Phase Noise in Signal Sources
This book contains a thorough treatment of phase noise, its relationship to thermal noise and associated subjects such as frequency stability. The design of low phase noise signal sources, including oscillators and synthesisers, is explained and in many cases the measured phase noise characteristics are compared with the theoretical predictions. Full theoretical treatments are combined with physical explanations, helpful comments, examples of manufactured equipment and practical tips. Overall system performance degradations due to unwanted phase noise are fully analysed for radar systems and for both analogue and digital communications systems. Specifications for the acceptable phase noise performance of signal sources to be used in such systems are derived after allowing for both technical and economic optimisation. The mature engineer whose mathematics may be somewhat rusty will find that every effort has been made to use the lowest level of mathematical sophistication that is compatible with a full analysis and every line of each mathematical argument has been set out so that the book may be read and understood even in an armchair. Due to a novel approach to the analytical treatment of narrow band noise, the book is simple to understand while simultaneously carrying the analysis further in several areas than any existing publication.
Inspec keywords: thermal noise; phase noise; frequency stability; oscillators; signal sources
Other keywords: phase noise; signal source; oscillator; synthesiser; frequency stability; thermal noise
Subjects: Other topics in statistics; Signal generators
In communications, radar and similar systems, signal sources are required as carriers for increasingly sophisticated baseband information. They are also required as local oscillators or pump sources for achieving frequency conversions. A simple source might consist of a crystal oscillator alone or perhaps a manually tuned oscillator. With the increased usage of the frequency spectrum, the permissible tolerance on the nominal frequency of signal sources is continually reduced. This has necessitated the development of more complex signal sources. For single frequency operation, these usually consist of crystal oscillators followed by amplifiers and frequency multiplying stages. Where manual or remote accurate selection of frequencies is required, frequency synthesisers are normally specified.
This chapter presents a review of modulation theory, including amplitude, phase and frequency modulation.
This chapter discusses the relationship between phase jitter and noise density.
In a radar or communication system using frequency modulation, it is natural to express any spurious angle modulation in terms of unwanted frequency deviation, as it is this which directly causes performance degradation. It is usually greatly preferable to work in terms of noise density, phase noise density or phase jitter. The use of the expression 'FM noise' is deprecated. A carrier with noise-like FM sidebands has sideband powers proportional to the phase modulation index and not to the frequency deviation. The operation of an FM demodulator is to produce an output power proportional to the square of the frequency deviation. It is only this operation which converts the random 'FM sidebands' into baseband noise power.
An oscillator is an inherently non-linear device. If it had an effective loop gain of exactly unity for all signal levels, an initial low level oscillation would never build up in amplitude. Some non-linearity must be present to reduce the effective loop gain to unity at the full output level. During each RF cycle, the instantaneous voltage will sweep over the full range and thus will normally experience this non-linearity. The effects of such non-linearity will include the generation of harmonics and intermodulation between any noise components which may be present and also between such noise components and the carrier. Due to flicker effects in the active device used, noise close to DC will tend to follow a 1/f power law with frequency. For example, a noise component in a 1 Hz bandwidth at a frequency of 5 Hz will be relatively large and due to the non-linearity will beat with the carrier to produce noise components at (f0 ± 5) Hz which will be of significant amplitude. The only other significant contribution to the noise output of a good oscillator would be expected to be the noise components existing initially at frequencies adjacent to f0. These would be identical in an ideal linear oscillator to those in a real somewhat non-linear oscillator. Thus, it is to be expected that, if a linear model were used to predict the carrier to noise ratio of an oscillator, the main error would be due to the neglect of the effects of 1/f noise transposed to small offset frequencies. Such a model should, therefore, be adequate to determine the performance of high quality oscillators except for very small offset frequencies.
At frequencies up to the order of 120-150 MHz, it is possible to use a quartz crystal as resonator and thus achieve simultaneously a high Q and good frequency stability and accuracy. At still higher frequencies the phase noise performance of a simple oscillator will be degraded both due to the higher value of f0 and simultaneously the lower Q of a suitable resonant circuit which can no longer be a quartz crystal. A further penalty is that the frequency accuracy and stability will be degraded. Thus it is apparent that a considerable improvement in performance might be achieved by using a crystal oscillator followed by a frequency multiplier to give the required output frequency. This would appear to be a beneficial tradeoff even if the multiplication process produced a phase noise degradation proportional to the square of the multiplication ratio. This degradation would be exactly offset by the f0 2 term in the numerator of the RHS of equation (6.1), leaving the improvement in Q as a bonus, to say nothing of the improved frequency stability. A further bonus is often available in that the noise figure of the transistor oscillator may be considerably better if the oscillator is operated at a sub-multiple of the required output frequency.
A better overall performance would be obtained if it were possible to take the performance shown by curve (a) up to an offset frequency of about 5 kHz and that of curve (b) at higher offset frequencies. In principle this would be possible by using source (b) to provide the final output, but to lock the phase of this source to that of the frequency multiplied 5 MHz source using a phase lock loop (PLL) with a natural frequency of about 5 kHz. The phase noise curves of the X-band VCO and the multiplied 5 MHz MO cross at about 25 kHz. If the X-band VCO were phase locked to the multiplied MO using a phase lock loop (PLL) with a natural frequency of about 25 kHz then the composite source would have an overall performance the graph of which would follow that of the multiplied 5 MHz MO up to 25 kHz and that of the X-band VCO for all higher offset frequencies. Thus, the overall phase noise performance of signal sources over an offset frequency range from the lowest to the highest offset frequencies may be greatly improved by the use of phase lock loops which will now be considered in more detail.
If a signal source is required to provide a large number of easily selected, accurately controlled and stable output frequencies with good phase noise performance, then the use of a synthesiser can hardly be avoided.
This chapter discusses the reciprocal relationships between phase noise and frequency stability.
This chapter discusses system phase noise requirements.
The symbols used in this Appendix are defined as they occur with the occasional exception of those given in the list which immediately precedes Chapter 1. As far as possible, the equation numbers given represent the expression occurring at the end of the first full (rather than simplified) derivation of each equation. It is hoped that this will facilitate the use of this summary for purposes of revision or reference.
For many years, it has been possible to build electronic amplifiers with an almost unlimited gain. If it were not for the effects of noise and interference, it would be possible to amplify the weakest of signals to any required level. Communication and radar systems would use low-power transmitters and would no longer be limited in range. In a sense, communication and radar engineering would become trivial.
In many communication or radar systems, the bandwidth occupied by the signal, and hence the bandwidth in which we are interested, is only a very small percentage of the centre frequency. The output noise from, for example, an IF filter will be white over most of the filter passband. Thus narrow-band white noise is both a simple and a practically interesting case. This Appendix considers the analysis of coloured noise by breaking the frequency band into a number of sub-bands, each with a different noise level.
This chapter discusses the Q of varactor-tuned oscillators.
This chapter discusses the phase noise performance of Gunn oscillators.
