tailieunhanh - Electric Circuits, 9th Edition P62

Electric Circuits, 9th Edition P62. Designed for use in a one or two-semester Introductory Circuit Analysis or Circuit Theory Course taught in Electrical or Computer Engineering Departments. Electric Circuits 9/e is the most widely used introductory circuits textbook of the past 25 years. As this book has evolved over the years to meet the changing learning styles of students, importantly, the underlying teaching approaches and philosophies remain unchanged. | 586 Active Filter Circuits assessment problem Objective 3 Understand how to use cascaded first- and second-order Butterworth filters For the circuit in Fig. find values of R Answer fl R2 il. and R2 that yield a second-order prototype Butterworth high-pass filter. NOTE Also try Chapter Problems and . Narrowband Bandpass and Bandreject Filters The cascade and parallel component designs for synthesizing bandpass and bandreject filters from simpler low-pass and high-pass filters have the restriction that only broadband or low- 2 filters will result. The Q of course stands for quality factor. This limitation is due principally to the fact that the transfer functions for cascaded bandpass and parallel bandreject filters have discrete real poles. The synthesis techniques work best for cutoff frequencies that are widely separated and therefore yield the lowest quality factors. But the largest quality factor we can achieve with discrete real poles arises when the cutoff frequencies and thus the pole locations are the same. Consider the transfer function that results o c 5 5 Ct c S t c suc s2 2 ycs to2 ------y. S2 is 0 . H s Eq. is in the standard form of the transfer function of a bandpass filter and thus we can determine the bandwidth and center frequency directly ß 2a c ÍOp D . From Eqs. and and the definition of Q we see that o Mc _ 1 ß 2cac 2 Figure An active high-O bandpass filter. Thus with discrete real poles the highest quality bandpass filter or bandreject filter we can achieve has Q 1 2. To build active filters with high quality factor values we need an op amp circuit that can produce a transfer function with complex conjugate poles. Figure depicts one such circuit for us to analyze. At the inverting input of the op amp we sum the currents to get V -V F a yo T sC Ri Narrowband Bandpass and Bandreject Filters 587 Solving for K S 15-54 At the node labeled