Nonlinear RLC Networks

Abstract

This article considers the question of existence and uniqueness of the response of nonlinear time‐varying RLC networks driven by independent voltage and current sources. It is proved that under certain conditions the response exists, is unique, and is defined by a set of ordinary differential equations satisfying some Lipschitz conditions. These conditions are of two types: (1) the network elements must have characteristics which satisfy suitable Lipschitz conditions and (2) the network must satisfy certain topological conditions. It should be noted that elements with nonmonotonic characteristics are allowed and that the element characteristics need to be continuous but not differentiable.

Memristor-The missing circuit element

“…Proof: Since the governing equations of a network containing only memristors are identical in form to the governing equations of a network containing only nonlinear resistors, the proof follows mututis mutandis the well-known proof given in [6], [7].…”

“…, b -n + 2 (9) kzl 7 We have assumed for simplicity that the mernristors are chargecontrolled. The proof can be easily modified to allow memristors characterized by arbitrary e curves.…”

Application of the mixed potential for formulating normal form equations for nonlinear rlc‐networks with ideal transformers

“…The last two terms describe the total instantaneous power W delivered from Ni to Nu. Therefore a more concise form of (8) …”

Book Review: Mathematical models in electrical circuitsrm: theory and applications

“…The history of nonlinear dynamic analyses of transistor circuitry extends back about three decades; some of the early efforts are [1,[4][5][6][7][8][9][20][21][22][23]. Many of those and more recent works concern qualitative properties such as existence, uniqueness, and stability of solutions, although considerable effort has also been expended toward computational problems.…”