Example: PMOS Circuit Analysis

Transcription

1 10//004 Example PMOS Circui Analysis.doc 1/8 Example: PMOS Circui Analysis Consider his PMOS circui: 5V K = 0. ma/v V = -.0 V + - V 10 K I V =4.0V 4K For his problem, we know ha he drain volage V = 4.0 V (wih respec o ground), bu we do no know he value of he volage source V. Le s aemp o find his value V! Firs, le s ASSUME ha he PMOS is in sauraion mode. Therefore, we ENFORCE he sauraion drain curren equaion I K ( V V ) =. Jim Siles The Univ. of Kansas ep. of EECS

2 10//004 Example PMOS Circui Analysis.doc /8 Now we mus ANALYZE his circui! 5V Q: Yikes! Where do we sar? I G A: The bes way o sar is by picking he low-hanging frui. In oher words, deermine he obvious and easy values. on ask, Wha is V?, bu insead ask, Wha do I know?! + - V 10 K I V =4.0V 4K There are los of hings ha we can quickly deermine abou his circui! I G = 0.0 V S = 5.0 ma V I V = = = 1 ma 4 4 V = V 10I = V 10 0 = V G G Therefore, we can likewise deermine: V = V V = = 10. V S S V = V V = V 50. V G S Jim Siles The Univ. of Kansas ep. of EECS

3 10//004 Example PMOS Circui Analysis.doc 3/8 Noe wha we have quickly deermined he numeric value of drain curren (I =1.0 ma) and he volage drain-o-source (V S =-1.0) Moreover, we have deermined he value V in erms of unknown volage V ( V = V 50. ). We ve deermined all he imporan suff (i.e., V,V S, I )! We can now relae hese values using our PMOS drain curren equaion. Recall ha we ASSUME sauraion, so if his assumpion is correc: I = K V V Insering ino his equaion our knowledge from above, along wih our PMOS values K=0. ma/v and V =-.0, we ge: ( ) I = K V V 10. = 0. V = V + 0. Be careful here! Noe in he above equaion ha hreshold volage V is negaive (since PMOS) and ha I and K are boh wrien in erms of milliamps (ma). Now, we solve his equaion o find he value of V! Jim Siles The Univ. of Kansas ep. of EECS

4 10//004 Example PMOS Circui Analysis.doc 4/8 50. = V + 0. ± 5 = V + 0. ± 5 0. = V Q: So V is boh 5 0. = 0 4. V and 5 0. = 4 3. V? How can his be possible? A: I s no possible! The soluion is eiher V =0.4 V or V = -4.3 V. Q: Bu how can we ell which soluion is correc? A: We mus choose a soluion ha is consisen wih our original ASSUMPTION. Noe ha neiher of he soluions mus be consisen wih he sauraion ASSUMPTION, an even meaning ha our ASSUMPTION was wrong. However, one (bu only one!) of he wo soluions may be consisen wih our sauraion ASSUMPTION his is he value ha we choose for V! For his example, where we have ASSUME ha he PMOS device is in sauraion, he volage gae-o-source V mus be less (remember, i s a PMOS device!) han he hreshold volage: V < V V < 0. V Jim Siles The Univ. of Kansas ep. of EECS

5 10//004 Example PMOS Circui Analysis.doc 5/8 Clearly, one of our soluions does saisfy his equaion ( V = 43. < 0. ), and herefore we choose he soluion V = 43. V. Q: oes his mean our sauraion ASSUMPTION is correc? A: NO! I merely means ha our sauraion ASSUMPTION migh be correc! We need o CHECK he oher inequaliies o know for sure. Now, reurning o our circui analysis, we can quickly deermine he unknown value of V. Recall ha we earlier deermined ha: V = V 50. And now, since we know ha he V =-4.3 V, we can deermine ha: V = V = = 077. V This soluion (V =0.77 V) is of course rue only if our original ASSUMPTION was correc. Thus, we mus CHECK o see if our inequaliies are valid: We of course already know ha he firs inequaliy is rue a p-ype channel is induced: V = 43. < 0. = V Jim Siles The Univ. of Kansas ep. of EECS

6 10//004 Example PMOS Circui Analysis.doc 6/8 And, since he excess gae volage is V V = 3. V, he second inequaliy: V = 10. > 3. = V V S shows us ha our ASSUMPTION was incorrec! Time o make a new ASSUMPTION and sar over! So, le s now ASSUME he PMOS device is in riode region. Therefore ENFORCE he drain curren equaion: i K V V V V = S S Now le s ANALYZE our circui! Noe ha mos of our original analysis was independen of our PMOS mode ASSUMPTION. Thus, we again conclude ha: I G = 0.0 ma V S = 5.0 V I V = = = 1 ma 4 4 V = V 10I = V 10 0 = V G G Jim Siles The Univ. of Kansas ep. of EECS

7 10//004 Example PMOS Circui Analysis.doc 7/8 Therefore, V = V V = = 10. V S S V = V V = V 50. V G S Now, insering hese values in he riode drain curren equaion: i = K ( V V ) VS V S 10. = 0. ( V ( ) )( 1) ( 1) 50. = ( V + ) 1 Look! One equaion and one unknown! Solving for V we find: ( ) 50. = V = V = V = V Thus, we find ha V = -5.0 V, so ha we can find he value of volage source V : V = V = V = V The volage source V is equal o zero provided ha our riode ASSUMPTION was correc. Jim Siles The Univ. of Kansas ep. of EECS

8 10//004 Example PMOS Circui Analysis.doc 8/8 To find ou if he ASSUMPTION is correc, we mus CHECK our riode inequaliies. Firs, we CHECK o see if a channel has indeed been induced: V = 50. < 0. = V Nex, we CHECK o make sure ha our channel is no in pinchoff. Noing ha he excess gae volage is V V = 50. ( 0). = 30. V, we find ha: V = 10. > 30. = V V S Our riode ASSUMPTION is correc! Thus, he volage source V = 0.0 V. Jim Siles The Univ. of Kansas ep. of EECS