APPLICATION NOTE
1
Equivalent Electrical Model
Crystal oscillators can be modelled as a series RLC circuit along with a parallel capacitor as shown in Figure 1.
Quartz crystal oscillators tend to operate towards their "series resonance".
Figure 1: Equivalent Electrical Model
The equivalent impedance of the crystal has a series resonance where Cs resonates with inductance, Ls at the
crystals operating frequency. This frequency is called the crystals series frequency, ƒs. As well as this series
frequency, there is a second frequency point established as a result of the parallel resonance created when Ls
and Cs resonates with the parallel capacitor Cp as described below:
Crystal Impedance against Frequency
R = R and X
LS
= 2πfL
s
X
CS
=1/2πfC
s
and X
CP
= 1/2πfC
p
Crystal Reactance against Frequency
X
S
= R
2
+(X
LS
-X
CS
)
2
X
CP
= 1/(2πfC
p
) and X
P
= (X
s
*X
CP
)/(X
s
+X
CP
)
