ECSE 334 Winter 2009 Midterm

1 v input transistors q1 and q2 provide gm1 gm2 2 mav

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Unformatted text preview: and Q2 which operate at VOV1 = VOV2 = 0.1 V. • Input transistors Q1 and Q2 provide gm1 = gm2 = 2 mA/V. Note: do not assume that transistors Q3 and Q4 have the same ( W ⁄ L ) . W 2 g m 1, 2 = μ n C ox ⎛ ----⎞ V OV 1, 2 = ( 200 μ A ⁄ V ) ⎝ L ⎠ 1, 2 ⎛ W⎞ ( 0.1V ) = 2mA ⁄ V ⇒ ⎛ W⎞ ------= 100 ⎝ L ⎠ 1, 2 ⎝ L ⎠ 1, 2 1 Now, I D 1, 2 = -- g m 1, 2 × V OV 1, 2 = 0.1mA . 2 Hence, I D 5, 6 = I D 1, 2 = 0.1mA and I D 3 = I D 1 + I D 2 = 0.2mA . Therefore, 2 I D 5, 6 2 ( 0.1mA ) ( W ⁄ L ) 5, 6 = ------------------------------- = ---------------------------------------------------- = 64 2 2 2 μ p C ox V OV 5, 6 ( 50 μ A ⁄ V ) ( 0.25V ) 2 ID3 2 ( 0.2mA ) ( W ⁄ L ) 3 = --------------------------- = ---------------------------------------------------------- = 32 2 2 2 μ n C ox V OV 3 ( 200 μ A ⁄ V ) ( 0.250V ) 2 I REF 2 ( 25 μ A ) ( W ⁄ L ) 4 = --------------------------- = ------------------------------------------------------- = 4 2 2 2 μ n C ox V OV 3 ( 200 μ A ⁄ V ) ( 0.25V ) ECSE334 - Prof. Anas Hamoui Midterm - SOLUTION page 2 of 7 ECSE334 Introduction to Microelectronics Winter 2009 b) Write the expression for the output resistance R o . Find its value. 1 1 r o 2 = ------------- = -------------------------------------------- = 40 k Ω –1 λn ID2 ( 0.25 V ) ( 0.1 mA ) 11 r o 6 = ------------- = ----------------------------------------- = 25 k Ω –1 λp ID2 ( 0.4 V ) ( 0.1 mA ) ∴ R o = r o 2 || r o 6 = 15.4 k Ω c) Write the expression for the differential voltage gain A d = v o ⁄ v id . Find its value. The small-signal current through Q1 and Q2 in Fig. 1 is: v id v id i d = --------------------------- = g m 1, 2 ----2 2 ( 1 ⁄ g m 1, 2 ) and, therefore, v o = ( 2 i d ) R o = ( g m v id ) R o where the factor 2 is due to the active load (Q5-Q6) which mirrors the current i d , thereby doubling the total current at the output. Hence, vo A d = ----- = g m 1, 2 R o = ( 2mA ⁄ V ) ( 15.4k Ω ) = 30.8V ⁄ V v id d) To improve the gain o...
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This note was uploaded on 02/08/2012 for the course ECSE 334 taught by Professor Anashamoui during the Spring '10 term at McGill.

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