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

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

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

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

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

Sallen-Key Band-pass Filter

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.,.

Standard Second Order Filter Note: For your design, let

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

Sallen-Key Low-pass Filters

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

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.