# hw13_sol - ECE 442 HW13 Solutions 1 a p 0 ID2 = f n(vO W...

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ECE 442 HW13 Solutions 1. a) λ p 0 I D 2 6 = fn ( v O ) ( W L ) 2 = 2 ( W L ) 1 I D 2 = 2 I D 1 = 2 mA V OV 3 = V I - V t = 0 . 6 - 0 . 4 = 0 . 2 V | A v | = 40 dB = 100 V V | A v | = g m R out = g m ( R L || r o 3 ) = 2 I D 3 V OV 3 ( R L || 1 λ n I D 3 ) 100 = 2 I D 3 0 . 2 × 10 k × 1 0 . 04 I D 3 10 k + 1 0 . 04 I D 3 Solving this equation yields the value of I D 3 = 1 . 67 mA . I D 2 = I D 3 + V O R L V O = R L ( I D 2 - I D 3 ) = 10 k ( 2 m - 1 . 67 m ) = 3 . 3 V I D 3 = 1 2 k 0 n ( W L ) 3 V 2 OV 3 ( 1 + λ n V O ) Solving this equation, we can obtain the value of ( W L ) 3 = 184 . 4 I D 2 = 1 2 k 0 p ( W L ) 2 V 2 OV 2 V OV 2 = s I D 2 1 2 k 0 p ( W L ) 2 = 0 . 523 V V G 2 = V CC - V OV 2 -| V tp | = 5 - 0 . 523 - 0 . 4 = 4 . 08 V R = V G 2 I REF = 4 . 08 1 m = 4 . 08 k Ω b) Using the formulas for swing as derived in class, in order to keep Q3 in saturation: v i - max V O - V OV 3 1 + A v = 3 . 3 - 0 . 2 1 + 100 = 30 . 7 mV In order to keep Q2 in saturation: v i - max V CC -| V OV 2 |- V O A v = 5 - 0 . 523 - 3 . 3 100 = 11 . 8 mV v i - max = min { 30 . 7 mV , 11 . 8 mV } = 11 . 8 mV 1

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2. a) v ID = v I 1 - v I 2 = 1 + 0 . 5 sin ( ω t ) - ( - 1 - 0 . 5 sin ( ω t )) = 2 + sin ( ω t ) V ID = 2 , v id = sin ( ω t ) v CM = v I 1 + v I 2 2 = 1 + 0 . 5 sin ( ω t ) + ( - 1 - 0 . 5 sin ( ω t )) 2 = 0 V CM = 0 , v cm = 0 The plot of the differential input is shown in Fig. 2a. The common-mode input is constant over time ( v CM = 0 ) . Figure 2a. Differential input voltage, vs time in μ s . b) v ID = v I 1 - v I 2 = 1 + 0 . 5 sin ( ω t ) - ( 1 - 0 . 5 sin ( ω t )) = sin ( ω t ) V ID = 0 , v id = sin ( ω t ) v CM = v I 1 + v I 2 2 = 1 + 0 . 5 sin ( ω t ) + ( 1 - 0 . 5 sin ( ω t )) 2 = 1 V CM = 1 , v cm = 0 The plot of the differential input is shown in Fig. 2b. The common-mode input is constant over time ( v CM = 1 ) . Figure 2b. Differential input voltage, vs time in μ s . c) Using the basic trigonometric identities:
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## This note was uploaded on 02/21/2010 for the course ECE 442 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.

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hw13_sol - ECE 442 HW13 Solutions 1 a p 0 ID2 = f n(vO W...

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