RLC Resonance Calculator
Generated infographic and interface snapshot for RLC Resonance Calculator
Find resonance, Q and bandwidth for any series or parallel tank circuit.
Free RLC Resonance Calculator Online — Big Das
The Big Das RLC Resonance Calculator computes resonant frequency, quality factor, 3 dB bandwidth and impedance at resonance for series and parallel RLC circuits — with a live impedance-vs-frequency plot.
What Is RLC Resonance?
A resistor, inductor and capacitor form a resonant circuit. At the resonant frequency f₀ the inductive and capacitive reactances cancel, so a *series
RLC reaches minimum impedance (just R) while a *parallel
RLC reaches maximum impedance. Q measures how sharp that resonance is: higher Q means a narrower passband or stopband.
How to Use the RLC Resonance Calculator
- Choose Series or Parallel topology.
- Enter the inductance with its unit (µH, mH or H).
- Enter the capacitance (nF, µF or mF).
- Enter the resistance (Ω or kΩ).
- Read f₀, Q, bandwidth, impedance at f₀ and both 3 dB frequencies instantly; the plot sweeps two decades above and below f₀.
Formulas Used
Resonant frequency (both topologies):
f0 = 1 / (2π · √(L · C))
Series RLC:
Q = (1/R) · √(L/C) = ω0·L / R
|Z(f0)| = R (minimum)
|Z(f)| = √(R² + (ωL − 1/ωC)²)
Parallel RLC (loss in series with L):
Q = R · √(C/L) = R / (ω0·L)
|Z(f0)| = L / (R·C) ≈ Q²·R (maximum, for high Q)
3 dB bandwidth:
BW = f0 / Q f_low ≈ f0 − BW/2 f_high ≈ f0 + BW/2
Worked Example
Series RLC with L = 10 mH, C = 100 nF, R = 10 Ω:
f₀ = 1 / (2π√(10×10⁻³ · 100×10⁻⁹)) ≈ 5.03 kHz
Q = (1/10)√(10×10⁻³ / 100×10⁻⁹) ≈ 31.6
BW = 5033 / 31.6 ≈ 159 Hz
|Z(f₀)| = 10 Ω (the resistor alone)
Put the same parts in parallel: Q = 10·√(100nF/10mH) ≈ 0.0316, the bandwidth balloons to ≈ 159 kHz, and |Z(f₀)| = L/(R·C) = 10 kΩ maximum.
Common Use Cases
Designing band-pass and band-stop filters
Tuning RF tank circuits and antenna matchers
Checking selectivity of oscillator networks
Estimating ringing and damping in switching converters
Coursework and lab verification for AC circuits classes
Frequently Asked Questions
Why does series resonance give minimum impedance but parallel give maximum?
At f₀ the reactances ωL and 1/ωC cancel. In series that leaves only R between the terminals; in parallel the circulating tank current means only a tiny current is drawn from the source, which appears as a very large impedance L/(R·C).
Can Q be zero or negative?
Not in a passive, physical circuit — Q requires positive R, L and C. The calculator rejects non-positive values rather than show a meaningless number.
Why is the 3 dB bandwidth f₀/Q?
At the two frequencies where reactance equals resistance the current (series) or voltage (parallel) falls to 1/√2 of its resonant value — the half-power or −3 dB points. Their separation works out to exactly f₀/Q.
Does the plot use a log scale?
Yes. Frequency and impedance are both logarithmic, sweeping two decades either side of f₀ so the resonance shape is visible regardless of component values.
What resistance should I use for a real inductor?
Use its DC resistance plus any explicit series resistor. Coil DCR dominates Q in most practical series tanks.