Amplifier Constant Gain and Noise

Transcription

1 Amplfe Constant Gan and ose by Manfed Thumm and Wene Wesbeck Foschungszentum Kalsuhe n de Helmholtz - Gemenschaft Unvestät Kalsuhe (TH) Reseach Unvesty founded 85

2 Ccles of Constant Gan (I) If s taken to be zeo, then Eq. 3.9 pedcts that the nput eflecton facto n of a two-pot wll be ndependent of the load eflecton facto L, and Eq pedcts that the output eflecton facto wll be ndependent of the souce eflecton facto., n 0 out 0 (3.46) nce such an nput and output ae decoupled, a smplfed and clea ccut desgn pocedue s possble.

3 Ccles of Constant Gan (II) In Fg. 3.9 t s shown how Eq. 3.4, whch s slghtly dffeently pesented n Eq. 3.47, can be assgned n a netwok. G Tu s undestood as the poduct of thee gan contbutons, whch can explctly be assgned to the tansfomaton netwok and the two-pot. G Tu u 0 L G G G G G Lu u, db 0, db G Lu, db L (3.47) G u Fg Unlateal powe gan G Tu of a two-pot connected as a matchng netwok. 3

4 Ccles of Constant Gan (III) Dependng on whethe the tansfomaton netwok mpoves o degades the matchng n compason wth the case n whch = L = 0, the esult s a matchng gan o a matchng loss. The gan contbuton G u, e.g. depends only on the eflecton facto of the souce, whch can be optmzed fo an appopate matchng ccut dung the ccut desgn, fo a gven. Fo =, G u = 0, fo L = 0, G Lu = (Eq. 3.47). One obtans the maxmum unlateal tansfe gan when the two-pot s matched n a complex conjugate fashon at both ends ( = *, L = *). 4

5 Ccles of Constant Gan (IV) ubsttuton nto Eq esults n: Tu, max, max 0 G G u G G Lu, max (3.48) The afoementoned pocedue fo ccut desgn now eles on all that could cause a constant G u (0 < G u < G u,max ) lyng on a ccle n the mth chat. The expesson fo G u s fomally the same as that fo G Lu, wth eplaced by L and by. Fo G Lu the same apples as fo G u. 5

6 Ccles of Constant Gan (V) The nfluence of the nput- ( = ) and output-matchng ( = ) on the gan G Tu can thus be descbed by a host of ccles of constant gan whose locaton n the mth chat s gven by d g g (3.49) wth R ju,max g The cente of the ccle of constant gan G les a dstance of d fom the md-pont of the mth chat n the decton of the vecto *. R s the ccle adus, g s the assocated nomalsed gan. G ju g Gju ;, j, o, j L G g (3.50) g ; d and R 0 degeneate 6

7 Examples fo G - Ccles G max =.3 db - plane G max =. db L - plane Fg Ccles of constant gan G u n the plane (top), G Lu n the L plane (bottom), fo a GaAs-MEFET chp CFY 0 at GHz wth =.56 (assumpton: = 0). Fo compason wth the values detemned fom Fg. 3.0 (G Tu,max = ( log.56 +.) db = 8.6 db fo = 0.65/68º and L = 0.6/7º), the values fo maxmal gan G T,max and the equed matchng ae gven fo an exact calculaton,.e. unde consdeaton of a non-zeo ( = 0.08): G T,max = G A,max = MAG = 8.9 db fo = 0.73/78º and L = 0.7/85º. 7

8 Amplfe ose (I) ose n Two-Pots Mcowave amplfes poduce an output sgnal even f no nput voltage s appled. The cause fo ths s the themal o Johnson nose of the amplfe, whch s chaactezed by the amplfe nose-fgue F. To detemne ths nose fgue one poceeds as follows: As shown n Fg. 3.a, the nput pot of a nosy two-pot s temnated by a nosy essto R whose nose chaactestcs can also be descbed, as shown n Fg. 3.b, by an extenal nose souce U and a noseless essto R. Fg. 3.. A nosy two-pot. 8

9 Amplfe ose (II) The followng well-known elaton esults: wth k U kTBR, (Boltzmann constant) (3.5) fo the detemnaton of the effectve value U of the nose voltage at known tempeatue T and bandwdth B. The ba epesents the tempoal mean value. nce wokng wth powes s geneally moe pleasant, and s useful n the followng dscusson, the maxmal nose powe P avalable to R s gven (load esstance = ntenal esstance): 3 J K P U 4R ; ; 4 0 / 74 / ktb (3.5) T C K B Hz P mw Hz dbm Hz 9

10 Amplfe ose (III) Fom these elatons, the nose fgue F of a two-pot s gven by the ato of total nose powe at the amplfe output, P o, and the avalable powe gan G A (Eq. 3.44) fom the two-pot multpled wth the nput powe P caused by R : F Po PG A (3.53) The avalable powe gan G A ca also be seen as the elaton between the powe avalable at the output, P, and the nput, P : 0

