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By Ken Budnick

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707/1)∗ 180/ pi = 45◦ . 1 APPROXIMATION LOSS FUNCTIONS Active filters use capacitors, resistors, and op-amps (in general, inductors are not used as they tend to be large at low frequencies and also radiate magnetic fields). They also require DC power supplies and have a frequency range limited by the quality of the operational amplifier used. , H($) = 1 . 1) This inversion turns an all-zero function into an all-pole transfer function. 2 r Bessel, r Butterworth, r Chebychev, and r Elliptical BUTTERWORTH APPROXIMATING FUNCTION A low-pass Butterworth approximation loss function, in magnitude squared form, is 2 2 A( j ω) = 1 + F( j ω) .

93 ≈ 3. 10: Third-order active filter Select the third-order normalized loss function A($) = ($ + 1)($2 + $ + 1) from the Butterworth tables. This is denormalized and transformed from a high-pass to a low-pass function by replacing $ with ω p /s . Since the passband attenuation is 3 dB, then ε = 1. 6000 +1 s A($)|$= 6000/s = A(s ) = 60002 6000 +1 . 38) The transfer function is H(s ) = 1 = A(s ) 1 6000 s +1 60002 s2 + 6000 s +1 = s3 (s + 6000)(s 2 + 6000s + 36 × 106 ) . 39) The first-order transfer function is E2 s s R s = = .

You may display both the pulse and its spectrum (time and frequency domain) simultaneously, by selecting Plot/Unsynchronize X-Axis from the Probe screen. Separate the two displayed book Mobk064 48 March 27, 2007 15:49 PSPICE FOR FILTERS AND TRANSMISSION LINES signals by pressing alt PP, and then apply ctrl X and ctrl V to a variable at the bottom. A decaying sine wave should be observed together with the 10 µs impulse. 3 FILTER AMPLITUDE RESPONSE The ABM Laplace part allows us to plot the frequency response for transfer functions derived from loss functions.

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