IEEE TRANSACTIONS ON EDUCATION, VOL. E-26, NO. 3, AUGUST 1983

A Graduate Course on Active, Digital, andSwitched Capacitor Filters

MANUEL M. SILVA, SENIOR MEMBER, IEEE

Abstract-This paper presents a solution to the problem of accom-modating the important new subject of switched capacitor networks inalready crowded electrical engineering curricula. This is achieved bycombining in a one-semester course three different, but related, subjects.This is made possible 1) by placing a strong emphasis on the underlyingprinciples that are common to active, digital, and switched capacitorfilters, and 2) by concentrating on the realization of these three typesof filters by simulation of passive ladder networks.

I. INTRODUCTIONE 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 de-sign was normally left to a limited number of specialists. Thissituation, however, has been dramatically changed by the ap-pearance of modern microelectronics technology which canrealize resistors and capacitors, but not inductors. Filters suit-able for microelectronic realization are, in contrast with pas-sive filters, a subject in which progress is taking place very rap-idly and which is of interest to the nonspecialist who must beable to select from the various new solutions now available forfiltering problems the one best suited to any given application.Active filters, employing resistors, capacitors, and opera-

tional amplifiers, and digitalfilters, are two important types ofmicroelectronic filters that have already found their way intomost electrical engineering curricula.Both active and digital filters have limitations. Active filters

can be realized as hybrid circuits, but not as monolithic inte-grated circuits since the time constants, defined by products ofresistances and capacitances, do not reach the required preci-sion. Digital filters, although realizable as monolithic circuits,are still too slow for many applications. A new and very in-teresting alternative to these two types of microelectronicsfilters 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 arenow defined by the switching frequency and by ratios of ca-pacitances, which can be obtained with high precision inmonolithic circuits. SC filters can be realized as MOS inte-grated circuits by using the same techniques that produceVLSI digital circuits. Thus, it is possible to integrate completesystems, 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, Univer-sidade Tecnica de Lisboa, 1096 Lisboa, Portugal.

electrical engineering curricula. This, however, must not bedone at the expense of dropping active and digital filters.These retain their importance for many applications, and,furthermore, many concepts associated with active and digitalfiltering 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 ofsuch a course is not straightforward in view of the wide area tobe covered which might encourage a superficial treatment of alarge number of topics. If this is to be avoided, suitable crite-ria will have to be used in the selection of a coherent set ofsubjects to be covered in depth. The establishment of suchcriteria and their application in the design of the course will beconsidered in this paper.The course described here has been taught once, in 1982, at

Lisbon University, as one of the elective subjects offered inthe first semester of the M.Sc. course on electrical and com-puter engineering.

II. CRITERIA AND OBJECTIVESTwo main criteria have presided over the organization of the

course.Filters with sampled signals (digital and SC filters) are nor-

mally obtained from analog filters (active or passive) by usingone of several transformations between the variables s and z;these transformations correspond to the replacement of con-tinuous-time integration by different forms of discrete-timeintegration. It follows from this that there are strong relation-ships between the three types of microelectronic filters to bestudied. The first criterion consisted of making extensive useof these relationships in the design of the course.The second criterion consisted of placing the greatest em-

phasis on the realization of the three types of filters by meth-ods based on the simulation of resistively terminated LC lad-der filters. These passive filters have a very low sensitivity ofthe transfer function to component variations. This low sen-sitivity is transferred to active, digital, and SC filters obtainedby simulation of passive ladder circuits. The methods usedare, basically, the same for the three types of filters. The em-phasis on simulation methods is not a serious restriction, sincenowadays virtually all high-performance filters are obtainedby these methods.One objective of the course is that the students will acquire

the ability to design high-performance active, digital, and SCfilters. These filters will be mostly realized by simulation ofpassive ladder circuits, which were obtained from tables orby using computer programs (passive filter synthesis is outside

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the scope of the course). In addition, the students must beable to evaluate critically the various options now available forthe filters for any given application.

It is intended that this course will lead to an integratedknowledge of the different filtering techniques, and that it willenable the students to transfer methods and results from filtersof one kind to filters of a different kind. It is also expectedthat the necessary background to start a research program willbe obtained from the course by those students who chose fortheir theses a subject in the area of microelectronic filters.

