Radio Frequency Integrated Circuit Design - Webs

Voltage-Controlled Oscillators
Q. In addition, as the capacitors become smaller, their value will be more
sensitive to parasitics. The frequency of oscillation for the Colpitts common-base
oscillator, as shown in Figure 8.10(a), taking into account transistor parasitics, is
given by
�osc ≈
1
√L� C 1C2 + C 1C�
C 1 + C 2 + C�
+ C��
275
(8.49)
For the Colpitts common-collector oscillator, as shown in Figure 8.10(b),
the frequency is given by
�osc ≈
1
√L� C 1C2 + C 2C�
C 1 + C 2 + C�
+ C��
For the −Gm oscillator, the frequency is given by
� osc ≈
1
√L� 2C� + C�
+ C� 2
(8.50)
(8.51)
Note that in the case of the −Gm oscillator, the parasitics tend to reduce
the frequency of oscillation a bit more than with the Colpitts oscillator.
8.14 Large-Signal Nonlinearity in the Transistor
So far, the discussion of oscillators has assumed that the small-signal equivalent
model for the transistor is valid. If this were true, then the oscillation amplitude
would grow indefinitely, which is not the case. As the signal grows, nonlinearity
will serve to reduce the negative resistance of the oscillator until it just cancels
out the losses and the oscillation reaches some steady-state amplitude. The
source of the nonlinearity is typically the transistor itself.
Usually the transistor is biased somewhere in the active region. At this
operating point, the transistor will have a particular g m . However, as the voltage
swing starts to increase during startup, the instantaneous g m will start to change
over a complete cycle. The transistor may even start to enter the saturation
region at one end of the swing and the cutoff region at the other end of the
voltage swing. Which of these effects starts to happen first depends on the
biasing of the transistor. Ultimately, a combination of all effects may be present.