An inductor and a capacitor exchange stored energy back and forth. At one specific frequency — the resonant frequency, f = 1/(2π√(LC)) — their reactances cancel exactly (X_L = X_C), leaving a circuit that behaves very differently at that frequency than at any other.
A series RLC circuit hits minimum impedance at resonance (current peaks) — this is the tuned circuit used to select a station in a radio. A parallel RLC "tank" circuit hits maximum impedance at resonance (current is blocked) — this is the shape used in oscillators and filters. Same formula for frequency, opposite effect on the circuit.
A tank circuit is an inductor and a capacitor wired in parallel, and the name is literal — energy sloshes between the two like liquid in a tank, the magnetic field of the coil charging the capacitor and the capacitor discharging back through the coil. At the resonant frequency that exchange is self-sustaining, the parallel combination presents its maximum impedance, and the circuit rejects everything else. That is why a tank sits in the collector of an oscillator to set its frequency, and across an antenna input to pick one station out of the band. Select Parallel RLC and solve for impedance to see the tank's Q and bandwidth alongside the resonant frequency — Q is what decides how sharply it discriminates between your signal and the one next to it.
Q factor measures how sharply the circuit responds around resonance — a higher Q means a narrower bandwidth and a more selective (but less forgiving of component drift) circuit. Bandwidth = resonant frequency ÷ Q, so a Q of 50 at 1 MHz gives a 20 kHz-wide response band.
Real inductors and capacitors are never exactly the value printed on them — a 5% tolerance part can shift your resonant frequency by roughly half that percentage. Expand Component Tolerance Analysis to see the resulting frequency range across your parts' tolerance band, and to snap your calculated values to the nearest real E6, E12, or E24 standard-series component.
Radio tuners, RF and antenna matching networks, oscillators, and low-pass/high-pass/bandpass filters all rely on the same LC resonance math. When solving for impedance, the sweep summary shows how the circuit behaves as you move away from resonance — useful for checking how forgiving a filter or tuner actually is in practice.
Flexible Solver: Solve for frequency, inductance, or capacitance with two known values.
Impedance Calculation: Includes resistance effects on impedance magnitude and phase angle.
Quality Factor: Calculate Q factor for circuit selectivity and bandwidth.
Component Snapping: Snap calculated values to standard component series (E6, E12, or E24).
Radio Tuning Circuits: design resonant circuits for radio receivers, select component values for specific frequencies, and optimize for bandwidth and selectivity.
Power Factor Correction: calculate capacitor values for reactive power compensation, design LC filters for AC circuits, and match impedance in power systems.
Filter Design: design LC low-pass and high-pass filters, calculate cutoff frequencies, and optimize for signal conditioning applications.
Antenna Tuning: design matching networks for antennas, tune impedance for maximum power transfer, and calculate resonant frequencies for different bands.
Solve for voltage, current, resistance, or power
Calculate electrical power and energy cost
Size wire for current and voltage drop
Decode or encode resistor color bands
Calculate mechanical stress, strain, and Young's modulus for engineering materials. Includes safety factor analysis.
Calculate beam deflection, bending moment, and reaction forces for various beam types and load configurations. Structural engineering tool.
Calculate concrete volume and required quantities of cement, sand, aggregate, and water. Supports standard and custom mix ratios.
Calculate pressure drop, flow rate, and fluid velocity in pipes. Supports Darcy-Weisbach and Hazen-Williams methods with minor losses.
Last updated