Chaos in a series circuit with a nonlinear capacitor and a nonlinear inductor

A generalized impedance converter (GIC) is presented in this paper as a programmable current source. A study of its properties and limitations is shown. Its current efficiency is compared with that of Howland topologies, and it is improved in this paper. The contribution of the operational amplifier static offsets to the current source is obtained by presenting typical values of these parameters, and an equivalent circuit with its differential and common modes is presented. The calculated and experimental GIC input impedances are obtained, showing its bandwidth limitation and proposing the possibility of extending the input impedance frequency response without varying its low-frequency value. In this paper, the GIC is used to provide constant current to a series sensor loop and a magnetoresistive current sensor (Wheatstone bridge), which are located within the GIC itself. In both cases, the GIC works under the DC regime, unlike usual AC use.

An elliptic filter is presented whose purpose is to detect an impending launch by listening for a 600-Hz tone characteristic of the auxiliary power units (APUs). These are activated between five and ten minutes prior to launch. The filter comprises the key element in an APU detection circuit, and it is implemented using a pair of generalized impedance converters (GIC) in cascade. The GIC configuration is highly insensitive to changes in both its passive and its active parameters, is capable of implementing a large variety of biquadratic filter functions, and is thus an excellent choice for active filters. The two GIC sections represent biquadratic factors which individually implement a high-pass and a low-pass notch filter. When placed in cascade, the result is a very narrow band elliptic filter. This paper includes measurements of the sensitivity of the filter to changes in its parameters. >

This paper presents a mathematical technique useful in the solution of certain nonlinear electrical and mechanical problems of practical importance. The mathematical procedure involves the formulation of the problem in terms of nonlinear integral equations, and, by its use, practical results may be obtained in many cases where the approximate solution of the integral equation may be effected by the assistance of the Laplace transform theory. No attempt is made to present a general theory, but instead the general method is illustrated by applying it to the solution of typical problems of technical importance such as the analysis of electric circuits with nonlinear resistance, nonlinear inductance, nonlinear capacitance, and to the steady-state solution of van der Pol's equation.

The transmission lines we consider are constructed from the nonlinear inductors and the nonlinear capacitors. In the first part of the paper, we additionally include linear ohmic resistors. The dissipation thus being taken into account leads to the existence of shocks-the traveling waves with the different asymptotically constant values of the voltage (the capacitor charge) and the current before and after the front of the wave. For the particular values of ohmic resistances (corresponding to strong dissipation), we obtain the analytic solution for the profile of a shock wave. Both the charge on a capacitor and current through the inductor are obtained as the functions of the time and space coordinate. For the case of weak dissipation, we obtain the stationary dispersive shock waves. In the second part of the paper, we consider a nonlinear lossless transmission line. We formulate the simple wave approximation for such a transmission line, which decouples left- and right-going waves. The approximation can also be used for the lossy transmission line considered in the first part of the paper to describe the formation of the shock wave (but, of course, not the shock wave itself).

Studying active filters is a basic composite part of student education in electronics and communication engineering. A methodology for designing active filters with a generalized impedance converter is proposed. Profound investigations of the considered model show that the circuits based on it are some of the lowest sensitivity active sections with great stability and possibilities for realizing high quality factors. Computer simulation with the product MicroCAP is used for investigating different types of active filters obtained on the basis of modifying the main model. These modifications allow low-pass, high-pass, pass-band and stop-band polynomial second-order sections and low-pass and high-pass elliptical second-order sections to be realized. Simulation results are given in tables and in graphical form and can be used in the educational process. Modeling increases the education effectiveness by extending the interests to the studied educational material and improves the motivation of the students.

A very high frequency (VHF) second order bandpass filter has been developed. The filter is based on a minimal transistor-only all-MOS high-frequency generalized impedance converter (GIC) that simulates a passive RLC ladder. The filter poles are obtained using the internal lumped capacitances of the MOS transistor. Using this structure a very high frequency filter is obtained consuming a small chip area. The center frequency is controlled by an external bias current to the circuit. Using the GIC, a bandpass filter can be implemented in MOS technology with center frequencies in excess of 50 MHz. The filter is simulated for center frequencies of 47 MHz, 54 MHz and 63 MHz. >

Recent works have introduced an effective technique to analyze nonlinear dynamics of a class LM of circuits containing ideal flux– or charge–controlled memristors and linear lossless elements (i.e. ideal capacitors and inductors). The technique, named Flux–Charge Analysis Method (FCAM), is based on analyzing the circuits in the flux–charge domain instead of the traditional voltage–current domain. Goal of this paper is to extend the FCAM to a larger class N of circuits containing also nonlinear capacitors and inductors. Nonlinear circuits with memristors and nonlinear lossless elements are widely used to several real nanoscale devices including the well-known Josephson junction. After deriving the constitutive relation in the flux–charge domain of each two–terminal element in N, the work focuses on a relevant subclass of N for which a state equation description can be obtained. State Equations (SE) formulation provides the fundamental basis for studying the chief features of the nonlinear dynamics: presence of invariant manifolds in autonomous circuits; coexistence of infinitely many different reduced–order dynamics on the manifolds; bifurcations due to changing of initial conditions for a fixed set of parameters, a.k.a. bifurcations without parameters.

