# The Characteristic-Resistance Method for Grounded Semi-Infinite Grids

@article{Zemanian1981TheCM, title={The Characteristic-Resistance Method for Grounded Semi-Infinite Grids}, author={Armen H. Zemanian}, journal={Siam Journal on Mathematical Analysis}, year={1981}, volume={12}, pages={115-138} }

A variety of existence and uniqueness theorems for the current flows in infinite electrical networks have been previously established, but there is virtually no information on how to compute those current flows under the practical requirement that the power dissipated and energy stored in the network be finite. This problem is addressed herein. It is shown that the characteristic-impedance method of analyzing lumped transmission lines can be adapted to semi-infinite half-plane resistive grids…

## 19 Citations

Infinite electrical networks with finite sources at infinity

- Mathematics
- 1987

Various physical situations leading to the exterior problem for partial differential equations are modeled by infinite electrical networks having finite-valued sources connected to extremities of the…

A finite-difference procedure for the exterior problem inherent in capacitance computations for VLSI interconnections

- Mathematics
- 1988

The computation of the capacitance coefficients of VLSI interconnection wires is an example of the exterior problem for Laplace's equation. However, the geometry is of a special sort in that the…

NONLIKEAR INFINITE NETKORKS AND RELATED OPES PROBLEMS

- Mathematics
- 1985

A brief survey is made of the current research status of the theory of nonlinear infinite electrical networks. Special attention is paid to the computational methods of solving for currents and…

A solution for an infinite electrical network arising from various physical phenomena

- Mathematics
- 1983

A procedure for determining the currents and voltages in a square or cubic grounded grid, wherein the grounding conductances can differ in quite arbitrary ways, is presented. Such a semi-infinite…

Computationally efficient determination of threshold voltages in narrow-channel MOSFETs including fringing and inversion effects

- Engineering
- 1989

A method for computing threshold voltages for narrow-channel MOSFETs based on infinite-network theory is presented. The technique enables a domain contraction down to a narrow strip containing the…

Analysis of v 'c) - c2$ = g in a Semi-Infinite Medium with an Irregular Boundary by Means of Network Manipulations

- Mathematics
- 1983

A finite-difference method for finding the finite-power solu- tion Cp of v 2+ - C'(J = g in a semi-infinite medium with an irregular boundary is established. The method is radically different from…

Nonlinear infinite networks and related open problems

- Mathematics1985 24th IEEE Conference on Decision and Control
- 1985

A brief survey is made of the current research status of the theory of nonlinear infinite electrical networks. Special attention is paid to the computational methods of solving for currents and…

Analysis of abla^2 phi - c^2 phi = g in a semi-infinite medium with an irregular boundary by means of network manipulators

- Mathematics
- 1983

A finite-difference method for finding the finite-power solution \phi of \nabla^{2} \phi - c^{2} \phi = g in a semi-infinite medium with an irregular boundary is established. The method is radically…

Infinite electrical networks: a reprise

- Physics
- 1988

A tutorial on resistive infinite electrical networks at an undergraduate level is presented. Rather than presenting a comprehensive survey on the wide variety of results existing in this subject, the…