Page 234 - Phase-Locked Loops Design, Simulation, and Applications

MIXED-SIGNAL PLL APPLICATIONS PART 1: INTEGER-N FREQUENCY
SYNTHESIZERS Ronald E. Best 141

Figure 6.16 The power spectral density of input phase jitter θ n,in . Noise below the corner
frequency f is called flicker noise. Noise above f is thermal noise.
c
c
When flicker noise is present, we get for the PSD of the noise signal

(6.11)

Now we get for the PSD of phase jitter the expression

(6.12)

Still assuming F = 6 dB we get for a modulating frequency f = f /10 the value
c
m

At a modulating frequency f = f /100, this would increase to −148 dBc/Hz.
m
c
We considered hitherto the very simple case where a noise source was modulating a carrier
signal at the input of a noiseless or of a real amplifier. Next, we have to examine the situation
where the noise source is fed to the input of an oscillator. The noise spectrum observed at the
oscillator output deviates considerably from that of a simple amplifier because the oscillator
has a frequency-dependent loop gain. In the vicinity of the resonant frequency the loop gain of
the oscillator is extremely high, hence the noise will be heavily amplified at those frequencies.