Inductance elements are also called self-inductance elements. If the magnetic flux generated by each of the two or more coils intersects with the other coil, these coils are called magnetic coupling or mutual induction. If it is assumed that these coils are stationary, and the resistance in the coils and the distributed capacitance between the turns are ignored, the coils with magnetic coupling can be expressed as idealized coupled inductors, or coupled inductors for short.
1. Series equivalent of coupled inductance
There are two ways to connect coupled inductors in series-forward and reverse. Sequential connection is the connection of different ends, as shown in Figure 1(a).
figure 1
After taking the mutual inductance voltage as a controlled voltage source, the circuit is shown in Figure 1(b), which can be obtained
where L=L1+L2+2M. It can be seen that the coupled inductance connected in series can be replaced by an equivalent inductance L, and the value of the equivalent inductance L is determined by the above formula.
Another series connection method of coupled inductors is reverse series connection. Reversed series connection is the end connection of the same name, as shown in Figure 2 (a), the circuit after taking the mutual inductance voltage as a controlled voltage source is shown in Figure 2 (b), which can be obtained from Figure 2 (b)
where L=L1+L2-2M
It can be seen that the coupled inductance connected in series can be replaced by an equivalent inductance L, and the value of the equivalent inductance L is determined by the above formula.
figure 2
2. T-type equivalent of coupled inductance
(1) The ends of the mutual inductance coils with the same name are connected together as shown in Figure 3. It is a circuit with three branches sharing a node and two branches of which have mutual inductance. It can be seen from the figure that the b end of L1 and the d end of L2 are The ends of the same name are connected together, and the voltages on the two coils are respectively
image 3
Mathematically transform the above two formulas, we can get
Draw the two-type T-type equivalent circuit as shown in Figure 3(b). In figure (b), there are three inductors without mutual inductance. Their self-inductance coefficients are L1-M, L2-M and M respectively, and they are connected to form a T-shaped structure, so they are called T-shaped mutual inductance coils. Decoupling equivalent circuit.
2. The different ends of the mutual inductance coils are connected together. Figure 4(a) has the same structure as Figure 3(a), except that the different ends of the two branches with mutual inductance are connected together, and the voltage on the two coils Respectively
Figure 4
also mathematically transform the above two formulas, we can get
The T-shaped equivalent circuit drawn is shown in Figure 5(b), where -M in the figure (b) is an equivalent negative inductance.
Figure 5
Using the above equivalent circuit, we can get the decoupling equivalent circuit of coupled inductors in parallel as shown in Figure 5 (a) and (c), as shown in Figure 5 (b) and (d) respectively. From Figure (b) (d), using the inductance series and parallel relationship without mutual inductance, the equivalent inductance of the coupled inductance in parallel when the same-named and different-named ends are connected can be obt