III. COURSE STRUCTURE AND CONTENTS

A. ProgramThe course includes the seven chapters listed below. The list

includes the approximate number of lecture hours devoted toeach chapter.

1) Filter transfer functions2) Filters with sampled signals3) Digital filters4) SC filters5) Active filters6) Operational simulation7) Direct simulation

5 h6h7 h6 h5 h7 h6 h

42 h

It can be seen that digital filters are studied before analogactive filters. One reason for choosing this order was the wishto conform to the modern approach of first teaching in thedigital simpler form those concepts that are common toanalog and digital systems. Another reason has to do with thestudents' motivation; they will initially be more receptive todigital filters, and, as the course progresses, they will becomeaware of the importance of analog filters since it is from thesethat the best quality digital filters are obtained, and alsobecause 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 sim-ulation methods. The matter in Chapter 1 is useful for active,passive, SC, and digital filters. Chapter 2, on filters withsampled signals, deals with both SC and digital filters. Chap-ters 3, 4, and 5 concentrate on the systems that implement thethree types of filters considered in this course. The realizationmethods are treated, in an integrated form in Chapters 6 and 7where simulation methods are applied in the realization ofactive, 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 ofthe frequency response (low-pass, bandpass, etc.), and withrespect to the form of realization (passive, active, etc.). Mostof the chapter. however, is devoted to the study of classicalapproximation theory (Butterworth, Chebyshev, Cauer) andthe frequency transformations that are used to transfer resultsfrom low-pass to other types of response.The main purpose of this first chapter is to teach some of

the basic concepts of electrical filtering since it is not expectedthat all students attending the course will have a prior knowl-edge of this subject. The students are assumed only to havestudied electronics, circuits, and systems theory at the under-graduate level.2) Filters with Sampled Signals: The previous chapter was

mainly concerned with the determination of the transfer func-tion T(s) of analog filters from the specifications. The presentchapter is devoted to obtaining the system function T(z) offilters with sampled signals.The chapter starts with a review of the properties of sampled

signals, with emphasis on signals sampled by pulses of finiteduration which occur in SC filters. Discrete-time systems areconsidered next, and the properties of the system function andof the frequency response are discussed.

Infinite impulse response (IIR) filters are considered, and itis pointed out that their system function T(z) is usually ob-tained from an analog transfer function T(s) by using a trans-formation between the variables s and z. This corresponds to areplacement of analog integration by numerical integration.The bilinear transformation, which corresponds to a trape-zoidal rule of integration, is most often used with digital filters.With SC filters, the LDI (lossless discrete integrator) trans-formation is very common, but BD (backward difference) andFD (forward difference) transformations are also used; thesethree transformations correspond to different rectangular rulesof integration.

Finite impulse response (FIR) filters are also considered, andT(z) is obtained by truncating an ideal impulse response usingdifferent types of windows.3) Digital Filters: Direct form realizations are introduced,

and it is shown that they are unsuitable for high-order filtersdue to high sensitivity of the response to the coefficients. Cas-cade and parallel forms using biquadratic sections are pre-sented as alternative realizations with moderate sensitivities.As a consequence of finite register length, both coefficients

and samples are quantized, and finite length arithmetic is con-sidered. 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 softwareimplementation using the integrated signal processor INTEL2920. This is a dedicated microprocessor belonging to a newgeneration of programmable signal processors which are ex-pected 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 two-phase clock is used to control the switches, and extensive useis made of "z-domain equivalent circuits," introduced byLaker.Integrators insensitive to parasitic capacitances are studied in

detail since these circuits are used in almost all practical SC fil-ters produced at present. Methods for replacing the elementsin RLC or in active-RC networks by SC equivalent circuits arebriefly mentioned, and it is pointed out that the circuits thusobtained are usually more sensitive to parasitic capacitancesthan SC filters with integrators.5) Active Filters: Sensitivity definitions and calculus are

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IEEE TRANSACTIONS ON EDUCATION, VOL. E-26, NO. 3, AUGUST 1983

introduced at this stage since sensitivity considerations play adominant role in this chapter and in the following ones.

It is shown that direct realization methods of active-RCfilters produce high-sensitivity circuits, and this led to the useof biquadratic. sections connected in cascade (this is quite sim-ilar to what has been found for digital filters).

