| R (Ω) | L (mH) | C (µF) | f (kHz) | V (V) | |Z| (Ω) | Phase (°) | f₀ (Hz) |
|---|---|---|---|---|---|---|---|
| 1000 | 10 | 1 | 1 | 5 | Varies by frequency | Varies by frequency | ≈ 1591.55 |
| 470 | 1 | 0.47 | 5 | 10 | Varies by frequency | Varies by frequency | ≈ 7323.02 |
- G = 1/R
- B = ωC − 1/(ωL)
- Enter R, L, and C values and select suitable units.
- Pick frequency input mode: f or ω.
- Provide f or ω, then press Calculate.
- Read complex impedance, magnitude, and phase above.
- Review resonance, Q, and bandwidth for design insights.
- Optional: enter voltage to estimate branch currents.
- Use CSV or PDF buttons to store your results.
1) Parallel RLC impedance in practice
A parallel RLC network models many real circuits: tuned receivers, anti-resonant traps, and high‑impedance sensor front ends. Unlike series networks, the parallel form often peaks in impedance at resonance, which is useful when you want to block a narrow frequency band or create a selective load for an amplifier.
2) What this calculator delivers
This tool computes complex impedance Z and admittance Y at a selected frequency. You get magnitude (|Z|), phase angle, and the conductance–susceptance view (G and B). It also estimates the ideal resonance frequency f0, quality factor Q, and bandwidth BW for quick selectivity checks.
3) Input data and unit handling
Enter R, L, and C in practical units such as kΩ, mH, and µF. Then choose either frequency f or angular frequency ω. If ω is entered, the calculator automatically converts to f = ω/(2π). This helps when you are working from control models or phasor-domain derivations.
4) Admittance-first thinking
Parallel networks are easiest to analyze using admittance. The total admittance is Y = 1/R + 1/(jωL) + jωC. The real part is conductance G = 1/R, while the imaginary part is susceptance B = ωC − 1/(ωL). When |Y| is known, impedance follows directly as Z = 1/Y.
5) Resonance and impedance peak
At ideal resonance, B becomes approximately zero because capacitive and inductive susceptances cancel. The resonant angular frequency is ω0 = 1/√(LC), and f0 = ω0/(2π). Near f0, the impedance magnitude can rise toward R, yielding a high‑impedance “anti‑resonance” point.
6) Q factor and bandwidth data
For a parallel RLC with R in parallel, a common estimate is Q = ω0RC (equivalently R/(ω0L)). Higher Q means a narrower peak and better selectivity. The approximate 3 dB bandwidth is BW = f0/Q, which simplifies to BW = 1/(2πRC). Use these values as design targets and to compare component choices.
7) Phase behavior across frequency
The sign of B determines whether the network looks capacitive or inductive. When B > 0, the current leads voltage and the impedance phase is negative. When B < 0, the current lags and the impedance phase is positive. Watching the phase transition around resonance is a reliable sanity check for your component values.
8) Using exported results for design records
Engineering work benefits from repeatable records. After computing results, download CSV for spreadsheets or PDF for reports and lab notes. If you provide an applied RMS voltage, the calculator also estimates branch currents in the resistor, inductor, and capacitor, supporting stress checks and component sizing.
1) What does “parallel RLC impedance” mean?
It is the combined opposition to AC of a resistor, inductor, and capacitor connected in parallel. The calculator returns Z as a complex number plus its magnitude and phase at the chosen frequency.
2) Why does impedance often peak at resonance in a parallel network?
At resonance, inductive and capacitive susceptances cancel, so the imaginary part of admittance approaches zero. The remaining conductance is mainly 1/R, making the overall impedance approach a maximum near R.
3) Should I enter frequency or angular frequency?
Either works. Use frequency when you think in Hz, and use angular frequency when your formulas are in rad/s. The calculator converts between them using ω = 2πf automatically.
4) What is the difference between impedance Z and admittance Y?
Impedance Z (ohms) relates voltage to current. Admittance Y (siemens) is its reciprocal and adds naturally for parallel branches. This calculator computes Y first, then inverts to get Z.
5) How accurate are Q and bandwidth values?
The reported Q and BW follow ideal, linear component assumptions and common high‑Q approximations. Real coils have series resistance and capacitors have ESR, which usually lowers Q and broadens the peak.
6) Can this calculator help with component stress checks?
Yes. If you enter an applied RMS voltage, it estimates branch currents through R, L, and C, plus total current. Use those values to evaluate heating, saturation risk, and reactive current levels.
7) What happens if values are extremely large or small?
The tool supports scientific notation and wide unit ranges, but extreme combinations can cause numerical limits or unrealistic results. If values look odd, check unit selections and try scaling components to practical magnitudes.