Time-varying Circuit Research Articles

The step recovery diode in series mode harmonic generation

The analysis of stop-recovery diode harmonic generators by means of a linear time-varying circuit model of the diode has been advocated previously and it has been demonstrated that a direct analogy exists for the purposes of predicting efficiency, terminating impedances and optimum idler combinations, between the shunt connected SRD and a three-terminal switch where the periodic variation in conductance may be related to the physical properties of the diode. In the present paper it is demons-trated that by suitably modifying the circuit equation to include the d.c. bias essential to the operation of the series connected SRD the linear time-varying circuit model may be applied to this circuit also, resulting in an analysis of comparable generality and ease of application to that obtained for the shunt generators. A basis is thus provided for the analysis of all forms of SRD harmonic generator and for the optimization of diode parameters for defined circuit configurations.

An analysis of time-varying circuits

Abstract The paper proposes a method for examining the stability and obtaining the response of the time-varying circuits involving differential equations of the order 2 or more, The method consists of first analysing the circuit by neglecting the time variation of its parameters and then taking it into account by introducing new variables which are suitably related to, and give the variation of the envelope and phase of, the response functions of the time-invariant network. These variables are obviously slowly varying quantities. The equations involving these variables can, by a little matrix manipulation, be put in a form which can be solved conveniently by Peano- Baker's method of solving d.e. with periodic coefficients. The proposed method has been illustrated by means of a simple-example of the Mathieu equation

Linear time-varying circuit analysis of the step-recovery diode harmonic generator†

Abstract Linear time-varying analysis of the step recovery diode harmonic generator is investigated to assess its value as a means of obtaining a very general and flexible technique for the evaluation of the circuit properties without recourse to analogue computation procedures. The approach is used to evaluate the effects of diode transition time and conducting resistance, and of source and terminating impedances and bias (conduction time). The effects of idler circuits on efficiency and terminating impedances are readily evaluated and the influence of idler loss characterized in a number of idler combinations for high-order multipliers. The effects of finite output circuit Q are also shown.

Theory for Some Asynchronous Time-Division Switches

A two-wire active asynchronous time-division switch has recently been proposed by J. O. Dimmick, T. G. Lewis, and J. F. O'Neill. The interrupted energy transfer from one filter to another is accomplished asynchronously in order that more efficient use may be made of processing time of talker pairs on the switching bus. After first formulating, in a concise mathematical fashion, the effect of passing a signal through such a randomly time-varying circuit, we focus attention on optimizing an important filter response function. Typically, two percent rms jitter in the transfer times yields αn output S/N of 30 dB independent of signal spectrum. The timing stabilization required to obtain small jitter is also discussed and an exact solution for exponential processing time is obtained. This latter result may be put to good use in studying the efficiency of the switch. Conservatively, asynchronous operation should increase traffic capacity threefold. Finally, a speech wave which passes through a sample-and-hold circuit with random sampling times is considered upon being reconstructed with a fixed filter. This is a model for a four-wire active asynchronous switch, and results are compared with the two-wire situation.

Stability of passive time-variable circuits

Stability of passive time-variable circuits

A method for realizing time-varying circuit elements

A practical method is presented for realizing time-varying circuit components whose instantaneous element values depend on externally generated digital control signals. These signals control the value of a discrete-state resistor in an operational amplifier circuit. The method was used to realize linear time-varying inductors and capacitors which were built and tested.

Time-varying circuits for noise measurement

A time-varying smoothing network with an increasing time constant provides good smoothing and fast initial response. A mathematical model evaluated by digital computer showed that a stepwise time constant increase gives fairly good results even with only two steps. For low-output detectors (e.g., Hall correlators) a continuously varying time constant may be realized by using an FET.

Theory of Unidirectionality and Conjugate Matching in Three-Port Time-Varying Reactance Circuits (Correspondence)

Theory of Unidirectionality and Conjugate Matching in Three-Port Time-Varying Reactance Circuits (Correspondence)

Noise in transistor mixers at low frequencies

The paper deals with the noise performance of transistor mixers at frequencies where reactive effects may be neglected (generally less than 0.1fT). The analysis involves the consideration of noise processes in a time-varying circuit, and the problem is treated by returning to the basic physical equations describing the transistor. The problem of noise in the transistor-base current is discussed in detail. The analysis allows a simple prediction of transistor-mixer noise figure at low frequencies, and the effects of variation in local-oscillator drive, source resistance, transistor parameters and operating current are readily predicted. The emphasis is on an engineering approach to the problem, and the results are presented in a form intended to facilitate the design of low-noise mixers.

