Elec and Comp Tech 62B Circuits and Systems Chapter 9 Active Filters 9/14/04

Overview Basic filter responses Filter response characteristics Active low-pass filters Active high-pass filters Active band-pass filters Active band-stop filters Filter response measurements 9/14/04 62Bchap9a

Basic Filter Responses A low-pass filter passes frequencies up to certain frequency, then attenuates frequencies above that frequency. 9/14/04 62Bchap9a

Basic Filter Responses The cutoff or critical frequency, fc, defines the end of the passband, and is where the output has dropped –3 dB 70.7% of the voltage 50% of the power Also called the “half power” or “3 dB down” point Since the filter response is from DC to fc the bandwidth (BW) = fc. The attenuation slope is determined by the number of poles, or bypass circuits 9/14/04 62Bchap9a

Roll-off Rate A single pole (bypass circuit), such as a RC filter, rolls off at a -20 dB/decade (same as a -6 db/octave) rate 2 poles produce a -40 db/decade, 3 poles produce -60 db/decade, and so on. 9/14/04 62Bchap9a

Transition Region The transition region is the span of frequencies in between the passband and the constant-slope roll-off Cascading multiple passive filter networks produces a large and gradual transition region, an undesirable filter characteristic. Active filters allow for multiple poles with a smaller transition region 9/14/04 62Bchap9a

High-Pass Filters A high-pass filter attenuates frequencies below fc and passes frequencies above fc. 9/14/04 62Bchap9a

Band-Pass Filters A band-pass filter has two critical frequencies, fc1 and fc2 BW = fc2–fc1 The center frequency fo = fc1fc2 9/14/04 62Bchap9a

Band-Stop Filters A band-pass filter has two critical frequencies, fc1 and fc2 BW = fc2–fc1 The center frequency fo = fc1fc2 9/14/04 62Bchap9a

Filter Response Characteristics In active filters, tailoring the feedback to alter the transition region defines the response characteristic. The most common are Butterworth, Chebyshev, and Bessel 9/14/04 62Bchap9a

Filter Response 9/14/04 62Bchap9a

Damping Factor The damping factor of an active filter circuit determines the response characteristic. The correct damping factor for the desired response depends on the number of poles For a 2nd-order (2 poles) Butterworth filter, the damping factor is 1.414 DF=2–R1/R2 9/14/04 62Bchap9a

Sallen-Key Low-Pass Filter A basic building-block for 2nd-order filters is the Sallen-Key filter. 9/14/04 62Bchap9a

Sallen-Key Parameters For simplicity, make CA=CB and RA=RB. Then, fc=1/2πRC 9/14/04 62Bchap9a

Sallen-Key Parameters For Butterworth damping factor of 1.414, R1/R2=.586, so if R2=1kΩ, R1=586 Ω 9/14/04 62Bchap9a

3rd & 4th-Order Low-Pass Filter All R and C filter values are equal R1 through R4 damping values are taken from tables (pg. 478) 9/14/04 62Bchap9a