except for the excitation magnetic flux. This can also be seen from the above magnetomotive force expression. In the figure below, we use magnetic lines of force of different colors to represent it.
After loading, the primary magnetic flux is the sum of the no-load excitation current magnetic flux φ1 and the magnetic flux φ11 caused by the load, and the two have the same direction.
Pay attention to the writing of the magnetic flux phi symbol, which may be deformed due to the recognition of the editor.
The excitation magnetic flux is a necessary condition for establishing electromagnetic conversion. At the same time, it can be seen that the primary current flows in from the same end and the secondary current flows out from the same end, which just keeps the energy in and out, and it can also be said that this maintains magnetic balance (cannot accumulate, accumulation means that the transformer core is saturated after a certain time).
On the contrary, we can easily know the ratio of the primary and secondary currents of the transformer by using the magnetomotive force expression. The inverse relationship is obtained in this way.
From this formula, it can be seen that the transformer is a variable current flow function from the secondary to the primary, and the variable current is the result of the secondary taking energy.
From the power point of view, the IP here does not include the excitation current, because we know from the principle that the excitation part cannot be transmitted. The excitation or excitation current only provides the conditions for energy transmission, and the load itself actively takes energy.
Ignoring the loss, the input power and output power are equal, and there is no need to store energy in the magnetic field. The transformer is an energy transmission device, not an energy storage device. In the actual transformer, high magnetic permeability materials are used to increase the excitation inductance to reduce the excitation current. The purpose of reducing the excitation current is to reduce copper loss and magnetic loss.
4. Reflected impedance
We clearly know that only the secondary coil has an actual load, and the primary side has no actual load, but when the load is connected, there is current and voltage on the primary side, which constitutes an equivalent impedance phenomenon.

Schematic diagram of transformer primary reflected impedance
When the output is loaded, the load takes energy through the transformer, and the input current will increase accordingly.
It is emphasized that the transformer is an energy transmission component. Only the excitation or exciting current causes energy storage, which cannot be transmitted to the secondary side for the load to use. When the transformer is loaded, the secondary current, that is, the magnetomotive force generated by the load current, is the demagnetizing magnetomotive force. Excitation is the basis for ensuring energy transmission. Without it, the secondary voltage will no longer exist, let alone energy transmission.
The working principle determines that the load cannot demand excitation energy for the load to use, so the primary coil of the transformer must be magnetically reset. Magnetic reset is the process of actively releasing energy by the primary excitation inductance, but it does not give it to the load, but to release it through a path that is physically connected to it. Since the core connection is an inductive connection, the excitation current is the basis for the operation of the transformer. Without it, how can the transformer establish a relationship between two things that are not physically connected?
5. Summary
But in terms of energy, the transformer is passive. It will not actively release energy to the load. Instead, the load connected to the secondary coil will demand energy from the source. It seems that the transformer is supplying energy, but it should be clear that this energy is not stored in the transformer. Instead, the primary side supplies energy synchronously in response to the load request while the load is demanding it. This is done synchronously.

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