CERAMIC RESONATOR PRINCIPLES
Principles of Operation for Ceramic Resonators
Equivalent Circuit Constants: Fig.1.2 shows the symbol for a ceramic resonator. The impedance and phase characteristics measured between the terminals are shown in Fig.1.5. This figure illustrates that the resonator becomes inductive in the frequency range between the frequency fr (resonant frequency), which provides the minimum impedance, and the frequency fa (antiresonant frequency), which provides the maximum impedance. It becomes capacitive in other frequency ranges. This means that the mechanical oscillation of a two terminal resonator can be replaced with an equivalent circuit consisting of a combination of series and parallel resonant circuits with an inductor L, a capacitor C, and a resistor R. In the vicinity of the resonant frequency, the equivalent circuit can be expressed as shown in Fig.1.4.
The fr and fa frequencies are determined by the piezoelectric ceramic material and its physical parameters. The equivalent circuit constants can be determined from the following formulas:
fr = fa = Qm = (Qm =
1
/2
1
/2
L 1 1 C L 1 C 1 C 0 / ( C
^{1}/2 Fr C1R1 Mechanical Q)
1 + C 0 ) = F
r
1+C
1 + C 0
Considering the limited frequency range of f r f f a , the impedance is given as Z=Re+jwLe (Le=0) as shown in Fig.1.5. The ceramic resonator should operate as an inductor Le(H) having the loss Re ().
Fig.1.1 shows comparisons for equivalent circuit constants between a ceramic resonator and a quartz crystal resonator. Note there is a large difference in capacitance and Qm which results in the difference of oscillating conditions when actually operated. The table in the appendix shows the standard values of equivalent circuit constants for each type of ceramic resonator.
Higher harmonics for other modes of oscillation exist other than the desired oscillation mode. These other oscillation modes exist because the ceramic resonator uses mechanical resonance. Fig.1.6 shows these characteristics.
8.8x10^{3 }
1.0x10^{3 }
385
72
8.6x10^{3 }
7.2x10^{3 }
2.1x10^{3 }
1.4x10^{4 }
14.5
4.2
4.4
5.9
0.015
0.005
0.007
0.027
256.3
33.3
36.3
39.8
5.15
2.39
2.39
5.57
9.0
17.6
8.7
4.8
1060
37.0
22.1
8.0
2734
912
1134
731
23000
298869
240986
88677
12
147
228
555
0.6
3
6
19
8.00MHz
FREQUENCY
L1 (µH) C1 (pF) C0 (pF) R1 () Qm
F (KHz)
Figure 1.1 Comparisons of equivalent
Circuit Constants for
Ceramic and Crystal Resonators
8.00MHz
453.5KHz
CRYSTAL 2.457MHz 4.00MHz
455KHz
CERAMIC RESONATOR
2.50MHz
4.00MH
z
1M 500k
100k 50k
Main Vibration Mode
Impedance between 2 terminals Phase ( ) = tan^{1 }X/R Z = R + jX ( R: real number, X: imaginary number)
Figure 1.2) Symbols for 2Terminal Ceramic Resonator
C1
L1
R1
Impedance Z ()
10
5
10
4
10
3
10
2
10
fr
fa
Phase ø (Deg.)
Impedance Z (Q)
1k 500
100 50
10 5
1
0
000 1.000 2.000 3.000 4.000 5.000 6.000 7.000 8.000 9.000 10.00
Frequency (MHz)
Figure 1.6) Spurious Characteristics for a Typical Ceramic Resonator (455 KHz)
10k 5k
Thickness Mode
430
440
450 Frequency (KHz)
460
470
C0
R1 : Equivalent Resistance L1 : Equivalent Inductance C1 : Equivalent Capacitance C0 : Inner Electrode Capacitance
+90
Figure 1.3) Electrical Equiv. Circuit for a Cer. Resonator
Re
Le
0

90
C
L
L
C
(Colpitts Oscillator)
(Hartley Oscillator)
C
CL1
CL2
L1
L2
Re : Effective Resistance Le : Effective Inductance
Figure 1.4) Equivalent Circuit for a Ceramic Resonator in
the Frequency Range of f f f ra
Figure 1.5) Impedance and Phase Characteristics for Ceramic Resonators
Figure 1.7) Basic configuration for an LC Oscillation Circuit
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TECHNICAL REFERENCE
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TECHNICAL REFERENCE