Design Of Pascal Filters

In the design of electronic system, Butterworth filters and Chebyshev filtesr aretwo kinds of the most commonly used filters. They are simple in design andadjustable. In the passband, Butterworth filter is maximally flat, but its attenuation atthe stopband is slow compared to that of Chebyshev filter; on the other hand, theattenuation of Chebyshev filter is better than that of Butterworth filter in the stopband,but the Chebyshev filter has equiripple characteristic in its passband. Therefore,people have been trying to find a new approximation method, whose transfer functionis nearly maximally flat in the passband and its stopband's attenuation is close to thatof the Chebyshev filter attenuation characteristic. In this paper, a new type of Pascalfilter design method is suggested, and the simulation verification is given to improvethe method is resultful.The innovative points of this paper are followed:1. Based on the characteristics of Pascal polynomial, the method to derive theapproximation of the transfer function is introduced and the magnitude response issimulated. For the given order, simulation results show that the ripple in thepassband is much less than that of Chebyshev filter and the attenuation in thestopband is larger than that of Buterworth filter.2. The method to design active Pascal filter is demonstrated. The frequency responseof the designed filter is simulated using Spice, which gives the simulation results,and further verifies the characteristics of the Pascal filter.3. Based on the derived transfer function, the procedures of passive Pascal filterdesign is listed. An example of 5th order Pascal lowpass passive filter design ispresented. Finally, the normalized Pascal passive filters of 2th to 10th order aresynthesized. In this paper, the method of a new type of Pascal filter design isproposed, and problems in the Pascal active and passive filter design solved.