Precision frequency sources such as quartz oscillators, masers, and passive atomic frequency standards are affected by phase and frequency instabilities including both random and deterministic components. It is of prime importance to have a comprehensive characterization of these instabilities in order to be able to assess the potential utility of each source. For that purpose, many parameters have been proposed especially for dealing with random fluctuations. Some of them have been recommended by the IEEE Subcommittee on Frequency Stability and later by Study Group 7 on "Standard Frequencies and Time Signals" of the International Radio Consultative Committee (CCIR). Others are not so widely used but show interesting capabilities. This paper aims at giving a broad review of parameters proposed for phase and frequency instability characterization, including both classical widely used concepts and more recent less familiar approaches. Transfer functions that link frequency-domain and time-domain parameters are emphasized because they provide improved understanding of the properties of a given time-domain parameter or facilitate introducing of new parameters. As far as new approaches are concerned, an attempt has been made to demonstrate clearly their respective advantages. To this end, some developments that did not appear in the original references ate presented here, e.g, the modified three sample variance Σ y 2(τ), the expressions of 〈δy- T 2〉, the intetpretation of structure functions of phase and its relations with Σ y 2(τ) and the Hadamard variance. The effects of polynomial phase and frequency drifts on various parameters have also been pointed out in parallel with those of random processes modeled by power-law spectral densities.

Characterization of phase and frequency instabilities in precision frequency sources: Fifteen years of progress

This is a survey paper which begins by the derivation of the general PLL noise equation and by dividing the additive noises into the passband group and the stopband group. In the following paragraphs the behavior of all the major sources of additive noises is investigated and the practical numerical values of the respective power spectral densities are given. In the terminating sections, guidelines for minimizing the additive noises in PLL systems and PLL frequency synthesizers are emphasized, and finally, phase-noise power spectral densities of several actual PLL frequency synthesizers are plotted in the normalized form. The paper is accompanied by a copious bibliography.

Noise Properties of PLL Systems

A new technique is presented which makes it possible to measure the inherent short-term stability of quartz crystal resonators in a passive circuit. Comparisons with stability measurements made on crystal controlled oscillators indicate that noise in the electronics of the oscillators very seriously degrades the inherent stability of the quartz resonators for times less than 1 s. A simple model appears to describe the noise mechanism in crystal controlled oscillators and points the way to design changes which should improve their short-term stability by two orders of magnitude. Calculations are outlined which show that with this improved short-term stability it should be feasible to multiply a crystal controlled source to 1 THz and obtain a linewidth of less than 1 Hz. In many cases, this improved short-term stability should also permit a factor of 100 reduction in the length of time necessary to achieve a given level of accuracy in frequency measurements.

Measurement of the Short-Term Stability of Quartz Crystal Resonators and the Implications for Crystal Oscillator Design and Applications

A photonic-delay line is used as a frequency discriminator for measurement of the phase noise - hence the short-term frequency stability - of microwave oscillators. The scheme is suitable for electronic and photonic oscillators, including the optoelectronic oscillator, mode lock lasers, and other types of rf and microwave pulsed optical sources. The approach is inherently suitable for a wide range of frequency without reconfiguration, which is important for the measurement of tunable oscillators. It is also insensitive to a moderate frequency drift without the need for phase locking.

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Photonic-delay technique for phase-noise measurement of microwave oscillators

In this paper we report the results of extensive research on phase modulation (PM) and amplitude modulation (AM) noise in linear bipolar junction transistor (BJT) amplifiers. BJT amplifiers exhibit 1/f PM and AM noise about a carrier signal that is much larger than the amplifiers thermal noise at those frequencies in the absence of the carrier signal. Our work shows that the 1/f PM noise of a BJT based amplifier is accompanied by 1/f AM noise which can be higher, lower, or nearly equal, depending on the circuit implementation. The 1/f AM and PM noise in BJTs is primarily the result of 1/f fluctuations in transistor current, transistor capacitance, circuit supply voltages, circuit impedances, and circuit configuration. We discuss the theory and present experimental data in reference to common emitter amplifiers, but the analysis can be applied to other configurations as well. This study provides the functional dependence of 1/f AM and PM noise on transistor parameters, circuit parameters, and signal frequency, thereby laying the groundwork for a comprehensive theory of 1/f AM and PM noise in BJT amplifiers. We show that in many cases the 1/f PM and AM noise can be reduced below the thermal noise of the amplifier.

Origin of 1/f PM and AM noise in bipolar junction transistor amplifiers

The high phase stability of atomic frequency standards has called for the development of associated electronic equipment of equivalent or superior stability. We have surveyed the performance of existing high quality frequency multipliers and R F amplifiers which operate in the range of 5 MHz to microwave frequencies. We were most interested in the phase noise in the range of Fourier  frequencies, f , of about Hz to l o t 3 Hz, since  most electronic servo systems in existing atomic frequency standards use modulation frequencies which fall within this range. This range also includes the passive linewidths of existing atomic frequency standards.

A. E. Wainwright

Papers

Flicker Noise of Phase in RF Amplifiers and Frequency Multipliers: Characterization, Cause, and Cure