A Graduate Course on Active, Digital, and Switched Capacitor Filters

104 IEEE TRANSACTIONS ON EDUCATION, VOL. E-26, NO. 3, AUGUST 1983 A Graduate Course on Active, Digital, and Switched Capacitor Filters MANUEL M. SILVA, SENIOR MEMBER, IEEE Abstract-This paper presents a solution to the problem of accommodating the important new subject of switched capacitor networks in already crowded electrical engineering curricula. This is achieved by combining in a one-semester course three different, but related, subjects. This is made possible 1) by placing a strong emphasis on the underlying principles that are common to active, digital, and switched capacitor filters, and 2) by concentrating on the realization of these three types of filters by simulation of passive ladder networks. I. INTRODUCTION E LECTRICAL filters have for many years been realized by passive circuits, using inductors, capacitors, and resistors. The theory of passive filters was well established, and filter design was normally left to a limited number of specialists. This situation, however, has been dramatically changed by the appearance of modern microelectronics technology which can realize resistors and capacitors, but not inductors. Filters suitable for microelectronic realization are, in contrast with passive filters, a subject in which progress is taking place very rapidly and which is of interest to the nonspecialist who must be able to select from the various new solutions now available for filtering problems the one best suited to any given application. Active filters, employing resistors, capacitors, and operational amplifiers, and digitalfilters, are two important types of microelectronic filters that have already found their way into most electrical engineering curricula. Both active and digital filters have limitations. Active filters can be realized as hybrid circuits, but not as monolithic integrated circuits since the time constants, defined by products of resistances and capacitances, do not reach the required precision. Digital filters, although realizable as monolithic circuits, are still too slow for many applications. A new and very interesting alternative to these two types of microelectronics filters is provided by switched capacitor filters (SC filters). These filters are made of capacitors, amplifiers, and switches, which are realized by MOS transistors. Time constants are now defined by the switching frequency and by ratios of capacitances, which can be obtained with high precision in monolithic circuits. SC filters can be realized as MOS integrated circuits by using the same techniques that produce VLSI digital circuits. Thus, it is possible to integrate complete systems, including filters, in one chip. It is already apparent that SC filters must be included in Manuscript received January 10, 1983; revised March 7, 1983. The author is with the Department of Electrical Engineering and the Centro de Electronica Aplicada, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, 1096 Lisboa, Portugal. electrical engineering curricula. This, however, must not be done at the expense of dropping active and digital filters. These retain their importance for many applications, and, furthermore, many concepts associated with active and digital filtering are necessary for a proper understanding of SC filters. This paper describes a one-semester course that combines the study of active, digital, and SC filters. The organization of such a course is not straightforward in view of the wide area to be covered which might encourage a superficial treatment of a large number of topics. If this is to be avoided, suitable criteria will have to be used in the selection of a coherent set of subjects to be covered in depth. The establishment of such criteria and their application in the design of the course will be considered in this paper. The course described here has been taught once, in 1982, at Lisbon University, as one of the elective subjects offered in the first semester of the M.Sc. course on electrical and computer engineering. II. CRITERIA AND OBJECTIVES Two main criteria have presided over the organization of the course. Filters with sampled signals (digital and SC filters) are normally obtained from analog filters (active or passive) by using one of several transformations between the variables s and z; these transformations correspond to the replacement of continuous-time integration by different forms of discrete-time integration. It follows from this that there are strong relationships between the three types of microelectronic filters to be studied. The first criterion consisted of making extensive use of these relationships in the design of the course. The second criterion consisted of placing the greatest emphasis on the realization of the three types of filters by methods based on the simulation of resistively terminated LC ladder filters. These passive filters have a very low sensitivity of the transfer function to component variations. This low sensitivity is transferred to active, digital, and SC filters obtained by simulation of passive ladder circuits. The methods used are, basically, the same for the three types of filters. The emphasis on simulation methods is not a serious restriction, since nowadays virtually all high-performance filters are obtained by these methods. One objective of the course is that the students will acquire the ability to design high-performance active, digital, and SC filters. These filters will be mostly realized by simulation of passive ladder circuits, which were obtained from tables or by using computer programs (passive filter synthesis is outside 0018-9359/83/0800-0104$01.00 © 1983 IEEE SILVA: GRADUATE COURSE ON FILTERS the scope of the course). In addition, the students must be able to evaluate critically the various options now available for the filters for any given application. It is intended that this course will lead to an integrated knowledge of the different filtering techniques, and that it will enable the students to transfer methods and results from filters of one kind to filters of a different kind. It is also expected that the necessary background to start a research program will be obtained from the course by those students who chose for their theses a subject in the area of microelectronic filters. III. COURSE STRUCTURE AND CONTENTS A. Program The course includes the seven chapters listed below. The list includes the approximate number of lecture hours devoted to each chapter. 