Electrical Resonance - LC Circuits

LC Circuits

Resonance of a circuit involving capacitors and inductors occurs because the collapsing magnetic field of the inductor generates an electric current in its windings that charges the capacitor, and then the discharging capacitor provides an electric current that builds the magnetic field in the inductor. This process is repeated continually. An analogy is a mechanical pendulum.

At resonance, the series impedance of the two elements is at a minimum and the parallel impedance is at maximum. Resonance is used for tuning and filtering, because it occurs at a particular frequency for given values of inductance and capacitance. It can be detrimental to the operation of communications circuits by causing unwanted sustained and transient oscillations that may cause noise, signal distortion, and damage to circuit elements.

Parallel resonance or near-to-resonance circuits can be used to prevent the waste of electrical energy, which would otherwise occur while the inductor built its field or the capacitor charged and discharged. As an example, asynchronous motors waste inductive current while synchronous ones waste capacitive current. The use of the two types in parallel makes the inductor feed the capacitor, and vice versa, maintaining the same resonant current in the circuit, and converting all the current into useful work.

Since the inductive reactance and the capacitive reactance are of equal magnitude, ωL = 1/ωC, so:

where ω = 2πf, in which f is the resonance frequency in hertz, L is the inductance in henries, and C is the capacitance in farads when standard SI units are used.

The quality of the resonance (how long it will ring when excited) is determined by its Q factor, which is a function of resistance. A true LC circuit would have infinite Q, but all real circuits have some resistance and smaller Q and are usually approximated more accurately by an RLC circuit.