Most of the material in this text stems from material developed and taught before my retirement in 2000 at the University of Maine. The purpose of writing this text is to document and organize material into one cohesive entity to illustrate a useful approach to preserving and teaching a modern version of the art of filter design. Strictly speaking, analog design procedures are essential to the design of high-speed sampling circuits such as the switched capacitor filter. So, in order to teach design procedures for high-performance digital devices, analog design considerations can not be totally ignored. In addition, active filter circuits (e.g., switched capacitors) offer competitive choices as alternatives to digital filters in many applications. In a sense, active filters are special-purpose analog computer signal processors.
Better courses need to be developed as techniques and curricula must evolve, and that is one of the purposes for writing this text. Another reason is that the material should also be useful for the practicing integrated circuit designer who wants to learn about the theory and design of active filters. The material presented here has practical use, and the text is organized so that specific procedures can be used for reference purposes.
Some material contained in this course is available in different texts and technical papers. However, most of the material has not been organized into a single text with sufficient examples and homework problems for anyone desiring to learn the subject on his or her own. So, with the encouragement of students and teaching colleagues, my special course notes have been assembled as a text on the subject of active filter design. The resulting text contains many practical procedures that are involved in the design and testing of active filter circuits. Some examples of previously unpublished topics are as follows:
1. An emphasis upon opamp gain redistribution in multiopamp
circuits to control dynamic range performance;
2. Precorrection for s-plane distortion introduced by sampled integrators in the switched capacitor circuit concept;
3. Broadband, multitone testing of switched capacitor circuits;
4. State variable implementation using switched capacitor procedures;
5. Examples showing that the state variable filter sensitivity is competitive to that obtained from the leapfrog topology;
6. LC network equivalences useful for leapfrog design procedures based upon prototype LC networks;
7. A useful algorithm that finds minimum order network functions (polynomial ratios) directly from specified loss functions.
From a teaching point of view, the material is organized as a one semester course divided into four subject areas of roughly 10 lectures (or 100 pages) each. Students are assumed to have completed junior-senior college years or to have experience working in the area of analog integrated circuit design. Required background includes basic courses in linear system theory and electronics, and it is helpful to have had experience using computer tools such as Matlab and SPICE or uCAP.
The first subject area (Chapters 1 through 3) reviews circuit analysis techniques, introduces the prototype concept together with frequency scaling and circuit transformations, and explores issues of nonideal opamp behavior. These subjects provide a background for circuit manipulation. For ease of understanding new ideas, all subsequent sections use only a simple frequency-dependent opamp model.
The second subject area (Chapters 4 and 5) introduces active circuits with emphasis upon the opamp and the state variable filter. Scaling for gain-frequency distribution and dynamic range is discussed and illustrated as a most important design consideration. The biquad circuit is only introduced as a special form of the state variable filter. Cascade synthesis procedures are illustrated, and fundamental differences between cascade and state variable filters are discussed. This provides background for subsequent development of the leapfrog structure.
The third subject area (Chapters 6 and 7) introduces sensitivity factors and methods used to estimate filter response parameter dependence upon component values. This leads to the leapfrog topology and the ability to design filters from LC prototypes in order to obtain responses that have low sensitivity to component nominal value variations. Procedures are then developed to convert the leapfrog circuits to switched capacitor implementations.
The fourth subject area (Chapter 8) introduces the student to the Approximation Problem. It provides a good closure to the topic to have some understanding of how to find a suitable network function. Topics include curve fitting to a generalized transmission function form, the use of an iterative active structure based on Fourier theory, and traditional polynomials such as the Butterworth, Chebyshev, and inverted Chebyshev polynomials, as well as a generalized polynomial form.
The goal of this course is to give readers a workable introduction to the active filter design area and to provide a foundation that is useful when and if they should pursue the subject at a more advanced level. The material is presented with sufficient detail so that readers should be able to handle a wide range of filter design problems in a practical and flexible manner. The course is not a ``look up the answer'' approach to filter design. It is a design course and provides that kind of experience (e.g., design examples are solved to find different candidate circuits, and discussion indicating why some are better solutions than are others is provided). Such reasons include undesired parasitic response (due to inadequate models), bad element value ratios, and possible tuning difficulties in production. Experience shows that the course is popular, and clearly, filter design is a popular subject with undergraduate engineers.
Finally, it should be emphasized that this material assumes that the student has access to and has learned how to use math tools such as Matlab and circuit simulators such as SPICE or uCAP. The text examples and homework rely heavily on the use of such tools. In particular, simulation is used extensively to evaluate the correctness of candidate designs. When proper modelling is used in the design process for linear filters, simulation is a valid tool used to measure the validity of a given design. Hence, simulation is sometimes referred to as a measured response. It is a fact that actual measurements for a properly constructed filter should virtually coincide with theoretically predicted responses. Thus, simulation is a valuable tool that is used extensively, especially for complex integrated circuits, where the cost of making a design error is prohibitive. There is no need to produce fabrication masks and special tools for circuit designs that do not even pass simulation measurement testing.
This text does not dwell significantly on how to use computer programs, but it does provide extensive examples of code used to compute various unusual procedures (e.g., polynomial manipulations). A CD for all example files, including the approximation program, apprx8, is included to facilitate work with text problems and examples.