Analyze parallel RLC tank circuits: resonant frequency, impedance, admittance, branch currents, phase angle, Q-factor, and bandwidth with live circuit, resonance curve, and phasor diagrams.
Analyze Impedance, Admittance, Branch Currents, and Anti-Resonant Peaks
Inductive branch current dominates (circuit appears inductive)
This RLC parallel resonance calculator instantly analyses a parallel RLC tank circuit at any frequency. Enter resistance R, inductance L, capacitance C, source voltage V, and frequency f to find the resonant frequency (fr = 1/2π√LC), maximum impedance Z = R, total admittance Y, individual branch currents (IR, IL, IC), phase angle φ, quality factor Q = R√(C/L), and bandwidth BW = fr/Q — with a live schematic, resonance curve, and phasor diagram. Use it for oscillator design, radio tuner analysis, band-stop filter sizing, and any circuit where a tank circuit is the key element.
| Quantity | Formula | At Resonance |
|---|---|---|
| Resonant Frequency | fr = 1 / (2π√(LC)) | — |
| Angular Frequency | ωr = 1 / √(LC) | — |
| Branch Current IR | IR = V / R | Minimum total source I |
| Branch Current IL | IL = V / (2πfL) | IL = IC |
| Branch Current IC | IC = V × 2πfC | IC = IL |
| Conductance | G = 1 / R | — |
| Net Susceptance | B = ωC − 1/(ωL) | B = 0 |
| Total Admittance | Y = √(G² + B²) | Y = G = 1/R (minimum) |
| Total Impedance | Z = 1 / Y | Z = R (maximum) |
| Quality Factor | Q = R√(C/L) | — |
| Bandwidth | BW = fr / Q | — |
| Phase Angle | φ = arctan(B/G) | φ = 0° |
A parallel RLC circuit (also called a tank circuit) places R, L, and C side by side across the same AC source. Every component shares the same voltage. At parallel resonance — sometimes called anti-resonance — the inductive and capacitive branch currents are equal in magnitude and exactly 180° out of phase, so they cancel. The reactive energy simply circulates between L and C without being drawn from the source. The result: impedance is maximised and the source current is minimised — the exact opposite of a series RLC circuit where impedance is minimised at resonance.
Parallel branches add as admittances (Y = 1/Z), not impedances. The three branch admittances are:
The quality factor Q determines how selective and how sharp the impedance peak is. For a parallel RLC circuit:
| Parallel RLC (Tank) | Series RLC | |
|---|---|---|
| Impedance at resonance | Maximum (= R) | Minimum (= R) |
| Current at resonance | Minimum (= V/R) | Maximum (= V/R) |
| Q-factor formula | Q = R√(C/L) ↑R → ↑Q | Q = (1/R)√(L/C) ↓R → ↑Q |
| Frequency formula | fr = 1/(2π√LC) | fr = 1/(2π√LC) |
| Admittance at resonance | Minimum (= G = 1/R) | Maximum |
| Phase angle at resonance | 0° (Isource in phase with V) | 0° (I in phase with V) |
| Below resonance | Inductive (I lags V) | Capacitive (I leads V) |
| Above resonance | Capacitive (I leads V) | Inductive (I lags V) |
| Main application | Oscillators, notch filters, tuners | Band-pass filters, tuned amplifiers |
| Component | Unit | Symbol | Common RLC Range |
|---|---|---|---|
| Inductance | Henry / millihenry / microhenry | H / mH / µH | µH for RF, mH for audio/power |
| Capacitance | Farad / microfarad / nanofarad / picofarad | F / µF / nF / pF | pF–nF for RF, µF for audio/power |
| Resistance | Ohm / kilohm / megaohm | Ω / kΩ / MΩ | Tens of Ω (low Q) to kΩ+ (high Q) |
A tank circuit is a parallel LC or RLC circuit that stores and exchanges energy between the inductor's magnetic field and the capacitor's electric field, like energy sloshing in a tank. Tank circuits are the core of LC oscillators and radio tuners.
At resonance the reactive currents (IL and IC) cancel inside the tank. No reactive current is drawn from the source — only the small IR. Since Z = V/Isource = V/IR = R, impedance is at its maximum.
Higher Q: Q = R√(C/L), so increasing R sharpens the resonance peak. This is the opposite of a series circuit where Q = (1/R)√(L/C) — larger R reduces Q.
Anti-resonance is simply another name for parallel resonance, emphasising that the circuit draws minimum current from the source (as opposed to series resonance where maximum current flows).
At resonance, IL = IC = Q × Isource. The reactive current circulates between L and C and can be Q times larger than the source current — important for component ratings.