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# 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 (anti-resonant 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.

8.8x103

1.0x103

385

72

8.6x103

7.2x103

2.1x103

1.4x104

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

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 2-Terminal Ceramic Resonator

Impedance Z ()

10

5

10

4

10

3

10

2

10

fr

fa

### 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

## ECS, INC. INTERNATIONAL 1105 S. RIDGEVIEW, OLATHE, KS 66062 • 913-782-7787 • 800-237-1041 • FAX 913-782-6991 • WWW.ECSXTAL.COM

TECHNICAL REFERENCE

88

TECHNICAL REFERENCE

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