Chapter06

Microelectronic Circuit Design

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CHAPTER 6 6.1 gate A V gate W I b gate W gates W P a avg / 4 5 . 2 / 10 = ) ( / 10 10 1 ) ( 5 - 5 μ = = = 6.2 ( a ) P avg = 100 2 x 10 7 gates = 5 W / gate ( b ) I = 5 x 10 -6 W / gate 2.5 V = 2 A / gate ( c I total = 2 A gate 2 x 10 7 gates () = 40 A 6.3 W P mW R I P V V V V b W P mW R I P V V V V a L H L H V V L H V V L H 109 10 10 0 3 . 3 | 0 | 0 | 3 . 3 ) ( 5 . 62 10 10 0 5 . 2 | 0 | 0 | 5 . 2 ) ( 5 2 5 2 5 2 5 2 = = = = = = = = = = = = 6.4 v O v I V H (3.3 V) V L (0V) 1.1 V (V REF ) 3.3V V + 6.5 v O v I V H (3.3 V) V L (0V) 1.1 V (V REF ) 3.3V V + Z = A ( ) = A 6-1
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6.6 v I A V V REF 6.7 V H = 3 V | V L = 0 V V IH = 2 V V IL = 1 V A V = dv O dv I = 3 V 1 V =− 3 6.8 v O v I V H (3 V) V L (0V) 1.33 V 3V V + Slope = +9 1.5 V 1.5 V 1.67 V 6.9 V NM V V V V V V NM V V V V V L REF IL OL H REF IH OH 2 = 0 2 = 2 0 3 = 2 5 = 2 5 = = = = = = 6.10 We would like to achieve the highest possible noise margins for both states and have them be symmetrical. Therefore V REF = 3.3/2=1.65 V. 6.11 V H = 3.3 V V L = V V IH = 1.8 V V OL 0.25 V V IL = 1.5 V V IH 3.0 V NM H = 3.0 1.8 = 1.2 V NM L = 1.5 0.25 = 1.25 V 6.12 V H = 2.5 V V L = 0.20 V 6-2
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6.13 V H =− 0.80 V | V L 1.35 V 6.14 V IH = V OH NM H 0.8 0.5 1.3 V V IL = NM L + V OL = 0.5 + − 2 ( ) = − 1.5 V 6.15 τ P = PDP/P = 10 -13 J/10 -4 W = 10 -9 s = 1 ns 6.16 () fJ W ns PDP c gate A V gate W x I b gate W gates x W P a avg 8 4 2 = ) ( / 60 . 1 5 . 2 / 10 4 = ) ( / 4 10 5 . 2 1 ) ( 6 - 5 = = = = μ 6.17 fJ W ns PDP c gate A V gate W I b gate W gates W P a avg 1 1 1 = ) ( / 4 . 0 5 . 2 / 1 = ) ( / 1 10 100 ) ( 8 = = = = 6.18 11 0 5 0 100 P 1 10 100 250 Slope = 1 Slope = 2 PDP 6-3
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6.19 () () () () () ( ) () () () ( ) () ( ) () ) RC RC t t t RC t RC t RC t RC t RC t t v v t v b RC RC t t t RC t RC t RC t RC t RC t t v t t v t v dt t dv RC t v dt t dv C t i t v R t i t v a f C r C c c C 20 . 2 9 ln | 1 . 0 ln exp 1 . 0 9 . 0 ln exp 9 . 0 | exp 1 0 0 ) ( 20 . 2 9 ln | 9 . 0 ln exp 1 = 1 . 0 1 . 0 ln exp 1 = 9 . 0 | exp 1 0 for 1 | | | ) ( % 90 % 10 % 10 % 10 % 90 % 90 % 10 % 90 % 10 % 10 % 90 % 90 = = = = = = = = = = = = = = = = = + = = + = 6.20 ( a ) V H = 2.5 V | V L = 0.20 V ( b ) V 10% = V L + 0.1 Δ V = 0.20 + 0.23 = 0.43 V t 10% 23 ns for v O V 90% = V L + 0.9 Δ V = 0.20 + 2.07 = 2.27 V t 90% 33 ns for v O t r = 33 23 = 10 ns For fall time: t 10% 2.5 ns for v O t 90% 0.8 ns for v O t f = 1.7 ns For v I , t 10% 0 ns t 90% 1 ns t r = ns t f ns c τ PHL 1.5 ns 0.5 ns = ns PLH 26 ns 21 ns = 5 ns ( d ) P = 1 + 5 2 ns = 3 ns 6.21 ns ns d ns ns V V c ns t ns t ns t ns t v ns t v ns t v ns t ns t v ns t V V V V v ns t V V V V b V V V V a P PLH PHL f r I f O O r O L O L L H 4 2 4 4 ) ( 4 | 4 | 07 . 1 2 36 . 1 78 . 0 1 | 1 1 0 , For 5 . 9 for 2 for 5 . 11 : time fall For 5 . 9 5 . 32 42 for 42 84 . 0 58 . 0 9 . 0 36 . 1 9 . 0 for 5 . 32 30 . 1 58 . 0 1 . 0 36 . 1 1 . 0 ) ( 36 . 1 | 78 . 0 ) ( % 50 % 90 % 10 % 90 % 10 % 90 % 90 % 10 % 10 = + = = = = = = = = + = Δ + = = + = Δ + = = = 6-4
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6.22 A + B () A + C AA + AC + BA + BC A + AC + BA + BC A1+C + AB + BC A + AB + BC A 1 + B + BC A + BC 6.23 Z = ABC + ABC + A BC Z = ABC ++ ABC + ABC + A BC Z = AB C + C + A + A BC Z = AB 1 + 1 BC Z = AB + BC 6.24 A B C Z 0000 0010 0100 0111 1000 1010 1101 1111 Z = AB+BC 6-5
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6.25 Z = A B C + ABC + A BC + AB C Z = CA B + AB + A B + () Z = B + A B + AB + Z = B + B + + B Z = 1 + A 1 Z = + A Z = C 1 Z = C 6.26 C Z Z C B A = 1 1 1 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 0 0 0 0 6-6
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6.27 A B C D Z 00000 00010 00100 00110 01000 01010 01100 01110 10000 10010 10100 10110 11000 11010 11100 11111 Z = AB + CD Z = AB CD Z = ABCD 6.28 A B C Z 1 Z 2 0000 1 0010 1 0100 0 0110 1 1000 0 1010 1 1101 1 1111 1 Z 1 = AB = AB Z 2 = AB + C 6.29 (a) Fanout = 2 (b) Fanout = 1 6-7
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6.30 t i(t) 1 ns 0.132 A 0 () ! 45 . 8
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Chapter06 - CHAPTER 6 6.1(a Pavg = 1W 10-5W gate = 10 W...

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