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

ACTIVE FILTER CIRCUITS 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 Active filters consist of op amps, resistors, and capacitors. 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 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 A prototype low-pass filter has component values of R1 = R2 = 1Ω and C = 1F, 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 The 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 Magnitude scaling can be used to alter component values without changing the frequency response of a circuit. © 2008 Pearson Education

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

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

15.2 Scaling The design of active low-pass and high-pass filters can begin with a prototype filter circuit. 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 The block diagram The circuit © 2008 Pearson Education

15.3 Op Amp Bandpass and Bandreject Filters An active broadband bandpass filter can be constructed using a cascade of a low-pass 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 Bandpass filters implemented in this fashion must be broadband filters (ωc2 » ωc1), 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. 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 An active broadband bandreject 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 The outputs are then fed into a summing amplifier, which can produce nonunity gain in the passband. Bandreject filters implemented in this way must be broadband filters (ωc2 » ωc1), 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 The block diagram 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 Higher order active filters have multiple poles in their transfer functions, resulting in a sharper transition from the passband to the stopband and 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. The block diagram The circuit © 2008 Pearson Education

15.4 Higher Order Op Amp Filters 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 Finding the roots of the denominator polynomial. Assigning the left-half plane roots to H(s). Writing 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 If 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