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Showing papers in "IEEE Transactions on Circuit Theory in 1963"


Journal ArticleDOI
George Zames1
TL;DR: An operator theory is outlined for the general, nonlinear, feedback loop and it is shown that feedback reduces distortion for band-limited inputs and an iteration whose rate of convergence is optimized is derived.
Abstract: An operator theory is outlined for the general, nonlinear, feedback loop. Methods for bounding system responses and investigating stability are introduced. An iterative expansion of the feedback loop, valid for large nonlinearities and unstable systems, is derived. The theory is applied to the study of nonlinear distortion in a class of amplifiers; it is shown that feedback reduces distortion for band-limited inputs. A model of the distortion is obtained, shown to be stable, and an iteration whose rate of convergence is optimized is derived.

129 citations


Journal ArticleDOI
D. Younger1
TL;DR: This paper establishes a relationship between these feedback arcs and order; in particular, such a minimum set of arcs is shown to be determined by a sequential ordering of the nodes which minimizes the number of arcs.
Abstract: A minimum feedback arc set is, for a directed graph, a minimum set of arcs which if removed leaves the resultant graph free of directed loops. This paper establishes a relationship between these feedback arcs and order; in particular, such a minimum set of arcs is shown to be determined by a sequential ordering of the nodes which minimizes the number of arcs, each of which enters a node that precedes in the ordering the node it leaves. From this relationship are developed some simple characteristics of such sets, as well as properties of the sequential orderings by which these minimum sets are determined. These properties form the basis of an algorithm for finding minimum feedback arc sets.

105 citations



Journal ArticleDOI
TL;DR: A procedure is developed for synthesizing a predistortion filter, a reconstruction filter, and a feedback filter for a base-band quantization system for narrow-band television signals so as to minimize a quantity representing the subjective effects of over-all system errors.
Abstract: One proposal for a base-band quantization system for narrow-band television signals incorporates linear predistortion and reconstruction, and a linear noise feedback loop around the quantizer. Using an additive noise model for the quantizer, a procedure is developed for synthesizing a predistortion filter ( H_1 ), a reconstruction filter ( H_2 ), and a feedback filter (F) for this system so as to minimize a quantity representing the subjective effects of over-all system errors. The feedback filter F is assumed to be a tapped delay line, whose tap weights are obtained through a rapidly converging iterative procedure on an IBM 7090 automatic computer. Explicit formulas are derived for the amplitude responses of the optimal H_1 and H_2 filters. The system functions for H_1 and H_2 are obtained through a least squares approximation program on the IBM 7090 computer. Based upon these system functions, passive, lumped parameter predistortion and reconstruction filters are designed.

43 citations


Journal ArticleDOI
TL;DR: In this paper, a realizability theory for n-ports having immittance matrices through the use of Schwartz's theory of distributions is developed, which relates the passivity of the n-port to the positive reality of the immittance matrix.
Abstract: This paper develops a realizability theory for n -ports having immittance matrices through the use of Schwartz's theory of distributions [1]. The development given here differs from other such theories, which relate the passivity of the n -port to the positivereality of the immittance matrix, in that the use of distribution theory produces a number of simplifications and leads to a comparatively concise yet rigorous realizability theory. This theory is based on but two postulates: 1) The n -port has a convolution representation; 2) The n -port is passive. Taken together, they are entirely equivalent to the properties of single-valuedness, linearity, time-invariance, continuity, passivity and causality. These two postulates are also necessary and sufficient for the immittance matrix of the n -port to exist and be positive-real. The last statement is the main conclusion of this paper. The concept of an n -port is extended here in that its driving and responding port variables may now be distributions as well as ordinary functions, this extension being made in a rigorous way. Also, a representation for positive-real matrices that is due to Youla [5] is exploited to obtain an explicit time-domain representation for passive n -ports having convolutions representations; this representation is shown to encompass the 1-port representations obtained by Konig and Meixner [4].

