P17E.pdf
2012.10.31
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Note
Principles of CERALOCK®
2
1. Equivalent Circuit Constants
Fig. 2-1 shows the symbol for a ceramic resonator. The
impedance and phase characteristics measured between
the terminals are shown in Fig. 2-2. This illustrates that
the resonator becomes inductive in the frequency zone
between the frequency Fr (resonant frequency), which
provides the minimum impedance, and the frequency Fa
(anti-resonant frequency), which provides the maximum
impedance.
Symbol
Impedance between Two Terminals Z=R+jx
(R : Real Component, X : Impedance Component)
Phase φ =tan-1X/R
2
Fig. 2-1 Symbol for the Two-Terminal CERALOCK®
It becomes capacitive in other frequency zones. This
means that the mechanical vibration of a two-terminal
resonator can be replaced equivalently with a
combination of series and parallel resonant circuits
consisting of an inductor : L, a capacitor : C, and a
resistor : R. In the vicinity of the specific frequency
(Refer to Note 1 on page 8), the equivalent circuit can be
expressed as shown in Fig. 2-3.
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2
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Fr and Fa frequencies are determined by the
piezoelectric ceramic material and the physical
parameters. The equivalent circuit constants can be
determined from the following formulas. (Refer to Note
2 on page 8)
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Fr
Fa
Frequency (kHz)
90
0
(2-1)
(2-2)
(2-3)
Fr=1/2π L1C1
Fa=1/2π L1C1C0/(C1+C0)=Fr 1+C1/C0
Qm=1/2πFrC1R1
-90
(Qm : Mechanical Q)
Considering the limited frequency range of Fr≦F≦Fa,
the impedance is given as Z=Re+jωLe (Le≧0) as shown
in Fig. 2-4, and CERALOCK® should work as an
inductance Le (H) having the loss Re (Ω).
Fig. 2-2 Impedance and Phase Characteristics of CERALOCK®
L1
C1
C0
R1
R1 : Equivalent Resistance
L1 : Equivalent Inductance
C1 : Equivalent Capacitance
C0 : Parallel Equivalent Capacitance
Fig. 2-3 Electrical Equivalent Circuit of CERALOCK®
Re
Le
Re : Effective Resistance
Le : Effective Inductance
Fig. 2-4 Equivalent Circuit of CERALOCK®
in the Frequency Band Fr≦F≦Fa
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