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 a change in 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 drawing) or
parallel (right drawing) 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 the parallel circuit (right), 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 left. 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. SPICEtype simulators use this or an even more sophisticated model to facilitate more
accurate calculations over a wide range of frequencies.
The
HamWaves.com website has a very sophisticated
calculator for coil inductance that allows you to en9ter the conductor diameter.
Equations (formulas) for combining inductors in series and parallel are given below. Additional equations are
given for inductors of various configurations.
SeriesConnected Inductors 
Total inductance of seriesconnected inductors is equal to the sum of the individual inductances. Keep
units constant.

Closely Wound Toroid 
Rectangular CrossSection

Coaxial Cable Inductance 

Straight Wire Inductance 
These
equations apply for when the length of the wire is much longer than the wire diameter
(look up wire diameter here). The ARRL
Handbook presents the equation for units of inches and µF:
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:

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:
a = wire radius,
l
= wire length parallel to ground plane h = height of wire above ground plane to bottom of wire

Parallel Line Inductance 

MultiLayer AirCore Inductance 
Wheeler's Formula:


ParallelConnected Inductors 
Total inductance of parallelconnected inductors is equal to the reciprocal of the sum of the reciprocals
of the individual inductances. Keep units constant.

Inductance Formula Constants and Variables 
The following physical constants and mechanical dimensional variables apply to equations on this page.
Units for equations are shown inside brackets at the end of equations; e.g.,
means lengths are in inches and inductance is in Henries. If no units are indicated, then any may be used
so long as they are consistent across all entities; i.e., all meters, all µH, etc.
C = Capacitance L = Inductance N = Number of turns W = Energy ε_{r} = Relative permittivity
(dimensionless) ε_{0} = 8.85 x 10^{12} F/m (permittivity
of free space) µ_{r} = Relative permeability (dimensionless) µ_{0}
= 4π x 10^{7}
H/m (permeability of free space)
1 meter = 3.2808 feet <—> 1 foot = 0.3048 meters 1 mm = 0.03937 inches <—>
1 inch = 25.4 mm
Also, dots (not to be confused with decimal points) are used to indicate
multiplication in order to avoid ambiguity.

Inductive Reactance 
Inductive reactance (X_{L}, in Ω) is proportional to the frequency (ω, in radians/sec,
or f, in Hz) and inductance (L, in Henries). Pure inductance has a phase angle of 90° (voltage leads
current with a phase angle of 90°).

Energy Stored in an Inductor 
Energy (W, in Joules) stored in an inductor is half the product of the inductance (L, in Henries) and the
current (I, in amp) through the device.

Voltage Across an Inductor 
The inductor's property of opposing a change in current flow causes a counter EMF (voltage) to form across
its terminals opposite in polarity to the applied voltage.

Quality Factor of Inductor 
Quality factor is the dimensionless ratio of reactance to resistance in an inductor.

SingleLayer Round Coil Inductance 
Wheeler's Formula for d >> a:
In general for a = wire radius:
Note: If lead lengths are significant, use the straight wire calculation to add that inductance.

SingleLayer Rectangular Coil Inductance 
This equation is too long to break up  click to enlarge:

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.


