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Circuit Theory, IEEE Transactions on

Issue 2 • Date March 1973

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Displaying Results 1 - 25 of 27
  • On poles and zeros of linear systems

    Page(s): 93 - 101
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    The problem of determining the poles and zeros of a linear system is considered. Also pointed out is that this problem is mathematically equivalent to the generalized eigenvalue problem of the formlambda Ax =Bx, which may be solved by means of some wellestablished numerical techniques. Two practical and reliable algorithms are presented. The first algorithm is more general than the second and can be effectively used to obtain the poles and zeros of a linear system even without knowing its state-space representation. The second algorithm assumes that the state-space equations of the system are known and takes full advantage of their special form. Both algorithms also offer considerable savings in computational effort when applied to multiple-input multiple-output systems. Several examples which illustrate the proposed methods and their computational characteristics are included. View full abstract»

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  • Active all-pass networks with constant resistance

    Page(s): 177 - 179
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    Two well-known active all-pass networks can be arranged to give a constant-resistive input impedance at one of their ports merely by making two resistance values equal. Sensitivity to termination errors is thus reduced with no sacrifice in the basic properties of the network. View full abstract»

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  • Relaxive One-Ports

    Page(s): 139 - 142
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    The impulse response of any finite lumped RC oneport that acts like a capacitor as frequency tends to infinity is completely monotonic. This property can be used to define a more general type of one-port, which we call "relaxive" one-ports. Their behavior is typical for various infinite and distributed RC networks. Characteristic representations for such one-ports in both the time and frequency domains are given, and a number of properties are established. View full abstract»

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  • An overshoot minimization technique for low-pass filters

    Page(s): 158 - 161
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    A method to reduce the overshoot of the step response of a low-pass filter by including in that response a constant times its second derivative is considered. A technique to determine the value of the constant that minimizes overshoot is presented and applied to four conventional filters. Results of the modification procedure are presented. View full abstract»

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  • An optimal property of the impulse invariant method

    Page(s): 173 - 174
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    This paper proves a new min-max optimum property of the impulse invariant method. In proving this, a method of digital filter design for band-limited inputs is also given. The design is carried out in the time domain. View full abstract»

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  • Minimal realization of biquadratic RC-transfer function

    Page(s): 144 - 147
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    The problem of minimal realization of a biquadratic transfer function possessing a pair of complex zeros in the left-half complex plane with maximum gain constant posed earlier by Lin and Siskind has been attempted. For the solution of this problem, a systematic synthesis procedure has been adopted and a relevant realizability theorem has been stated and proved. It has been possible always to realize the theoretical maximum value of gain constant. Furthermore, several examples show that the method requires fewer elements in comparison with other well-known methods. View full abstract»

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  • On the properties of continuants and sensitivity computations

    Page(s): 167 - 169
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    Properties of continuants under differentiation are investigated and closed-form formulas are obtained for the differentiation of the ratio of two continuants with respect to an independent parameter. These results are applied to the sensitivity analysis of ladder-type as well as certain nonladder-type structures. View full abstract»

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  • Roundoff noise and attenuation sensitivity in digital filters with fixed-point arithmetic

    Page(s): 174 - 175
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    A general expression is established which relates the output roundoff noise generated by a fixed-point multiplier in a digital filter to the sensitivity of the filter attenuation with respect to the corresponding multiplier coefficient. It confirms that filters with low sensitivity of the attenuation also produce less roundoff noise. View full abstract»

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  • Synthesis of nonoriented 2n-terminal communication nets with prescribed terminal capacity matrices of two-port flows

    Page(s): 107 - 113
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    The realization of nonoriented communication nets satisfying requirements of two commodities is investigated in this paper. A necessary condition for a requirement matrix to be a terminal capacity matrix of a communication net is found. A method of synthesizing a2n-terminal net with the use of a special configuration is presented. The results based on graph theory are more convenient than those of linear programming. Whenever a realization is obtained, it is an optimum realization. The procedures which convert a2n-terminal net into a2(n+ 1)-terminal net are also discussed. View full abstract»