Summary form only given. In the course of the last decade, interest in the generation of high power chaos has grown substantially. This development was largely enhanced by the range of possible applications which among others include coding, ultra-wide-band (UWB) spread spectrum communication systems as well as detection and radar. Also a new field of research has opened up with the realisation that the interaction between E-M radiation and live tissue should be investigated more closely, either using high power microwave pulses, low power chaos for dosimetry purposes and THz radiation for diagnosis of some malignant growth. So far various methods have been tried in search for suitable sources of high-power chaos. For example 30 ns high-power pulses have been obtained by feeding an amplitron with anharmonic signals. Similarly chaotic oscillations have been generated by hard driving a relativistic BWO, initial simulation results being obtained using MAGIC2D. Others used a smooth anode magnetron to achieve somewhat similar results; also the effect of a time-delayed feedback in both klystrons and TWTs on generating chaos has been investigated. In our own research group we investigated the generation of chaos using plasma filled diodes. As a result of all the above research effort we have decided that a more systematic approach to the generation of high-power chaos would not be out of place. In our contribution we propose to discuss what we consider to be the essential requirements for the generation of high-power chaos. High power, of whatever kind, can only be achieved using high voltages and currents; this immediately brings us into the realm of relativistic kinematics, since in practice we would be operating in the region of 500 kV and above. It would appear that the magnetic field invariably plays a crucial role in the interaction process. We are going to show, using the simplest possible means, why it should be so, especially as far as the energy volume density in the interaction space is concerned. We have shown already that chaos can be generated in a plasma-filled diode even without the presence of a magnetic field; therefore an addition of plasma is likely to facilitate the development of chaos via the usual cascade of bifurcations. These are the three points which we propose to discuss more fully as part of our presentation

Time-invariantn-port networks are considered which are constructed from linear resistors and transformers, and nonlinear inductors and capacitors. A port property is sought which is analogous to the symmetry of the impedance matrix obtained in the linear case. Such a property is found using a stochastic characterization: with all resistors assumed to be at the one temperature and modelled to include the usual thermal noise, a fluctuating noise voltage will be observed at the ports of the networks. With some reasonable restrictions on the nature of the nonlinearities in the reactive elements, the vector of such noise voltages is shown to constitute what is known as a reversible stochastic process; in the linear case, reversibility holds if and only if the impedance matrix is symmetric.

In single-sided and double-sided ladder networks containing nonlinear inductors and capacitors, the nonlinearities have to be closely matched. This can be done by using a gyrator and nonlinear capacitance to simulate each nonlinear inductance.

The procedure of calculating dynamic modes of electric circuits containing nonlinear inductances and capacitances is proposed. The procedure is based on the explicit methods of differential equations integration and requires calculating a linear circuit at every solving step, decreasing the computation time as compared to usual iterative methods. The method is illustrated by calculation of the transformer activation process.

We present the main results of theoretical and experimental developments of noise and chaos generators for Noise Radar (NR), which is part of Noise Radar Technology (NRT), in the Laboratory for Nonlinear Dynamics of Electronic Systems (LNDES), O. Ya. Usikov Institute for Radiophysics and Electronics, National Academy of Sciences of Ukraine (IRE NASU) since 1990. The Principles of Dynamical Chaotization is considered for generation of random/chaotic/noise signals in a wide range of frequencies: from P-band up to W-band. Various approaches to the chaos generators design are briefly described. P-band chaotic waveform oscillator with time-delayed feedback of ring type is described. Generation of noise signals directly in oscillatory systems containing a non-linear active electronic component is the most promising approach to design of a simple and efficient NR transmitter. Applications of Field Programmable Gate Array (FPGA) and Arbitrary Waveform Generators (AWG) for digital generation of pseudo-random signals are presented. Experimental testing showed high efficiency of FPGA-based pseudo-random signals for applications in radar with variety of sounding waveforms. The Chaos generators presented can be also used as a source of modulating signal in Voltage Controlled Oscillator (VCO) based NR transmitter.

High accurate and wideband current excitation for bioimpedance health monitoring systems

In nonlinear capacitors, inductors and resistors, general equations holding among the voltages and currents at different frequencies are derived. These are obtained only on the assumption that the characteristics for the nonlinear elements are single-valued. The well-known Manley-Rowe relation is the lowest order and simplest ones among these equations. But, even then, the relations are more extensive, in the sense that the number of the voltage generators may be arbitrary.

Instantaneous charge/flux transfers may occur in switched electrical circuits when the switch configuration changes. Characterization of such state discontinuities is a classical issue in circuit theory which, typically, is based on the so-called charge and flux conservation principle. This paper proposes a general state transfer principle for arbitrary switching port-Hamiltonian systems. This new principle coincides with the charge and flux conservation principle in the special case of linear RLC circuits, but also covers circuits with nonlinear capacitors and inductors, and of arbitrary topology. Moreover, the new principle is applied to switching mechanical systems.