TABLE OF CONTENTS This section describes the basics of phase-noise analysis and applies the analysis to oscillator design. A phase-noise modeling technique is developed that will allow mathematical operations to be performed on phase-noise curves. Frequency modulation (FM) waveform theory is investigated so that the relationship between narrowband FM and single-sideband phase noise is established. Various measurement relationships to phase noise are explained so that an engineer can interpret between oscillator stability specifications that use these measurements. With the establishment of several phase-noise relationships, a general mathematical description for oscillators is developed. Finally, the phase-noise power slopes of an oscillator are modeled.
A study of FM theory typically begins with a mathematical model for an FM waveform. Equation (3.28) mathematically describes an FM waveform as a function of time:
where
| V p | = maximum amplitude (V); |
| t | = time variable (sec); |
| ? | = modulation index; |
| ? m | = angular frequency of modulation, which is usually less than the carrier frequency (rad/s); |
| ? m | = 2 ? f m; |
| ? c | = angular frequency of the carrier, usually greater than modulation frequency (rad/s); |
| ? c | = 2 ? f c. |
The FM waveform function in (3.28) allows frequency, phase, and phase-noise relationships to be developed. The argument of the cosine function in (3.28) is the instantaneous phase. The derivative of instantaneous phase with respect to time is frequency; therefore, the study of frequency-stability analysis includes the study of instantaneous phase. The derivative of the...
