Electrical & Electronics
RLC Impedance & Resonance Calculator
Calculate series or parallel RLC impedance, phase, resonance, quality factor and bandwidth with a frequency plot.
Your inputs
Your results
- Impedance magnitude · |Z|
- —
- Phase shift
- —
- Real part · Re(Z)
- —
- Imaginary part · Im(Z)
- —
- Resonant frequency
- —
- Quality factor · Q
- —
| Inductive reactance · XL | — |
|---|---|
| Capacitive reactance magnitude · XC | — |
| Resonance bandwidth | — |
Both axes are logarithmic. Frequency is normalized to f0; the marker shows the entered frequency when it is in range.
Z = R + j(ωL − 1/(ωC))Compare RLC impedance, resonance and damping
Explore how an ideal resistor, inductor and capacitor behave at a chosen sinusoidal frequency. Select a series circuit or three parallel branches, then compare complex impedance, phase, resonance, quality factor and bandwidth. The selected resistor represents the entire modeled loss in that topology. The tool excludes winding resistance, capacitor losses, parasitic capacitance and loading by another circuit.
Step by step
- Choose series or parallel and inspect the diagram. Enter positive resistance, inductance, capacitance and frequency. The fields default to Ω, mH, nF and Hz; check each unit before comparing a result with a component specification.
- Read impedance magnitude together with its real and imaginary parts. A positive imaginary part is inductive; a negative one is capacitive. The phase describes voltage relative to current, not the output phase of an unspecified filter.
- Compare the entered frequency with resonance and inspect the impedance curve. Change frequency or connection while keeping the component values, then compare quality factor and bandwidth. Print the results when you want to retain the chosen inputs and model.
Settings and limits
- Connection and resonance
- In series, impedances add. In parallel, branch admittances add before inversion to obtain impedance. Resonance is f0 = 1 / (2π√(LC)) in both ideal models. At resonance, reactive terms cancel and impedance equals R; the series curve has a minimum, while the parallel curve has a maximum.
- Quality factor and bandwidth
- Series Q = √(L/C) / R, while parallel Q = R × √(C/L). Increasing the same resistor therefore reduces series Q but increases parallel Q. The displayed bandwidth is f0 / Q for series-current or parallel-impedance resonance. It is not automatically the bandwidth of a loaded voltage-output filter.
- Reading the plot
- Both axes are logarithmic and frequency is normalized to resonance. The plotted range extends from 0.01 to 100 times f0. The marker appears only when the entered frequency is within that range; a missing marker does not mean the numeric calculation failed.
Worked example
Enter R = 100 Ω, L = 10 mH, C = 100 nF and f = 1000 Hz. In series, the impedance magnitude is about 1531.98 Ω and phase is −86.2574°. Switch to parallel without changing those values to obtain about 54.7423 Ω and +56.8096°.
| RLC | |Z| | φ | Q | BW |
|---|---|---|---|---|
| R + L + C | 1531.98 Ω | −86.2574° | 3.16228 | 1591.55 Hz |
| R ∥ L ∥ C | 54.7423 Ω | +56.8096° | 0.316228 | 15915.5 Hz |
Both connections have resonance near 5032.92 Hz. Series Q is 3.16228 with bandwidth 1591.55 Hz; parallel Q is 0.316228 with bandwidth 15915.5 Hz. Near resonance both impedances approach 100 Ω, although their curves and damping differ. The table compares the two models at the original frequency.
Questions and troubleshooting
Why does the same network change from capacitive to inductive?
Connection matters. Below resonance, the series capacitor contributes the larger impedance magnitude, while the parallel inductor provides the lower-impedance branch. Compare the sign of the imaginary result and the phase after switching topology rather than transferring a series interpretation to parallel.
Can I model an inductor's winding resistance separately?
This tool has one resistor in the selected ideal topology. A resistor across parallel branches is not equivalent to resistance in series with the inductor. Use an appropriate circuit model for winding loss, capacitor loss or additional source and load resistance.
Why are results blank or the curve missing?
Every component and the frequency must be strictly positive and produce finite results. Check missing entries, unsupported unit suffixes and extreme values. Enter a valid numeric case again; the tool clears the previous results and plot when an input cannot be calculated.