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  • Explicit formula for elements in ideal pulse compression transmission line networks

    Page(s): 150 - 153
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    The explicit formulaZ_m =m(m +1)/2is proved for the characteristic impedances of a cascade ofntransmission lines whose open-circuited voltage transfer function is optimally designed to compress a time-limited signal by the factorn+1. In the proof, use is made of the relationship between the synthesis procedure and the generation of sequences of polynomials orthogonal on the unit circle through a recurrence formula. Furthermore, it is shown that the impedance variation in the resulting realization is very close to the global minima for these ideal pulse compression networks with the additional desirable feature of a monotonic line realization. View full abstract»

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  • The reactive-active filters

    Page(s): 113 - 119
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    A synthesis procedure is proposed for designing RC active filters containing grounded gyrators and negative impedance convertors. Under suitable hypotheses, the sensitivity to variations of the component values of these filters is shown to be equivalent in the passband to that of traditional reactive-passive filters. Moreover, an approximate formula is derived under the same hypotheses for calculating the output noise power in the passband. Measured results of a prototype are included. View full abstract»

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  • Synthesis of dispersive networks for pulse compression using iterative technique

    Page(s): 147 - 150
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    A method is presented for automatic computation of transfer functions approximating to a quadratic phase characteristic in an equiripple manner for any prescribed minimum phase error. The program is based on a recently introduced method for the approximation of a linear phase characteristic in which only linear equations are involved. The characterization of the best nonlinear Chebyshev approximation of an arbitrary phase characteristic is discussed and it is shown that the necessary and sufficient conditions are fulfilled for the resulting solution to be unique and to represent the best Chebyshev approximation of a quadratic phase characteristic. By suitable modification the procedure described can also be used for determining the equiripple approximation of a linear slope group delay characteristic. View full abstract»

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  • Planarization by transformation

    Page(s): 169 - 171
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    A new approach to star-polygon transformations is introduced. For star-connectedR-networks and for a certain class of polygon-connectedR-networks the "terminal value" is defined. This concept allows for an elegant derivation of the necessary and sufficient conditions for the existence of a polygon-into-star transformation. The related formulas appear to be simple and easy to remember. More important, the terminal value turns out to be a useful tool in the search for planar equivalents and in the recognition of transformable polygon structures. Simplicity is the only reason for the restriction to resistance networks. The study of the general RLC case does not bring out any new aspects. View full abstract»

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  • Distributed RC impedances of constant phase

    Page(s): 153 - 154
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    Exact realizations of input impedances with substantially frequency-independent phase angles over a finite frequency range are given in the form of linear distributed RC structures. The theory of these networks is outlined and some results concerning their design and performance are given. View full abstract»

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  • Complementary transformation of feedback systems

    Page(s): 137 - 139
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    A transformation denoted by complementary transformation is developed, which maps a certain class of polynomials given in linear decomposition onto itself without changing the roots of the polynomials. This transformation applied on the characteristic equation of systems with one amplifier and one feedback network results in equivalent systems having the same relation between the eigenfrequencies and the network elements as the original systems. View full abstract»

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  • On the design of gradient algorithms for digitally implemented adaptive filters

    Page(s): 125 - 136
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    The effect of digital implementation on the gradient (steepest descent) algorithm commonly used in the mean-square adaptive equalization of pulse-amplitude modulated data signals is considered. It is shown that digitally implemented adaptive gradient algorithms can exhibit effects which are significantly different from those encountered in analog (infinite precision) algorithms. This is illustrated by considering the often quoted result of stochastic approximation that to achieve the optimum rate of convergence in an adaptive algorithm the step size should be proportional to1/n, wherenis the number of iterations. On closer examination one finds that this result applies only whennis large and is relevant only for analog algorithms. It is shown that as the number of iterations becomes large one should not continually decrease the step size in a digital gradient algorithm. This result is a manifestation of the quantization inherent in any digitally implemented system. A surprising result is that these effects produce a digital residual mean-square error that is minimized by making the step size as large as possible. Since the analog residual error is minimized by taking small step sizes, the optimum step-size sequence reflects a compromise between these competing goals. The performance of a time-varying gain sequence suggested by stochastic approximation is contrasted with the performance of a constant step-size sequence. It is shown that in a digital environment the latter sequence is capable of attaining a smaller residual error. View full abstract»

