Rev Page of Mini Tutorial MT One Technology Way P PDF document - DocSlides

Rev  Page of Mini Tutorial MT  One Technology Way P PDF document - DocSlides

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Page of Mini Tutorial MT 202 One Technology Way P O Box 9106 Norwood MA 02062 9106 USA Tel 7813294700 Fax 7814613113 wwwanalogcom Allpass Filters by Hank Zumbahlen Analog Devices Inc IN THIS MINI T ID: 22136

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Rev. | Page of Mini Tutorial MT 202 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 Allpass Filters by Hank Zumbahlen, Analog Devices, Inc. IN THIS MINI TUTORIAL Allpass filters , consisting of first order allpass filters and second order allpass filters, require only one operational amplifier ( op amp . Allpass filters are one of multiple discrete circuits described in a series of mini tutorials INTRODUCTION TO ALLP ASS FILTERS In most cases, the amplitude respon se of a filter is of primary concern. Another type of filter that leaves the amplitude of the signal intact but introduces phase shift is called an allpass filter. The purpose of this filter is to add phase shift (delay) to the response of the circuit. T he amplitude of an allpass is unity for all frequencies. The phase response, however, changes from 0 to 360 (for a 2 pole filter) as the frequency is swept from 0 to infinity. One use of an all pass filter is to provide phase equalization, typically in p ulse circuits. It also has application in single side band, suppressed carrier (SSB SC) modulation circuits. The transfer function of an allpass filter is (1) Note that an allpass transfer function can be synthesized as AP = H LP BP + H HP = 1 2H BP (2) FIRST ORDER ALLPASS The general form of a first order allpass filter is shown in Figure . If the function is a simple RC high pass ( Figure ), the circuit has phase shift that goes from 180 at 0 Hz. and at high frequency. It is 90 at = 1/RC. The resistor may be made variable to allow adjustment of the delay at a particular frequency. If the function is changed to a low pass function ( Figure ), the filter is still a first order allpass and the delay equations still hold, but the signal is inverted, changing from 0 at dc to 180 at high frequency. Figure . First Order Allpass Filter SECOND ORDER ALLPASS A second order allpass circuit shown in Figure was first described by Delyiannis ( see the References section ). The main attraction of this circuit is that it only requires one op amp. Remember also that an allpass filter can also be reali zed as 1 B P. Figure Second Order Allpass Filter One may use any of the band pass realizations discussed in this series of mini tutorials to build the filter, but be aware of whether the BP inverts the phase or not. In ad dition, be aware that the gain of the BP section must be 2. To this end, the dual amplifier band pass filter DABP ) structure is particularly useful, since its gain is fixed at 2. To select an op amp we primarily need to concern ourselves with the bandwidth. The rule of thumb is that the open loop gain of the amp at the resonant frequency should be at least 20 dB. Also, since there is a capacitor in the feedback network, a current feedback amplifier is probably not appropriate. Figure and Figure summarize design equations for various active filter realizations. In all cases, H, , Q, and are given, taken from the design tables. (A) R1 R1 OUT IN (B) R1 R1 OUT IN 10400-002 R4 R2 OUT R1 R3 IN 10400-003
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MT 202 Mini Tutorial Rev. | Page of FIRST ORDER ALLPASS DESIGN EQUATIONS RC RC IN Figure . RC Tan Shift Phase FRC RC Delay Group Delay at dc = 2 RC Given a phase shift of at a frequency = F TAN RC Figure design is the same as Figure except the sign of the phase changes. Figure . SECOND ORDER ALLPASS DESIGN EQUATIONS Figure . IN To design the filter, c hoose C. k = 2πF REFERENCES Delyiannis , T. High Q Factor Circuit with Reduced Sensitivity , Electronic Letters, Volume 4, December 1968. p. 577. Zumbahlen, Hank. Linear Circuit Design Handbook . Elsevier. 2008. ISBN: 978 7506 8703 REVISION HISTORY /12 Revision 0: Initial Version R1 R1 OUT IN 10400-003 R1 R1 OUT IN 10400-005 R4 R2 OUT R1 R3 IN 10400-006 2012 Analog Devices, Inc. All rights reserved. Trademarks and registered trademarks are the property of their respective owners. MT10400 4/12(0)

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