DESIGN AND DEVELOPMENT OF MEDICAL ELECTRONIC ...

ACTIVE FILTERS 61we recommend that you try the two and three op-amp topologies that will allow you moreability to “tweak” the end result. In addition, a good way of designing well-behaved filters isto base them on one of the various active filter building blocks offered by analog IC vendors.For example, Burr-Brown (now part of Texas Instruments) offers the UAF42, a universalactive filter that can be configured for a wide range of low-pass, high-pass, and bandpassfilters. It implements filter functions through a state-variable topology with an invertingamplifier and two integrators. The integrators include on-chip 1000-pF capacitors trimmedto 0.5%. This solves the difficult problems of obtaining tight-tolerance low-loss capacitors.The UAF42 is available in 14-pin DIP and SOL-16 surface-mounted packages.Burr-Brown’s free DOS-compatible FilterPro program lets you design Butterworth,Chebyshev, and Bessel filters, enter the desired performance, and then obtain the passivevalues required. You can force the program to use the nearest 1% resistors, set some resistorvalues, enter realistic or measured capacitor values, and then plot the actual gain/phase versusfrequency performance. Similarly, Microchip’s Windows-based FilterLab lets you designSallen–Key or multiple-feedback low-pass filters with either Butterworth, Chebyshev, orBessel responses using their MCP60x family of single-supply op-amps.Maxim also offers a line of state-variable filter ICs, the MAX274 and MAX275. TheseICs have independent cascadable second-order sections that can each implement all-polebandpass or low-pass filter responses, such as Butterworth, Bessel, and Chebyshev, and isprogrammed by four external resistors. The MAX274 has four second-order sections, permittingeighth-order filters to be realized with center frequencies up to 150 kHz. TheMAX275 has two second-order sections, permitting fourth-order filters to be realized withcenter frequencies up to 300 kHz. Both filters operate from a single 5-V supply or fromdual 5-V supplies. A free DOS-based filter design program is available from Maxim tosupport the development of applications based on the MAX274 state-variable filter IC.State-variable filter realizations have the distinct advantage that they provide simultaneouslow-pass, bandpass, and high-pass outputs from the same filter circuit. In addition,the filter parameters are independent of each other. For example, the cutoff frequency ofthe active-feedback state-variable filter circuit of Figure 2.14 is given by1f C 2π(R3 )(C1)where R3 R4 and C1 C2. As shown in the ac-sweep PSpice simulation analysis ofFigure 2.15, this filter yields simultaneous low-pass and high-pass responses with a -3-dBcutoff frequency f C and a bandpass response centered at the same frequency. In this example,the resistor values selected for R4 and R6 give the filter a cutoff frequency of approximately50 Hz. The Butterworth response on a state-variable filter gives it a value Q -3 dB and anin-band gain of the bandpass filter equal to Q ( 0.707), making all curves cross at thesame point.Since the cutoff frequency of a state-variable filter depends on the value of two resistors(R3 and R4 in the prior example), it is relatively easy to design a tunable filter by substitutingthese resistors by two tracking variable resistors. The filter can also be made tohave a cutoff frequency that is proportional to a control voltage by using circuits that presenta variable resistance as a function of an input voltage.Although FETs and variable transconductance amplifiers can be used as voltagedependentresistors, better results are easier to achieve using analog multipliers in serieswith a resistor as the control elements. The circuit of Figure 2.16 shows how R3 and R4of the circuit of Figure 2.14 have been replaced by two Analog Devices AD633 precisionanalog multipliers. The transfer function of the AD633 is given byV out (x 1 x 2)(y 1 y 2 ) z10V