1FIGURE 1. Two-Pole Low-Pass Filter Using UAF42.NOTE: A UAF42 and two external resistors make a unity-gain, two-pole, 1.25dB rippleChebyshev low-pass filter. With the resistor values shown, cutoff frequency is 10kHz.Although active filters are vital in modern electronics, theirdesign and verification can be tedious and time consuming.To aid in the design of active filters, Burr-Brown provides aseries of FilterPro™ computer-aided design programs. Us-ing the FILTER42 program and the UAF42 it is easy todesign and implement all kinds of active filters. The UAF42is a monolithic IC which contains the op amps, matchedresistors, and precision capacitors needed for a state-variablefilter pole-pair. A fourth, uncommitted precision op amp isalso included on the die.Filters implemented with the UAF42 are time-continuous,free from the switching noise and aliasing problems ofswitched-capacitor filters. Other advantages of the state-variable topology include low sensitivity of filter parametersto external component values and simultaneous low-pass,high-pass, and band-pass outputs. Simple two-pole filterscan be made with a UAF42 and two external resistors—seeFigure 1.The DOS-compatible program guides you through the de-sign process and automatically calculates component values.Low-pass, high-pass, band-pass, and band-reject (or notch)filters can be designed.Active filters are designed to approximate an ideal filterresponse. For example, an ideal low-pass filter completelyeliminates signals above the cutoff frequency (in the stop-band), and perfectly passes signals below it (in the pass-band). In real filters, various trade-offs are made in anattempt to approximate the ideal. Some filter types areoptimized for gain flatness in the pass-band, some trade-offgain variation or ripple in the pass-band for a steeper rate ofattenuation between the pass-band and stop-band (in thetransition-band), still others trade-off both flatness and rateof roll-off in favor of pulse-response fidelity. FILTER42supports the three most commonly used all-pole filter types:Butterworth, Chebyshev, and Bessel. The less familiar In-verse Chebyshev is also supported. If a two-pole band-passor notch filter is selected, the program defaults to a resonant-circuit response.Butterworth (maximally flat magnitude). This filter has theflattest possible pass-band magnitude response. Attenuationis –3dB at the design cutoff frequency. Attenuation beyondthe cutoff frequency is a moderately steep –20dB/decade/pole. The pulse response of the Butterworth filter has mod-erate overshoot and ringing.Chebyshev (equal ripple magnitude). (Other transliterationsof the Russian Heby]ov are Tschebychev, Tschebyscheffor Tchevysheff). This filter response has steeper initial rateof attenuation beyond the cutoff frequency than Butterworth.A1R250kΩA2A3R450kΩUAF4211R150kΩRF115.8kΩRF215.8kΩC11000pFC21000pF13 8 7 142VINR350kΩVO1FILTER DESIGN PROGRAM FORTHE UAF42 UNIVERSAL ACTIVE FILTERBy Johnnie Molina and R. Mark Stitt (602) 746-7592APPLICATION BULLETIN®Mailing Address: PO Box 11400 • Tucson, AZ 85734 • Street Address: 6730 S. Tucson Blvd. • Tucson, AZ 85706Tel: (602) 746-1111 • Twx: 910-952-111 • Telex: 066-6491 • FAX (602) 889-1510 • Immediate Product Info: (800) 548-6132©1991 Burr-Brown Corporation AB-035C Printed in U.S.A. July, 1993SBFA0022This advantage comes at the penalty of amplitude variation(ripple) in the pass-band. Unlike Butterworth and Besselresponses, which have 3dB attenuation at the cutoff fre-quency, Chebyshev cutoff frequency is defined as the fre-quency at which the response falls below the ripple band.For even-order filters, all ripple is above the dc-normalizedpassband gain response, so cutoff is at 0dB (see Figure 2A).For odd-order filters, all ripple is below the dc-normalizedpassband gain response, so cutoff is at –(ripple) dB (seeFigure 2B). For a given number of poles, a steeper cutoff canbe achieved by allowing more pass-band ripple. TheChebyshev has more ringing in its pulse response than theButterworth—especially for high-ripple designs.Inverse Chebyshev (equal minima of attenuation in the stopband). As its name implies, this filter type is cousin to theChebyshev. The difference is that the ripple of the InverseChebyshev filter is confined to the stop-band. This filter typehas a steep rate of roll-off and a flat magnitude response inthe pass-band. Cutoff of the Inverse Chebyshev is defined asthe frequency where the response first enters the specifiedstop-band—see Figure 3. Step response of the InverseChebyshev is similar to the Butterworth.Bessel (maximally flat time delay), also called Thomson.Due to its linear phase response, this filter has excellentpulse response (minimal overshoot and ringing). For a givennumber of poles, its magnitude response is not as flat, nor isits initial rate of attenuation beyond the –3dB cutoff fre-quency as steep as the Butterworth. It takes a higher-orderBessel filter to give a magnitude response similar to a givenButterworth filter, but the pulse response fidelity of theBessel filter may make the added complexity worthwhile.Tuned Circuit (resonant or tuned-circuit response). If atwo-pole band-pass or band-reject (notch) filter is selected,the program defaults to a tuned circuit response. When band-pass response is selected, the filter design approximates theresponse of a series-connected LC circuit as shown in Figure4A. When a two-pole band-reject (notch) response is se-lected, filter design approximates the response of a parallel-connected LC circuit as shown in Figure 4B.CIRCUIT IMPLEMENTATIONIn general, filters designed by this program are implementedwith cascaded filter subcircuits. Subcircuits either have atwo-pole (complex pole-pair) response or a single real-poleresponse. The program automatically selects the subcircuitsrequired based on function and performance. A programoption allows you to override the automatic topology selec-tion routine to specify either an inverting or noninvertingpole-pair configuration.FIGURE 3. Response vs Frequency for 5-pole, –60dBStop-Band, Inverse Chebyshev Low-Pass FilterShowing Cutoff at –60dB.FILTER RESPONSE vs FREQUENCYNormalized Frequencyf /100Cf /10Cf C10f C+100–10–20–30–40–50Filter Response (dB)5-Pole Chebyshev3dB RippleRippleFILTER RESPONSE vs FREQUENCYNormalized Frequencyf /100Cf /10Cf