By John A. Richards
The various sensible options constructed for treating platforms defined via periodic differential equations have arisen in several fields of program; con sequently a few techniques haven't regularly been recognized to staff in parts that will gain considerably from them. moreover, fresh analytical tools are computationally dependent in order that it now turns out an opportune time for an applications-oriented e-book to be made to be had that, in a feeling, bridges the fields within which equations with periodic coefficients come up and which attracts jointly analytical tools which are applied without problems. This ebook seeks to ftll that position, from a user's and never a theoretician's view. The complexities of periodic platforms frequently call for a computational procedure. Matrix remedies as a result are emphasised right here even supposing algebraic tools were incorporated the place they're valuable of their personal correct or the place they identify homes that may be exploited via the matrix method. The matrix improvement given calls upon the nomenclature and remedy of H. D'Angelo, Linear Time various platforms: research and Synthesis (Boston: Allyn and Bacon 1970) which bargains with time-varying structures quite often. it is suggested for its modernity and accomplished method of platforms research through matrix tools. because the current paintings is applications-oriented no try has been made to be whole theoretically when it comes to proposing all proofs, life theorems etc. those are available in D'Angelo and vintage and well-developed treatises akin to McLachlan, N. W. : concept and alertness of Mathieu services.
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Additional info for Analysis of periodically time-varying systems
16) where IN Lm is the minimal value and IN L M is the maximal value of the INL characteristic of the DI A converter. M * 100 = • If the percentual errors of the different current sources are given [1Ideal F;, i = 1 ... 2N - 1], one can state that the difference between the upper and the lower limit for the INL characteristic has to be larger than the maximum current source error. 17) • The INL error of the D/A converter will be minimal if IN Lm and IN LM are located symmetrically around zero. 19) Once the lower bound of the INL error is given, the (near) optimal switching sequence can be determined by using an INL bounded algorithm.
Although this implementation improves the overall linearity of the OJ A converter, it is still not optimal. In [Marqu ISSCC98] a switching scheme has been presented that preserves the simple row and column decoder but further reduces the INL error. The presented OJA converter has a 6-2-4 segmented architecture where the 6 most significant bits are implemented using a row and column decoder. Instead of using only one current source, the current is generated by four current sources that are placed symmetrically around the center of the array.
Although this implementation provides a simple and inherently monotonic D/A conversion, it has some major drawbacks. 1: The resistor string architecture occupied silicon area becomes fairly large. For a ten bit DIA converter, 1023 resistors and 1024 switches are required. Furthermore, the delay through the switching network poses a severe limitation on the update rate of the DIA converter. The integral non linearity error is directly related to the matching precision of the used resistors. Due to uncertainties during processing, the values of the resistors in the resistor string will not be equal.