EE 311: Junior EE Lab Sallen-Key Filter Design

1. EE 311: Junior EE Lab Sallen-Key Filter Design J. Carroll 9/17/02

2. Background Theory • Filter applications include: • power supplies to attenuate undesirable ripple • audio circuits for bass and treble control • band limiting a signal before it is sampled • Four basic filter types: • high-pass • low-pass • band-pass • band-reject or notch

3. Background Theory • Filters fall in one of two categories: • Passive: consist of only passive elements • i.e., resistors, inductors and capacitors • Active: consist of passive and active devices • such as transistors or op-amps • can’t amplify output of passive filter to produce active filter • op-amps typically chosen over transistors • All things equal, active filters have responses equal to or better than conventional passive filters • reduced insertion loss • can amplify desired frequencies • simple design and ease of tuning • does not require the use of inductors

4. Band-pass Filter Performance • Center (Resonant) Frequency • frequency for maximum filter gain, the geometric mean of the two half-power frequencies • Lower and Upper Cutoff Frequencies • half-power frequencies are 3dB less than the gain at the center frequency • Maximum Gain, • ratio of to at the filter's center or resonant frequency, often expressed in dB • Bandwidth • difference between the upper and lower filter cutoff frequencies, closely related to the passband

5. Band-pass Filter Performance • Quality Factor • dimensionless figure of merit used to measure the selectivity of a filter expressed as ratio of center frequency to bandwidth

6. Sallen-Key Band-pass Filter

7. Equal Component Sallen-Key Filter In order to ensure stability of the filter, we must ensure that the poles of the transfer function lie in the left-half of the complex s-plane, or . Thus, we must ensure that the gain of the op-amp is less than 3, i.e., .

8. Standard Second Order Filter Note: For your design, let

9. Frequency Scaling • Frequency scaling is a method of changing a filter’s frequency of operation • This method is extremely useful once one has designed a filter with a satisfactory response (i.e., ) and then merely wants to change, for example, the center frequency • To increase the center frequency of a filter without affecting any of its other characteristics (i.e., ), we can simply divide all frequency determining capacitors or divide all frequency determining resistors by the desired scaling factor • As an example, to triple the center frequency, divide all capacitor values by 3 or divide all resistor values by 3

10. Sallen-Key Low-pass Filters

11. Pass all frequencies from zero up to the corner frequency, and blocks all frequencies above this value • In actual filters, there is a transition region between the passband and the stopband • The frequency response of the low-pass filter is not, however, as straightforward to analyze as that of the band-pass filter • For quality factors less than 0.5, the poles of the transfer function are real • For quality factors greater than 0.5, the poles are complex • For quality factors >0.707, the frequency response peaks above just beyond the corner frequency • This peak can be quite large for large quality factors • Quality factors =0.707 produces a maximally flat response, i.e., the sharpest fall-off near the corner without any peaks larger than Sallen-Key Low-pass Filters

12. Closing Remarks • Let’s quickly examine the Pre-lab questions • Make sure you work all of the problems, especially the PSpice problems • See the class website for various resources related to this lab, including PDF documents, M-files, filter design programs, etc.