RLC Parallel Resonance Calculator
Parallel tank resonance, Q, bandwidth and dynamic impedance including inductor ESR.
What it does
A parallel “tank” circuit has its highest impedance at resonance. Including the inductor’s series resistance (ESR) shifts the resonance slightly and sets the real-world Q.
Where it's used
Oscillator tanks, IF filters and antenna matching networks.
How to use it
- Enter the parallel resistance (the load or loss across the tank).
- Enter L and C.
- Optional: enter the inductor’s series resistance from its datasheet.
The formula explained
- f₀
- resonant frequency (shifted slightly by the inductor’s r)
- Q
- R·√(C/L) for the parallel tank
- BW
- f₀ / Q
- r
- inductor series resistance (ESR)
Worked example
A small RF tank: 10 µH and 100 pF.
Inputs:
- Parallel resistance R: 50k Ω
- Inductance L: 10u H
- Capacitance C: 100p F
- Inductor series resistance (ESR): 2 Ω
The calculator gives:
- Resonant frequency f₀: 5.033 MHz
- Ideal f₀ (r = 0): 5.033 MHz
- Quality factor Q: 79.057
Tips and common mistakes
- A larger parallel resistance gives a sharper tank.
- For air-core coils the ESR often limits Q more than anything else.
- Stray capacitance of the board adds to C at high frequencies.
Questions people ask
Why is the Q lower than the parallel resistor alone suggests?
Two losses act together: the parallel resistance and the coil’s own series resistance. In the example each one alone would give a Q of about 158, and together they give about 79.
What is the impedance of the tank at resonance?
The coil’s loss acts like a parallel “dynamic resistance” L / (C × r) — 50 kΩ in the example. In parallel with the 50 kΩ resistor that gives 25 kΩ at resonance.
Where are parallel tank circuits used?
In LC oscillators, in intermediate-frequency filters in radios, and in antenna matching. The tank passes signals near f₀ with little loss and shorts others to ground.
Related Reactive & RLC calculators
- Capacitors in Series
- Capacitors in Parallel
- Inductors in Series
- Inductors in Parallel
- RLC Resonant Frequency
- RC Time Constant
- Capacitor Reactance
Enter your values to get the result with the formula, substituted values and an explanation of each step.