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I I v -I L ----_ -_ _ _ 2 2 I D E A L VOLTAOE AW.FlER Fig. 1. RC active filter with ideal voltage amplifier.The choice of D(s) may be so made that the pole sensitivity due to change in the gain of the voltage amplifier is minimum. Considering a secondorder transfer function, letHswhere the poles s1 and s: are at -r k j x . The H may be assumed equal to unity without loss of generality so thatFor this second-order transfer function, let D(s) be of first order having a real negative root. Therefore,Then.In terms of the RC admittances,. (9)For realizing yl(s) and y2(s), K has been assumed equal to unity.minimized.The sensitivity of T(s) with respect to K may now be calculated [ 2 ] and =- K x b 2Thus, the real and imaginary parts of the sensitivity may be separated as sq. = ~ 2 K p 2 -2pr + r2 + x' ( K + P For stability of bandwidth, the real part of the root sensitivity should be made minimum by a suitable choice of p . Differentiating Sqr with respect to p and equating to zero, we obtain the conditionSince p is real and positive,as for a narrow-band filter, r << x . Similarly, for the stability of the center frequency, the imaginary part of the root sensitivity can be minimized This leads to the same condition, i.e.,Substituting this value of p into (13), the root sensitivity for a narrow-band filter with K = 1 is obtained asTo achieve the stabilization of center frequency and bandwidth, the foregoing process of minimizing the root sensitivity can be adopted for the synthesis of an active RC filter employing a voltage amplifier. Hakim [4] has shown a different technique to obtain a prescribed pole sensitivity by realizing a conjugate complex phantom zero using a control parameter K which is not the gain of the amplifier but is some function of the gain of the amplifier. The freedom to prescribe the pole sensitivity is also overshadowed [3] by the inconvenient structures resulting.The Horowitz decomposition [SI minimizes sensitivity but this minimization occurs only for certain structures, basically Linvill configurations. Therefore, the Horowitz technique is not general [3] for minimizing the pole sensitivity of different active network configurations. The technique presented here is general and the pole sensitivity can be calculated and minimized with respect to any parameter of the realized network. This technique can also be used to obtain the prescribed pole sensitivity for other structures.The method is applicable to low-pass and high-pass filters as well. REFERENCES[I] S. S. Hakim, "RC active filters using an amplifier as the active element," Proc. Inst.[2] P. J. McVey, "Sensitivity in some simple RC active network," Proc. Inst. Elec. Eng., [31 R. W. Newcomb, A c h e Integrured Circuit Synthesis.Englewood Cliffs, N. J.:[4] S. S. Hakim, "Synthesis of RC active filters with prescribed pole sensitivity," Proc.[SI 1. M. Horowitz "Optimization of negative-impedance conversion methods of active

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Laplacian operators used in the literature for digital image processing are not rotationally invariant. We examine the anisotropy of 3 x 3 Laplacian operators for images quantized in square pixels, and find the operator which has the minimum overall anisotropy.

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Abstract. An exact solution to the Laplace equation is derived for the distribution of electric potential within a long cylinder carrying a circular constriction along its axis. The expression obtained for the potential distribution is reduced to a form which may be readily evaluated and is highly accurate for a ratio of constriction radius to cylinder radius approaching unity. Exact expressions both for the electric current density within the constriction and for the spreading resistance (i.e., the increase in resistance of the cylinder due to constriction of current flow lines) are also obtained.

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Abstract.. ,,9...A.WVe-descrftw a control structure for building an Image Understanding System. This system can deal with objects with diverse appearances when consistent spatial relations exist between objects. By accumulating consistent predictions originated from existing instances, our system can dynamically reason about what to do in order to construct interpretations of the image:f n nis paper, we -have discussed parts of the proposed system -the representation of spatial knowledge, the accumulation of evi. deuce, the focus of attention mechanism, and the integration of constraints for top. down control.