Kirchoff's Voltage Research Articles

A Time-Mode Translinear Principle for Nonlinear Analog Computation

This work proposes a novel translinear principle based on time domain processing of signals. The exponential relationship between voltage and time in an RC circuit is exploited to implement a logarithmic voltage-to-time converter and an exponential time-to-voltage converter. These circuits are the time domain analogs of the voltage mode translinear circuits that exploit the exponential relationship between current and voltage in BJTs and subthreshold MOS transistors. Just as Kirchoff's voltage laws provide a natural form of addition for the voltage-mode translinear principle, the progression of time can also be a natural source of addition for the proposed time-mode analog of this principle. In this work a time-mode adder circuit is used to realize a translinear principle in time. This paper describes the theory behind this time-mode translinear principle. Furthermore, the design of nonlinear circuit functions, e.g., multiplication and power law, based on the time-mode translinear principle is described. Simulation and measurement results for a two-input single quadrant multiplier are presented. The chip was fabricated in a 180 nm CMOS process with simulation results agreeing closely with experimental results. We also present error analysis for such circuits and provide a brief discussion on future prospects of this approach.

Adaptive‐cross‐approximation‐based acceleration of transient analysis of quasi‐static partial element equivalent circuits

A new formulation of the partial element equivalent circuit (PEEC) method is presented, which is well suited to be combined with compression and matrix–vector product acceleration techniques. In particular, taking advantage of the rank-deficiency of the magnetic and electric field couplings, the adaptive cross approximation (ACA) technique is firstly, adopted to compress PEEC interaction matrices, namely partial inductances and coefficients of potential matrices. Differently from the use of ACA in conjunction with the method of moments, in this study, magnetic and electric field couplings are kept distinct, thus allowing to efficiently compress both magnetic and electric field interaction matrices. Secondly, the compressed matrices are used to accelerate the transient analysis of PEEC circuits. Indeed, Kirchoff voltage and current laws are enforced to PEEC circuits so that matrix–vector products involving the interaction matrices can be significantly accelerated in virtue of their compression, thus leading to very good speed-ups when using iterative solvers like the generalised method of residuals algorithm. Numerical results demonstrate the validity, accuracy and performance of the proposed approach in terms of both memory usage saving and transient analysis speed-up.

Generalized Kirchoff's Current and Voltage Law Formulation for Coupled Circuit–Electromagnetic Simulation With Surface Integral Equations

In this paper, a new formulation for coupled circuit-electromagnetic (EM) simulation is presented. The formulation employs full-wave integral equations to model the EM behavior of two- or three-dimensional structures while using modified nodal analysis to model circuit interactions. A coupling scheme based on charge and current continuity and potential matching, realized as a generalization of Kirchoff's voltage and current laws, ensures that the EM and circuit interactions can be formulated as a seamless system. While rigorous port models for EM structures can be obtained using the approach discussed herein, it is shown that the coupling paradigm can reveal additional details of the EM-circuit interactions and can provide a path to analysis-based design iteration.

A new algorithm for the reconfiguration of distribution feeders for loss minimization

The authors report a power-flow-minimum heuristic algorithm for determining the minimum loss configuration of radial distribution networks. The algorithm is based on the concept of optimum flow pattern which is determined by solving the KVL and KCL (Kirchoff's voltage and current laws) equations of the network. The optimum flow pattern of a single loop formed by closing a normally open switch is found, and the flow pattern is established in the radial network by opening a closed switch. This process is repeated until the minimum loss configuration is obtained. A simple, fast and approximate power flow method has also been developed to assist the reconfiguration algorithm. The proposed reconfiguration algorithm has been found to give better network configuration than those obtained by some other methods. >

Minimum Vertex Potential Principle

We consider the problem of minimizing a sum of vertex potentials of a finite directed graph for which 1) there is a directed path from a base vertex to every other vertex, 2) each arc is assigned a minimum rise potential constraint, and 3) Kirchoff's voltage law is satisfied. It is pointed out that a solution exists if and only if the sum of the minimum rise potential constraints about every cycle is nonpositive; and if a solution exists, an optimum is obtained by setting the potential at every vertex equal to the maximum sum of minimum rises taken over all paths to the vertex. Thus, the solution is easily obtained by finding a maximum distance tree. The intuitive simplicity of the result together with several ready physical applications make it seem worth mentioning.