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

 

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8 Evaluate the Crystal for Margin

If a crystal with more appropriate motional properties is needed, it is possible to evaluate the compatibility of a crystal resonator with the oscillator based on the motional properties of the crystal.

The critical transconductance (gmcrit) is the minimum transconductance required by the oscillator to maintain a stable oscillation for a given crystal and load capacitance that can be calculated by the following formula:

Equation 15. gmcrit=4 × Rload× ω2 × (C0+CL)2
Equation 16. Where:  Rload= Rm × 1+C0+CLoad2 and ω=2πf

The gain margin (Gainmargin) can then be calculated by the following formula and the resulting ratio should be greater than 5 to ensure there is enough margin to start and maintain oscillation.

Equation 17. Gainmargin= gmgmcrit