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A simple circuit for direct current (dc) measurement using a transformer is proposed. The circuit is based on nonlinear effects in the transformer ferromagnetic core, and it provides information about the current magnitude and polarity. The circuit is analyzed applying piecewise-linear model of the core magnetization curve. An averaged-circuit model and the circuit transfer function are presented. Good linearity and wide measurement range are obtained. Design guides for reduction of the output voltage ripple are given. Measurement error within 0.25% of the full scale is achieved.

A new procedure is presented that very rapidly determines whether or not a dc operating point exists for a series-parallel network of continuous, strictly monotonically increasing resistances having possibly limited domains and/or ranges. This is accomplished without any attempted computation of the operating point. If such exists, it will be unique. The procedure does not involve any manipulation of the characteristic curves of the resistors other than the asymptotes to which they tend. As a result, it is easily programmed and rapidly executed. The test is extendable to series-parallel networks of nonmonotonic resistors, but in this case the test is only for existence - not for uniqueness. Index Terms - Monotone resistors, nonlinear networks, operating points, series-parallel networks.

A fast and convergent iteration method for piecewise-linear analysis of nonlinear resistive circuits is presented. Most of the existing algorithms are applicable only to a limited class of circuits. In general, they are either not convergent or too slow for large circuits. The new algorithm presented in the paper is much more efficient than the existing ones and can be applied to any piecewise-linear circuit. It is based on the piecewise-linear version of the Newton-Raphson algorithm. As opposed to the Newton-Raphson method, the new algorithm is globally convergent from an arbitrary starting point. It is simple to understand and it can be easily programmed. Some numerical examples are given in order to demonstrate the effectiveness of the proposed algorithm in terms of the amount of computation.

This paper presents new results concerning the stability of operating points of dc circuits. We define two classes of unstable operating points and develop criteria for identifying the class to which a given operating point belongs. We also show, by employing results from degree theory, that if a circuit possesses n structurally stable operating points (n has been shown previously to be odd), then 1/2(n - 1) of these operating points must be unstable and hence physically unobservable. A special case of this result proves that any bistable circuit must posses at least three operating points.

A new method of modeling PWM converters operating in continuous mode (CCM) is introduced. The procedure of deriving the models consists of three steps. First, static voltage and current transfer functions of the idealized switching part of the converters are found. Second, the linearization of these transfer functions at the operating point is carried out and the idealized switching part is replaced by dependent current and voltage sources. Third, the equivalent average resistance (EAR) of parasitic resistances and equivalent average voltage (EAV) of offset voltage sources of switches are determined using the principle of energy conservation. The method leads to linear dc and small-signal circuit models of a PWM converter. The obtained models give the same dc and small-signal characteristics as the state-space averaging method. To illustrate the method, the analysis of the PWM flyback converter is given, taking into account parasitic resistances of the transformer, the filter capacitor, the switch, and the diode as well as the diode threshold voltage. Design equations for dc voltage transfer function, efficiency, and small-signal characteristics are derived.

This paper develops a constructive homotopy-based methodology for finding all or multiple dc operating points of nonlinear circuits and systems. Several sufficient conditions for the connectivity of all the solutions along a single homotopy path are derived. These conditions offer criteria to determine an initial guess from which all the solutions can be obtained by following the single homotopy path. For the class of nonlinear circuits and systems in which all of the solutions lie on several homotopy paths, a new systematic method to explicitly construct a starting point for each homotopy path is developed. From a practical viewpoint, the constructive method developed does not require the difficult task of finding a good initial guess and is applicable to general nonlinear circuits and systems. From a methodological viewpoint, the constructive method developed is applicable to general homotopy methods with different homotopy functions. One particularly important feature of the developed constructive method is that when this method is applied to a dc problem with box constraints, it is very computationally efficient because it locates only feasible solutions satisfying the given box constraints. The proposed method is applied to several test examples with promising results. Index Terms--DC operating points, homotopy methods, nonlinear circuits and systems.

The switch-mode dc-to-ac inverter using dc-to-dc converter configuration has many advantages over the traditional bridge-type inverter. The previously presented circuit with nonlinear robust control works only for resistive load and its output voltage has considerable distortion near the zero-crossing point. A novel bidirectional circuit with nonlinear robust control is proposed in this paper to overcome those drawbacks. This inverter can dynamically stabilize the output voltage, i.e., the output voltage of the inverter remains dynamically unchanged when subjected to large disturbances in the input voltage or output load. The stability analysis is presented. The closed-loop control system under P control, PI control, PD control, and PID control of the voltage loop for different types of loads are investigated. The results show that the PD control is the best choice. The performance of the circuit is also studied. Computer simulation and experimental results are provided. Index Terms--Control techniques, dc-ac power conversion, dynamic response, pulse width modulation inverters.