Robust Functional Testing for VLSI Cellular Neural Network Implementations [Transaction Briefs] - Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 44, NO. 2, FEBRUARY 1997 161 Fig. 5 illustrates that doubling the number of segments per unit distance to 1000/50 cm (while using a 150 V triangular pulse at the input) gives less attenuation, in support of the theory that as a transmission line is approached, solitons propagate without excessive attenuation. Fig. 6 shows that if the input amplitude goes to 300 V, while keeping the 100 ps transitions, two solitons result assuming 1000/50 cm, as noted in . This shows that it is important to employ appropriate inputs, and an ample number of segments per unit distance, more than suggested for simple edge sharpening in  or . V. CONCLUDING COMMENTS Simulations can have nonlinear inductance and can include frequency-dependent parameters using the above method. Computer advances in conjunction with a simple algorithm render the method quite accessible. Furthermore, it is possible to extend the method to nonuniform lines involving abrupt bends or encounters with other objects. APPENDIX A Differentiation equation s n F (s) = 1 0� d n dt n f(t)e �st dt (A1) where n is a positive integer, and F (s) is a Laplace transform of f(t). For example, p s can be expressed as s= p s where from Table I in the text (using � = �0.5) the inverse Laplace transform of 1=s0:5 is 1= p �t; (A1) readily shows that the transform of ps is 1=(2p�t1:5) which agrees with Table I using � = �1.5. REFERENCES  N. Seddon and E. Thornton, “A high-voltage, short risetime, pulse sharpener,” Rev. Sci. Instrum., vol. 59, no. 11, pp. 2497–2498, Nov. 1988.  C. R. Wilson, M. M. Turner, and P. W. Smith, “Pulse sharpening in a uniform LC ladder network containing nonlinear ferroelectric capacitors,” IEEE Trans.