SLLA549 July 2021 TCAN4550 , TCAN4550-Q1 , TCAN4551-Q1

9 Calculate the Startup Time and Quality Factor

The ability of the crystal to sustain oscillation can be determined by the Quality Factor (Q) which is the ratio of the initial stored energy and the amount of energy lost in one radian cycle of oscillation. A higher Q factor will have less energy loss and longer sustained oscillation before the resonation dies out. Calculate the Quality factor (Q) by the following formula:

Equation 18.

Q = \frac{2 π \times F_{s} \times L_{m}}{R_{m}}

The time it takes the oscillations to start and stabilize is also of importance. Several factors such as the drive level, load resistance, and the magnitude of the closed loop gain can impact the startup time (τ) of the oscillations which can be calculated by the following formula:

Equation 19.

τ = \frac{2 \times L_{m}}{R_{L o a d} + R_{n e g}}