JAMES W NILSSON SUSAN A RIEDEL ELECTRIC CIRCUITS

JAMES W. NILSSON & SUSAN A. RIEDEL ELECTRIC CIRCUITS EIGHTH EDITION

CHAPTER 15 ACTIVE FILTER CIRCUITS © 2008 Pearson Education

CONTENTS 15. 1 First-Order Low-Pass and High-Pass Filters 15. 2 Scaling 15. 3 Op Amp Bandpass and Bandreject Filters 15. 4 High Order Op Amp Filters 15. 5 Narrowband Bandpass and Bandreject Filters © 2008 Pearson Education

15. 1 First-Order Low-Pass and High-Pass Filters Ø Active filters consist of op amps, resistors, and capacitors. Ø They can be configured as low-pass, high- pass, bandpass, and bandreject filters. © 2008 Pearson Education

15. 1 First-Order Low-Pass and High-Pass Filters Ø They overcome many of the disadvantages associated with passive filters. © 2008 Pearson Education

15. 1 First-Order Low-Pass and High-Pass Filters A first-order low-pass filter © 2008 Pearson Education

15. 1 First-Order Low-Pass and High-Pass Filters A general op amp circuit © 2008 Pearson Education

15. 1 First-Order Low-Pass and High-Pass Filters A first-order high-pass filter © 2008 Pearson Education

15. 1 First-Order Low-Pass and High-Pass Filters ØA prototype low-pass filter has component values of R 1 = R 2 = 1Ω and C = 1 F, and it produces a unity passband gain and a cutoff frequency of 1 rad/s. © 2008 Pearson Education

15. 1 First-Order Low-Pass and High-Pass Filters ØThe prototype high-pass filter has same component values and also produces a unity passband gain and a cut-off frequency of 1 rad/s. © 2008 Pearson Education

15. 2 Scaling Ø Magnitude scaling can be used to alter component values without changing the frequency response of a circuit. © 2008 Pearson Education

15. 2 Scaling Ø For a magnitude scale factor of km, the scaled (primed) values of resistance, capacitance, and inductance are © 2008 Pearson Education

15. 2 Scaling Ø Frequency scaling can be used to shift the frequency response of a circuit to another frequency region without changing the overall shape of the frequency response. © 2008 Pearson Education

15. 2 Scaling For a frequency scale factor of kf , the scaled (primed) values of resistance, capacitance, and inductance are © 2008 Pearson Education

15. 2 Scaling Ø Components can be scaled in both magnitude and frequency, with the scaled (primed) component values given by © 2008 Pearson Education

15. 2 Scaling Ø The design of active low-pass and high- pass filters can begin with a prototype filter circuit. Ø Scaling can then be applied to shift the frequency response to the desired cutoff frequency, using component values that are commercially available. © 2008 Pearson Education

15. 3 Op Amp Bandpass and Bandreject Filters Constructing the Bode magnitude plot of a bandpass filter © 2008 Pearson Education

15. 3 Op Amp Bandpass and Bandreject Filters A cascaded op amp bandpass filter (a) The block diagram (b) The circuit © 2008 Pearson Education

15. 3 Op Amp Bandpass and Bandreject Filters Ø An active broadbandpass filter can be constructed using a cascade of a lowpass filter with the bandpass filter’s upper cutoff frequency, a high-pass filter with the bandpass filter’s lower cutoff frequency, and (optionally) an inverting amplifier gain stage to achieve nonunity gain in the passband. © 2008 Pearson Education

15. 3 Op Amp Bandpass and Bandreject Filters Ø Bandpass filters implemented in this fashion must be broadband filters (ω ( c 2 » ωc 1), so that the elements of the cascade can be specified independently of one another. © 2008 Pearson Education

15. 3 Op Amp Bandpass and Bandreject Filters Example: Designing a Broadband Bandpass Op Amp Filter. Ø Design a bandpass filter for a graphic equalizer to provide an amplification of 2 within the band of frequencies between 100 and 10, 000 Hz. Use 0. 2µF capacitors. © 2008 Pearson Education

15. 3 Op Amp Bandpass and Bandreject Filters Constructing the Bode magnitude plot of a bandreject filter © 2008 Pearson Education

15. 3 Op Amp Bandpass and Bandreject Filters Ø An active broadbandreject filter can be constructed using a parallel combination of a low-pass filter with the bandreject filter’s lower cutoff frequency and a high-pass filter with the bandreject filter’s upper cutoff frequency. © 2008 Pearson Education

15. 3 Op Amp Bandpass and Bandreject Filters Ø The outputs are then fed into a summing amplifier, which can produce nonunity gain in the passband. Ø Bandreject filters implemented in this way must be broadband filters (ω ( c 2 » ωc 1), so that the low-pass and high-pass filter circuits can be designed independently of one another. © 2008 Pearson Education

15. 3 Op Amp Bandpass and Bandreject Filters A parallel op amp bandreject filter (a) The block diagram (b) The circuit © 2008 Pearson Education

15. 4 Higher Order Op Amp Filters The bode magnitude plot of a cascade of identical prototype first-order filters © 2008 Pearson Education

15. 4 Higher Order Op Amp Filters Ø Higher order active filters have multiple poles in their transfer functions, resulting in a sharper transition from the passband to the stopband thus a more nearly ideal frequency response. © 2008 Pearson Education

15. 4 Higher Order Op Amp Filters A cascade of identical unity-gain low-pass filters. (a) The block diagram (b) The circuit © 2008 Pearson Education

15. 4 Higher Order Op Amp Filters Ø The transfer function of an nth–order Butterworth low-pass filter with a cutoff frequency of 1 rad/s can be determined from the equation: © 2008 Pearson Education

15. 4 Higher Order Op Amp Filters By ØFinding the roots of the denominator polynomial. ØAssigning the left-half plane roots to H(s). ØWriting the denominator of H(s) as a product of first- and second- order factors. © 2008 Pearson Education

15. 4 Higher Order Op Amp Filters Defining the transition region for a low-pass filter © 2008 Pearson Education

15. 5 Narrowband Bandpass and Bandreject Filters An active high-Q bandpass filter © 2008 Pearson Education

15. 5 Narrowband Bandpass and Bandreject Filters A high-Q active bandreject filter © 2008 Pearson Education

15. 5 Narrowband Bandpass and Bandreject Filters ØIf a high-Q, or narrowband, bandpass, or bandreject filter is needed, the cascade or parallel combination will not work. Instead, the circuits shown previously are used with the appropriate design equations. © 2008 Pearson Education

THE END © 2008 Pearson Education