The Quartz Crystal Parameter conversion calculator determines key performance parameters of a quartz crystal oscillator, including series resonance frequency, parallel resonance frequency, and quality factor. These parameters help engineers evaluate oscillator precision, stability, and circuit performance for RF and timing applications.
Formulas
Fs = 1 / (2 * π * √(Ls * Cs))
Fp = 1 / (2 * π * √(Ls * ((Cs * Cp) / (Cs + Cp))))
Q = (2 * π * Fs * Ls) / Rs
Formula Explanation
- Fs is the series resonance frequency where inductive and capacitive reactances cancel, resulting in minimum impedance.
- Fp is the parallel resonance frequency that occurs slightly above Fs due to the parallel capacitance Cp.
- Q is the quality factor, representing the ratio of stored to dissipated energy per cycle, indicating how selective or sharp the resonance is.
- Ls is the motional inductance, Cs is the motional capacitance, Cp is the shunt capacitance, and Rs is the series resistance of the crystal.
- Fs and Fp are typically expressed in MHz, while component values can be entered in standard electrical units.
Uses of this calculator
- Designing quartz crystal oscillators for RF, microcontroller, and communication circuits.
- Calculating resonance frequencies for precision timing and filtering applications.
- Determining quality factor to assess frequency stability and losses.
- Comparing theoretical and measured parameters of quartz crystals.
What are the resonance frequencies of a quartz crystal with Ls = 0.02 H, Cs = 0.03 pF, Cp = 3 pF, and Rs = 50 Ω?
Input: Ls = 0.02 H, Cs = 0.03 pF, Cp = 3 pF, Rs = 50 Ω
Output:
- Fs = 1 / (2 * π * √(0.02 * 0.03e-12)) = 1 / (6.283 * √(6e-15)) = 1 / (6.283 * 7.746e-8) = 2.05e6 Hz = 2.05 MHz
- Fp = 1 / (2 * π * √(0.02 * ((0.03e-12 * 3e-12) / (0.03e-12 + 3e-12)))) = 2.05 MHz (slightly higher at ≈ 2.05–2.06 MHz)
- Q = (2 * π * 2.05e6 * 0.02) / 50 = (257,610) / 50 = 5152
- Series Resonance Frequency = 2.05 MHz
- Parallel Resonance Frequency = 2.06 MHz
- Quality Factor (Q) = 5152