6. Introduction to Transistor Amplifiers: Concepts and Small-Signal Model

Transcription

1 6. ntoucton to anssto mples: oncepts an Small-Sgnal Moel Lectue notes: Sec. 5 Sea & Smth 6 th E: Sec. 5.4, 5.6 & Sea & Smth 5 th E: Sec. 4.4, 4.6 & EE 65, Wnte203, F. Najmaba

2 Founaton o anssto mples oltage ample eques o / const. 2 examples below MOS tanse uncton s NO lnea o / can be negate mnus sgn epesents a 80 o phase sht n satuaton, howee, tanse uncton looks lnea but shte F. Najmaba, EE65, Wnte 203, nto to mps 2/32

3 Founaton o anssto mples 2 n satuaton, tanse uncton appea to be lnea ppoxmate the tanse uncton wth a tangent lne at pont Q wth a slope o : S S s gs lnea elatonshp o s S S an gs F. Najmaba, EE65, Wnte 203, nto to mps 3/32

4 Founaton o anssto mples 3 Let us conse the esponse NMOS emans n satuaton at all tmes an s a combnaton o a constant alue an a sgnal gs : gs F. Najmaba, EE65, Wnte 203, nto to mps 4/32

5 he esponse to a combnaton o gs can be oun om the tanse uncton F. Najmaba, EE65, Wnte 203, nto to mps 5/32

6 Response to the sgnal appeas to be lnea Response o S s also mae o a constant pat S an a sgnal esponse pat s. onstant pat o the esponse, S, s ONLY elate to, the constant pat o the nput Q pont on the tanse uncton o peous sle. o.e., gs 0, then s 0 he shape o the tme ayng poton o the esponse s s smla to gs. o.e., s s popotonal to the nput sgnal, gs F. Najmaba, EE65, Wnte 203, nto to mps 6/32

7 lthough the oeall esponse s non-lnea, the tanse uncton o the sgnal s lnea! onstant: Bas Sgnal an esponse s gs S S s gs Non-lnea elatonshp among these paametes ppoxmately Lnea elatonshp among these paametes F. Najmaba, EE65, Wnte 203, nto to mps 7/32

8 mpotant Ponts an entons! Sgnal: We want the esponse o the ccut to ths nput. Bas: State o the system when thee s no sgnal. o Bas s constant n tme may ay extemely slowly compae to sgnal o Pupose o the bas s to ensue that MOS s n satuaton at all tmes. Response o the ccut an ts elements to the sgnal s eent than ts esponse to the Bas o to Bas sgnal: o Sgnal chaactestcs o elements ae eent,.e. elatonshps among gs, s, s eent om elatonshps among, S,. o Sgnal tanse uncton o the ccut s eent om the tanse uncton o total nput Bas sgnal. boe obseatons & conclusons equally apply to a BJ n the acte moe! F. Najmaba, EE65, Wnte 203, nto to mps 8/32

9 ssues n eelopng a tanssto ample:. Fn the chaactestcs o the elements o the sgnal whch can be eent than the chaactestcs equaton o bas. o hs wll lea to eent ccut conguatons o bas esus sgnal 2. ompute ccut esponse to the sgnal o Focus on unamental tanssto ample conguatons 3. How to establsh a Bas pont bas s the state o the system when thee s no sgnal. o Stable an obust bas pont shoul be eslent to aatons n µ n ox W/L, t o β o BJ ue to tempeatue an/o manuactung aablty. o Bas pont etals mpact small sgnal esponse e.g., gan o the ample. F. Najmaba, EE65, Wnte 203, nto to mps 9/32

10 Sgnal cut We wll n sgnal chaactestcs o aous elements. 2 n oe to use ccut theoy tools, we wll use the sgnal chaactestcs o aous elements to assgn a ccut symbol. e.g., o We wll see that the oe sgnal chaactestcs s lnea so o sgnals, oe can be moele as a ccut theoy essto. o n ths manne, we wll ae at a sgnal ccut.

11 Bas an Sgnal cuts Bas & Sgnal Bas Sgnal only Bas Sgnal - Bas? MOS R... : : R R, S R R,, gs,... MOS R... : : R,, R S,, MOS R... : : gs,, s,, F. Najmaba, EE65, Wnte 203, nto to mps /32

12 Fnng sgnal ccut elements -- Ressto Ressto oltage uent Equaton Bas Sgnal: R R R R R Bas: R R R R R Sgnal: R R R R?? R R R R R R R R R R essto emans as a essto n the sgnal ccut. F. Najmaba, EE65, Wnte 203, nto to mps 2/32

13 Fnng sgnal ccut elements -- apacto apacto oltage uent Equaton Bas Sgnal: /t Bas: /t Sgnal: c c?? c t t t c t c capacto emans as a capacto n the sgnal ccut. o Snce const., 0,.e., capacto acts as an open ccut o bas ccut. F. Najmaba, EE65, Wnte 203, nto to mps 3/32

14 Fnng sgnal ccut elements S & S nepenent oltage souce oltage uent Equaton Bas Sgnal: S S S const Bas: S S S const Sgnal: s S S s S S?? s S S 0 s 0, s 0 Smlaly: n nepenent oltage souce becomes a shot ccut! n nepenent cuent souce becomes an open ccut! F. Najmaba, EE65, Wnte 203, nto to mps 4/32 Execse: Show that epenent souces eman as epenent souces

