Realistic Quartz Crystal Oscillator BVD Model

@Muse - Here is the updated circuit using realistic component parameters based on the complete **Butterworth–Van Dyke (BVD)** quartz crystal equivalent model: ### Key Changes to Match Real-Life Operation 1. **Complete BVD Crystal Model**: - **Motional Resistance (#Rm = $20\text{ }\Omega$)**: Represents the internal acoustic dissipation (ESR). - **Motional Inductance (#Lm = $25\,\mu\text{H}$)** and **Motional Capacitance (#Cm = $10\text{ pF}$)**: Determine the primary mechanical resonance frequency: $$f_s = \frac{1}{2\pi\sqrt{L_m C_m}} \approx 10.07\text{ MHz}$$ - **Shunt Capacitance (#C0 = $3\text{ pF}$)**: Represents the physical electrostatic capacitance of the electrodes and package holding the quartz crystal. 2. **Realistic Load Capacitors (#C1, #C2 = $22\text{ pF}$)**: - Standard crystal load capacitance is $C_L \approx 12\text{–}18\text{ pF}$. With two $22\text{ pF}$ capacitors in series: $$C_L \approx \frac{C_1 \cdot C_2}{C_1 + C_2} + C_{\text{stray}} \approx 11\text{ pF} + C_{\text{stray}} \approx 13\text{–}16\text{ pF}$$ 3. **Oscillation Behavior**: - The $\pi$-network formed by the crystal and #C1 / #C2 introduces an exact $180^\circ$ phase shift around $12\text{ MHz}$, complementing the $180^\circ$ inversion of #U1. - If starting from an initial DC state, pressing #SW1 briefly kicks the high-$Q$ resonator into clean rail-to-rail digital switching at #out.

published 6 hours ago