Quality Factor Calculator Formula

Understand the math behind the quality factor calculator. Each variable explained with a worked example.

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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

VariableDescriptionDefault
inductance_uhInductance(µH)100
capacitance_pfCapacitance(pF)100
resistanceSeries Resistance(Ω)5
l_hDerived value= inductance_uh / 1000000calculated
c_fDerived value= capacitance_pf / 1000000000000calculated

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
  1. 01sqrt(L/C) = sqrt(0.0001 / 1e-10) = sqrt(1e6) = 1000
  2. 02Q = 1000 / 5 = 200
  3. 03f_0 = 1.59 MHz, BW = 7958 Hz

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