AN95089 Datasheet, PDF (4/19 Pages) Ramtron International Corporation – BLE Crystal Oscillator Selection and Tuning Techniques

PSoC® 4/PRoC™ BLE Crystal Oscillator Selection and Tuning Techniques
2.3 Crystal Equivalent RLC Circuit
Figure 4 shows the equivalent RLC circuit of the crystal.
Figure 4. Equivalent RLC Circuit of the Crystal
Inverting Amplifier
R
XI
XO
CL
C0
L_M
RM
C_M
Where,
RM = Motional resistance of the crystal
C0 = Shunt capacitance
CL = Load capacitance
CM = Motional capacitance
LM = Motional inductance
This circuit represents parallel resonant mode. The frequency of oscillation is derived from Equation 2:
Equation 2:
Where
is the series resonant frequency of the oscillator and is the frequency of oscillation.
2.3.1
Equivalent Series Resistance (ESR)
This resistance represents the resistive element of the quartz crystal equivalent circuit. It is the equivalent impedance
of the crystal at its natural resonant frequency (series resonance). The gain of the oscillator amplifier directly depends
on the ESR: the higher the ESR value, the higher will be the gain required by the oscillator amplifier to oscillate at the
desired frequency.
Internal oscillator circuits in every chip are designed to work with a maximum specified value of ESR such that the
biasing point of the amplifier becomes unstable, resulting in oscillations.
The ESR for a crystal is given by the following equation:
Equation 3:
See the crystal datasheet for the ESR value. Its value depends on the crystal frequency and usually varies from 20 Ω
to 100 Ω.
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Document No. 001-95089 Rev. *A
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