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# CERAMIC RESONATOR PRINCIPLES

## Basic Oscillating Circuits

Generally, the oscillating circuits can be grouped into the following three types:

• 1.

Positive feedback

• 2.

Negative resistance element

• 3.

Delay of transfer time or phase in the case of ceramic resonators, quartz crystal resonators, and LC oscillators, positive feedback is the circuit of choice.

Among the positive feedback oscillation circuits using LC, the tuning type anti-coupling oscillation circuit, by Colpitts and Hartley, are typically used. See Fig. 1.7.

fOSC

=

1

/2

L

1

*

[(C

L1

*

C L 2 ) / ( C

L1

+ C L 2 ) ]

## Hartley Circuit

fOSC

=

1

/2

C ( L 1 + L 2 )

In a ceramic resonator oscillator, the inductor is replaced by a ceramic resonator, taking advantage of the fact that the resonator becomes inductive between resonant and anti-resonant frequencies. The most commonly used circuit is the Colpitts circuit.

The operating principle of these oscillation circuits can be seen in Fig.2.1.

Oscillation occurs when the following conditions are satisfied.

In Fig.1. 7, a transistor, which is the most basic amplifier, is used.

Loop gain: G =

Phase amount:

=

+

= 360˚ • n (n = 1,2,…)

The oscillation frequencies are approximately the same as the resonance

f r e q u e n c y o f t h e c i r c u i t c o n s i s t i n g o f L , C

L1

,

and C

L2

in the Colpitts

## In a Colpitts circuit, an inversion of

= 180˚ is used, and it is inverted

c i r c u i t o r c o n s i s t i n g o f L 1 , L 2 , a n d C i n t h e H a r t l e y c i r c u i t . T h e s e

more than

= 180˚ with L and C in the feedback circuit. The operation

frequencies can be represented by the following formulas.

with a ceramic resonator can be considered as the same.

• 

1

40

30

### Possible to Oscillate

Amplifier Gain Phase Shift: 1

R

f

20

Phase

90

Feedback Network Transfer Function: Phase Shift: 2

10

0

• -

10

### Phase (deg)

Oscillating conditions Loop gain G =  Phase Shift T = 1+1 = 360˚ • n(n = 1,2, …)

Figure 2.1) Principles of Oscillation

CL1

Ceramic Resonator

CL2

• 2

Figure 2.2) Basic Oscillation Circuit with Inverters

• -

20

• -

30

• -

40

3.90

4.00M VDD = +5V

C

L1

=C

L2

= 30pF

IC: CD4069UBE

4.00 Frequency (KHz)

• -

90

4.10

40

30

### Impossible to Oscillate

90

20

0.01

• 

1

IC

• 2

Ceramic Resonator

Z

in

[ 1 M ( ) ] - j / w [ 8 1 0 9 ( F ) ]

Loop Gain (dB)

10

0

• -

10

Phase

Phase (deg)

Z 0 = 5 0

Vector Voltmeter

• -

20

### Gain

• -

90

V

in

S.S.G.

• -

30

4.00M VDD = +2.7V

C

L1

=C

L2

= 30pF

Loop gain G =  Phase Shift T = 1+1 = 360˚ • n(n = 1,2, …)

• -

40

3.90

IC: CD4069UBE

4.00 Frequency (KHz)

4.10

Figure 2.3) Measuring Circuit Network for Loop-Gain and Phase Shift

Figure 2.4) Measured Results of Loop Gain and Phase Shift

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TECHNICAL REFERENCE

89

TECHNICAL REFERENCE

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