Electric Circuits, 9th Edition P61. 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. | 576 Active Filter Circuits Thus we can design a fourth-order low-pass filter with any arbitrary cutoff frequency by starting with a fourth-order cascade consisting of prototype low-pass filters and then scaling the components by kf tt t. to place the cutoff frequency at any value of desired. Note that we can build a higher order low-pass filter with a nonunity gain by adding an inverting amplifier circuit to the cascade. Example illustrates the design of a fourth-order low-pass filter with nonunity gain. Example Designing a Fourth-Order Low-Pass Op Amp Filter Design a fourth-order low-pass filter with a cutoff frequency of 500 Hz and a passband gain of 10. Use 1 xF capacitors. Sketch the Bode magnitude plot for this filter. Solution We begin our design with a cascade of four prototype low-pass filters. We have already used Eq. to calculate the cutoff frequency for the resulting fourth-order low-pass filter as rad s. A frequency scale factor of kf will scale the component values to give a 500 Hz cutoff frequency. A magnitude scale factor of ktJl permits the use of 1 xF capacitors. The scaled component values are thus R 0 C 1 xF. Finally add an inverting amplifier stage with a gain oiRf Ri 10. As usual we can arbitrarily select one of the two resistor values. Because we are already using fl resistors let R fl then Rf IQRi fl. The circuit for this cascaded the fourth-order low-pass filter is shown in Fig. . It has the transfer function x F 4 _s _ The Bode magnitude plot for this transfer function is sketched in Fig. . Figure The cascade circuit for the fourth-order low-pass filter designed in Example . Higher Order Op Amp Filters 577 Figure The Bode magnitude plot for the fourth-order low-pass filter designed in Example . By cascading identical low-pass filters we can increase the asymptotic slope in the transition and control the location of the .
