An Accurate and Efficient Computation of Poles and Zeros of Transfer Functions for Large Scale Analog Circuits and Digital Filters

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26220%2F21%3APU137706" target="_blank" >RIV/00216305:26220/21:PU137706 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/978-981-15-9209-6_8" target="_blank" >https://doi.org/10.1007/978-981-15-9209-6_8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-981-15-9209-6_8" target="_blank" >10.1007/978-981-15-9209-6_8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

An Accurate and Efficient Computation of Poles and Zeros of Transfer Functions for Large Scale Analog Circuits and Digital Filters

Popis výsledku v původním jazyce

The poles and zeros of a circuit transfer function can be efficiently computed solving the generalized eigenvalue problem, which could be transformed into the standard eigenvalue problem to be solved by a suitably modified QR algorithm. In this way, the poles and zeros can be obtained for any linear circuit or a nonlinear circuit linearized at an operating point (using the Laplace transform), or for any digital filter (using the Z transform). Both the reduction of the generalized eigenvalue problem to the standard form and the iterative procedures of the QR algorithm are very sensitive to the numerical precision of all calculations. The numerical accuracy is especially critical for the two kinds of circuits: the microwave circuits characterized by huge differences among the magnitudes of the poles and zeros, and the large scale circuits, where the errors of poles and zeros are increased by the extreme number of arithmetic operations and frequent multiplicity of the poles and zeros as well. In this chapter, two illustrative examples of the reduction of the general eigenvalue problem (the first for analog and the second for digital circuit) and using the QR algorithm are shown first. After that, four circuits of various sizes are analyzed: simpler microwave low noise amplifier, larger power operational amplifier, more complex example with a 272 integrated operational amplifier, and the most difficult analysis of a distributed oscillator. A meticulous comparison of the obtained results shows that a usage of newly implemented 128-bit arithmetics in GNU Fortran or C compilers with partial pivoting can assure both efficient and enough accurate procedures for computing the poles and zeros of the circuit transfer function.

Název v anglickém jazyce

An Accurate and Efficient Computation of Poles and Zeros of Transfer Functions for Large Scale Analog Circuits and Digital Filters

Popis výsledku anglicky

The poles and zeros of a circuit transfer function can be efficiently computed solving the generalized eigenvalue problem, which could be transformed into the standard eigenvalue problem to be solved by a suitably modified QR algorithm. In this way, the poles and zeros can be obtained for any linear circuit or a nonlinear circuit linearized at an operating point (using the Laplace transform), or for any digital filter (using the Z transform). Both the reduction of the generalized eigenvalue problem to the standard form and the iterative procedures of the QR algorithm are very sensitive to the numerical precision of all calculations. The numerical accuracy is especially critical for the two kinds of circuits: the microwave circuits characterized by huge differences among the magnitudes of the poles and zeros, and the large scale circuits, where the errors of poles and zeros are increased by the extreme number of arithmetic operations and frequent multiplicity of the poles and zeros as well. In this chapter, two illustrative examples of the reduction of the general eigenvalue problem (the first for analog and the second for digital circuit) and using the QR algorithm are shown first. After that, four circuits of various sizes are analyzed: simpler microwave low noise amplifier, larger power operational amplifier, more complex example with a 272 integrated operational amplifier, and the most difficult analysis of a distributed oscillator. A meticulous comparison of the obtained results shows that a usage of newly implemented 128-bit arithmetics in GNU Fortran or C compilers with partial pivoting can assure both efficient and enough accurate procedures for computing the poles and zeros of the circuit transfer function.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

20201 - Electrical and electronic engineering

Projekt

<a href="/cs/project/GA20-26849S" target="_blank" >GA20-26849S: Nové algoritmy pro přesnou, efektivní a robustní analýzu rozsáhlých systémů</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Transactions on Engineering Technologies: World Congress on Engineering and Computer Science 2019

ISBN

978-981-15-9208-9

Počet stran výsledku

16

Strana od-do

1-16

Počet stran knihy

206

Název nakladatele

Springer

Místo vydání

Singapore

Kód UT WoS kapitoly

—