Resonance & Impedance

Capacitors and inductors naturally oscillate at a set frequency, and this interaction also generates an impedance (similar electrical effect to a resistor).

• Resonant Frequency: fo = 1 / (2π × √(L × C))
• Inductive Reactance: XL = 2πLf
• Capacitive Reactance: XC = 1 / 2πCf
• Series Impedance: ZS = XL - XC
• Parallel Impedance: ZP = 1 / ZS

Where frequency (f) is in Hertz (Hz), inductance (L) is in Henries (H), capacitance (C) is in Farads (F), and Impedance (Z) is in Ohms (Ω).

Notes:

• Because the phase of inductive and capacitive reactance are opposite one another, they subtract instead of add when in series.
• The impedance of a series circuit will be essentially zero at the resonance frequency, making a “band pass” filter.
• The impedance of a parallel circuit will be essentially infinite at the resonance frequency, making a “band stop” filter.