TABLE OF CONTENTS The concept of ? ? modulation was first employed in oversampling analog-to digital (A/D) and digital-to-analog (D/A) converters [1, 2]. Oversampling data converters operate at a much higher sampling rate than the Nyquist rate, which is twice the signal bandwidth. In a ? ? A/D converter, the ? ? modulator modulates the analog input into a digital code, either a single-bit or multibit word. Advanced semiconductor technology is better suited for providing fast digital circuits than for providing precise analog circuits. Taking advantage of ever-increasing IC speed, ? ? techniques trade resolution in time for resolution in amplitude and, thus, allow imprecise analog circuits to be used. ? ? techniques have also found applications in frequency synthesis, which is the main topic of this chapter. In a fractional- N frequency synthesizer, a ? ? modulator can be used to control the loop divider such that the fractional spurs can be randomized and shifted to a higher frequency band where they can be easily removed by the loop LPF. In this chapter, the basic concept of ? ? modulation is first introduced. Then, various ? ? modulator topologies for frequency-synthesis applications are presented, and their performances are compared.
This section provides an overview of the basic concepts necessary to understand ? ? modulators. First, oversampling techniques are described, followed by a description, in general terms, of how a feedback loop can result in noise shaping in...
