ECSE 334 Winter 2009 Midterm

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

## This note was uploaded on 02/08/2012 for the course ECSE 334 taught by Professor Anashamoui during the Spring '10 term at McGill.

Ask a homework question - tutors are online