In this paper we suggest a method to calculate the first integrals of a special system of the first order of differential equations. Then we use the method for finding the solutions of some differential equations such as, the differential equation of RLC circuit

The Cochrun–Grabel (C–G) method, an algorithm for finding the characteristic polynomial of a circuit containing reactances, has so far been restricted to circuits not employing mutual inductances. In this paper we present an intuitive, yet rigorous, proof of the Cochrun-Grabel method for a general RLC circuit, and we extend the method to allow the analysis of an RLC circuit containing mutual in...

In this appendix, the frequency characteristics of the RLC circuit model and the KLM model are compared via numerical simulations. To facilitate the comparison, the piezoelectric crystal was assumed to be lossless, air backed, and radiating into a homogeneous lossless region. This was done to simplify the analysis since closed form expressions for the element values in the RLC circuit model hav...

The limiting factor for high-performance systems is being set by interconnection delay rather than transistor switching speed. The advances in circuits speed and density are placing increasing demands on the performance of interconnections, for example chip-to-chip interconnection on multichip modules. To address this extremely important and timely research area, we analyze in this paper the ci...

The interaction of a gravitational wave with a system made of an RLC circuit forming one end of a mechanical harmonic oscillator is investigated. We show that, in some configurations, the coherent interaction of the wave with both the mechanical oscillator and the RLC circuit gives rise to a mechanical quality factor increase of the electromagnetic signal. When this system is used as an amplifi...

This paper aims to explore RLC equivalent circuit synthesis method for reduced-order models of interconnect circuits obtained by Krylov subspace based model order reduction (MOR) methods. To guarantee pure RLC equivalent circuits can be synthesized, both the structures of input and output incidence matrices and the block structure of the circuit matrices should be preserved in the reduced-order...

A wide-band physical and scalable 2equivalent circuit model for on-chip spiral inductors is developed. Based on physical derivation and circuit theory, closed-form formulas are generated to calculate the RLC circuit elements directly from the inductor layout. The 2model accurately captures ( ) and ( ) characteristics beyond the self-resonant frequency. Using frequency-independent RLC elements, ...

In this paper we suggest a method to calculate the first integrals of a special system of the first order of differential equations. Then we use the method for finding the solutions of some differential equations such as, the differential equation of RLC circuit.