11 Amplfe ose (IV) Wth Eq. 3.53, the nose fgue F can be wtten as the elaton of the sgnal-to-nose atos (R) of the nput and output sgnals: G A P P (3.54) Often the nose fgue s gven as a logathmc quantty (F). The defnton s: P P R F P P o R o (3.55) nce the avalable powe at the nput depends on the souce mpedance and not the load mpedance, the nose fgue F also only depends on the souce mpedance (o the souce eflecton facto ). F 0log( F) db (3.56)

12 Amplfe ose (V) Fo sees connecton of multple amplfe pots, the total nose fgue s detemned as shown n Fg. 3.. Hee, P s agan the avalable nput nose powe, whle P n and P n epesent the nose powe components due to the ndvdual amplfe stages. These ae uncoelated and can thus be added. The total nose powe at the amplfe goup output, P o,tot, s gven by: Po, TOT GA GA P Pn Pn (3.57) Fg. 3.. ees connecton of two amplfe two-pots.

13 Amplfe ose (VI) Thus the total nose fgue of a two-stage amplfe s gven by: P P P o, TOT n n F P G A G A P G A P G A G A (3.58) o whee F F n Z PG A F P F and F G A F P F n Z PG A (3.59) (F Z : addtonal nose fgue wth T e = F Z T 0 the effectve nose tempeatue) Fom these elatons the nose fgue of abtaly complex amplfe chans can be detemned by ecuson: 3

14 Amplfe ose (VII) F tot F F Fn G G G G A A A An (3.60) Fom Eq t s evdent that the contbuton to the total nose fgue of nose fgue F of the second stage s negatvely weghted by the gan of the fst stage. On the othe hand t can be sensble to athe put up wth a hghe fst stage gan and smultaneously hghe nose fgue F to suppess the nose of the second stage. 4

15 Ccles of Constant ose (I) Ccles of Constant ose The nose fgue of a two-pot can be epesented by Eq. 3.6, whee = R /Z 0 s the nose essto nomalsed to the efeence esstance Z 0 Y = G +jb s the souce admttance, and Y O = G O +jb O s the nput admttance whch causes the lowest nose fgue (the ndex O stands fo optmal). R F Fmn Y YO Fmn ys yo G g 0 O O 0 O O y Y Z g jb y Y Z g jb (3.6) 5

16 Ccles of Constant ose (II) If Y and Y O ae expessed by and O, then a nose fgue esults that s dependent on F mn,, O and : F e. g. Y, Y Y O O Z0 F 4 O mn O (3.6) 6

17 Ccles of Constant ose (III) The fou values F mn, and the ampltude and phase of O ae known as nose paametes and ae ethe commonly gven by tanssto manufactues o can be expementally detemned. Ths s done by adjustng the mpedance of the souce (e.g. wth vaable sees and paallel tansmsson lnes) untl mnmal nose appeas at the output. ZT (3.63) 7

18 Ccles of Constant ose (IV) The value of can be measued by a netwok analyse; the calbaton condtons ensue that = O. The thus detemned nose fgue epesents F mn. Fom the aleady detemned values, the nomalsed nose esstance can be detemned by settng to zeo and conductng a futhe nose measuement F( = 0): F 0 F O mn 4 O (3.63) 8

19 Ccles of Constant ose (V) The mnmum nose fgue F mn n db ses oughly lnealy wth the opeatng fequency, and depends on the collecto o dan cuent. As a typcal example of the fequency- and cuent-dependence, Fg. 3.3 shows the nose behavou of the GaAs-FET ATF036. Fg Gan and mnmum nose fgue of the GaAs-FET ATF036. Left: plotted vesus fequency. Rght: plotted vs. dan cuent. 9

20 F Ccles (I) The appopate fo a desed nose fgue can be detemned fom Eq. 3.6, whch s the mplct ccle equaton fo the vecto. ome manpulaton esults n the explct fom n Eq. 3.64, whee s the nose fgue paamete and F s the desed nose fgue. O O (3.64) whee O mn F F 4 O (3.65) 0

21 F Ccles (II) Thus the cente pont vecto C F and adus R F of the nose ccle ae: C F O (3.66) R F O (3.67) These ccles can be dawn on a mth chat as shown n Fg Fo the specal case of F = F mn ( I = 0) the ccle becomes a pont at = O. Accodng to Eq. 3.66, the centes of the futhe nose ccles le on the staght connectng lnes between the ogn and the pont O.

22 F Ccles (Example) - plane - plane Fg ose ccles fo a 4 GHz tanssto. Fg ose ccles and ccles of constant gan n a dagam fo a GaAs-FET at 4 GHz (- - - gan, --- nose).