43 citations


Journal ArticleDOI
TL;DR: In this paper, a passive driving point impedance can be built from RL or RC elements to vary in magnitude nearly as \omega^k and to have a nearly constant angle at k\pi/2 over an arbitrarily wide frequency range, |k| \leq 1.
Abstract: A passive driving point impedance can be built from RL or RC elements to vary in magnitude nearly as \omega^k and to have a nearly constant angle at k\pi/2 over an arbitrarily wide frequency range, |k| \leq 1 . Except at the extreme ends, the successive positions of the network poles (along the negative frequency axis) are taken in the ratio \rho , in which \rho in the range 6 to 25 determines an approximation error in the range 1 per cent to 10 per cent. The zeros of an arbitrarily wide-band network lie between poles, in the ratio \rho^k from a pole. A series string of parallel RL or RC pairs can be used to realize the impedance, according to whether k is positive or negative. The R/L or 1/RC of successive pairs are in the ratio \rho , and the resistors of successive pairs are in the ratio \rho^k . One pair "at" each band edge, the "corrector" or "compensation" impedance, is specified by different ratios, so as to account for band-edge effects. An experimental admittance constructed with five capacitors and five resistors approximated an \omega^{1/2} admittance at a constant 45° angle to within the measurement accuracy of \pm 1 per cent in magnitude and \pm 1° in phase over the frequency range 50 cps to 10,000 cps.

40 citations


Journal ArticleDOI

33 citations


Journal ArticleDOI
TL;DR: In this paper, a special class of biquadratic impedance functions, called bridge networks, are defined, which are realizable by unbalanced bridge networks composed of these five elements, one of the reactive elements being in the cross arm of the bridge.
Abstract: An important class of biquadratic impedance functions consists of those functions realizable as the driving-point impedance of a network consisting of three resistors, one inductor, and one capacitor. This paper presents a study of a special subclass of these, namely, those realizable by unbalanced bridge networks composed of these five elements, one of the reactive elements being in the cross arm of the bridge. Such a network will, under suitable conditions, realize certain biquadratic impedance functions not obtainable by other networks composed of the same numbers of elements. Specific formulas are given for the synthesis of such bridge networks, together with a statement of the exact conditions upon the coefficients of the biquadratic impedance function for the physical realizability of such bridge networks.

32 citations


Journal ArticleDOI
TL;DR: In this article, the authors proved that a lumped-constant network is supposed to be excited by means of one or more sinusoidal sources with the same frequency, and obtained a multiterminal network including only reactive elements.
Abstract: The following two theorems are proved: Theorem I: A lumped-constant network is supposed to be excited by means of one or more sinusoidal sources with the same frequency. Here we take out all resistive elements and voltage sources from the network. Then we obtain a multiterminal network including only reactive elements. For this network, let n = number of terminal-pairs, E_k = voltage drop across the K -th terminal-pair. The mean value of reactive energy T stored in this network is given by T = \frac {1}{2j} \Sum_{k=1}^{n}(\bar{E}_k \frac{d}{d\omega} I_k + \bar{I}_k \frac{d}{d\omega} E_k) . Theorem II: Suppose that an n -terminal-pair reactance network terminated by resistances is driven by a sinusoidal source. Let E_0 = emf of generator, S = voltage reflection coefficient at driving terminal-pair, R_1 = inner resistance of generator, R_k = resistance terminating K -th terminal-pair, D_k = the ratio of E_0 to the voltage measured across the resistance R_k . Then the mean value of the reactive energy stored in the network is given by T = \frac{|E_0|^2}{4R_1} |S|^2 \frac{d}{d\omega} (-\arg S) + \Sum_{k=2}{n} \frac {|E_0|^2}{R_k |D_k|^2 } \frac {d}{d\omega} (\arg D_k) . Some additional remarks, especially on the special but rather practical forms derived from these two theorems, are described.

28 citations


Journal ArticleDOI
TL;DR: In this article, a synthesis procedure is developed to generate dc configurations of new (as well as existing) electronic bistable circuits using a controlled-resistance (conductance) model.
Abstract: In this report a synthesis procedure is developed to generate the dc configurations of new (as well as existing) electronic bistable circuits. Of particular interest are those semiconductor configurations employing three-terminal active devices which in themselves are not potentially bistable. To accomplish the above task, devices and/or electronic mechanisms are modeled in a unified manner using a controlled-resistance (conductance) model. In a systematic fashion, all possible combinations of two threeterminal device configurations are inspected and a drastic simplification to six basic configurations is made without loss of generality. Particular devices are next introduced and further eliminations are made. From the remaining possible bistable configurations, existing bistable circuits are generated together with at least two new circuits. Bistable operation of these two new circuits is confirmed by experiment.

