Inductor

From HvWiki

A coil of wire with a useful amount of inductance.

Contents 1 Read-world inductor equivalent 2 Theory 2.1 Current Rise 2.2 Inductive Kick 2.3 Energy Storage 2.4 Impedance 2.5 Equivalent Inductance 3 Skin effect 4 Design 5 Measuring Inductance 5.1 LR Circuit

Read-world inductor equivalent

Theory

Current Rise

Inductive Kick

Energy Storage

The energy stored in an inductor depends on the current flowing through it and its inductance.

Impedance

Impedance of inductors can be represented as resistance in the complex number domain.

Z_L = jωL

Here ω stands for rotational frequency. This is useful when there is a sinusoidal current source supplying energy to the inductor.

Example:

v(t) = v_maxcos(ωt + θ)

becomes, using Euler's formula

V = V_maxe^{j(ωt + θ)}

and thus since Z = jωL and

where which can then be converted back to a real number

i(t) = i_maxsin(ωt + θ)

Equivalent Inductance

Equivalent inductance, L_eq, of inductors connected in series is simply the sum of inductances.

Equivalent inductance, L_eq, of inductors connected in parallel is thus

Skin effect

For frequencies above 50 kHz the skin effect should be taken into consideration.

Design

Measuring Inductance

There are inductance meters available (often as LCR meters) that make measuring inductance easy. For those who only want to measure inductance for a one-off, there are other ways.

LR Circuit

If an inductor is connected in series with a resistor it acts as a frequency dependent voltage divider.

The voltage dropped across the resistor is given by

so that

Therefore

And X_L = ωL = 2πfL so