Jan R. Westra

Oscillators and Oscillator Systems

The first € price and the £ and

Resonance-mode selection and crosstalk elimination using resonator-synchronised relaxation oscillators

price are net prices, subject to local VAT. Prices indicated with * include VAT for books; the €(D) includes 7% for Germany, the €(A) includes 10% for Austria. Prices indicated with ** include VAT for electronic products; 19% for Germany, 20% for Austria. All prices exclusive of carriage charges. Prices and other details are subject to change without notice. All errors and omissions excepted. J.R. Westra, C.J.M. Verhoeven, A. van Roermund Oscillators and Oscillator Systems

Effect-oriented modelling of noise in relaxation oscillators

In many applications, electro-mechanical resonators, such as crystals or micro-machined resonating structures, are used as a frequency-selective element in oscillators. These mechanical resonators often have many resonance modes and suffer from large crosstalk. The reliable selection of the desired resonance mode, at the same time coping with the large crosstalk is often a problem in integrated circuits, especially when the spacing between resonance modes is only small. In this paper, a method is presented that uses the selectivity and the time-discrete character of relaxation oscillators to solve both problems.

Fundamentals of oscillator design

In this paper, a new modelling method is introduced for the description of the influence of noise in relaxation oscillators. Although the noise behaviour of relaxation oscillators is principally difficult to analyse, mainly due to the non-linear character of these oscillators, in this paper a method is presented for describing the influence of noise by using simple filter models that can be interpreted very easily. The presented models are effect-oriented models, rather than a cause-oriented models, which gives the designer the freedom to match the noise model to a specific application.

Noise in oscillators

The primary goal of the designer of every technical system is to achieve a certain functionality. At the highest level in the design of this technical system, the designer is not interested in the technology that is used to implement this functionality. It could as well be implemented as a mechanical system as an electronic system, or as a chemical system. At the highest level, the behavior of the system can be described as a set of mathematical equations. The actual design of the system comes down to the implementation of these equations using one technology or another.

Noise in second-order oscillators

One of the most important signal specifications for an oscillation is its spectral purity. In every oscillator application there is a limit on the noise that can be allowed to contaminate the oscillation. Therefore this, and the following two chapters are devoted to noise. In this chapter, general descriptions are given of the influence of noise on oscillations. Section 4.2 starts with a mathematical description of contaminations of oscillations. Section 4.3 specifically zooms in on the noise behavior of oscillators. In this section, the mathematical fundamentals of Section 4.2 are used as a basis. In the five subsections of Section 4.3, various noise measures are presented that are often used in literature. Some of these noise measures can effectively describe the noise behavior whereas others should be avoided. Using the results of the subsections describing the various noise measures, the results from the rest of the chapter can be compared to results already known from literature. In the last section, the Bennet model is introduced. This model can be used advantageously for noise calculations in oscillators. In Chapter 5, this model is used for the description of the influence of noise in first-order oscillators.

Classification of oscillators

In the previous chapter, we concentrated completely on the noise behavior of oscillators using a first-order timing reference. In this section, we concentrate on the class of oscillators using a second-order timing reference. In Chapter 3, a complete classification of this class of oscillators is given, which is used in this chapter as a guideline. We have seen that we can distinguish the classes of second-order relaxation oscillators and second-order harmonic oscillators. First, in Section 6.2, the class of second-order relaxation oscillators is covered. It is shown that this class of oscillators is not very interesting from a high-performance point of view, although it incorporates many well-known oscillators. After that, in Section 6.3, the noise behavior of the second-order harmonic oscillators is described. Finally, the chapter is summarized in Section 6.4

Noise in first-order oscillators

In order to achieve a hierarchical design methodology, a classification of oscillators is of utmost importance. In a good classification, we should be able to give the properties of an oscillator once we know its place in the classification. Vice versa, starting at the top of the classification, we should be able to make strategic design decisions, being aware of both the possibilities and the impossibilities of the circuits at lower levels of the hierarchy. In this chapter, a classification of oscillators is presented, that is the completion to partial classifications, made earlier by Boon [1], Doorenbosch [2] and Verhoeven [8].

Oscillators and Oscillator Systems Classification, Analysis and Synthesis

After the general description of the influence of noise on oscillations given in the previous chapter, a general treatment of noise in first-order oscillators is presented in this chapter. Earlier, descriptions of the influence of noise in oscillators in general and first-order oscillators specifically were given by Hajimiri and Lee, Verhoeven, and others, in [1, 2, 4–7, 9, 13–17]. Now, better methods are present for describing the noise behavior of first-order oscillators specifically. Insight has evolved and the theory described in [14] has been extended. The noise behavior of second-order oscillators is covered in Chapter 6.