Lecture #26. Small Signal Model
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1 ecture #6 ANNOUNCEMEN he lowest H grade will be dropped for each student OUNE Sall-signal MOSFE odel MOSFE scaling elocity uration Short-channel MOSFEs EE30 ecture 6, Slide Sall Signal Model Conductance paraeters: g g d D D G const D G D const λ D0 µ C ( EE30 ecture 6, Slide
2 nclusion of Additional Parasitics EE30 ecture 6, Slide 3 Cutoff Frequency f ax is the frequency where the MOSFE is no longer aplifying the input signal Obtained by considering the sall-signal odel with the output terinals short-circuited, and finding the frequency where i out / i in f ax g πc µ ( π ncreased MOSFE operating frequencies are achieved by decreasing the channel length EE30 ecture 6, Slide 4
3 MOSFE Scaling MOSFEs have scaled in size over tie 970 s: ~ 0 µ oday: ~50 n Reasons: Speed Density EE30 ecture 6, Slide 5 Benefit of ransistor Scaling as (decreased ective R Gate area as (decreased load C herefore, RC (iplies faster switch EE30 ecture 6, Slide 6
4 Circuit Exaple CMOS nverter dd... 3 C C... dd τ d 3 τ d : propagation delay 0 t EE30 ecture 6, Slide 7 τ d ( pull down delay + Cdd pull up delay dp C pull down delay dd dn pull up delay τ d C ( + dd 4 dn dp τ d is reduced by increasing D R N and R P dd on d ( dd g dd EE30 ecture 6, Slide 8
5 elocity Saturation velocity uration has large and deleterious ect on the D of MOSFES v µ + << : v µ >> : v µ EE30 ecture 6, Slide 9 MOSFE - with elocity Saturation C µ ( long - channel / EE30 ecture 6, Slide 0
6 Solving for D d d 0, ( ( / A sipler and ore accurate D is: D / d v µ EE30 ecture 6, Slide Drain Saturation oltage D D n + E f E >> - n then the MOSFE is considered long-channel. his condition can be isfied when is large, or is close to EE30 ecture 6, Slide
7 EXAMPE: Drain Saturation oltage Question: At gs.8, what is the D of an NFE with 3 n, 0.5, and d 45 n for (a 0 µ, (b u, (c 0. µ, and (d 0.05 µ Solution: Fro,, and, µ n is 00 c - s -. v /µ 8 04 /c + 3 / d. D + EE30 ecture 6, Slide 3 D + (a 0 µ, D (/.3 + / (b µ, D (/.3 + /8 -. (c 0. µ, D (/.3 + / (d 0.05 µ, D (/.3 + / EE30 ecture 6, Slide 4
8 D with elocity Saturation Substituting D for in equation gives: D C ( µ long - channel D ery short channel case: D C µ n v C ( ( << / D is proportional to rather than ( EE30 ecture 6, Slide 5 inear region: Suary: NMOSFE - C µ ( E n Saturation region: Cµ ( D ( E n E v n v / µ c/s for electrons c/s for holes EE30 ecture 6, Slide 6
9 ery-short-channel MOSFEs f E << - n : D D ( n E < Cµ E( Cv ( D is not sensitive to o increase D (for faster circuit operation, we ust increase C ( - n, i.e. reduce and n n n EE30 ecture 6, Slide 7 ds (A/µ Short- vs. ong-channel MOSFE ds ( Short-channel MOSFE: D is proportional to - n rather than ( - n D is lower than for long-channel MOSFE Channel-length odulation is apparent 0.5 µ t 0.4 gs.5 gs.0 gs.5 gs.0 ds (µa/µ EE30 ecture 6, Slide 8.0 µ gs.5 t 0.7 ds ( gs.0 gs.5 gs.0
10 elocity Overshoot hen is coparable to or less than the ean free path, soe of the electrons travel through the channel without experiencing a single scattering event projectile-like otion ( ballistic transport he average velocity of carriers exceeds v e.g. 35% for 0. µ NMOSFE Effectively, v and E increase when is very sall EE30 ecture 6, Slide 9 PMOSFE - with elocity Saturation inear region: C µ ( + E p Saturation region: Cµ ( D E p p EE30 ecture 6, Slide 0
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