##### From CMOS Current-Mode Circuits for Data Communications

## 6.5 Noise Characteristics of Phase-Locked Loops

In this section, we investigate the noise characteristics of phase-locked loops in the lock state from a system point of view. Such an analysis provides us with the critical insight of the noise behavior of phase-locked loops.

### 6.5.1 Phase Noise of Oscillators

It is well understood that ring VCOs suffer from poor phase noise mainly due to their low quality factor and a large number of noise sources [189]. The noise of VCOs(CCOs) largely affects the timing jitter of PLLs, subsequently the BER of clock and data recovery operation. In this section, we briefly review the mathematical treatment of the phase noise of oscillators. Readers are referred to the cited references for an in-depth treatment of the phase noise of oscillators.

#### Leeson Model

Perhaps the most widely cited early work on phase noise analysis of oscillators is the empirical expression given by Leeson [190]. It predicts the power of the single-side-band (SSB) phase noise of a *LC* tank oscillator

(6.32) | |

where ? * ?* is the frequency offset from the oscillation frequency * ? _{o,} Q* is the quality factor of the oscillator,

*F*is the excess noise factor,

*k*is Boltzmann's constant,

*T*is absolute temperature in degrees Kelvin,

*P*is the average power loss of the oscillator, and is the corner frequency between 1/

_{s}*f*

^{2}and 1/

*f*

^{3}regions, as shown in Fig. 6.85. It is seen that 1/

*f*

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