Tuned Circuits
Used extensively in radio and electronics, tuned circuits are the major components in filters,
oscillators andfrequency selective networks.
Inductive Reactance
The impedance of an air wound coil is given by the following formula:
Where Xl is the inductive reactance in ohms, f is the frequency in hertz and L the inductance of the
coil in Henrys. An inductor wound on an iron or ferrite core will have a different value.
Capacitive Reactance
This is similar to the inductor, with C
in farads and f in hertz. The capacitive reactance will be in ohms.
Parallel Tuned Circuit
A tuned circuit arranged as a parallel combination of an inductor and capacitor, will have a resonant
frequency, Fr that is calculated with the following equation.
Fr is given in ohms when L is in Henrys and C in Farads.
Hartley Oscillator
The Hartley oscillator uses two coils (or a single centre tapped coil) and a parallel tuning capacitor. The
frequency of oscillation is given by :
Fosc is in ohms when L is in Henrys and C in Farads.
Colpitts Oscillator
The Colpitts oscillator uses two capacitors and a single coil, the oscillator frequency is determined
by:
The formula is the same as the resonant circuit for both the Hartley and Colpitts oscillators,
expect that the total inductance is summed in the Hartley case and the capacitors are added in series in the
Colpitts oscillator. An example is shown in the
analysis section.
Air Spaced Coil
An inductor made with a few turns of coiled wire has the following inductance :
Here L is the inductance in uH (1uH
= 1/1000000 of an Henry), n is the number of turns on the coil, r is the radius of the coil in inches, and l
(small L ) is the length of the coil in inches. As this becomes rather tedious to work out the inductance it
is easier to know what inductance you require, and then work out the number of turns for the coil. The formula is
rearranged as follows :
Using the above dimensions, this gives the number of turns for the coil.
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