Radio Frequency Integrated Circuit Design - Webs

Voltage-Controlled Oscillators
V tank = i fundRp = kI AVERp
283
(8.74)
Thus, equations to predict oscillation amplitude have now been derived.
By comparing (8.73) and (8.74) to (8.68), it can be seen that a given amount
of dc current will lead to more current at the fundamental frequency in the
case of the resistive tail as opposed to the current tail.
8.17 Phase Noise
A major challenge in most oscillator designs is to meet the phase noise requirements
of the system. An ideal oscillator has a frequency response that is a simple
impulse at the frequency of oscillation. However, real oscillators exhibit ‘‘skirts’’
caused by instantaneous jitter in the phase of the waveform. Noise that causes
variations in the phase of the signal (distinct from noise that causes fluctuations
in the amplitude of the signal) is referred to as phase noise. The waveform of
a real oscillator can be written as
V osc = A cos [� o t + � n (t)] (8.75)
where � n (t) is the phase noise of the oscillator. Here amplitude noise is ignored
because it is usually of little importance in most system specifications. Because
of amplitude limiting in integrated oscillators, typically AM noise is lower than
FM noise. There are several major sources of phase noise in an oscillator, and
they will be discussed next.
8.17.1 Linear or Additive Phase Noise and Leeson’s Formula
In order to derive a formula for phase noise in an oscillator, we will start with
the feedback model of an oscillator as shown in Figure 8.33 [7].
From control theory, it is known that
Nout(s)
Nin(s)
= H1(s)
1 − H(s)
(8.76)
where H(s) = H 1(s)H2(s). H(s) can be written as a truncated Taylor series:
Figure 8.33 Feedback model of an oscillator used for phase-noise modeling.