5h 1) Filter transfer functions 6h 2) Filters with sampled signals 7h 3) Digital filters 6h 4) SC filters 5h 5) Active filters 7h 6) Operational simulation 6h 7) Direct simulation 42 h It can be seen that digital filters are studied before analog active filters. One reason for choosing this order was the wish to conform to the modern approach of first teaching in the digital simpler form those concepts that are common to analog and digital systems. Another reason has to do with the students' motivation; they will initially be more receptive to digital filters, and, as the course progresses, they will become aware of the importance of analog filters since it is from these that the best quality digital filters are obtained, and also because there are applications for which analog filters are indispensable. This syllabus, as a result of the two criteria referred to in the previous section, shows an emphasis on those aspects that are common to different types of filters, and an emphasis on simulation methods. The matter in Chapter 1 is useful for active, passive, SC, and digital filters. Chapter 2, on filters with sampled signals, deals with both SC and digital filters. Chapters 3, 4, and 5 concentrate on the systems that implement the three types of filters considered in this course. The realization methods are treated, in an integrated form in Chapters 6 and 7 where simulation methods are applied in the realization of active, digital, and SC filters. More detailed comments on each chapter of the course will now be given. 1) Filter Transfer Function: This chapter includes a review of various types of filters, both with respect to the shape of the frequency response (low-pass, bandpass, etc.), and with respect to the form of realization (passive, active, etc.). Most of the chapter. however, is devoted to the study of classical approximation theory (Butterworth, Chebyshev, Cauer) and the frequency transformations that are used to transfer results from low-pass to other types of response. The main purpose of this first chapter is to teach some of 105 the basic concepts of electrical filtering since it is not expected that all students attending the course will have a prior knowledge of this subject. The students are assumed only to have studied electronics, circuits, and systems theory at the undergraduate level. 2) Filters with Sampled Signals: The previous chapter was mainly concerned with the determination of the transfer function T(s) of analog filters from the specifications. The present chapter is devoted to obtaining the system function T(z) of filters with sampled signals. The chapter starts with a review of the properties of sampled signals, with emphasis on signals sampled by pulses of finite duration which occur in SC filters. Discrete-time systems are considered next, and the properties of the system function and of the frequency response are discussed. Infinite impulse response (IIR) filters are considered, and it is pointed out that their system function T(z) is usually obtained from an analog transfer function T(s) by using a transformation between the variables s and z. This corresponds to a replacement of analog integration by numerical integration. The bilinear transformation, which corresponds to a trapezoidal rule of integration, is most often used with digital filters. With SC filters, the LDI (lossless discrete integrator) transformation is very common, but BD (backward difference) and FD (forward difference) transformations are also used; these three transformations correspond to different rectangular rules of integration. Finite impulse response (FIR) filters are also considered, and T(z) is obtained by truncating an ideal impulse response using different types of windows. 3) Digital Filters: Direct form realizations are introduced, and it is shown that they are unsuitable for high-order filters due to high sensitivity of the response to the coefficients. Cascade and parallel forms using biquadratic sections are presented as alternative realizations with moderate sensitivities. As a consequence of finite register length, both coefficients and samples are quantized, and finite length arithmetic is considered. The effects of truncation and rounding are compared, and quantization noise and limit cycles are discussed. Hardware implementation is considered, and the method of distributed arithmetic is presented. Also included is software implementation using the integrated signal processor INTEL 2920. This is a dedicated microprocessor belonging to a new generation of programmable signal processors which are expected to have widespread application in the future. 4) SCFilters: SC networks are introduced, and methods for analyzing them are developed. It is assumed that a twophase clock is used to control the switches, and extensive use is made of "z-domain equivalent circuits," introduced by Laker. Integrators insensitive to parasitic capacitances are studied in detail since these circuits are used in almost all practical SC filters produced at present. Methods for replacing the elements in RLC or in active-RC networks by SC equivalent circuits are briefly mentioned, and it is pointed out that the circuits thus obtained are usually more sensitive to parasitic capacitances than SC filters with integrators. 