Lecture 0: Small Sgnal Dece Parameters 06009 Lecture 9, Hgh Speed Deces 06
Lecture : Ballstc FETs Lu: 0, 394 06009 Lecture 9, Hgh Speed Deces 06
Large Sgnal / Small Sgnal e I E c I C The electrcal sgnal s often small. be BE Dde the total oltage/current nto a large (DC) and small (AC) sgnal. We are manl nterested n the small sgnal part. We can make a Talor expanson around the bas oltage. Nonlnear constant bas current oltage and lnear AC arng sgnal current/oltage. E I E e f BE, f BE be f Bas Current BE I E Sgnal Current be C I C c f f BE, be IC be BE f BE 06009 Lecture 9, Hgh Speed Deces 06 3
port parameters E C B port E C I I E C e c f f BE, f f BE BE, be BE be f f BE BE 0 0 z z z z Can transform to dfferent parameter sets 06009 Lecture 9, Hgh Speed Deces 06 4
Y,z,ABCD,h,g Admttance z z Impedance z z A C ABCD/ cascade/ aparameters g g Inerse hbrd parameters B D g g h h Hbrd parameters bparameters b b h h b b 06009 Lecture 9, Hgh Speed Deces 06 5
Conerson between parameter sets From Electrc Crcuts, J. W. Nlsson and S.A. Redel 06009 Lecture 9, Hgh Speed Deces 06 6
Shunt/Seres addton Shunt b Seres z b a z a c z c c = a b z c = z a z b 06009 Lecture 9, Hgh Speed Deces 06 7
Cascade, Serer/Parallel addtons Cascade Seres/parallel h b ABCD a ABCD b ABCD c ABCD c = ABCD a ABCD b h a h c h c = h a h b gparameters parallel/seres: g c =g a g b 06009 Lecture 9, Hgh Speed Deces 06 8
DC parameters models g d = 0 0 g m g d gs ds = gg gd dg dd gs ds g gs d ds b c = I c β t 0 I C t 0 be ce = bb bc cc be ce b be c ce If we know the parameters for one confguraton we can calculate the parameters for a dfferent confguraton! s sg d dg 06009 Lecture 9, Hgh Speed Deces 06 9
Indefnte Admttance Matrx e e c c 3 e b c ee be ce eb bb ec bc cc e b c b b If e = c = b = : how large s e b and c? CE: bb, bc,, cc Wh s ce ec =0 If e = and b = c =0 : how large s e b c? Wh s ee be ce =0 : ee, ec, cc, ce All rows and columns hae to sum up to zero! 06009 Lecture 9, Hgh Speed Deces 06 0
CS/CC/CG CS/CD/CG confguratons Same for FETs but wth: C D E S B G From Rado Electroncs, L. Sundström, G. Jönsson and H. Börjesson 06009 Lecture 9, Hgh Speed Deces 06
Yparameters for common gate transstor s d = g m g d g d (g m g D ) g d sg dg = ss sd ds dd sg dg s sg d dg 06009 Lecture 9, Hgh Speed Deces 06
Hbrd pmodel : Crcut Representaton Crcut representaton of parameters A transstor (three termnal dece) alwas hae a common termnal ( ) Hbrd p representaton pf parameters. ald f there s a common termnal. One current source less. usuall hae a drect phscal nterpretaton. 06009 Lecture 9, Hgh Speed Deces 06 3
Tme Harmonc Sgnals jw be BE ~ e ~ c e I E c I C Use complex notaton for small sgnal oltages. If nput terms are snusodal, the output wll also be snusodal ampltude & phase shft. complex matrx ee ce ec cc ~ ~ be E be C be E C BE ~ ~ be be be ~ bee ~ e ~ bee ~ e jw jw jw jw Goal s to dentf the dfferent parameters from fundamental transstor phscs Ampltude & phase 06009 Lecture 9, Hgh Speed Deces 06 4
Complex small sgnal parameters We wll determne that the parameters can be wrtten as real an magnar parts, wth the magnar parts correspondng to capacte elements. Intrnsc (quas statc) parameters for a FET. g d = jωc gg jωc dg gs g m jωc dg g d jωc dd = gg gd gs ds dg dd ds Where g m, C gg, C dg orgnates from the phscs of the transstor. The dfferent parameters thus depend of w, GS, DS and the geometr of the transstors. 06009 Lecture 9, Hgh Speed Deces 06 5
Current Gan h port Maxmum current gan s short crcuted h = =0 = = Appl a test oltage to the nport: h = =0 = The current gan tpcall decreases wth frequenc h = corresponds to the transton frequenc, f T. 06009 Lecture 9, Hgh Speed Deces 06 6
Power Gan I Transducer Gan S P n P a,l port P L L Power aalable from source: Pa,s Power delered at load: P L P a,s P L G T = P L P a,s Transducer Gan Power gan can be seen as a two step process: Power s delered from the source to the nput of the transstor Power s delered from the output of the transstor to the load G T = 4Re L Re s s L To maxmze the transducer gan we must correctl select the source and load mpedances! 0600 Lecture 9, Hgh Speed Deces 06 7
Power Gan II S S [] L [] L n out n = L Dece nput mpedance as seen from the source out = s Dece nput mpedance as seen from the load Maxmum power transfer requres that both the source and the load are conjugated matched s = n L = out 06009 Lecture 9, Hgh Speed Deces 06 8
Maxmum Gan Aalable and Stable G T,max = K K K = Re Re Re > If K>: The transstor s uncondtonall stable G T,max = K K = MAG K: Rollet Stablt factor Ths s the Maxmum Aalable Gan If K<: For maxmum gan, the transstor s unstable. B addng shunt resstances to and we can make K=. The maxmum gan s then G T,max = Ths s the Maxmum Stable Gan Ths corresponds to n / out beng negate for optmal s / L. The power gan tpcall decreases wth frequenc. G T,max = corresponds to the maxmum oscllaton frequenc, f max. Need two functons to descrbe G T,max (w). Not used for extrapolaton. 06009 Lecture 9, Hgh Speed Deces 06 9
Unlateral Gan K = Re Re Re > A nonzero can cause a dece to be unstable. We can alwas elmnate through a passe, lossless feedback network. The maxmum transducer gan of ths network s called Mason s unlateral gan, U. Example: caused b a capactor can be cancelled b a nductor (at one frequenc) Ths ges one equaton ald for all alues of. U = 4 Re Re Re Re U = also ges f max Ths s the same as from MSG/MAG. U s the same for CC/CG/CS stages. 06009 Lecture 9, Hgh Speed Deces 06 0