Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki (Dec 2019)

SYNTHESIS OF QUASI BAND LADDER TRANSFORMING HIGH ORDER FILTERS

  • A. E. Kurochkin

DOI
https://doi.org/10.35596/1729-7648-2019-126-8-30-37
Journal volume & issue
Vol. 0, no. 7-8
pp. 30 – 37

Abstract

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The purpose of the work, the results of which are presented in the article, was to develop a computerized mathematical model of the ladder filter to study the features of the synthesis of matching chains of any order on its basis. To achieve this goal, all the synthesis tasks were solved, including the choice of the prototype, frequency transposition, calculation of the poles of the transfer function of the prototype, calculation of the poles of the transfer function of the filter, calculation of the reflection coefficient of the filter, the calculation of the input resistance of the filter, the implementation of the ladder chain by the Cauer method and denormalization of the values of the elements of the ladder chain. Modeling of characteristics of ladder filters of any high order with frequency characteristic of Chebyshev on the computer with 32-bit operating system is carried out. It is shown that the use of standard mathematics leads to a significant increase in the error of matching of loads at increasing the order of the chain. To increase the accuracy of calculations it is proposed to use software that allows implementing mathematical operations on variables with any length of the mantissa. There are computer libraries where numbers are presented in the form of string type variables and arithmetic operations are carried out on them according to school rules “ in a column ” . Once the calculations are completed, the strings are converted back to normal numbers. The article considers the application of the variant of BigNumber library for high level JavaScript language. To estimate the accuracy of the calculation it is proposed to apply the property of antimetric ladder structure. From the presented results of the calculation it follows that in order to obtain not less than 15 reliable digits after the decimal point for the parameters of the n-th order filter it is necessary to increase the length of the variable mantissa to the value 2n.

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