Digital Frequency Synthesis Demystified : DDS and Fractional-N PLLs (Demystified) (Demystified)

?? In-depth coverage of modern digital implementations of frequency synthesis architectures ?? Numerous design examples drawn from actual engineering projects ?? The accompanying CD includes digital frequency synthesis design tools and an electronic version of the book Digital frequency synthesis is used in modern wireless and communications technologies such as radar, cellular telephony, satellite communications, electronic imaging, and spectroscopy. This is book is a comprehensive overview of digital frequency synthesis theory and applications, with a particular emphasis on the latest approaches using fractional-N phase-locked loop technology. The design tools in the accompany CD allow readers to work through the examples in this book for a realistic simulation of actual design using digital frequency synthesis. ??In-depth coverage of modern digital implementations of frequency synthesis architectures ??Numerous design examples drawn from actual engineering projects ??The accompanying CD includes digital frequency synthesis design tools and an electronic version of the book

Chapter One

Introduction to Frequency Synthesis

1-1 Introduction and Definitions

This text deals with emerging modem digital techniques used to generate and modulate sine waves. These waveforms are used in almost all radio applications, communications, radar, digital communications, electronic imaging, and more. Such techniques either build the waveform from the "ground up" digitally (i.e., generate all the signal parameters such as phase, frequency, and amplitude digitally) and deal with the very fundamental nature of the waveform and its features (direct digital synthesis) or are part of the digital heart of modern phase-locked loop (PLL) sjnithesizers. This might seem, and is indeed, a common and known subject. Sine waves are truly natural waveforms and trigonometric functions that are well known and have been researched for a long time. Furthermore, frequency sjnithesis is quite a mature technology with extensive literature and comprehensive coverage in the professional meetings. Why another text on the subject? What is new besides application-specific integrated circuit {ASIC) technologies and silicon densities, geometry, and integration?

While the above statements are true, there is a continuous evolution in the technology. The generation of accurate waveforms plays a crucial role in almost all electronic equipment, from radar to home entertainment equipment, so the importance of the subject is clear. Clearly, the most important reason for the utilization of the now extremely popular PLL synthesizers in consumer electronics and other very popular applications at extremely low cost (and the popularization of frequency synthesis from consumer products all the way to complex requirements) is the advance of digital technology; integrated, high densities; and low-cost silicon single-PLL chips and ASICs. However, parallel to the advance of traditional PLL synthesis, there emerged other synthesis techniques, mainly digital in nature, direct digital synthesis (DDS) and fractional-N PLL synthesis. Thus, the classical PLL synthesizer is now being supplemented with a sizable element of digital technology and digital signal processing (DSP). Indeed the application of DSP techniques to frequency synthesis is still at an early stage.

The generation of sine waves by using digital methodologies requires generating the waveform from the ground up. This is fundamentally different from the PLL synthesizer, where the signal is available from an oscillator. It goes back to the very basic structure of the waveform itself and deals with its very basic characteristics rather than manipulates signals that have already been generated by an oscillator. Surprisingly, some of these very basic mathematical issues are being resolved only lately.

Unfortunately, in these specific fields, there is a lack of complete understanding of the mathematics as well as the standard implementation of working hardware. The operation of a direct digital synthesizer is far from intuitive, and its artifacts are sometimes alien to our (conservative or standard) thinking. Indeed, in this ongoing research effort, we have tried to recruit some very skilled professional mathematicians in the search for (1) effective sine read-only memory (ROM) (the transformation of ψ to sin ψ) compression algorithms (indeed, the same old trigonometric functions; see Chap. 7), (2) a "minimal" amount of data necessary to represent the waveform, such as to meet a specific level of accuracy, and (3) a general formulation for the performance of DDS. We have not had much luck or enthusiasm.

We understand that this might not be the most exciting topic for mathematicians, but it has tremendous importance for electronics, radio, and radar designers. The challenge has to be met within the electronics community, and we have attempted to present a comprehensive introduction.

Although there are many excellent books on PLL synthesis (see References), mostly published in the 1980s, note that this is the first attempt to write a comprehensive text on the subject of digital frequency synthesis, direct digital synthesis, and digital and fractional-N synthesis; and the number of sources is not overwhelming in this newly emerging technological discipline. We have found a paucity of literature in the field; and even though many articles have begun to appear in the last few years and the technology attracts much attention in professional meetings, comprehensive texts and bibliographies are needed. This is what this text attempts to supply. Every attempt is made to present a very comprehensive, updated bibliography.

Because of the paucity of literature, in this text we attempt to present an intuitive approach supplemented by many examples, in the hope that this book fills a current need as expressed to us by many young and beginning designers as well as others who are not familiar with the details and lack an intuitive understanding.

In this text, frequency synthesizer is defined as a system that generates one or many frequencies derived from a single time base (frequency reference), in such a way that the ratio of the output to the reference frequency is a rational fraction. The frequency synthesizer output frequency preserves the long-term frequency stability (the accuracy) of the reference and operates as a device whose function is to generate frequencies that are multiples of the reference frequency (multiples by a single or many numbers). These multiples may be whole or fractions; but since only linear operations are used (in the frequency domain), these numbers can only be rational. A frequency synthesizer, as defined here, can thus generate an output frequency of, say, X/Y (where X and Y are whole numbers) times the reference frequency, but not, for example, π times the reference frequency (π is not a rational number).

Three main, conventional techniques are being used currently for sine-wave synthesizers and are common throughout the industry. The most common and most popular technique uses the phase-locked loop synthesis. PLL synthesizers can be found in the most sophisticated radar systems or the most demanding satellite communications terminals as well as in car radios and stereo systems for home entertainment. The PLL is a feedback mechanism locking its output frequency to a reference. PLL synthesizers gained popularity for their simplicity and economics.

