Lectur 22. RF and Microwave Circuit Design Γ-Plane and Smith Chart Analysis. ECE 303 Fall 2005 Farhan Rana Cornell University
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1 ctur RF ad Micrwav Circuit Dig -Pla ad Smith Chart Aalyi I thi lctur yu will lar: -pla ad Smith Chart Stub tuig Quartr-Wav trafrmr ECE 33 Fall 5 Farha Raa Crll Uivrity V V Impdac Trafrmati i Tramii i ω t ( t R [ V ] l + ad Dfi a piti dpdt rflcti cfficit a: k k + k ( i a cmplx umbr f magitud vr gratr tha uity Dfi a rmalid impdac a: Th: R + X Nrmalid ritac Nrmalid ractac + r + ECE 33 Fall 5 Farha Raa Crll Uivrity
2 k -Pla (Cmplx Pla Imag ( ( ( cmplt full rvluti i th cmplx pla wh it pha g thrugh k + Thrfr, impdac i pridic with ditac with a prid qual t half-wavlgth R ( l ECE 33 Fall 5 Farha Raa Crll Uivrity -Pla with Nrmalid Ractac Curv ( R + + X Th rd curv idicat th valu f th rmalid ractac X ( th -pla Frm th curv ca radff th valu f X ( l ECE 33 Fall 5 Farha Raa Crll Uivrity
3 -Pla with Nrmalid Ritac Curv ( R + + X Th blu curv idicat th valu f th rmalid ritac R ( th -pla Frm th curv ca radff th valu f R ( l ECE 33 Fall 5 Farha Raa Crll Uivrity -Pla with Nrmalid Ritac ad Ractac Curv Th Smith Chart ( ( R + + X Th Smith Chart abl t rad-ff valu f bth th rmalid ritac R ( ad th rmalid ractac X ( valu th -pla l ECE 33 Fall 5 Farha Raa Crll Uivrity 3
4 V ad Matchig fr Maximum Pwr I may micrwav ad RF circuit it i HIGH dirabl t b abl t trafr maximum pibl tim-avrag pwr t a lad impdac: I + V R + X _ V ω t ( t R [ V ] What i th tim-avrag pwr dlivrd t th lad? * P ( ( ( R [ ] R t V t I t V I V + V V R R[ ] + ( R + R + ( X + X Maximum tim-avrag pwr dlivrd t th lad: * V + R + X P ( t i maximid wh: R R r X * X P ( t V max 8 R ECE 33 Fall 5 Farha Raa Crll Uivrity ad Matchig i Tramii i V V ω t ( t R [ V ] + l + Hw d gt th maximum tim-avrag pwr dlivrd t th lad? Th quivalt circuit i: V ( l Pwr dlivrd t th lad will b maximid if pwr dlivrd t th trafrmd impdac (-l i maximid Mut hav th impdac (- l matchd t th urc impdac, i.. * ( l ECE 33 Fall 5 Farha Raa Crll Uivrity
5 Exampl: ad Matchig i Tramii i - I V V ω t ( t R [ V ] 5 Ω l 5 Ω Supp: 5 Ω Ω 5 Ω Ω Hw d gt th maximum tim-avrag pwr dlivrd t th lad? Nd (- l matchd t th urc impdac 5 Ω STEP : Firt fid STEP : Fid l uch that th impdac (-l ha a ral part f 5 Ω ( l 5 + X ( l ( l. + X ( l ECE 33 Fall 5 Farha Raa Crll Uivrity Exampl: ad Matchig i Tramii i - II Fid th dird l uig Smith Chart (. (. 667 ( l. +.8 x l.83 ( l ( l ECE 33 Fall 5 Farha Raa Crll Uivrity 5