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  • Spectral modes of the generalized transform

    Page(s): 164 - 165
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    Spectral modes for the generalized transform are developed. These spectra are invariant to cyclic shift of the input sequence and possess sequency resolution in their squared terms. They cannot, however, be called energy spectra as there are cross terms, some of which are negative. View full abstract»

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  • Filters approximating ideal amplitude and arbitrary phase characteristics

    Page(s): 120 - 124
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    The closed-form solution is derived for the scattering transfer functionS_{12}(p)of a resistively terminated lossless reciprocal two-port prototype network of degree2nwhich satisfies the following constraints:|S_{12}(jomega) | leq 1|S_{12}({pm}j{omega}_i) | = 1 , i = 1 rightarrow narg S_{12}({pm}j{omega}_i) = pm psi({omega}_i), i = 1 rightarrow nwhere theomega_iare arbitrary andpsi(omega)is any odd function. The solution is obtained in terms of the arbitrary phase polynomials of the first and second kinds, which are capable of being generated through simple recurrence formulas. View full abstract»

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  • An approximation method for time domain synthesis of linear networks

    Page(s): 142 - 144
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    Time domain synthesis of linear networks requires approximation of functions with a finite sum of weighted exponentials. In this paper an error function, obtained by orthonormal filtering, suitable to numeric optimization, is evaluated. The error function is the integrated squared difference between the obtained function and the desired one. The procedure can be used to form an optimum set of basis exponentials to an ensemble of functions. Finally, the procedure is illustrated with some simple examples. View full abstract»

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  • A note on the transition (rise) time versus line length in coaxial cables

    Page(s): 165 - 167
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    A tutorial discussion is given on the relation between the shape of the transition (rise) time versus length curve and that of the frequency domain attenuation. An analysis is developed in terms of hypothetical cable attenuation responses having a frequencyfdependence off^m, wheremis a constant0 <m < 1. It is shown that if thef^mlaw prevails, then the transition time depends on the lengthlasl^{1/m}. Practical applications are made toRG 58C/U, RG 59B/U, andRG 63B/U. View full abstract»

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  • Electrical noise in low-pass FDNR filters

    Page(s): 154 - 158
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    The electrical noise performance of generalized impedance converter (GIC) low-pass ladder structures is derived. The concept of frequency-dependent negative-resistance (FDNR) elements has allowed low-sensitivity high-order low-pass ladder structures to be realized directly from the corresponding LC prototype. The electrical noise appearing at the output of the low-pass FDNR realization is derived for the equiterminated low-pass Butterworth realization, and it is shown that the output noise power spectral density may be obtained from a suitable noise model of the GIC. Experimental verification of the output noise spectral density is given. View full abstract»

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  • A numerical algorithm to design multivariable low-pass equiripple filters

    Page(s): 161 - 164
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    The designs of low-pass equiripple filters employing lumped, as well as distributed, elements are obtained by numerical methods. The number of ripples is restricted to be equal to the number of elements in the filter. The solution of a set of simultaneous nonlinear equations gives the element values directly. The technique has been used to design a wide variety of filters of practical interests. View full abstract»

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  • On tuning the group delay of an active RC all-pass resonator

    Page(s): 172 - 173
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    A general expression is presented for the frequencyomega_0of the delay maximum of an all-pass resonator composed of an active bandpass resonator and a summing amplifier. This expression is a function of the resonant frequency and pole-q. Through an example using the multiple feedback bandpass resonator, a procedure is presented for aligning the delay response of the corresponding allpass circuit without monitoring delay. View full abstract»

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