Filter Dispersion. with respect to frequency otherwise signal dispersion (and thus signal distortion) will result. Right?

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1 3/1/005 Filter Diperion.doc 1/6 Filter Diperion Any ignal that carrie ignificant information mut ha ome non-zero bandwidth. In other word, the ignal energy (a well a the information it carrie) i pread acro many frequencie. If the different frequencie that comprie a ignal propagate at different velocitie through a microwave filter (i.e., each ignal frequency ha a different delay τ ), the output ignal will be ditorted. We call thi phenomenon ignal diperion. Q: I ee! The phae delay τ ( ) of a filter mut be a contant with repect to frequency otherwie ignal diperion (and thu ignal ditortion) will reult. Right? A: Not necearily! Although a contant phae delay will inure that the output ignal i not ditorted, it i not trictly a requirement for that happy event to occur. Thi i a good thing, for a we hall latter ee, building a good filter with a contant phae delay i very difficult! Jim Stile The Univ. of Kana Dept. of EECS

2 3/1/005 Filter Diperion.doc /6 For example, conider a modulated ignal with the following frequency pectrum, exhibiting a bandwidth of B Hertz. V ( ) Now, let likewie plot the phae delay function τ ( ) of ome filter: τ ( ) V ( ) Note that for thi cae the filter phae delay i nowhere near a contant with repect to frequency. Jim Stile The Univ. of Kana Dept. of EECS

3 3/1/005 Filter Diperion.doc 3/6 However, thi fact alone doe not necearily mean that our ignal would uffer from diperion if it paed through thi filter. Indeed, the ignal in thi cae would be ditorted, but only becaue the phae delay τ ( ) change ignificantly acro the bandwidth B of the ignal. Converely, conider thi phae delay: τ ( ) V ( ) A with the previou cae, the phae delay of the filter i not a contant. Yet, if thi ignal were to pa through thi filter, it would not be ditorted! The reaon for thi i that the phae delay acro the ignal bandwidth i approximately contant each frequency component of the ignal will be delayed by the ame amount. Compare thi to the previou cae, where the phae delay change by a precipitou value τ acro ignal bandwidth B : Jim Stile The Univ. of Kana Dept. of EECS

4 3/1/005 Filter Diperion.doc 4/6 τ ( ) V ( ) τ Now thi i a cae where diperion will reult! Q: So doe τ need to be preciely zero for no ignal ditortion to occur, or i there ome minimum amount τ that i acceptable? A: Mathematically, we find that diperion will be inignificant if: τ 1 A more pecific (but ubjective) rule of thumb i: Or, uing = πf : π τ < 5 f τ < 0.1 Jim Stile The Univ. of Kana Dept. of EECS

5 3/1/005 Filter Diperion.doc 5/6 Generally peaking, we find for wideband filter where filter bandwidth B i much greater than the ignal bandwidth (i.e., B B ) the above criteria i eaily atified. In other word, ignal diperion i not typically a problem for wide band filter (e.g., preelector filter). Thi i not to ay that τ ( ) i a contant for wide band filter. Intead, the phae delay can change ignificantly acro the wide filter bandwith. What we typically find however, i that the function ( ) τ doe not change very rapidly acro the wide filter bandwidth. A a reult, the phae delay will be approximately contant acro the relatively narrow ignal bandwidth B. τ ( ) V ( ) Jim Stile The Univ. of Kana Dept. of EECS

6 3/1/005 Filter Diperion.doc 6/6 Converely, a narrowband filter where filter bandwidth B i approximately equal to the ignal bandwidth (i.e., B B ) can (if we re not careful!) exhibit a phae delay which likewie change ignificantly over filter bandwidth B. Thi mean of coure that it alo change ignificantly over the ignal bandwidth B! τ ( ) V ( ) Thu, a narrowband filter (e.g., IF filter) mut exhibit a near contant phae delay τ ( ) in order to avoid ditortion due to ignal diperion! Jim Stile The Univ. of Kana Dept. of EECS