5) Active Filters: Sensitivity definitions and calculus are 106 IEEE TRANSACTIONS ON EDUCATION, VOL. E-26, NO. 3, AUGUST 1983 introduced at this stage since sensitivity considerations play a dominant role in this chapter and in the following ones. It is shown that direct realization methods of active-RC filters produce high-sensitivity circuits, and this led to the use of biquadratic. sections connected in cascade (this is quite similar to what has been found for digital filters). Biquadratic sections are not studied here. Most students will probably have been introduced to them in previous courses, and in accordance with the criteria already discussed, this course concentrates on the realization of high-performance filters by simulation methods. However, it is desirable to include here a discussion of the decomposition of the transfer function in second-order factors since this is an important subject with interest to different types of filters, and it is a subject not likely to have been dealt with before by the students. Multifeedback filters with "follow-the-leader" configuration are referred to here in view of their low sensitivity. Study of the "leapfrog" structure, however, is left to Chapter 6, since it can in most cases be regarded as resulting from an operational simulation of a passive ladder circuit. The chapter ends with a discussion of Orchard's conjecture which is behind almost all modern methods for the realization of electric filters. It is shown that doubly terminated LC ladder filters with frequencies of maximum power transfer in the passband have very low sensitivities. If these passive filters are simulated by active-RC, digital, or SC circuits, the low-sensitivity properties are preserved. 6) Operational Simulation: In this chapter and in the next one, the simulation methods are presented and applied to the realization of active, digital, and SC filters. The criteria discussed before are thus applied in full here. Operational simulation does not attempt to preserve the topology of the passive circuit; instead, the form of the equations describing the passive filter is transferred to the circuit or system that performs the simulation (the signal flow graph is preserved). "Leapfrog" structures using integrators are derived from passive ladders. Active-RC, digital, and SC integrators are then used to obtain filters that preserve the low sensitivity of the original ladder. The linear transformation method [9], [10] is also presented in this chapter. It is believed that this method has a high educational value since it includes, as special cases, various other simulation methods, and can thus provide much insight into these methods. As an application of the linear transformation method, wave active and wave digital filters are derived. 7) Direct Simulation: With direct simulation methods, the passive circuit topology is preserved. There is therefore a oneto-one correspondence between the passive filter components and subnetworks of the simulating filter. Direct simulation methods make extensive use of two-port immittance converters and inverters to simulate inductors and supercapacitors (elements with admittance proportional to s2). These are studied here, and multiport converters [11 ] useful for the simulation of floating inductors and of inductor networks are also included. The methods of inductor simulation and of impedance con- version (Bruton's method) are described, and different circuits realizing simulated inductors and supercapacitors are compared. The simulation of transformed ladder prototypes [12] is also included. It is shown that this method can be used to realize both active and SC filters. B. Bibliography There is no textbook available that follows the approach taken in this course. In fact, most textbooks are devoted to only one type of filter; in those textbooks that include more than one type of filter they are treated separately. Thus, the course had to be supported by different references, [1 ]-[5] (naturally only parts of these textbooks are relevant to the above program). Some supplementary material can be found in [6]-[12]. (Papers [9]-[12] deal with subjects that were included in the course and are not available in textbooks.) The references that apply to each chapter of the course are indicated as follows: Chapter 1: Chapter 2: Chapter 3: Chapter 4: Chapter 5: Chapter 6: Chapter 7: [1 ], [5 ], and [7]. [1], [2], [7],and [8]. [2], [3], [7], and [8]. [1]. [1], [4], [5],and [6]. [1], [4], [5], [9], and [10]. [4], [5], [11], and [12]. IV. PROJECTS A significant part of the course work is devoted to the realization of projects that consist of the design and testing of filters. These correspond to applications in which the teaching staff has some experience and must be of intermediate complexity, i.e., of fourth to sixth order. Typical examples are filters for telephony, telegraphy, and data MODEM's. The students are encouraged to submit projects of their own choice, subject to the condition that they must be compatible with the objectives of the course. The projects are normally suitable for groups of two students. The projects are conditioned by the same criteria that determined the course structure. Thus, the same filter will be realized in three different forms: digital, active RC, and SC. These different realizations will in most cases employ simulation methods. The approximation and synthesis of the passive filters to be simulated require the use of tables [11 ] and computer programs, namely the FILSYN [12] program package. The projects entail building and testing discrete component prototypes of the active-RC and SC versions of the filter. Software implementation of the digital filter version has been done, in