Biquadratic sections are not studied here. Most students willprobably have been introduced to them in previous courses,and in accordance with the criteria already discussed, thiscourse concentrates on the realization of high-performance fil-ters by simulation methods. However, it is desirable to includehere a discussion of the decomposition of the transfer functionin second-order factors since this is an important subject withinterest to different types of filters, and it is a subject notlikely to have been dealt with before by the students.Multifeedback filters with "follow-the-leader" configura-

tion are referred to here in view of their low sensitivity. Studyof the "leapfrog" structure, however, is left to Chapter 6, sinceit can in most cases be regarded as resulting from an opera-tional 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 realizationof electric filters. It is shown that doubly terminated LC lad-der filters with frequencies of maximum power transfer in thepassband have very low sensitivities. If these passive filters aresimulated by active-RC, digital, or SC circuits, the low-sensi-tivity properties are preserved.

6) Operational Simulation: In this chapter and in the nextone, the simulation methods are presented and applied to therealization of active, digital, and SC filters. The criteria dis-cussed 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 equa-tions describing the passive filter is transferred to the circuitor system that performs the simulation (the signal flow graphis preserved)."Leapfrog" structures using integrators are derived from pas-

sive ladders. Active-RC, digital, and SC integrators are thenused to obtain filters that preserve the low sensitivity of theoriginal ladder.The linear transformation method [9], [10] is also pre-

sented in this chapter. It is believed that this method has ahigh educational value since it includes, as special cases, vari-ous other simulation methods, and can thus provide much in-sight into these methods. As an application of the linear trans-formation method, wave active and wave digital filters arederived.

7) Direct Simulation: With direct simulation methods, thepassive circuit topology is preserved. There is therefore a one-to-one correspondence between the passive filter componentsand subnetworks of the simulating filter.

Direct simulation methods make extensive use of two-portimmittance converters and inverters to simulate inductors andsupercapacitors (elements with admittance proportional to s2).These are studied here, and multiport converters [11 ] usefulfor the simulation of floating inductors and of inductor net-works are also included.The methods of inductor simulation and of impedance con-

version (Bruton's method) are described, and different cir-cuits realizing simulated inductors and supercapacitors arecompared.The simulation of transformed ladder prototypes [12] is

also included. It is shown that this method can be used torealize both active and SC filters.

B. BibliographyThere is no textbook available that follows the approach

taken in this course. In fact, most textbooks are devoted toonly one type of filter; in those textbooks that include morethan one type of filter they are treated separately. Thus, thecourse had to be supported by different references, [1 ]-[5](naturally only parts of these textbooks are relevant to theabove program). Some supplementary material can be foundin [6]-[12]. (Papers [9]-[12] deal with subjects that were in-cluded 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: [1 ], [5 ], and [7].Chapter 2: [1], [2], [7],and [8].Chapter 3: [2], [3], [7], and [8].Chapter 4: [1].Chapter 5: [1], [4], [5],and [6].Chapter 6: [1], [4], [5], [9], and [10].Chapter 7: [4], [5], [11], and [12].

IV. PROJECTSA significant part of the course work is devoted to the real-

ization of projects that consist of the design and testing of fil-ters. These correspond to applications in which the teachingstaff has some experience and must be of intermediate com-plexity, i.e., of fourth to sixth order. Typical examples arefilters for telephony, telegraphy, and data MODEM's. The stu-dents are encouraged to submit projects of their own choice,subject to the condition that they must be compatible withthe objectives of the course. The projects are normally suit-able for groups of two students.The projects are conditioned by the same criteria that deter-

mined the course structure. Thus, the same filter will berealized in three different forms: digital, active RC, and SC.These different realizations will in most cases employ simula-tion methods.The approximation and synthesis of the passive filters to be

simulated require the use of tables [11 ] and computer pro-grams, 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 beendone, in the first run of the course, using a general-purposecomputer. It is expected that in the future the digital filterswill be implemented in integrated signal processor chips (e.g.,INTEL 2920).The report on the project has a large weight in the final clas-

sification. It was felt, however, that the assessment shouldalso include a written test, since successful completion of theproject does not necessarily guarantee the achievement of the

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main objective of the course: a deep insight into the basic prin-ciples which are common to different types of filters.