26 citations




Journal ArticleDOI
TL;DR: A method is described for the (insertion loss) design of wide-band band-pass filters to exhibit arithmetically symmetrical characteristics to correct the truncation error by a compensating function.
Abstract: A method is described for the (insertion loss) design of wide-band band-pass filters to exhibit arithmetically symmetrical characteristics. The method consists of a periodic transformation of the frequency variable, truncation of the resulting infinite product in the characteristic function, and finally, correcting the truncation error by a compensating function. The last step involves a certain amount of numerical or graphical approximation, but the required accuracy is usually quite easy to satisfy by elementary methods. As a special case, the design of constant group delay band-pass filters is also described.



Journal ArticleDOI
TL;DR: In this article, it was shown that a positive real function containing a parameter n^2 \geq 0 in the form of a linear function can be realized as the input impedance of a non-bilateral passive two-port terminated in a loaded n: 1 ideal transformer.
Abstract: It is shown that a positive real function containing a parameter n^2 \geq 0 in the form of a linear function can be realized as the input impedance of a nonbilateral passive two-port terminated in a loaded n: 1 ideal transformer. The same impedance can also be synthesized by a pair of bilateral two-ports, each of which is terminated in a loaded n: 1 or 1 : n ideal transformer. The method of synthesis for the case where n^2 is a complex variable is also given. It is found that any two positive real functions can be realized as the open-circuit and the short-circuit driving-point impedances of a nonbilateral two-port or, under additional conditions, of a bilateral two-port.

Journal ArticleDOI
TL;DR: In this article, a general large-signal analysis for frequency multiplication with abrupt-junction varactors is presented, where a Fourier-series representation of the current, the nonlinear elastance and the voltage is used to obtain exact closed-form solutions.
Abstract: This paper presents a general large-signal analysis for frequency multiplication with "lossy" abrupt-junction varactors. A Fourier-series representation of the current, the nonlinear elastance and the voltage is used to obtain exact closed-form solutions. Lossless coupling networks are considered in the theory so that the performance limits obtained will be fundamental to the varactor itself. Additional circuit losses can be added quite simply to find the expected performance in a practical case. Idler currents (currents flowing at frequencies other than the input and output frequencies) are shown to be necessary for multiplication by integers greater than two with abrupt-junction varactors. The effects of these currents are included in the general theory and a particular case, the tripler, is completely solved to demonstrate the procedures involved and to show the performance limits set by varactor and idler losses. Graphs which show the comparative theoretical performance of several multipliers are presented.

Journal ArticleDOI
TL;DR: In this paper, a set of conditions that guarantee stability of a single nonlinear element in an arbitrary linear, time-invariant circuit is presented. But the stability criterion is not applicable for physical circuits containing nonlinear elements, since there are bounded inputs that can burn out the nonlinear component.
Abstract: In a mixer, modulator or parametric amplifier the quiescent state (no signal) is a driven state, for the local oscillator, carrier, or pump is always on. Thus asymptotic stability in the sense used by control engineers is not applicable. The usual linear circuit stability criterion-every bounded input gives a bounded output-is also unsatisfactory for physical circuits containing nonlinear elements because we know that there are bounded inputs that can burn out the nonlinear element. Consequently this paper begins with the stability criteria: 1) operation is always within the allowable dynamic range of the nonlinear element; 2) a periodic steady state with the same period as the pump (LO or Carrier) is approached asymptotically. The class of circuits discussed consists of a single nonlinear element in an arbitrary linear, time-invariant circuit. For this class a set of conditions that guarantees stability is derived. Special emphasis is placed on circuits where the nonlinear element is reactive because these elements present additional mathematical problems. An example is given to show the applicability of the conditions to a specific circuit.

