Introduction to the calculation method of coil inductance

In the process of switching power supply circuit design or circuit testing, the inductance of the coil or wire and the number of turns of the coil are often calculated in order to adjust and improve the circuit parameters. The following lists only a variety of coil inductance calculation methods for reference, and the derivation process is not prepared to be introduced in detail here.
When performing circuit calculations, the SI international unit system is generally used, that is, the magnetic permeability is the product of relative magnetic permeability and vacuum magnetic permeability, that is: μ=μrμ0, where the relative magnetic permeability μr is a coefficient without units, and the unit of μ0 vacuum magnetic permeability is H/m.

Several typical inductors

1. Inductance of a straight conductor with a circular cross section

in:

L: Inductance of a straight conductor with a circular cross section [H]

l: Cable length [m]

r: conductor radius [m]

μ0: vacuum magnetic permeability, μ0=4π10-7 [H/m]

[Explanation] This is the calculation formula under the condition of l>>r. When there is a magnetic bead outside the circular cross-section straight conductor, it is referred to as a magnetic bead. The inductance of the magnetic bead is μr times the inductance of the circular cross-section straight conductor. μr is the relative magnetic permeability of the magnetic core, μr=μ/μ0, μ is the magnetic permeability of the magnetic core, also known as the absolute magnetic permeability, μr is a unitless constant, which is easy to obtain through actual measurement.

2. Inductance of coaxial cable

The coaxial cable is shown in Figure 2-33, and its inductance is:

in:

L: Inductance of coaxial cable [H]

l: length of coaxial cable [m]

r1: outer diameter of the inner conductor of the coaxial cable [m]

r2: Inner diameter of coaxial cable outer conductor [m]

μ0: vacuum magnetic permeability, μ0=4π10-7 [H/m]

【Note】 This formula ignores the thickness of the outer conductor of the coaxial cable.

3. Inductance of two-wire transmission line

[page]Among them:

L: Inductance of the transmission line [H]

l: length of the transmission line [m]

D: Distance between transmission lines [m]

r: Radius of the transmission line [m]

μ0: vacuum magnetic permeability, μ0=4π10-7 [H/m]

【Note】 The application conditions of this formula are: l >> D, D >> r.

4. Mutual inductance between two parallel straight wires

Two parallel straight wires are shown in Figure 2-34, and their mutual inductance is:

in:

M: Mutual inductance of transmission line [H]

l : length of transmission line [m]

D: Distance between transmission lines [m]

r: Radius of the transmission line [m]

μ0: vacuum magnetic permeability, μ0=4π10-7 [H/m]

【Explanation】 The application conditions of this formula are: >> D, D >> r.

5. Inductance of the ring

in:

L: Inductance of the ring [H]

R: radius of the ring [m]

r: radius of the circular cross section [m]

μ0: vacuum magnetic permeability, μ0=4π10-7 [H/m]

【Note】 The application condition of this formula is: R >> r.