15 Summay o sgnal ccut elements Resstos& capactos: o apacto act as open ccut n the bas ccut. he Same nepenent oltage souce e.g., : Eectely goune nepenent cuent souce: epenent souces: Non-lnea Elements: o oes & tansstos? Eectely open ccut he Same eent! F. Najmaba, EE65, Wnte 203, nto to mps 5/32

16 oe Sgnal Response Bas Sgnal : s exp n Bas : s exp n Sgnal : s exp n s exp n exp n s exp n? exp n eent equaton! equaton s non-lnea! Relate to bas alue,! F. Najmaba, EE65, Wnte 203, nto to mps 6/32

17 oe small-sgnal moel: F. Najmaba, EE65, Wnte 203, nto to mps 7/32 exp n? n n n n n n n n << exp :... 2! exp Exapnson : aylo Sees 2 n

18 Fomal eaton o small sgnal moel F. Najmaba, EE65, Wnte 203, nto to mps 8/ ! a a >> 2 2 a << Small sgnal means: a a a g Sgnal Bas o element, : Bas o element, : Sgnal o element a, a : a g a a a a... 2!... 2! aylo Sees Expanson a a

19 eaton o oe small sgnal moel F. Najmaba, EE65, Wnte 203, nto to mps 9/32 n S e n S n S e n e S n S n S e e S n S n S n n e n e S n n n n / oe can be eplace wth a essto n the sgnal ccut!

20 Small sgnal moel s chaactestcs Small sgnal moel s equalent to appoxmatng the non-lne chaactestcs cue by a lne tangent to the cue at the bas pont n F. Najmaba, EE65, Wnte 203, nto to mps 20/32

21 eaton o MOS small sgnal moel MOS equatons:, S G 0 Sgnal Bas o MOS,, S :, S, G 0 Bas o MOS,, S :, S, G 0 Sgnal o MOS, gs, s : g gs, s, g 0, S aylo Sees Expanson n 2 aables, S, S S, S S S..., S gs S, S s, S gs S, S s F. Najmaba, EE65, Wnte 203, nto to mps 2/32

22 eaton o MOS small sgnal moel 2 F. Najmaba, EE65, Wnte 203, nto to mps 22/32 s S gs S S,,, S S t ox n L W λ µ m O t S t ox n S t ox n g L W L W S S ,, λ µ λ µ o S S S t ox n t ox n S L W L W S S , 2, λ λ λ λ λ µ λ µ λ 0 g o s gs m g

23 MOS small sgnal ccut moel nput open ccut 0 an g g m gs s o Statement o KL wo elements n paallel g m o gmo >> λ λ O O O F. Najmaba, EE65, Wnte 203, nto to mps 23/32

24 PMOS small sgnal moel s entcal to NMOS PMOS* NMOS PMOS small-sgnal ccut moel s entcal to NMOS o We wll use NMOS ccut moel o both! o Fo both NMOS an PMOS, whle 0 an 0, sgnal quanttes:, gs, an s, can be negate! F. Najmaba, EE65, Wnte 203, nto to mps 24/32 Execse: ee PMOS small sgnal moel ollow eaton o NMOS small-sgnal moel

25 eaton o BJ small sgnal moel BJ equatons: B 2, E / β Sgnal Bas o BJ B,,, E : B, 2, E Bas o BJ B,,, E : B, 2, E Sgnal o BJ b, c, be, ce : b g be, c g 2 be, ce B s s e e We nee to peom aylo Sees Expanson n 2 aables o both B an. E b, E be c 2, E be 2 E, E ce F. Najmaba, EE65, Wnte 203, nto to mps 25/32

26 eaton o BJ small sgnal moel 2 B s / β e E s e B / β s e s e E s e E B s / β e, E π 2, E s e E, E g m b, E be π be 2 s E, E e, E E o be b c gmbe π ce o F. Najmaba, EE65, Wnte 203, nto to mps 26/32

27 BJ small sgnal ccut moel be b c gmbe π ce o essto, π, between B & E Statement o KL wo elements n paallel π B g m We ollow S&S: be s enote as π o E Smla to NMOS/PMOS, the small ccut moel o a PNP BJ s the same as that o a NPN. F. Najmaba, EE65, Wnte 203, nto to mps 27/32

28 ltenate BJ small sgnal ccut moel F. Najmaba, EE65, Wnte 203, nto to mps 28/32 π π π π π β β β g g m B B m g m Moel β b Moel

29 Summay o tanssto small sgnal moels g m 2 O o λ F. Najmaba, EE65, Wnte 203, nto to mps 29/32

30 Example : onstuct the sgnal ccut an eplace the tanssto wth ts small-sgnal moel assume capactos ae shot o sgnal. S 0 R emans aps shot Goun at the bottom F. Najmaba, EE65, Wnte 203, nto to mps 30/32 Replace MOS wth ts small sgnal moel

31 Example 2: onstuct the sgnal ccut an eplace the tanssto wth ts small-sgnal moel assume capactos ae shot o sgnal. S 0 aps shot Goun at the bottom 00k 33k 24.8 k Flp PMOS Replace MOS wth ts small sgnal moel F. Najmaba, EE65, Wnte 203, nto to mps 3/32

32 Example 3: onstuct the sgnal ccut an eplace the tanssto wth ts small-sgnal moel assume capactos ae shot o sgnal. S 0 aps shot S 0 hs makes S an open ccut Replace MOS wth ts small sgnal moel F. Najmaba, EE65, Wnte 203, nto to mps 32/32