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Mini Tutorial MT-218 One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Tel: 781.329.4700 • Fax: 781.461.3113 • www.analog.com One could also adjust the output for maximum output, which also occurs at resonance, but this is usually not as precise, especially at lower values of Q where there is a less pronounced peak. Multiple Feedback Band-Pass Design Example by Hank Zumbahlen, Analog Devices, Inc. MULTIPLE FEEDBACK BAND-PASS DESIGN EQUATIONS IN THIS MINI TUTORIAL − H ω0 s A multiple feedback band-pass is designed in this mini tutorial, one in a series of mini tutorials describing discrete circuits for op amps. s + αω 0 s + ω 0 2 2 OUT C4 C3 R1 R2 Figure 2. VO = V IN R5 C3 R2 10423-001 IN 1 1 R1 C4 1 1 + + C3 + C4 R5 C3 C4 R1 R2 +s C3 C4 R5 −s OUT C4 10423-002 IN The multiple feedback topology is widely used as a band-pass filter because it offers a simple and reliable band-pass implementation, especially below a Q of 20 or so. The schematic of a multiple feedback band-pass filter is shown in Figure 1. R1 R5 s2 Design Flow Figure 1. Multiple Feedback Band-Pass Choose C3. In this example, a filter is designed with an arbitrarily chosen center frequency (F0) of 1 kHz and a Q of 10. The amplifier gain is arbitrarily set at 1 (0 dB). Note that this does not mean that the output will have a gain less than or equal to the input. In fact, there will be a gain of 10 (20 dB) due to the peaking of the Q of the filter function. Then k = 2 π F0 C3 C4 = C3 Using the design equations in the Multiple Feedback Band-Pass Design Equations section, one can calculate the appropriate component values. Note that the calculated component values most likely are not standard values. Select the closest standard values. While this causes some errors, it is typically within specifications. If not, tuning may be required. Tuning of the resonant frequency, F0, is possible by making R2 variable. The Q of the circuit (see MT-210) can be adjusted (with R5) as well, but this also changes F0. Tuning of F0 can be accomplished by monitoring the output of the filter with the horizontal channel of an oscilloscope, with the input to the filter connected to the vertical channel. The display is a Lissajous pattern. This pattern is an ellipse that collapses to a straight line at resonance, since the phase shift is 180°. R1 = 1 Hk R2 = 1 (2 Q − H ) k R5 = 2Q k When selecting the op amp, look for an amp with a gainbandwidth product sufficient to support the output. In this case, the F0 is 1 kHz. The peaking due to the filtering function is 20 dB. A 20 dB pad is added to this as a safety fact. Therefore, an op amp with at least 40 dB of open-loop gain at 1 kHz is needed. For this example, an AD711 is arbitrarily chosen. The open-loop gain of the AD711 is shown in Figure 3. The open-loop gain at 1 kHz is on the order of 65 dB, well over the requirement. Rev. 0 | Page 1 of 2 Mini Tutorial 80 60 60 40 40 20 20 10 0 –20 10 100 1k 100k 10k 1M –40 –20 10M –50 10 FREQUENCY (Hz) 100 1k 10k 100k 10k 100k FREQUENCY (Hz) Figure 5. Figure 3. Open-Loop Gain of the AD711 180 If the open-loop gain of the op amp is too low, a phenomenon known as Q multiplication takes place and the response of the filter is affected. The final design for the filter is shown in Figure 4. The standard values for the resistors have been substituted. Note that this circuit is shown in National Instrument’s Electronic Workbench. A version of this program can be downloaded from the Analog Devices website. In addition, a group of ready-entered circuits, including this filter, can be download from the same page. 90 PHASE (Degrees) MULTIPLE FEEDBACK BAND-PASS FILTER FINAL DESIGN 135 45 0 –45 –90 –135 –180 10 XBP1 100 1k FREQUENCY (Hz) IN – C1 R1 15.8kΩ 10nF 1% V3 + 1V p 1kHz – 0° Figure 6. OUT + – REFERENCES C2 10nF Jung, Walter G., editor. 2006. Op Amp Applications Handbook, Newnes, ISBN 0-916550-26-5. R3 316kΩ 1% 2 R2 806Ω 1% 3 Kester, Walt, editor. 1992. Amplifier Applications Guide, Analog Devices, Inc. ISBN: 0-916550-10-9. 4 U1 6 AD711KN 7 Zumbahlen, Hank, editor. 2007. Basic Linear Design, Analog Devices, Inc. ISBN 0-916550-28-1. 1 5 V1 12V V2 12V Figure 4. The voltage of this circuit is shown in Figure 5; the phase response is shown in Figure 6. 10423-004 + 10423-006 RL = 2kΩ C = 100pF –20 –30 0 0 –10 10423-005 80 20 GAIN (dB) 100 PHASE MARGIN (Degrees) 100 10423-003 OPEN LOOP GAIN (dB) MT-218 Zumbahlen, Hank. “Phase Relations in Active Filters.” Analog Dialogue, Vol. 14, No. 4, 2008. Zumbahlen, Hank, editor, 2008. Linear Circuit Design Handbook, Newnes, ISBN 978-0-7506-8703-4. REVISION HISTORY 2/12—Revision 0: Initial Version ©2012 Analog Devices, Inc. All rights reserved. Trademarks and registered trademarks are the property of their respective owners. MT10423-0-2/12(0) Rev. 0 | Page 2 of 2