Radio Frequency Integrated Circuit Design - Webs

286 Radio Frequency Integrated Circuit Design
are completely switched, int is the noise current injected into the oscillator from
the biasing network during this time. During transitions, the transistors act like
an amplifier, and thus collector shot noise icn from the resonator transistors
usually dominates the noise during this time. The total input noise becomes
|Nin(s)| 2 ≈ kT +
2
int R p
� + i
2
2
cnR p (1 − �) (8.88)
where R p is the equivalent parallel resistance of the tank. Thus, we can define
an excess noise factor for the oscillator as excess noise injected by noise sources
other than the losses in the tank:
F = 1 +
2
int R 2
p icn � +
2kT R p (1 − �)
kT
(8.89)
Note that as the Q of the tank increases, R p increases and noise has more
gain to the output; therefore, F is increased. Thus, while (8.85) shows a decrease
in phase noise with an increase in Q, this is somewhat offset by the increase
in F. If noise from the bias icn is filtered and if fast switching is employed, it
is possible to achieve a noise factor close to unity.
Now (8.86) can be rewritten as
PN =� |H1|�o
(2Q��)� 2
�FkT 2PS�
(8.90)
Note that in this derivation, it has been assumed that flicker noise is
insignificant at the frequencies of interest. This may not always be the case,
especially in CMOS designs. If � c represents the flicker noise corner where
flicker noise and thermal noise are equal in importance, then (8.90) can be
rewritten as
PN =� |H1|�o
(2Q��)� 2
�FkT �c
1 +
2PS�� ���
(8.91)
It can be noted that (8.91) predicts that noise will roll off at slopes of −30
or −20 dB/decade depending on whether flicker noise is important. However, in
real life, at high frequency offsets there will be a thermal noise floor. A typical
plot of phase noise versus offset frequency is shown in Figure 8.34.
It is important to make a few notes here about the interpretation of this
formula. Note that in the derivation of this formula, it has been assumed that