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

2. 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

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

4. 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

5. 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

6. 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

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

8. 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

9. 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

10. 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

11. Filter Response
9/14/04
62Bchap9a

12. 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

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

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

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

16. 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