V. CONCLUSIONSThis paper describes a course on microelectronic filters

which includes active, digital, and SC filters. This is not, how-ever, a course divided into three parts; if the three differenttypes of filters were treated independently, the coveragewould have to be unacceptably superficial. A unified treat-ment was used, instead, and this made it possible to success-fully 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 stu-

dents, and the final assessment, based on a project report andon a written examination, has shown that the course objectiveshave been achieved.

REFERENCES

[II M. S. Ghausi and K. R. Laker, Modern Filter Design: Active RCand Switched Capacitor. Englewood Cliffs, NJ: Prentice-Hall,1981.

[2] A. V. Oppenheim and R. W. Schafer, Digital Signal Processing.Englewood Cliffs, NJ: Prentice-Hall, 1975.

[31 A. Peled and B. Liu, Digital Signal Processing. Theory, Designand Implementation. New York: Wiley, 1976.

[41 L. T. Bruton, RC-Active Circuits Theory and Design. EnglewoodCliffs, NJ: Prentice-Hall, 1980.

[51 A. S. Sedra and P. 0. Brackett, Filter Theory and Design: ActiveandPassive. Portland, OR: Matrix, 1978.

[61 G. Daryanani, Principles ofActive Network Synthesis and Design.New York: Wiley, 1976.

[71 H. Y.-F. Lam, Analog and Digital Filters: Design and Realization.Englewood Cliffs, NJ: Prentice-Hail, 1979.

[8] L. R. Rabiner and B. Gold, Theory and Application ofDigitalSignalProcessing. Englewood Cliffs, NJ: Prentice-Hall, 1975.

[91 H. G. Dimopoulos and A. G. Constantinides, "Linear transfor-mation active filters," IEEE Trans. Circuits Syst., vol. CAS-25,pp. 845-852, Oct. 1978.

[101 M. S. Piedade and M. M. Silva, "A note on hnear transformationactive filters," Proc. IEE, vol. 128, part G, pp. 180-181, Aug.1981.

[11] M. M. Silva, "Multiport converters and inverters," Int. J. CircuitTheory App!., voL 6, pp. 243-252, July 1978.

[121 M. S. Piedade and M. M. Silva, "New lowpass and bandpass activefilters derived from passive ladder prototypes," in Proc. IEEE Int.Symp. Circuits Syst., Houston, TX, Apr. 1980, pp. 557-561.

[131 R. Saal and W. Entenmann, Handbook ofFilter Design, AEGTelefunken, Berlin, Germany, 1979.

[14] G. Szentirmai, "FILSYN-A general purpose filter synthesisprogram," Proc. IEEE, voL 65, pp. 1443-1458, Oct. 1977.

Manuel M. Silva (M'76-SM'81) was born inPonta Delgada, Azores, in 1943. In 1967 he re-ceived the degree in electrical engineering fromthe Instituto Superior Tecnico, Lisboa, Portugal.He was a graduate student at Imperial Collegeof Science and Technology, London, England,and obtained the Ph.D. degree from the Univer-sity of London, London, England, in 1976.He is an Associate Professor of Electrical En-

gineering at the Instituto Superior Tecnico andis the head of the Research Group on Analog

and Digital Filters at the Centro de Electr6nica Aplicada, Instituto Su-perior Tecnico. He was one of the organizers of the IEEE Portugal Sec-tion and is now its Chairman.

Short Notes

A Microprocessor-Based Digital Control Course

E. LUQUE, 1. SERRA, AND L. MORENO

Abstract-A microprocessor-based digital control laboratory coursehas been developed at the Autonomous University of Barcelona. Themicroprocessor controller interfaces directly to an analog computer.The introduction of the microprocessor in a closed-loop system allowsgreat flexibility in the types of algorithms that can be used in stand-alone controllers. Some experiments have been carried out with theaim of improving the student's understanding of the digital controlconcepts. A brief description of the algorithms, with main emphasison their discrete realization, and details of each laboratory experi-ments are given. The philosophy underlying the course is the activeparticipation 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.

1. INTRODUCTIONWhen the students reach the Digital Control Systems course

developed at the Autonomous University of Barcelona, theyhave already taken a preliminary course in linear systemtheory, including time response, frequency response, stability,and controller design. They have also had a course in intro-duction to computer sciences, and have had some hardware andsoftware 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 tech-

nique 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 anddynamic 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-

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