High-frequency response of a CG amplifier
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- Cathleen Sherman
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1 Hgh-requency respnse a G apler between surce & grund between dran & grund w-pass lter Md-band p w-pass lter db Input Ple Output Ple n sb
2 Hgh- respnse a G apler Exact Slutn ( db sb ( / : Nde ( / : Nde n sg sg r g s r g s an be sled t nd / sg
3 Hgh- respnse a G apler Exact Slutn ( pact slutn can be und by gnrng r (.e., r Nde sg sg : g / g / g sg sg ( s s sg sg s g g ( sg sg / g ltage dder ( /g and sg Input Ple sg s sg /( g sg Nde : s g ( g s Md-band Gan Output Ple sg sg ( g s ( sg / g s
4 Open-rcut Te-nstants Methd as as H ( s bs bs b... ω ω p p as as... ( s / ω ( s / ω p p... b can be und by the pen-crcut te-cnstants ethd.. Set sg. nsder each capactr separately, e.g., j (assue thers are pen crcut! 3. Fnd the ttal resstance seen between the ternals the capactr, e.g., j (treat grund as a regular nde. 4. b Σ n j j j apprxatn t H s: H π b
5 db Hgh- respnse a G apler te-cnstant ethd (nput ple n sb τ [ ( r /( g n sg r ] Ternals n. nsder : r g r r g r r g r. Fnd resstance between apactr ternals
![r ] Ternals n.](/docs-images/46/21629724/images/page_5.jpg "nsder : r g r r g r r g r.")
6 Hgh- respnse a G apler te-cnstant ethd (utput ple n db sb τ [ r ( g sg ]. nsder : r ( g r ( g. Fnd resstance between apactr ternals
![sb τ [ r ( g sg ].](/docs-images/46/21629724/images/page_6.jpg "nsder : r ( g r ( g.")
7 Hgh-requency respnse a G apler db n sb M ( r sg / g g r ( r τ τ H n [ [ sg π b ( r r /( g ( g π ( τ τ sg ] r ] parsn te-cnstant ethd wth the exact slutn (r sg / g / g sg ( g s n ( sg / g s Input ple : Output ple : M ω p / τ ω p / τ
8 Hgh-requency respnse a S apler db s between utput and nput! sb s shrted ut. Input Ple? Output Ple?
9 Mller s There I ( (, /( I I /, /( I ( ( nsder an apler wth a gan wth an pedance attached between nput and utput and eel the presence nly thrugh I and I We can replace wth any crcut as lng as a current I lws ut and a current I lws ut.
10 Mller s There stateent I an pedance s attached between nput and utput an apler wth a gan, can be replaced wth tw pedances between nput & grund and utput & grund Other parts the crcut
11 / ( / ( / ( n Exaple Mller s There: Inertng apler n n p ( Opp : ecall r EE, s large Slutn usng Mller s there: / n /
12 pplyng Mller s There t apactrs / ( / ( j ω arge capactr at the nput r >>
13 Hgh-requency respnse a S apler Usng Mller s There Use Mller s There t replace capactr between nput & utput ( wth tw capactrs at the nput and utput. d g( r g n, db, ( [ g ( r ],, ( / * [ / g ( r ] Nte: appears n the nput (, as a uch larger capactr. * ssung g >>
14 Hgh- respnse a S apler Mller s There and te-cnstant ethd n [ g ( r ] db Input Ple ( n : Output Ple ( : r τ n sg τ ( r π H b ( r n sg
![( r ] db Input Ple ( n : Output](/docs-images/46/21629724/images/page_14.jpg "Ple ( : r τ n sg τ ( r π H b ( r")
15 Hgh- respnse a S apler Exact slutn Slng the crcut (nde ltage ethd: b b sg n n ( db g sg ( r db ( s ( b s b ( r s [ g ( r ] / g Mller & te-cnstant ethd:. Sae b and sae H as exact slutn b nsg ( r π H. lthugh, we get the sae H, there s a substantal errr n nddual nput and utput ples. 3. Mller apprxatn dd nt nd the zer!
16 Mller s There s Mller s pprxatn Fr Mller There t wrk, rat / (apler gan shuld be calculated n the presence pedance. In ur analyss, we used d-band gan the apler and gnred changes n the gan due t the eedback capactr,. Ths s called Mller s pprxatn. In the Opp exaple the gan the chp,, reans cnstant when s attached (utput resstance the chp s sall. Because the apler gan n the presence s saller than the dband gan (we are n the hgh- prtn the gan Bde plt, Mller s apprxatn erestates, and underestates, There s a substantal errr n nddual nput and utput ples. Hweer, b and H are estated well. Mre prtantly, Mller s pprxatn sses the zer ntrduced by the eedback resstr (Ths s prtant r stablty eedback aplers as t aects gan and phase argns. Frtunately, we can calculate the zer the transer unctn easly (next slde.
17 Fndng the zer the S apler By dentn, g er : ( s s z Because, zer current wll lw n r, db and 3 By K, a current g wll lw n. 4 Oh s law r ges: g s z g s z
18 er S apler can play an prtant rle n stablty eedback aplers Snce the nput ple s at /(πτ /(π n sg Sall sg can push p t ery large alues! p p z p z p ase > z >> p p ase p > z > p
19 autn: The te cnstant ethd apprxatn t H (see S&S page 74. n b Σ j j j ω Snce, b ω ω ω ω ω p p H H p p Ths s the crrect rula t nd H Hweer, S&S ges a derent rula n page 7 (cntradctng rulas pp74. Ignre ths rula (S&S Eq ω H ω p ω p ω p3... Dscussns (and se cnclusns re Mller s there n Exaples 9.8 t 9. are ncrrect. The dscrepancy between H r Mller s apprxatn and exact slutn s due t the use Eq (Nt Mller s ault!
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