Microwave Filter

Filter Design
of 20
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
  RF Engineering – Passive Circuit Microstrip Filter Design 1.0 Introduction to Filter A filter is a network that provides perfect transmission for signal with frequencies incertain passand region and infinite attenuation in the stopand regions! uch idealcharacteristics cannot e attained# and the goal of filter design is to appro$imate the idealrequirements to within an acceptale tolerance! Filters are used in all frequenc% rangesand are categori&ed into three main groups' ã (ow)pass filter *(PF+ that transmit all signals etween DC and some upper limit ω c and attenuate all signals with frequencies aove ω c ! ã ,igh)pass filter *,PF+ that pass all signal with frequencies aove the cutoff value ω c and re-ect signal with frequencies elow ω c ! ã .and)pass filter *.PF+ that passes signal with frequencies in the range of ω /  to ω 0  andre-ect frequencies outside this range! 1he complement to and)pass filter is the and)re-ect or and)stop filter!2n each of these categories the filter can e further divided into active and passive t%pe!1he output power of passive filter will alwa%s e less than the input power while activefilter allows power gain! 2n this la we will onl% discuss passive filter! 1he characteristicof a passive filter can e descried using the transfer function approach or the attenuationfunction approach! 2n low frequenc% circuit the transfer function *,* ω ++ description isused while at microwave frequenc% the attenuation function description is preferred!Figure /!/a to Figure /!/c show the characteristics of the three filter categories! 3ote thatthe characteristics shown are for passive filter! Figure 1.1A  – A low)pass filter frequenc% response! F! 4ungMa% 0556/ A Filter  ,* ω + 7 / * ω +7 0 * ω + ( ) ( )( ) ω ω ω  /0 V V  H   = ( )( )        −= ω ω  /0/5 05 V V  Log n Attenuatio ω c 8,* ω +8 ω /1ransfer functionAttenuation9d. ω 5 ω c :/505:5;5  RF Engineering – Passive Circuit Microstrip Filter Design Figure 1.1B  – A high)pass filter frequenc% response! Figure 1.1C  – A and)pass filter frequenc% response! 2.0 Realization of Filters At frequenc% elow /!5<,&# filters are usuall% implemented using lumped elements suchas resistors# inductors and capacitors! For active filters# operational amplifier issometimes used! 1here are essentiall% two low)frequenc% filter s%ntheses techniques incommon use! 1hese are referred to as the image)parameter method *2PM+ and theinsertion)loss method *2(M+! 1he image)parameter method provides a relativel% simplefilter design approach ut has the disadvantage that an aritrar% frequenc% responsecannot e incorporated into the design! 1he 2PM approach divides a filter into a cascadeof two)port networks# and attempt to come up with the schematic of each two)port# suchthat when comined# give the required frequenc% response! 1he insertion)loss method egins with a complete specification of a ph%sicall% reali&ale frequenc% characteristic#and from this a suitale filter schematic is s%nthesi&ed! Again we will ignore the image parameter method and onl% concentrate on the insertion loss method# whose design procedure is ased on the attenuation response or insertion loss of a filter! 1he insertionloss of a two)port network is given %' ( ) 0 //loadtodeliveredPower sourcethefromavailalePower ω  Γ −=== load inc IL  P  P  P  *0!/+=here Γ   is the reflection coefficient looking into the filter *we assume no loss in thefilter+! F! 4ungMa% 05560 ω Attenuation9d. 5 ω c :/505:5;5 ω c 8,* ω +8 ω /1ransfer function ω / 8,* ω +8 ω   /1ransfer function ω 0 ω Attenuation9d. 5 ω / :/505:5;5 ω 0  RF Engineering – Passive Circuit Microstrip Filter Design Design of a filter using the insertion)loss approach usuall% egins % designing anormali&ed low)pass protot%pe *(PP+! 1he (PP is a low)pass filter with source and loadresistance of / Ω  and cutoff frequenc% of / Radian9s! Figure 0!/ shows the characteristics!2mpedance transformation and frequenc% scaling are then applied to denormali&e the (PPand s%nthesi&e different t%pe of filters with different cutoff frequencies! Figure 2.1  – A normali&ed (PP filter network with unit% cutoff frequenc% */Radian9s+!(ow)pass protot%pe *(PP+ filters have the form shown in Figure 0!0 *Analternative network where the position of inductor and capacitor is interchanged is alsoapplicale+! 1he network consists of reactive elements forming a ladder# usuall% knownas a ladder network! 1he order of the network corresponds to the numer of reactiveelements! 2mpedance transformation and frequenc% scaling are then applied to transformthe network to non)unit% cutoff frequenc%# non)unit% source9load resistance and to other t%pes of filters such as high)pass# and)pass or and)stop! E$amples of high)pass and and)pass filter networks are shown in Figure 0!: and Figure 0!; respectivel%!R  Figure 2.2  – (ow)pass protot%pe using (C elements! F! 4ungMa% 0556: A Filter  ,* ω + 7 / * ω +7 0 * ω + R   >/R  (  >/Attenuation9d. ω 5 ω c  > / :/505:5;5(   / >g 0 ( 0 >g ; C / >g / C 0 >g : R  ( > g  3?/ /(   / >g / ( 0 >g : C / >g 0 C 0 >g ; R  ( > g  3?/ g 5 > /  RF Engineering – Passive Circuit Microstrip Filter Design Figure 2.3  – E$ample of high)pass filter# note the position of inductor and capacitor isinterchanged as compared with low pass filter! Figure 2.4  – E$ample of and pass)filter# the capacitor is replaced with parallel (Cnetwork while the inductor is replaced with series (C network! 3.0 Brief Overview of ow! ass rotot#$e Filter %esign &sing u'$ed (le'ents 1here are a numer of standard approaches to design a normali&ed (PP of Figure 0!: thatappro$imate an ideal low)pass filter response with cutoff frequenc% of unit%! Among thewell known methods are' ã Ma$imall% flat or .utterworth function! ã Equal ripple or Che%shev approach! ã Elliptic function!=e will not go into the details of each approach as man% ooks have covered them!2nterested reader can refer to reference @:# which is a classic te$t on network anal%sis or @;# a more advance version! 1he asic idea is to appro$imate the ideal amplituderesponse 8,* ω +8 0  of an amplifier using pol%nomials such as .utterworth# Che%shev#.essel and other orthogonal pol%nomial functions! 1his is usuall% given as' +*/+* +*+* ω ω ω ω   N ooio  P C  K V V  H  +== *:!/+,ere 4  o  and C o  are constants and P  3 * ω + is a pol%nomial in ω  of order 3! 4  o  and C o  areusuall% dependent on the t%pe of pol%nomial used! A comparison of appro$imating the(PP amplitude response with .utterworth# .essel and Che%shev pol%nomials isillustrated in Figure :!/! F! 4ungMa% 0556; ( 0 ( / C / C  3 C 0 ( 0 ( / C / ( : C : C  3 (  3
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks