Radio Frequency Integrated Circuit Design - Webs

Voltage-Controlled Oscillators
C par = C S
1 + 1
Q 2
=
2pF
1
1 +
2.2097 2
= 1.66 pF
This results in a new resonator resonant frequency of
1
� =
√LC 1
=
= 7.76150 Grad/sec
par √10 nF � 1.66 pF
This is a frequency of 1.2353 GHz, which is close to a 10% change in
frequency. The oscillating frequency is determined by resonance of the loop,
which in this case results in a 5% change in frequency as seen in Example 5.2.
This discrepancy, which can be verified by a simulation of the original circuit
of Figure 8.18(a), is due to the phase shift in the nonideal capacative feedback
path. While calculating frequency shifts and explaining them is of interest to
academics, it is suggested that for practical designs, the simple calculations be
used since parasitics and nonlinear effects will cause a downward shift of frequency.
Further refinement should come from a simulator.
8.8.3 Negative Resistance Analysis of −Gm Oscillator
The analysis of the negative resistance amplifier, shown in Figure 8.9, and the
more common differential form in Figure 8.22(c) is somewhat different. The
small-signal equivalent model for this circuit is shown in Figure 8.19. Note
that one transistor has had the normal convention reversed for V� .
An expression for the current that flows into the circuit can be written
as follows:
Figure 8.19 Small-signal equivalent model for the negative resistance cell in the negative
resistance oscillator.
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