Stability of passive time-variable circuits

Lyapunov's second method is used to show that circuits composed of a finite connection of linear, passive, time-variable elements are necessarily stable. Such connections may involve transformers and gyrators as circuit elements, as well as the conventional resistors, inductors and capacitors. An equivalent structure is determined, using only time-variable gyrators to interconnect constant elements consisting of unit capacitors and unit resistors. Using this model, asymptotic stability and uniform asymptotic stability of the original circuit may be investigated. Examples are given to illustrate the methods and concepts.

Transients in Periodically Time-Varying Circuits

Transients in Periodically Time-Varying Circuits

The step-recovery diode in harmonic generation: a linear time-varying circuit model

A circuit model of the step-recovery diode is proposed based on the known conduction properties of the device. This model permits analysis of harmonic generation circuits with greater generality than has hitherto been possible and is used to estimate the efficiency and optimum terminating conditions of a high-order frequency multiplier.

Equivalent Circuits for Two-Dimensional Magnetic Fields: I - The Static Field

These papers describe electric circuit analogs for the 2-dimensional magnetic fields of synchronous machines. Although finite difference solutions of the differential equations are introduced to establish the mathematics, equivalent circuits are also deduced from elementary field and circuit theory familiar to electrical engineers. A simple resistive circuit is constructed to represent the static magnetic field with the ability to introduce any known currents and iron saturation. For the sinusoidally time-varying case, an RC analog is shown to represent the usual coupled circuit, and provides a most versatile tool for predicting eddy currents. Both the static and time-varying equivalent circuit should prove useful in the design of synchronous machines for the solution of magnetic problems for which numerical methods are necessary.

Useful time-variable circuit-element equivalences

Because time-variable circuit elements have properties not possessed by time-invariant ones, such as the ability to modulate or amplify with low noise, it is useful to have different ways of looking at them. Here we present general equivalences for time-variable inductors, capacitors, resistors and gyrators, using time-invariant elements and time-variable transformers, which allow various properties to be determined and interpreted on physical grounds.

The analysis and synthesis of a class of linear time-varying networks

Networks of certain types of time-varying circuit elements can be treated analytically in essentially the same way as networks of fixed-parameter elements, and for such networks the known theory of network analysis and synthesis of fixed-parameter elements can be considered as a special case of a more general theory. A few of the details of the extension to the general theory are considered, and an outline of the theory is presented.

Some Aspects of Perturbational Analysis of Time-Varying Circuits

A method of iterative analysis of a wide class of time-varying networks is considered. The unknown steady-state node voltages (mesh currents) are obtained in the form of infinite series, the convergence of which is investigated. Formally the method is suitable for analyzing nonselective time-variable networks.

Perception of Sounds Characterized by a Rapidly Changing Resonant Frequency

The perception of sounds characterized by a moving resonance was investigated a series of experiments. Stimuli were generated by exciting a tuned circuit with a short train of pulses of repetition rate 100/sec. The resonant frequency of the tuned circuit was changed in a piecewise linear manner over a 500-cps range. Subjects matched the test stimuli by adjusting the resonant frequency of a fixed (i.e., nonvarying in time) resonant circuit until the test and comparison stimuli were judged to be most alike. Results indicate a strong tendency for subjects to adjust the frequency of the fixed resonant circuit until it is close to the terminal resonant frequency of the time-varying circuit. This tendency depended to some extent on the direction and rate of the frequency change in the test stimulus. The implications of the results for auditory theory and speech perception are discussed briefly.

Resonance phenomena in time-varying circuits

ASA logical continuation of the studies of systems with fixed parameters, there has been increasing interest in systems whose parameters are functions either of the dependent variable (nonlinear systems) or of the independent variable (time-varying systems). A general approach to the analysis of time-varying systems is so difficult, that at the present stage of development in this field one is restricted to the solution of relatively simple problems arising in practical applications.

Four methods for the analysis of time-variable circuits

THE GENERAL theory of electric circuits whose component parameters are linear and constant has been extensively developed and is well understood. In recent years, considerable attention and effort has been directed to the analysis and performance of circuits whose parameters vary with the time. Many of the most important and interesting problems of circuit theory involve variable. parameters. For example, the equivalent circuits of the microphone transmitter, the condenser microphone, the induction generator, the superregenerator and of many other practical devices contain parameters that are time-varying. Many systems in mechanical and acoustical engineering in which the compliance or the inertia parameters vary with the time lead to the same mathematical formulation of their behavior as do the time-varying circuit problems.

The response of linear networks to suddenly applied stationary random noise

IN RECENT years time-varying circuits have attracted considerable attention in the literature, <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> but little seems to have been done <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> for those cases in which the input to such circuits is a random one.