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Page-94 - v GS 1 = v 1 = V DD> ¯ V t → M1 is ON v GS 2...

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Finally, from KVLs in no. 3. above, we have v o = V DD + v DS 3 = V DD . So, when v 1 is LOW and v 2 is HIGH, the output is HIGH. We can go back and ±nd the state of M2. We will ±nd M2 to be OFF (left for students). v 1 = V DD , v 2 = 0 We ±rst ±nd v GS and state of all transistors by using KVLS in no. 1 above. v GS 1 = v 1 = V DD > ¯ V t M1 is ON v GS 2 = v 2 v DS 1 = v DS 1 < ¯ V t M2 is OFF i D 2 = 0 v GS 3 = v 1 V DD = 0 > ¯ V t M3 is OFF i D 3 = 0 v GS 4 = v 2 V DD = V DD < ¯ V t M4 is ON In the above, we used the fact that v DS 1 0. Since i D 2 = 0, by KCLs in no. 2 above , i D 1 = i D 2 = 0. Also, i D 3 + i D 4 = i D 2 = 0 leading to i D 4 = 0. We add the value of i D to the table above and look for transistors that are ON and have i D = 0. These transistors have to be in Triode region with v DS = 0. v GS 1 = v 1 = V DD > ¯ V t M1 is ON i D 1 = 0 v DS 1 = 0 v GS 2 = v 2 v DS 1 = v DS 1 < ¯ V t M2 is OFF i D 2 = 0 v GS 3 = v 1 V DD = 0 > ¯ V t M3 is OFF i D 3 = 0 v GS 4 = v 2 V DD = V DD < ¯ V t M4 is ON i D 4 = 0 v DS 4 = 0 Finally, from KVLs in no. 3. above, we have v o = V DD + v DS 4 = V DD . So, when v 1 is HIGH and v 2 is LOW, the output is HIGH. v 1 = V DD , v 2 = V DD We ±rst ±nd v GS and state of all transistors by using KVLS in no. 1 above.
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Unformatted text preview: v GS 1 = v 1 = V DD > ¯ V t → M1 is ON v GS 2 = v 2 − v DS 1 = V DD − v DS 1 → M2 is ? v GS 3 = v 1 − V DD = 0 > − ¯ V t → M3 is OFF → i D 3 = 0 v GS 4 = v 2 − V DD = 0 > − ¯ V t → M4 is OFF → i D 4 = 0 From KCLs in no. 2 above , i D 2 = i D 1 = i D 3 + i D 4 = 0. We add the value of i D to the table above and look for transistors that are ON and have i D = 0. These transistors have to be in Triode region with v DS = 0. v GS 1 = v 1 = V DD > ¯ V t → M1 is ON i D 1 = 0 → v DS 1 = 0 v GS 2 = v 2 − v DS 1 = V DD − v DS 1 = V DD > ¯ V t → M2 is ON i D 2 = 0 → v DS 2 = 0 v GS 3 = v 1 − V DD = 0 > − ¯ V t → M3 is OFF → i D 3 = 0 v GS 4 = v 2 − V DD = 0 > − ¯ V t → M4 is OFF → i D 4 = 0 ECE65 Lecture Notes (F. Najmabadi), Fall 2009 94...
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