I am a Mathematician and I am looking for some good reference about overdamped networks in electronics (the electrical circuit system). It must have some theory about overdamped networks and some concrete examples which include elementary derivations of the corresponding system of equations governing the time behaviour of the electrical system written in the matrix-vector form:

*Lï+Ri+Di=O*

where **L**, **R**, **D** are nxn matrices, **i** is the n-vector of current, __for n>1 or (more important to me) very large n__.

Some details:

The natural modes of a linear passive time-invariant n-port are

given by the Lagrange’s equilibrium equation in matrix form which may be

obtained by writing Kirchoff’s loop equations for all n dynamically independent loops of the system.

*Lï+Ri+Di=O. (1)*

The operators *L,R *and **D**≠ 0 represent the effective loop inductance, resistance and elastance respectively; and **i** is an n-vector loop charges **(1).**

The loop current n-vector is produced by the small initial conditions

prevailing at the time t = 0. No sustained source is applied.

__Overdamped system__ is one in which all three matrices **L**, **R** and **D** are symmetric positive definite and all the eigenvalues λ of the quadratic eigenvalue problem (λ^{2}* **L**+λ* **R**+**D**)x=0, x≠ 0, are real and negative.

One good workbook is

Dare A. Wells, Schaum’s Outline of Theory and Problems of Lagrangian Dynamics, 1967., Chapter 15,

but I need a book with the corresponding theory about overdamped networks and some examples like in the mentioned Schaum’s Outline.

## Comments rated to be Good Answers:

Re: A reference for Overdamped Networks (systems) in Electronics" by Rixter on 10/29/2017 3:53 PM (score 3)