Another sjnithesizer technique is known as direct analog (DA) frequency S5nithesis. In this technique, a group of reference frequencies is derived from the main reference; and these frequencies are mixed and filtered, added, subtracted, or divided according to the required output. However, there are no feedback mechanisms in the basic technique.

The DA frequency synthesis technique offers excellent spectral purity, especially close to the carrier, and excellent switching speed, which is a critical parameter in many designs and determines how fast the synthesizer can hop from one frequency to another.

The DA technique is usually much more complicated than PLL to execute and is therefore more expensive. DA sjnithesizers found applications in medical imaging and spectrometers, fast-switching antijam communications and radar, electronic warfare (EW) simulation, automatic test equipment (ATE), radar cross-section (RCS) measurement, and such uses where the advantages of the DA technique are a must at a premium cost.

The third technique, which is the focus of this book, is direct digital synthesis (DDS), which is a digital signal processing (DSP) discipline and uses digital circuitry and techniques to create, manipulate, and modulate a signal, digitally, and eventually convert the digital signal to its analog form by using a digital-to-analog converter (DAC).

Although the direct digital S5nithesizer [sometimes referred to as numerically controlled oscillator (NCO)] was invented almost 30 years ago (see Ref. 9 and Chap. 10), it started to attract attention only in the last 10 to 12 years. Due to the enormous evolution of digital technology and its tools, the technique evolved remarkably into an economical, high-performance tool and is now a major frequency synthesis method used by almost all S5nithesizer designers from instrument makers to applications like satellite communications, radar, medical imaging, and cellular telephony and amateur radios (most of which are anything but amateur).

Direct digital synthesizers offer fast switching speed, high resolution (the step size ofthe synthesizer), small size and low power, good economics, and the reliability and producibility of digital designs. In addition, since the signal is manipulated digitally, it is easy to modulate and achieve accuracies not attained by analog techniques and to conveniently interface with the computing machines that usually control the synthesizer.

Another focal point of this text is the description of fractional-N PLL synthesis. This technique resembles DDS in almost all aspects and operates as a DDS "inside" the PLL architecture. Please note that in many designs, more than one synthesis technique is being utilized, and the designer "hybridizes" the design so that the advantage is taken of each technique being used and its weaknesses are suppressed. So it is quite common (and applications can be expected to grow) to see combinations of PLL and DDS or DA and DDS, and from time to time all three techniques are used in one design. Thus the basic three techniques indeed complement one another and enable the up-to-date competent designer to use all as needed to optimize the design as the applications and demands increase with the system complexity.

This text has 10 chapters. Chapter 1 is a general introduction and short description of frequency synthesis techniques. Chap. 2 deals with synthesizer system analysis, and Chap. 3 addresses measurement techniques pertinent to frequency synthesis. Chapter 4 details a variety of DDS technologies and deals with the quantization effects, their artifacts, and representations in DDS. Chapter 5 discusses PLL principles and the details of fractional-N PLL synthesis of various complexities. Chapters 6, 7, and 8 deal in detail with the cardinal components of DDS, namely, accumulators of binary and binary-coded decimal (BCD) structure, ROM lookup tables and ROM compression algorithms, and digital-to-analog converters. Chapter 9 gives a short review of state-of-the-art reference oscillators and what we consider some remarkable instruments or products on the market that are directly related to digital frequency generation.

Chapter 10 is special, as it refers to a reprint of the original 1971 article by Tierney, Rader, and Gold that lacked off the DDS industry (Ref. 8), including some footnotes. This article is special not only because of its pioneering nature but also for the fact that it deals with all the cardinal issues of the subject. The chapter also includes a description of the programs contained on the accompanying CDROM.

1-2 Synthesizer Parameters

Like any other engineering product, a frequency synthesizer (FS) needs to meet a set of specifications. In the following, a list of the most common specifications is provided followed by a definition and industry standard conventions. Obviously, for different applications, different specifications are more important than others, and it is up to the designer to design for efficiency and economy. While a FS for a car radio needs to be moderately accurate, extremely reliable, very small and simple, and very inexpensive, a FS used in magnetic resonance imaging (MRI) must be very accurate, must have very high spectral purity, must be able to hop from frequency to frequency very quickly, and needs different modulation capabilities. While consumer electronic products need to operate in extreme environmental conditions (one expects the car radio to operate when powered up in extreme heat or cold conditions, and the vibrations of the cars are severe), the MRI spectrometer operates in a laboratory-controlled environment with little temperature variation and almost no shock or mechanical vibrations.

Designers are therefore required to compare their specifications to the best economical and practical solution. The specifications are divided into two groups: those that are related to the topics of this book and others that are more general and are beyond our scope. All the following sections pertain to generic specifications.

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Excerpted from Digital Frequency Synthesis Demystified by Bar-Giora Goldberg Copyright © 1999 by LLH Technology Publishing. Excerpted by permission of Newnes. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site. · In-depth coverage of modern digital implementations of frequency synthesis architectures
· Numerous design examples drawn from actual engineering projects
· The accompanying CD includes digital frequency synthesis design tools and an electronic version of the book

Digital frequency synthesis is used in modern wireless and communications technologies such as radar, cellular telephony, satellite communications, electronic imaging, and spectroscopy. This is book is a comprehensive overview of digital frequency synthesis theory and applications, with a particular emphasis on the latest approaches using fractional-N phase-locked loop technology. The design tools in the accompany CD allow readers to work through the examples in this book for a realistic simulation of actual design using digital frequency synthesis.

· In-depth coverage of modern digital implementations of frequency synthesis architectures
· Numerous design examples drawn from actual engineering projects
· The accompanying CD includes digital frequency synthesis design tools and an electronic version of the book