Journal ArticleDOI
TL;DR: In this article, it was shown that the bicubic impedance inherent in a five-element minimum-resistance bridge network automatically reduces to a biquadratic function under certain conditions.
Abstract: One form of the five-element minimum-resistance bridge network consists of equal resistors in one pair of opposite side-arms of a bridge structure, equal inductors in the other pair of opposite side-arms, and a capacitor in the cross-arm. This gives a biquadratic impedance, since, by virtue of the equal impedances in opposite cross-arms, the bicubic impedance inherent in such a network automatically reduces to a biquadratic function. It is shown in this paper that, if such a network is generalized to the extent of having opposite elements in the bridge of unequal magnitude, but still of the same kind, the impedance will still reduce to a biquadratic function under certain conditions. These conditions are determined explicitly, together with formulas for the synthesis of such a network.



Journal ArticleDOI
TL;DR: In this paper, the stability of linear time varying conductance-capacitance networks is studied and several sufficient conditions for their stability are given, in particular, instability can occur only if both the G matrix and the C matrix are time varying.
Abstract: This paper studies the stability of linear time varying conductance-capacitance networks. Several sets of sufficient conditions for their stability are given. In particular, instability can occur only if both the G matrix and the C matrix are time varying. In the limit of very large pump frequencies, the stability of periodic piecewise constant networks is determined by a simple relation. The design of unstable G-C networks is explained and illustrated by two examples. In the second example the q vector (whose components are sums of charges on condensers in certain cut sets) has components that behave like sine waves modulated by increasing exponentials.

Journal ArticleDOI
TL;DR: In this paper, it was shown that many of the frequency response concepts associated with time-invariant linear systems can be extended in a meaningful manner to time-varying, discrete-time linear systems.
Abstract: It is shown that many of the frequency response concepts associated with time-invariant linear systems can be extended in a meaningful manner to time-varying, discrete-time linear systems. Generalized frequency domain representations of the input and output are introduced along with a generalized frequency response or transfer function relating input and output. In addition, generalizations of bandwidth, gain bandwidth product, and Parseval's (Plancherel's) theorem are introduced. The key to these developments is the use of a decomposition of the system matrix based on its singular values.

Journal ArticleDOI
TL;DR: This paper is envisaged as the first of a series of three papers dealing with binary random processes and their application in the analysis of simple filters containing a randomly switched parameter.
Abstract: When a binary random process is sampled by an independent random pulse process a new binary process is generated. Statistical properties of this new binary process are investigated in this paper. Two methods of sampling are considered, according as an even or odd number of zeros of the binary process being sampled occur between successive sampling pulses. When the binary process is one in which the number of zeros in a given time interval obeys the Poisson distribution, and the time intervals between successive sampling pulses are independent, then the time intervals between successive zeros of the output binary process are also statistically independent, in which case all statistical properties of the output process are obtained. By iteration of this sampling procedure it is shown that a whole class of binary random processes, all having statistically independent intervals, is made accessible. The autocorrelation function of the output binary process is obtained in the case where an arbitrary binary process is sampled by a pulse process having independent intervals. The mean rate of the output process is discussed when the sampling intervals are not independent. Four special cases are considered as examples. Finally a brief description of an experimental sampling device and some results obtained with it, is given. This paper is envisaged as the first of a series of three papers dealing with binary random processes and their application in the analysis of simple filters containing a randomly switched parameter.

Journal ArticleDOI
TL;DR: In this paper, the negative conductance is distributed along a quarter wave transmission line rather than lumped at the terminals to determine the oscillation frequency and power output of a tunnel diode oscillator.
Abstract: The tunnel diode oscillator in which the negative conductance is distributed along a quarter wave transmission line rather than lumped at the terminals is analyzed to determine the oscillation frequency and power output. The analysis assumes a parabolic variation of negative conductance with bias voltage and an operating frequency high enough so the equivalent linearization technique of Kryloff and Bogoliuboff can be applied. The analysis indicates that the distributed oscillator should give 2/3 the power at \pi/2 times the frequency and at 2 times the load resistance of a lumped oscillator with the same total inductance capacitance and negative conductance. Series parasitic resistance is shown primarily to decrease the output power while series parasitic inductance and shunt capacitance of the transmission line primarily decrease the output frequency. Measurements of output frequency on experimental oscillators are in quantitative agreement with the analysis while measurements of output power are in qualitative agreement.