6 Exampl: ad Matchig i Tramii i - III V V 5 Ω 5 Ω ω t R V l ( t [ ] S if l.83 th th quivalt circuit i: Ω 5 Ω l Ω V ( But w hav a prblm! W hav b abl t match th ral part f th impdac t th urc but w dd up with a uwatd ractiv trm Hw d w gt rid f thi uwatd ractac? Awr: U tub tur ECE 33 Fall 5 Farha Raa Crll Uivrity Stub Tur i Micrwav Circuit Stub tur, a th am uggt, ar hrt tub f tramii li that ar ud t cacl ut uwatd ractac i micrwav circuit l A p-circuit tub ( l X ( k l ct It ha a capacitiv impdac fr hrt lgth ad i ud t cacl uwatd iductiv ractac l A hrt-circuit tub ( l X ( k l ta It ha a iductiv impdac fr hrt lgth ad i ud t cacl uwatd capacitiv ractac X X capacitiv iductiv iductiv 3 5 capacitiv kl 3 5 kl ECE 33 Fall 5 Farha Raa Crll Uivrity 6
7 ad Matchig Uig Sri Stub Tur V 5 Ω 5 Ω l.83 Ω l l 5 Ω Nd: ( l 9 ( l. 8 Hav: + ( l Ω V ( l ( l - 9 Ω Ω What lgth l f th tub mut b ch t gt a ractac f 9? ( l ct( k l kl l ECE 33 Fall 5 Farha Raa Crll Uivrity ( ( + ad Matchig Uig Stub Tur: Smith Chart Op-Circuit tub tur a Smith Chart ( l 9 ( l. 8 l.8 x ECE 33 Fall 5 Farha Raa Crll Uivrity 7
8 Admittac ad Nrmalid Admittac Smith Chart R + + X ( + ( r l ECE 33 Fall 5 Farha Raa Crll Uivrity ad Matchig Uig Paralll Stub Tur - I V 5 Ω 5 Ω Ω Nd: ( l l ( l l 5 Ω + D ( l + 5 D ( l Nd: ( l ( l ( l 5 D 5 ( l D V 5 Ω ( l ( l It i mr uful hr t wrk with admittac rathr tha impdac wh u paralll tub ic admittac f circuit lmt i paralll add ECE 33 Fall 5 Farha Raa Crll Uivrity 8
9 (. 5 (. 667 ad Matchig Uig Paralll Stub Tur - II ( 5. ( ( l ( l..8 x l.67 ECE 33 Fall 5 Farha Raa Crll Uivrity ad Matchig Uig Paralll Stub Tur - III S what d w hav far: V 5 Ω 5 Ω l.67 Ω l Nd:.8 ( l + ( l 5 l Hav: V ( l ( l ECE 33 Fall 5 Farha Raa Crll Uivrity ( l 5 Ω ( ( l 5 5 What lgth l f th tub mut b ch t gt a ractac f +.8/5? ( l kl.6 5 Ω ( l ( k l ta.8 5 l.7 l ( l
10 Op-Circuit tub tur a Smith Chart ( ( + ad Matchig Uig Paralll Stub Tur - IV x ( ( ( l +.8 ( l l.7 ECE 33 Fall 5 Farha Raa Crll Uivrity Stub i Micrwav Circuit: Sm Pictur Phtgraph f a GH lctric igl-tub tur with varactr did tuig lmt A GaN amplifir chip with radial tub fr GH prati GH micr-fabricatd rcfigurabl tub tur GH micr-fabricatd MEMSwitchd tub tur ECE 33 Fall 5 Farha Raa Crll Uivrity
11 ECE 33 Fall 5 Farha Raa Crll Uivrity V l Quartr-Wav Trafrmr ( ( k k + + Supp th lgth l f th tramii li i quartr-wavlgth: l l k ( ( k k l l l A quartr-wavlgth lg tramii li ivrt th rmalid impdac Actual impdac at -/ : ECE 33 Fall 5 Farha Raa Crll Uivrity Quartr-Wav Trafrmr: O a Smith Chart ( ( Supp: ( ( x
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