HW3%20Solution

HW3%20Solution - 1. Figure 1 shows an enhance NMOS...

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1. Figure 1 shows an enhance NMOS inverter, assuming γ=0.4, 2|φf|=0.6V, V T0 =0.43V (all the following questions are adopting such constants unless special hint), kn’=115μA/V 2 and λ=0, calculate V OH , V OL , VM for the inverter. Figure 1 Solution: V OL : To calculate V OL , we set V IN = V DD = 2.5V. We expect V OUT to be low, so we can make the assumption that M2 will be saturated and M1 will be in the linear region. For M2: ' 2 2 2 2 2 2 . .( ) .(1 ) 2 n D GS T DS k W I V V V L λ = - + , whereby 2 T V can be approximated as 2 T V derived in above process, which is equal to 2.5-1.765=0.735(V). For M1: ' 2 1 1 1 1 1 1 1 . .[2( ) ] 2 n D GS T DS DS k W I V V V V L = - - Set 2 D I = 1 D I , we get OUT V =0.285V. (Hint, more accurately, we can still consider the body effect of M2, and form 2 equations to solve both OUT V and 2 T V , which is also considered to be correct) V M : To calculate V M we set V M = V IN = V OUT ; therefore both M1 and M2 are in saturation region since their V G = V D , and we have following equations:
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' 2 2 2 2 2 2 . .( ) .(1 ) 2 n D GS T DS k W I V V V L λ = - + = ' 2 2 2 . .( 0.735) 2 n DD M k W V V L - - ' 2 1 1 1 1 1 . .( ) .(1 ) 2 n D GS T DS k W I V V V L = - + = ' 2 1 0 1 . .( ) 2 n M T k W V V L - Set 1 D I = 2 D I , we get M V = 0.984V. 2. Still referring to question 1, calculate V
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HW3%20Solution - 1. Figure 1 shows an enhance NMOS...

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