8/29/2019 Electronic Circuits and Devices EC4050 Active Filters M.Yuvaraj ACTIVE LOW-PASS FILTERS • Filters that use op-amps as the active element provide several advantages over passive filters (R, L, and C elements only). • The op-amp provides gain, so the signal is not attenuated as it passes through the filter. 1 8/29/2019 Single-Pole Filter • Single-Pole filter provides a roll-off of -20 dB/decade above the critical frequency • The critical frequency of the single-pole filter is fc = 1/(2πRC). • The op-amp in this filter is connected as a noninverting amplifier with the closed-loop voltage gain in the passband set by the values of R1 and R2. Sallen-Key Low-Pass Filter • The Sallen-Key is one of the most common configurations for a secondorder (two-pole) filter, also known as a VCVS (voltage-controlled voltage source) filter. • Notice that there are two low-pass RC circuits that provide a roll-off of -40 dB/decade above the critical frequency (assuming a Butterworth characteristic). • A unique feature of the Sallen-Key low-pass filter is the capacitor that provides feedback for shaping the response near the edge of the passband. • The critical frequency for the Sallen-Key filter is 2 8/29/2019 • The component values can be made equal so that RA = RB = R and CA = CB = C. • In this case, the expression for the critical frequency simplifies to • As in the single-pole filter, the op-amp in the second-order Sallen-Key filter acts as a noninverting amplifier with the negative feedback provided by resistors R1 and R2. • The damping factor is set by the values of R1 and R2, thus making the filter response either Butterworth, Chebyshev, or Bessel. • For example, the damping factor of 1.414 required for a second-order Butterworth response. Example • Determine the critical frequency of the Sallen-Key low-pass filter, and set the value of for an approximate Butterworth response 3 8/29/2019 Cascaded Low-Pass Filters ACTIVE HIGH-PASS FILTERS • Single-Pole Filter • A high-pass active filter with a -20 dB/decade roll-off. • The negative feedback circuit is the same as for the low-pass filters. 4 8/29/2019 The Sallen-Key High-Pass Filter • The components RA, CA, RB, and CB form the two-pole frequency-selective circuit. • Notice that the positions of the resistors and capacitors in the frequencyselective circuit are opposite to those in the low-pass configuration. • As with the other filters, the response characteristic can be optimized by proper selection of the feedback resistors, R1 and R2. Example • Choose values for the Sallen-Key high-pass filter to implement an equal-value second-order Butterworth response with a critical frequency of approximately 10 kHz. 5 8/29/2019 Cascading High-Pass Filters ACTIVE BAND-PASS FILTERS • band-pass filters pass all frequencies bounded by a lower-frequency limit and an upper-frequency limit and reject all others lying outside this specified band. • A band-pass response can be thought of as the overlapping of a lowfrequency response curve and a high-frequency response curve. 6 8/29/2019 Cascaded Low-Pass and High-Pass Filters • One way to implement a band-pass filter is a cascaded arrangement of a high-pass filter and a low-pass filter. • The critical frequency of each filter is chosen so that the response curves overlap sufficiently. • The critical frequency of the high-pass filter must be sufficiently lower than that of the low-pass stage. This filter is generally limited to wide bandwidth applications. • The lower frequency fc1 of the passband is the critical frequency of the high-pass filter. The upper frequency fc2 is the critical frequency of the low-pass filter. The center frequency of the passband is the geometric mean of fc1 and fc2. 7 8/29/2019 Multiple-Feedback Band-Pass Filter • The two feedback paths are through R2 and C1. • Components R1 and C1 provide the low-pass response, and R2 and C2 provide the high-pass response. • The maximum gain, A0, occurs at the center frequency Multiple-Feedback Band-Stop Filter • Notice that this configuration is similar to the band-pass except that R3 has been moved and R4 has been added. 8 8/29/2019 Reference • Electronics Principles by Albert Malvino and David J Bates • Electronic Devices by Thomas L Floyed • Microelectronic circuits by Adel S Sedra, Kenneth Carless Smith 2010, Oxford University Press 9
