seriesresonant

Series resonance refers to the condition in a series RLC circuit where the inductive reactance X_L and the capacitive reactance X_C cancel each other (X_L = X_C). When this occurs, the impedance of the circuit is minimized and is essentially equal to the series resistance R. Consequently, the current drawn from the source is at its maximum for that circuit, given by I = V / R. A small R yields a high circulating current and a high quality factor.

The resonant frequency is determined by the values of the inductor L and capacitor C: ω0 = 1 / √(LC) in radians per second, and f0 = 1 / (2π√(LC)) in hertz. The circuit behaves as a highly selective element near f0, which makes it useful as a frequency-tuning component. The quality factor Q of a series resonant circuit is Q = ω0 L / R = 1 / (R) √(L / C); a higher Q indicates a narrower bandwidth, with the approximate bandwidth given by Δω = ω0 / Q.

Applications of series resonance include filters and tuning circuits in radio receivers, oscillators, and impedance-matching networks. In a typical setup, a series resonant branch is placed in series with a load so that the branch presents a low impedance at the desired frequency, effectively passing that frequency while attenuating others (a band-pass effect). Real-world performance is limited by non-idealities such as the equivalent series resistance of the inductor and the equivalent series resistance and parasitics of the capacitor, which broaden the resonance and reduce peak current.