the first run of the course, using a general-purpose computer. It is expected that in the future the digital filters will be implemented in integrated signal processor chips (e.g., INTEL 2920). The report on the project has a large weight in the final classification. It was felt, however, that the assessment should also include a written test, since successful completion of the project does not necessarily guarantee the achievement of the IEEE TRANSACTIONS ON EDUCATION, VOL. E-26, NO. 3, AUGUST 1983 main objective of the course: a deep insight into the basic principles which are common to different types of filters. V. CONCLUSIONS REFERENCES [II [2] [31 [41 [51 [61 G. Daryanani, Principles of Active Network Synthesis and Design. [71 [8] This paper describes a course on microelectronic filters which includes active, digital, and SC filters. This is not, however, a course divided into three parts; if the three different types of filters were treated independently, the coverage would have to be unacceptably superficial. A unified treatment was used, instead, and this made it possible to successfully accommodate the whole matter in a one-semester course. Another salient feature of the course is the emphasis on modern methods based on simulation of passive ladder filters, which leads to high performance filters. During its first run, the course was well received by the students, and the final assessment, based on a project report and on a written examination, has shown that the course objectives have been achieved. M. S. Ghausi and K. R. Laker, Modern Filter Design: Active RC and Switched Capacitor. Englewood Cliffs, NJ: Prentice-Hall, 1981. A. V. Oppenheim and R. W. Schafer, Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975. A. Peled and B. Liu, Digital Signal Processing. Theory, Design and Implementation. New York: Wiley, 1976. L. T. Bruton, RC-Active Circuits Theory and Design. Englewood Cliffs, NJ: Prentice-Hall, 1980. A. S. Sedra and P. 0. Brackett, Filter Theory and Design: Active andPassive. Portland, OR: Matrix, 1978. 107 [91 [101 [11] [121 [131 [14] New York: Wiley, 1976. H. Y.-F. Lam, Analog and Digital Filters: Design and Realization. Englewood Cliffs, NJ: Prentice-Hail, 1979. L. R. Rabiner and B. Gold, Theory and Application ofDigital SignalProcessing. Englewood Cliffs, NJ: Prentice-Hall, 1975. H. G. Dimopoulos and A. G. Constantinides, "Linear transformation active filters," IEEE Trans. Circuits Syst., vol. CAS-25, pp. 845-852, Oct. 1978. M. S. Piedade and M. M. Silva, "A note on hnear transformation active filters," Proc. IEE, vol. 128, part G, pp. 180-181, Aug. 1981. M. M. Silva, "Multiport converters and inverters," Int. J. Circuit Theory App!., voL 6, pp. 243-252, July 1978. M. S. Piedade and M. M. Silva, "New lowpass and bandpass active filters derived from passive ladder prototypes," in Proc. IEEE Int. Symp. Circuits Syst., Houston, TX, Apr. 1980, pp. 557-561. R. Saal and W. Entenmann, Handbook ofFilter Design, AEG Telefunken, Berlin, Germany, 1979. G. Szentirmai, "FILSYN-A general purpose filter synthesis program," Proc. IEEE, voL 65, pp. 1443-1458, Oct. 1977. Manuel M. Silva (M'76-SM'81) was born in Ponta Delgada, Azores, in 1943. In 1967 he received the degree in electrical engineering from the Instituto Superior Tecnico, Lisboa, Portugal. He was a graduate student at Imperial College of Science and Technology, London, England, and obtained the Ph.D. degree from the University of London, London, England, in 1976. He is an Associate Professor of Electrical Engineering at the Instituto Superior Tecnico and is the head of the Research Group on Analog and Digital Filters at the Centro de Electr6nica Aplicada, Instituto Superior Tecnico. He was one of the organizers of the IEEE Portugal Section and is now its Chairman. Short Notes A Microprocessor-Based Digital Control Course 1. INTRODUCTION E. LUQUE, 1. SERRA, AND L. MORENO When the students reach the Digital Control Systems course developed at the Autonomous University of Barcelona, they have already taken a preliminary course in linear system theory, including time response, frequency response, stability, and controller design. They have also had a course in introduction to computer sciences, and have had some hardware and software experience with the Rockwell 6502 microprocessor. The Digital Control Systems course is divided into two parts. In the first part, the students learn about the following topics: * Sampled data system theory using the z-transform technique and the state space formulation. * Nonlinear system theory using the describing function method and the phase-plane technique. * An introduction to optimum control theory, including concepts such as maximum principle of Pontryagin and dynamic programming of Bellman. The second part is an experimental course which is the objective of this report. The introduction of a microprocessor in a closed-loop sys- Abstract-A microprocessor-based digital control laboratory course has been developed at the Autonomous University of Barcelona. The microprocessor controller interfaces directly to an analog computer. The introduction of the microprocessor in a closed-loop system allows great flexibility in the types of algorithms that can be used in standalone controllers. Some experiments have been carried out with the aim of improving the student's understanding of the digital control concepts. A brief description of the algorithms, with main emphasis on their discrete realization, and details of each laboratory experiments are given. The philosophy underlying the course is the active participation of the students. Manuscript received November 1, 1982; revised March 9, 1983. The authors are with the Department of Electricity and Electronics, Autonomous University of Barcelona, Bellaterra, Barcelona, Spain. 0018-9359/83/0800-0107$01.00 © 1983 IEEE