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.
When
used in
series (left) or
parallel
(right) with its circuit compliment, a capacitor, the inductorcapacitor 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.
Realworld
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.
Parallel Inductors 
Inductors in parallel combine in the same manner as parallel resistors.

Straight Wire 
These equations apply for when the length of the wire is much longer than the wire diameter.
For lower frequencies  up through about VHF, use this formula:
Above VHF, skin effect causes the ¾ in the top equation to approach unity (1), so use this equation:

L = inductance (μH)
l = length (mm)
d = wire
diameter (mm) 
The ARRL Handbook presents this equation for units in inches:
Use the same VHF frequency point as above for changing the 0.75 to a 1 
L=inductance (μH)
b = length (in.)
a = wire
radius (in.) 
Look up wire diameter here.

Coaxial Cable 

D = outer radius d = inner radius 

z = length (ft) 

z = length (m) 
Closely Wound Toroid 
(units
in inches)

SingleLayer AirCore


Wheeler's Formula

(units in inches)
Where: 
d and z are in inches N = number of turns 
Note: 
If lead lengths are significant, use the straight wire calculation to add that inductance. 

Multilayer AirCore Coil 
Inductance[μHenry] =
,
^{1}
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


Inductive Reactance 
X_{L}=jωL

Series Inductors 
Inductors in series combine in the same manner as series resistors.
Ls = L1 + L2 + ··· + Ln
W = 1/2 Li ^{2}
X _{L}
= 2 π f L L = inductance (H) v = voltage (V)
W = energy (J)

"Q" Factor 
 Q = F_{0}/F_{3db}
 Q = E_{stored} / E_{loss_per_cycle}
 Parallel Circuit:
Q = R/(2*π*F_{0}*L)
 Series Circuit:
Q = (2*π*F_{0}*L)/R
 1/Q_{load} = 1/Q_{ext} + 1/Q_{tank}

Where: 
L = inductance E = energy ext = external

Finding the Equivalent "R_{Q}" 
Since the "Q" of an inductor is the ratio of the reactive component to the
resistive
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.



Straight Wire Parallel to Ground Plane w/One End Grounded 
The ARRL Handbook presents this equation for a straight wire suspended above a ground plane, with one end grounded
to the plane:
L = inductance (μH) a = wire radius (in.) b = wire length parallel to ground plane (in.) h =
wire height above ground plane (in.) 