Quality Factor Calculator Formula
Understand the math behind the quality factor calculator. Each variable explained with a worked example.
Formulas Used
Quality Factor (Q)
q_val = (1 / resistance) * sqrt(l_h / c_f)Resonant Frequency
resonant_freq = 1 / (2 * pi * sqrt(l_h * c_f))Bandwidth
bandwidth = resistance / (2 * pi * l_h)Variables
| Variable | Description | Default |
|---|---|---|
inductance_uh | Inductance(µH) | 100 |
capacitance_pf | Capacitance(pF) | 100 |
resistance | Series Resistance(Ω) | 5 |
l_h | Derived value= inductance_uh / 1000000 | calculated |
c_f | Derived value= capacitance_pf / 1000000000000 | calculated |
How It Works
Quality Factor (Q)
Q = (1/R) x sqrt(L/C)
Also: Q = f_0 / Bandwidth
Higher Q means less energy loss, sharper resonance, and narrower bandwidth.
Worked Example
100 uH, 100 pF, 5 ohms series resistance.
inductance_uh = 100capacitance_pf = 100resistance = 5
- 01sqrt(L/C) = sqrt(0.0001 / 1e-10) = sqrt(1e6) = 1000
- 02Q = 1000 / 5 = 200
- 03f_0 = 1.59 MHz, BW = 7958 Hz
Frequently Asked Questions
What is a good Q value?
Depends on application. RF filters often need Q > 100. Audio filters may use Q of 1-10.
What limits Q in practice?
Component losses: inductor wire resistance, capacitor ESR, and radiation losses.
Q of a single component?
For an inductor: Q = XL/R. For a capacitor: Q = 1/(2pi x f x C x ESR).
Ready to run the numbers?
Open Quality Factor Calculator