Eliminating Excessive Summands and Multipliers in the Difference Sensitivity Expressions for Linear Electric Circuits
Abstract
Formulas for simultaneously separating homogeneous parameters (resistances, conductances, and controlled voltage and current sources) in the ratios and differences of circuit determinants are proposed. These formulas are used in constructing rational fractional expressions without mutually eliminating summands and excess multipliers. In separating identical parameters from the ratio of circuit determinants, excess multipliers in the numerator and denominator of the sensitivity function are eliminated, and in separating them from the difference, identical summands with the opposite signs are localized (grouped), due to which they can be eliminated without applying additional computation efforts. An algorithm for obtaining non-excess symbolic sensitivity expressions is developed, which is intended to be used for any circuit functions, including the transfer functions for voltage and current, and for mutual and input resistances and conductances. An example of constructing a non-excess sensitivity function for an active low-pass filter is considered. The sensitivity functions obtained using the difference formula, the generalized Bode formula, and the proposed algorithm are compared.
References
2. Филаретов В.В. Топологический анализ электронных схем методом выделения параметров. — Электричество, 1998, № 5, с. 43-52.
3. Курганов С.А., Филаретов В.В. Обобщенные безызбыточ- ные формулы для чувствительности схемных функций линейных электрических цепей. - Электричество, 2017, № 2, с. 44-50.
4. Курганов С.А., Недорезов М.В., Филаретов В.В. Анализ чувствительности каскадных электронных схем делением их на части. — Международ. сб. науч. тр. «Синтез, анализ и диагностика электронных цепей». Ульяновск: УлГТУ, 2018, вып. 15, с. 64—76.
5. Hoang S. Direct topological method in network sensitivity analysis. — Archiwum Elektrotechniki, 1975, vol. 21, iss. 4, pp. 767—784.
6. Тимкин Ю.В. Анализ электронных схем методом двунаправленных графов. М.: Энергоатомиздат, 1985, 256 с.
7. Филаретов В.В. Топологический анализ электронных схем методом выделения ветвей и дуг. — Электричество, 1992, № 7, c. 31—37.
8. Филаретов В.В. Синтез оптимальных формул схемных функций электрических цепей. — Электричество, 1995, № 4, c. 36—43.
9. Mandache L., Iordache M., Dumilriu L., Sirbu I., Niculae D. Sensitivity analysis of analog circuits based on a modified nodal approach. Proc. of Intern. Conf. on Optimization of Electrical and Electronic Equipment, May 22—24, 2014, Moieciu, Romania, pp. 83—88.
#
1. Bode G. Teoriya tsepei i proektirovaniye usilitelei s obratnoi svyaz’yu/Per. s angl. (Theory of Chains and Planning of Strengtheners Ticker-Coil/Trans. from Eng.). Moscow, GIIL, 1948, 641 p.
2. Filaretov V.V. Electrichestvo — in Russ. (Electricity), 1998, No. 5, pp. 43-52.
3. Kurganov S.A., Filaretov V.V. Electrichestvo — in Russ. (Electricity), 2017, No. 2, pp. 44-50.
4. Kurganov S.A., Nedorezov M.V., Filaretov V.V. Mezhdunarod. sb. nauch. tr. «Sintez, analiz i diagnostika elektronnykh tsepei» (Intern. collection of scienstific papers «Synthesis, analysis and diagnosis of electronic circuits»). Ul'yanovsk State Technical University, 2018, iss. 15, pp. 64-76.
5. Hoang S. Direct topological method in network sensitivity analysis. — Archiwum Elektrotechniki, 1975, vol. 21, iss. 4, pp. 767-784.
6. Timkin Yu.V. Analiz elektronnykh skhem metodom dvunapravlennykh grafov (Analysis of electronic circuits by the method of bi-directional graphs). Moscow, Energoatomizdat, 1985, 256 p.
7. Filaretov V.V. Electrichestvo — in Russ. (Electricity), 1992, No. 7, pp. 31-37.
8. Filaretov V.V. Electrichestvo — in Russ. (Electricity), 1995, No. 4, pp. 36-43.
9. Mandache L., Iordache M., Dumitriu L., Sirbu I., Niculae D. Sensitivity analysis of analog circuits based on a modified nodal approach. Proc. of Intern. Conf. on Optimization of Electrical and Electronic Equipment, May 22-24, 2014, Moieciu, Romania, pp. 83-88.
