Frequency Bandwidth Calculator

The frequency bandwidth calculator will provide you with the upper and lower cutoff frequencies and the frequency bandwidth.

Bandwidth1.5915 kHzf₀ ÷ Q — the width between the half-power points

Resonant frequency15.9155 kHz1 ÷ 2π√(LC) — where the two reactances cancel exactly

At 15.9155 kHz10 Ωtotal impedance

Inductive reactance X_L100 Ωrises with frequency

Capacitive reactance X_C100 Ωfalls with frequency

Net reactance-28.4217 fΩzero — the circuit is at resonance and looks purely resistive

Phase angle0°current leads the voltage

Q factor10the sharpness of the resonance

Characteristic impedance √(L/C)100 Ω

Current1 Aat its maximum — at resonance only R limits the current

Voltage across the inductor100 VHIGHER than the supply — a series resonant circuit genuinely does this, by a factor of about Q, and it can destroy components rated only for the supply voltage

Voltage across the capacitor100 V

Real power dissipated10 Wonly the resistance dissipates — reactance stores and returns energy without loss

Power factor1cos of the phase angle

At four times the capacitance7.9577 kHzhalf the frequency — f₀ goes as the inverse square root of both L and C

The formula

f₀ = 1 ÷ 2π√(LC); Z = √(R² + (X_L − X_C)²); Q = (1/R)√(L/C)

Voltages larger than the supply

Inductive reactance rises with frequency and capacitive reactance falls, so there is exactly one frequency where they cancel. At that resonance a series circuit looks purely resistive, its impedance is at a minimum, and the current is at a maximum.

The consequence that alarms people the first time they measure it: the voltage across the inductor and across the capacitor can each be far larger than the supply voltage, by roughly a factor of Q. They are equal and opposite, so they cancel as far as the source is concerned — but they are individually real, and a capacitor rated for the supply voltage will fail. This is a genuine hazard in resonant circuits, not a measurement artefact.

Q measures how sharp the resonance is, and equals √(L/C) divided by the resistance. High Q means a narrow bandwidth and large internal voltages; low Q means a broad, gentle response. Only the resistance dissipates power — reactance stores energy and gives it back, which is why a reactive load draws current without consuming energy and why power factor matters to utilities.