"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 8, 2018

contents of issue      DOI  10.30898/1684-1719.2018.8.16     full text in English (pdf)  

UDC 621.372, 532.59



V. N. Biryukov

Southern Federal University, Bol’shaya Sadovaya, 105/42, Rostov-on-Don 344006, Russia 


The paper is received on August 13, 2018 


Abstract. Currently employed time-domain simulation methods, which are based on trapezoidal rule (TR), or backward differentiation formulas (BDF), reveal to be both poorly accurate and inefficient when employed to simulate oscillating circuits. Only L-stable methods can solve stiff systems of ordinary differential equations (SODE) of most practical circuits and only P-stable methods can solve SODE of oscillation circuits. A trapezoidal rule is P-stable, but isn’t L-stable. BDFs are L-stable, but do not have P-stability. This paper presents a one-step multi-stage backward differentiation formula (TR-BDF4) of a second-order, as a generalization of the TR-BDF composite scheme. This scheme is equivalent to singly diagonally implicit Runge-Kutta (SDIRK) methods of special type, and regarded as the one-step analogs of the multi-step methods, the backward differentiation formulas (BDFs). TR-BDF4' method is A(π/2)-stable, is not P-stable, but it has an interval of periodicity (0; 0.37). Unlike the conventional BDFs and TR-BDF the TR-BDF4 at small steps maintains the accuracy of the trapezoidal formula at the imaginary axis.

It is further shown that the implicit difference schemes solvable by Gauss-Seidel iterations have some similar properties.

Keywords: oscillating circuits, nonlinear differential equations, error analysis.


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For citation:

V. N. Biryukov. On the best methods for time domain analysis of RF circuits. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2018. No. 8. Available at http://jre.cplire.ru/jre/aug18/16/text.pdf

DOI  10.30898/1684-1719.2018.8.16