Calculation
Q = √(L/C)/R; f₀ = 1/(2π√(LC))
Quality factor compares resonant reactance with total series resistance.
Dubbel Elektrotechnik, Schwingkreise und Filter
Series RLC circuit quality factor
Quality factor compares resonant reactance with total series resistance.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Quality factor Q — Dimensionless ratio of reactance at resonance to total series resistance.
- Series resistance R — Total loss-producing series resistance including coil winding, capacitor ESR and wiring.
- Inductance L — Effective inductance near the calculated resonance frequency.
- Capacitance C — Effective series capacitance near the calculated resonance frequency.
Example
R=20 Ω, L=100 mH and C=100 µF give f₀≈50.33 Hz and Q≈1.58.
Assumptions and limits
Linear lumped series RLC circuit with frequency-independent equivalent values; parasitics, loading and tolerances are excluded.
Understand Series RLC circuit quality factor
This calculator evaluates how sharply an idealised series circuit selects around resonance. It complements the RLC current calculator with a dimensionless damping and selectivity measure.
What does this quantity describe?
At f₀=1/(2π√LC), inductive and capacitive reactance are equal. Series quality Q=ω₀L/R=1/(ω₀CR)=√(L/C)/R compares that reactance with all effective series loss.
Formula and variables
Q = √(L/C)/R; f₀ = 1/(2π√(LC))
f₀ = 1/(2π√(LC))Q = ω₀L/RQ = 1/(ω₀CR)Q = √(L/C)/R
| Symbol / input | Meaning |
|---|---|
| Quality factor Q | Dimensionless ratio of reactance at resonance to total series resistance. |
| Series resistance R | Total loss-producing series resistance including coil winding, capacitor ESR and wiring. |
| Inductance L | Effective inductance near the calculated resonance frequency. |
| Capacitance C | Effective series capacitance near the calculated resonance frequency. |
Choose the inputs correctly
R must include every series loss effective at resonance, including winding resistance and capacitor ESR. L and C are effective values near f₀, not unchecked ideal ratings at another frequency.
How to use the calculator
Estimate L and C, determine f₀, then enter total R effective there. Use Q for option comparison and verify actual response by measurement.
Worked example
R=20 Ω, L=100 mH and C=100 µF give f₀≈50.33 Hz. √(L/C)=31.62 Ω, so Q≈1.58.
Understand the result and units
Greater Q means lower relative damping and sharper resonance, but can also create high component voltages and greater tolerance sensitivity.
R in Ω, L with henry prefixes and C with farad prefixes; Q is dimensionless. Resonance follows from coherent SI values.
Typical applications
Teaching resonance and damping, and preliminary comparison of series filters, tuned circuits and laboratory resonators.
Assumptions, limits and common mistakes
Lumped linear equivalent with frequency-independent R, L and C. Source/load damping, parasitics, skin effect, core loss and tolerances are excluded.
Common mistake: Do not use only a drawn resistor while omitting winding and ESR losses. Higher Q is not automatically better because it can create voltage magnification and narrow tolerances.
Frequently asked questions
What is “Series RLC circuit quality factor” used for?
Teaching resonance and damping, and preliminary comparison of series filters, tuned circuits and laboratory resonators.
Where do the input values come from?
R must include every series loss effective at resonance, including winding resistance and capacitor ESR. L and C are effective values near f₀, not unchecked ideal ratings at another frequency.
What does the result not cover?
Lumped linear equivalent with frequency-independent R, L and C. Source/load damping, parasitics, skin effect, core loss and tolerances are excluded.