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    AUTOMATED DESIGN OF TWO-ZERO RATIONAL CHEBYCHEV FILTERS

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    Author
    Le, Kha Hien
    Issue Date
    1981
    Keywords
    Chebyshev systems -- Mathematical models.
    Filters (Mathematics)
    Advisor
    Kerwin, William J.
    
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    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    The Rational Chebyshev Function was first introduced by Bernstein (1926), used by Sharpe (1953), then later by Heldman (1955) to design elliptic-characteristic filters. Namely for a filter of order N, we have N/2 equal ripples in the passband and N/2 equal ripples in the stopband of the magnitude response. Here, the same mechanics are used but are now producing a new and different type of response. It has N/2 ripples in the passband but only one ripple in the stopband for all orders. As N increases from three, the result is a substantial saving in number of capacitors in the passive ladder realization of the above function as compared to that of traditional elliptic filters of the same order N. It also has been discovered that the above ladder's element values can be expressed as explicit expressions involving only the coefficients of the transfer function. These expressions can also be used for other types of filters. Numerically, the design can be carried out by a Fortran program or a set of programs on a programmable calculator. The design is termed automated because the user needs only to give the three specifications: the filter order N, the stopband zeros Z, and the passband ripple amount R(p). The program automatically selects the starting point for the given case and proceeds. The numerical results of the above programs over a range of specifications has led to a surprising and simple expression relating the above specifications to the minimum stopband attenuation. This is a useful relationship for the designer to estimate the zero position when using the programs.
    Type
    text
    Dissertation-Reproduction (electronic)
    Degree Name
    Ph.D.
    Degree Level
    doctoral
    Degree Program
    Graduate College
    Electrical Engineering
    Degree Grantor
    University of Arizona
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