This calculator determines the series resonance frequency (Fs), parallel resonance frequency (Fp) and quality factor (Q) of a quartz crystal using its equivalent circuit values. It helps to understand the behavior of crystal oscillators in electronic circuits.
Ideal for electronic engineers, oscillator designers and students who wish to analyze the frequency stability and losses of a crystal used in RF or watchmaking assemblies.
Formulas
Fs = 1 / (2 × π × √(Ls × Cs))
Fp = 1 / (2 × π × √(Ls × ((Cs × Cp) / (Cs + Cp))))
Q = (2 × π × Fs × Ls) / Rs
Explanation of formulas
- Fs corresponds to the series resonance frequency where the impedance of the crystal is minimum.
- Fp represents the parallel resonance frequency where the crystal acts as a high impedance resonator.
- Q indicates the quality of the crystal, the higher it is, the greater the frequency stability.
- The parameters Ls, Cs, Cp and Rs come from the equivalent electrical model of the crystal.
10 MHz quartz crystal resonance calculation
Input : Ls = 0.03 H, Cs = 0.02 pF, Cp = 4 pF, Rs = 25 Ω
Exit :
- Fs ≈ 9.99 MHz
- Fp ≈ 10.00 MHz
- Q ≈ 7.5 × 10⁴
Benefits and uses
- Rapid analysis of the main parameters of a quartz crystal.
- Allows you to design precise and stable oscillators.
- Useful for comparing the performance of different crystals.
- Facilitates the teaching and understanding of resonance circuits.