NONINTEGER EXPONENTS IN ELECTRONIC-CIRCUITS .2. MEMORY EFFECTS IN THEFRACTAL IMMITTANCE

The transient behavior in the fractal admittance acting as a non-integ er-rank differential/integral operator, Y(s) is-proportional-to s(a) w ith -1 < a < 1 and a not-equal 0, is examined from the point of view o f memory effects by employing the distributed-relaxation-time model. T he internal state of the diode is found to be represented by the curre nt spectrum i (lambda, t) with respect to the carrier relaxation rate lambda, leading to a general formulation of the long-time-tail memory behavior characteristic of the operator. One-to-one correspondence is found among the input voltage in the past v(-t), the short-circuit cur rent i(sc)(t) and the initial current spectrum i (lambda, 0) within th e framework of the Laplace-type integral transformation and its invers e, assuring that each response retains in principle the entire informa tion on the corresponding input, such as the functional form, the magn itude, the onset time, and so forth. The current and voltage responses are exemplified for various single-pulse voltage inputs. The response s to the pulse-train inputs corresponding to different ASCII codes are found to be properly discriminated between one another, showing the p otentials of the present memory effects.