Anderson Electronics, Inc. - Tutorial (Motional Capacitance & Motional Inductance)

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Motional Capacitance & Motional Inductance
The parallel and series resonant equivalent circuits of a crystal appear as follows whereas:

Co = Shunt Capacitance
Cl = Load Capacitance
Rs = Series Resistance
L1 = Motional Inductance

Normally crystal designs for oscillators, specifically VCXOs, maximize C1 to achieve required frequency adjustment/pullability and reduced impedance, Rs. As C1 is maximized, L1 is reduced, a requirement for suppressing spurious modes. C1 is governed by electrode area/diameter and registration/alignment of the two metal plates. Conversely, Co negates the effect of increasing pullability by increasing Cm through electrode size.

In filter crystal design, C1 is selected to achieve a specific bandwidth. In fundamental mode crystals bandwidth is inversely proportional to C1 meaning that as C1 is reduced, bandwidth increases. C1 tolerance must also be considered, but generally:

BW (KHz.) = 0.5/ C1 (fF)

C1 = 0.5/BW (KHz.)

Equivalent Circuit of a Resonator

Equivalent Circuit Parameter Relationships

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