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Quartz
Crystal Theory 
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The Equivalent Circuit
L1
 Dynamic or Motional Inductance (mH)
C1  Dynamic or Motional
Capacitance (fF) (1015
F)
R1  Equivalent Series
Resistance (ohms)
C0  Parallel or Static
Capacitance (pF) 

Note 1: L1,
C1 and R1 are not true
electrical components. They are apparent values of inductance, capacitance and resistance
which serve to model mechanical / piezoelectric of the vibrating crystal in the region of
resonance.
Note 2: In all cases the units shown in brackets are those normally
used for ATcut crystals.
Note 3: It is necessary to use consistent units in the equations, i.e.
Farads, Henries, etc.
Circuit Equations  Basic Crystals
Circuit Equations  with external load
Frequency Deviation  series to load: 

Note 1: Series
Capacitance (CL) increases the frequency.
Note 2: The effect of a trimmer may be readily assessed by
calculating D and D' for CL and CL'
and subtracting.
Note 3: Units are correct for C1,
C0 and CL in Farads. 

Trim Sensitivity: 

The above graph shows the effect of external load capacitance on the trim sensitivity of a
representative 20MHz fundamental mode crystal. Notice the large frequency shift with small
load changes when fundamental mode crystals are operated at low load capacitance's.
Overtone mode crystals are generally less affected by external loads. A rough
approximation is to reduce the fundamental mode trim sensitivity by a factor of the
overtone mode crystal.
Apparent Series Resistance (with CL): 

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