Inductors are passive devices used in electronic circuits to store energy in the form of a magnetic field. They
are the compliment of capacitors, which store energy in the form of
an electric field. An ideal inductor is the equivalent of a short circuit (0 ohms) for direct currents (DC), and
presents an opposing force (reactance) to alternating currents (AC) that depends on the frequency of the current.
The reactance (opposition to current flow) of an inductor is proportional to the frequency of the current flowing
through it. Inductors are sometimes referred to as "coils" because most inductors are physically constructed of
coiled sections of wire.
The property of inductance that opposes current flow is exploited for the purpose of preventing signals with
a higher frequency component from passing while allowing signals of lower frequency components to pass. This is
why inductors are sometimes referred to as "chokes," since they effectively choke off higher frequencies. A common
application of a choke is in a radio amplifier biasing circuit where the collector of a transistor needs to be supplied
with a DC voltage without allowing the RF (radio frequency) signal from conducting back into the DC supply.
used in series (left) or parallel
(right) with its circuit compliment, a capacitor, the inductor-capacitor combination forms a circuit that resonates
at a particular frequency that depends on the values of each component. In the series circuit, the impedance to
current flow at the resonant frequency is zero with ideal components. In parallel circuits (right), the impedance
to current flow is infinite with ideal components.
inductors made of physical components exhibit more than just a pure inductance when present in an AC circuit.
A common circuit simulator model is shown to the right. It includes the actual ideal inductor with a parallel resistive
component that responds to alternating current. The DC resistive component is in series with the ideal inductor,
and a capacitor is connected across the entire assembly and represents the capacitance present due to the proximity
of the coil windings.
Equations (formulas) for combining inductors in series and parallel are given below.
Additional equations are given for inductors of various configurations.
The HamWaves.com website has a very
sophisticated calculator for coil inductance that allows you to enter the conductor diameter.
|Inductors in series combine in the same manner as series resistors.
= L1 + L2 + ··· + Ln
W = 1/2 Li2
= 2 π
L = inductance (H)
v = voltage
W = energy (J)
Where: L = inductance
- Q = F0/F3db
- Q = Estored / Eloss_per_cycle
- Parallel Circuit:
Q = R/(2*π*F0*L)
- Series Circuit:
Q = (2*π*F0*L)/R
- 1/Qload = 1/Qext + 1/Qtank
E = energy
ext = external
|Finding the Equivalent "RQ"
|Since the "Q" of an inductor is the ratio of the reactive component to the
component, an equivalent circuit can be defined with a resistor in parallel with the inductor. This equation
is valid only a a single frequency, "f," and must be calculated for each frequency of interest.
|Multilayer Air-Core Coil
| Inductance[μHenry] =
L = inductance (µH)
r = mean radius of coil (in)
z = physical length of coil winding (in)
N = number of turns
d = depth of coil (outer radius minus inner radius) (in)
1: Thanks to Wayne H. for correcting
the 0.8 factor, which used to be 0.5