Multiport Cases Research Articles

Extremal Length and Width of Blocking Polyhedra, Kirchhoff Spaces and Multiport Networks

Various facts about the extremal length (EL) and extremal width (EW) of a one-port network on a Kirchhoff space due to Anderson, Duffin and Trapp and their relation to blocking pairs of polyhedra are unified and extended to the multiport case. The definitions of EL and EW are extended to all pairs of blocking polyhedra $(G,H)$ on coordinates E given a symmetric positive definite matrix R. It follows that $\text{EW}^{ -1} = \min \{ x^t Rx | x \in G \} , \text{EL}^{ -1} = \min \{ z^t R^{-1} z | z \in H \} $ and $\text{EL} \cdot \text{EW} = 1$. A Kirchhoff space on coordinates $(E,P)$ where P is called the set of ports is a subspace that represents a matroid on $E \cup P$ in which P is independent and co-independent. Given any nonzero vector $\omega $ on port coordinates P, we extend Fulkerson’s construction of a blocking pair from orthogonal subspaces with one distinguished coordinate to Kirchhoff spaces which model multiport networks. For $\omega $ and positive definite R a pair of minimization problems with reciprocal values are derived from Kirchhoff spaces. When R is diagonal these problems coincide with the $\text{EW}^{ - 1} $ and $\text{EL}^{ - 1} $ problems for the blocking pair from Kirchhoff spaces. In the case of a multiport resistor network, EW is the power dissipated when the voltage vector $\omega $ is applied to the ports.

A theory of Q‐reciprocal and quasi‐reciprocal multiports

AbstractTwo notions: quasi‐reciprocity and Q‐reciprocity as generalizations of classical reciprocity are introduced and examined for the multiport case. A number of theorems and properties characterizing a class of Q‐reciprocal multiports are stated. A way of extending to quasi‐reciprocal networks some results proved under the assumption of reciprocity is presented as an example of application.

Characterization of time-invariant network elements

We present a discussion on the definitions and characterizations of the four basic types of time-invariant electrical network elements, namely: resistors, inductors, capacitors and memristors, including the nonlinear multiport cases.

Two scattering matrix programs for active circuit analysis

What's a diamond to an ape, do you think? It's nothing to be eaten by a monkey. --- Thai poem The philosophy is advanced of having two programs to cover a given area, one for quick routine calculations and one to handle general cases Thus, two scattering matrix programs are described for the area of computer-aided analysis of active circuits. Both programs rest upon an iterative use of cascade loading, a connection previously proven to incorporate any arbitrary connection. One program, GENERAL, covers the multiport case and through an incorporation of the generality of the scattering matrix handles any physical network. GENERAL proceeds by finding the scattering matrix of interconnections through the use of the indefinite admittance and by iteratively cascade loading such interconnections with componenets. The other (time-shared) program, SPEEDY, is a fast 2-port version. SPEEDY's time advantage comes about by programming the specific results for the most typical design connections (to which the program is limited). These are the series-parallel and cascade connections for 2-ports interpreted in terms of scattering parameters. SPEEDY contains two unique subroutines: one for all possible 2-port connections and one for converting common emitter scattering parameters to those for common base or collector.