Page 232 - Phase-Locked Loops Design, Simulation, and Applications

MIXED-SIGNAL PLL APPLICATIONS PART 1: INTEGER-N FREQUENCY
SYNTHESIZERS Ronald E. Best 140

This is the noise power within the frequency interval from 10,000 to 10,001 Hz relative to
the carrier frequency. Next S *(f ) is to be computed. We get
θθ
m

Hence, S *(f ) becomes
m dB
θθ

We conclude that the noise power within a bandwidth of 1 Hz at offset frequency f = 10
m
kHz is 120 dB below carrier power. Furthermore, we see that the mean square value of phase
2
perturbation within a bandwidth of 1 Hz at modulating frequency f = 10 kHz is 10 −12 rad .
m
For the rms value of phase perturbation in that frequency interval we get

To avoid confusion with the standards used in practically all books and papers on
frequency synthesizers, we will nevertheless use the familiar unit dBc/Hz for power density
of phase jitter, although this unit has been shown to be somewhat incorrect.

As mentioned earlier, real amplifiers add further noise. Noise performance of amplifiers is
specified by noise figure F which is defined by

(6.10)

in other words, F is the ratio of signal-to-noise at the output to signal-to-noise at the input. For
a real amplifier S , (f ) becomes larger than S , (f ) by factor F; thus, we now have
θθ out m θθ out m

When we assume F = 6 dB, S , (f ) increases by 6 dB, thus
θθ out m dB

In real amplifiers, we are not only confronted with thermal noise, but there is always
another noise source called flicker noise. Flicker noise is also referred to as 1/f noise, because
the power spectral density of flicker noise varies with amplifier, however, at frequencies
below a corner frequency denoted as f [cf. Fig. 6.16]. For operational amplifiers, for example,
c
f can be on the order of 10 Hz to some kHz. In oscillators, f can easily extend into the MHz
c c
region.