ch07_solutions

# Il 2 k r v dd v tn v tp 29 v dd k r v tn v tp 29 k r

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IL = 2 K R V DD - V TN + V TP ( 29 - V DD - K R V TN + V TP ( 29 K R + 3 K R - 1 ( 29 K R + 3 = 0 0 lim K R 1 V IL = lim K R 1 2 2 K R V DD - V TN + V TP ( 29 - V DD - K R V TN + V TP ( 29 1 2 K R + 3 + V TN K R + 3 K R + 3 + 1 2 K R - 1 ( 29 K R + 3 lim K R 1 V IL = V DD - V TN + V TP ( 29 - V DD - V TN + V TP ( 29 1 4 + 2 V TN 2 = 3 V DD + 5 V TN + 3 V TP 8 V OH = 2 V IH + V DD - V TN - V TP 2 = 7 V DD + V TN - V TP 8 NM L = V IL - V OL = 3 V DD + 5 V TN + 3 V TP 8 - V DD - V TN + V TP 8 = V DD + 3 V TN + V TP 4 NM H = V OH - V IH = 7 V DD + V TN - V TP 8 - 5 V DD + 3 V TN + 5 V TP 8 = V DD - V TN - 3 V TP 4

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7-256 7.95 a ( 29 For V DD = 5 V , V TN = 1 V , V TP = - 1 V t P = 0.322 C K n | d t P dK n = - 0.322 C K n 2 = - t P K n | S K n t P = K n t P d t P dK n = - 1 t P t P S K n t P K n K n = - K n K n = - - 0.25 ( 29 = + 0.25 | A 25% decrease in K n will cause a 25% increase in propagation delay. b ( 29 Assuming a symmetrical inverter with V DD = 5V and V TN = 0.75V, t P = C K n V DD - V TN ( 29 ln 4 V DD - V TN V DD - 1 + 2 V TN V DD - V TN t P = C K n 5 - 0.75 ( 29 ln 4 5 - 0.75 5 - 1  + 2 0.75 ( 29 5 - 0.75 = 0.289 C K n d t P dV TN = t P V DD - V TN ( 29 + C K n V DD - V TN ( 29 - 4 V DD 4 V DD - V TN V DD - 1 + 2 V DD V DD - V TN ( 29 2 d t P dV TN = 0.289 C 5 - 0.75 ( 29 K n + C K n 5 - 0.75 ( 29 - 4 5 4 5 - 0.75 5 - 1 + 2 5 ( 29 5 - 0.75 ( 29 2 = 0.120 C K n S V TN t P = V TN t P d t P dV TN = 0.75 K n 0.289 C 0.120 C K n = 0.311 t P t P 2245 S K n t P V TN V TN = 0.311 0.1 0.75  = 0.0415 = 4.15%. A 13% increase in V TN causes an 4.2% increase in t P . 7.96 *PROBLEM 7.96 - INVERTER DELAY VS RISETIME VDD 1 0 DC 5 V1 2 0 PULSE (0 5 0 0.1N 0.1N 25N 50N) MN1 3 2 0 0 MOSN W=4U L=2U AS=16P AD=16P MP1 3 2 1 1 MOSP W=4U L=2U AS=16P AD=16P C1 3 0 1PF * V2 4 0 PULSE (0 5 0 0.2N 0.2N 25N 50N) MN3 5 4 0 0 MOSN W=4U L=2U AS=16P AD=16P MP3 5 4 1 1 MOSP W=4U L=2U AS=16P AD=16P C3 5 0 1PF * V3 6 0 PULSE (0 5 0 0.5N 0.5N 25N 50N) MN5 7 6 0 0 MOSN W=4U L=2U AS=16P AD=16P MP5 7 6 1 1 MOSP W=4U L=2U AS=16P AD=16P
7-257 C5 7 0 1PF * V4 8 0 PULSE (0 5 0 1N 1N 25N 50N) MN7 9 8 0 0 MOSN W=4U L=2U AS=16P AD=16P MP7 9 8 1 1 MOSP W=4U L=2U AS=16P AD=16P C7 9 0 1PF * V5 10 0 PULSE (0 5 0 2N 2N 25N 50N) MN9 11 10 0 0 MOSN W=4U L=2U AS=16P AD=16P MP9 11 10 1 1 MOSP W=4U L=2U AS=16P AD=16P C9 11 0 1PF * .OP .TRAN 0.025N 50N .MODEL MOSN NMOS KP=5E-5 VTO=0.91 GAMMA=0.99 +LAMBDA=.02 TOX=41.5N +CGSO=330P CGDO=330P CJ=3.9E-4 CJSW=510P .MODEL MOSP PMOS KP=2E-5 VTO=-0.77 GAMMA=0.5 +LAMBDA=.05 TOX=41.5N +CGSO=315P CGDO=315P CJ=2.0E-4 CJSW=180P .PROBE V(2) V(3) V(4) V(5) V(6) V(7) V(8) V(9) V(10) V(11) .END t r τ P 0.1 ns 4.6 ns 0.2 ns 4.6 ns 0.5 ns 4.7 ns 1 ns 4.9 ns 2 ns 5.1 ns
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