MC145225 MC145230
30
MOTOROLA RF/IF DEVICE DATA
2
1
2
1
2
1
Rs
Ls
Cs
Re
Xe
Co
X1
Figure 23. Crystal Resonator Equivalent Circuit
NOTE: Values are supplied by crystal manufacturer (parallel
resonant crystal).
Figure 24. Overtone Crystal Equivalent Circuit
2
1
L1s
C1s
R1s
Co
L3s
C3s
R3s
L5s
C5s
R5s
Because of the acoustic properties of the crystal
resonator, the crystal “tank” responds to energy not only at its
fundamental frequency, but also at specific multiples of the
fundamental frequency. In the same manner that a shorted or
open transmission line responds to multiples of the
fundamental frequency, the crystal “tank” responds similarly.
A shorted half–wave transmission line (or closed acoustic
chamber) will not only resonate at its fundamental frequency,
but also at odd multiples of the fundamental. These are called
the overtones of the crystal and represent frequencies at
which the crystal can be made to oscillate. The equivalent
circuit of an overtone crystal is shown is Figure 24.
The components for the appropriate overtone are
represented by 1, 3, and 5. The fundamental components are
represented by 1, and those of importance for the third and
fifth overtones, by 3 and 5.
Fundamental Mode
The equivalent circuit for the Colpitts oscillator operating in
the fundamental mode is shown in Figure 25.
C3 is selected to provide a small reduction in the inductive
property of the crystal. In this manner, the frequency of the
oscillator can be “pulled” slightly. The biasing combination of
M1R1 and M2R2 provide the ability to start operation with a
higher than normal operating current to stimulate crystal
activity. This “kick start” current is nominally four times the
normal current. An internal counter times the application of
the “kick start” and returns the current to normal after the time
out period.
The mutual conductance (transconductance) of the
transistor Q1 is useful in determining the conditions
necessary for oscillation. The nominal value for the
transconductance is found from the formula
Ie
26
gm =
where Ie is the emitter current in mA.
The operation of the oscillator can be described using the
concept of “negative resistance”. In a normal tuned circuit,
any excitation tends to be dissipated by the resistance of the
circuit and oscillation dies out. The resistive part of the crystal
along with the resistance of the wiring and the internal
resistance of C1, C2, and C3, make up this “damping”
resistance. Some form of energy must be fed back into the
circuit to sustain oscillation. This is the purpose of the
amplifier.
Figure 25. Fundamental Mode Colpitts Oscillator Equivalent Circuit
C3
C2
C1
R1
R2
Q1
M1
+V
Oscb
Osce
Frequency Synthesizer
I1
200/800
μ
A
R1s
Co
C1s
Rst
M2
L1s
0
0
0