13.1 Frequency Stability and Noise

When frequency stability is used to specify clock performance, it is generally understood as referring to frequency change. This corresponds to drift or aging over time in oscillators. Frequency stability also includes the concept of frequency variation. For telecommunications systems, frequency and phase stability are specified using statistical definitions.

Noise must be analyzed if we are to assess the statistical clock performance. More detailed specifications of frequency stability are needed for this goal. The basic PLL analysis described in Chapter 5 did not consider the noise of signals and circuits. Spurious characteristics were introduced in the DDS analysis in Chapter 11. Only digital signal analysis was used, however, and the concept of noise was not considered. This chapter describes the influence of random electrical noise as well as measures to evaluate and specify noise in clocks.

13.2 Relationship Between Sine Wave and Noise

13.2.1 Noise in the Frequency Domain

A common ideal sine wave generated by a signal source has a single frequency component. We must accept, however, that the amplitude, frequency, and phase of a practical sine will include noise. The power of a sine wave is concentrated on just its fundamental frequency f _o if the wave can be expressed as

If this signal is analyzed with a spectrum analyzer, the measured frequency domain spectrum is as shown in Figure 13.1. A single peak exists at f _o and its magnitude is related to the effective power. The practical spectrum looks...