ECSE 334 Winter 2009 Midterm

# 1v all nmos and pmos devices have their substrate

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Unformatted text preview: Fig. 3a Question 2: [30 marks] Consider the folded-cascode amplifier in Fig. 3. Assume that: • All MOSFETs are biased in the saturation region with V OV = 0.1V . • All NMOS and PMOS devices have their substrate (body) connected to ground and VDD, respectively. • γ = 0 and λ = 0 , in your dc calculations. • gmb = 0, in your small-signal analysis. • Current sources IBIAS1 and IBIAS2 have incremental output resistances of R L 1 and R L 2 , respectively. • Capacitances C L 1 and C L 2 model the parasitic capacitances at nodes X and OUT, respectively, except for the parasitic (internal) capacitances of the MOSFETs. • Do not neglect C db in the MOSFET small-signal models. a) Find the value of transconductances gm1 and gm2 of transistors Q1 and Q2, respectively. I D 1 = I BIAS 1 – I BIAS 2 = 0.375mA ⇒ g m 1 = ( 2 I D 1 ) ⁄ V OV = ( 2 × 0.375mA ) ⁄ ( 0.1V ) = 7.5mA ⁄ V I D 2 = I BIAS 2 = 1mA ⇒ g m 2 = ( 2 I D 2 ) ⁄ V OV = ( 2 × 0.75mA ) ⁄ ( 0.1V ) = 15mA ⁄ V b) Write an expression for resistances R 1 and R 2 at midband frequencies. RL2 1 R 1 ≅ -------- ⎛ 1 + -------- ⎞ gm2 ⎝ r⎠ o2 R 2 ≅ ( R L 1 || r o 1 ) + r o 2 [ 1 + g m 2 ( R L 1 || r o 1 ) ] c) Write an expression of the midband voltage gains A M 1 ≡ v x ⁄ v in and A M ≡ v o ⁄ v s . v in = v s i d = g m 1 v in (see circuit diagram in Fig. 3a) v x = i d ( r o 1 || R L 1 || R 1 ) ⇒ A M 1 = v x ⁄ v in = – g m 1 ( r o 1 || R L 1 || R 1 ) v o = i d ( R L 2 || R 2 ) ⇒ A M = v o ⁄ v s = – g m 1 ( R L 2 || R 2 ) ECSE334 - Prof. Anas Hamoui Midterm - SOLUTION page 5 of 7 ECSE334 Introduction to Microelectronics Winter 2009 RL1 X R1 CL1 RS Cgd1 IN Cdb1 Cdb2 Cgs1 Cgs2 Cgd2 R2 RL2 OUT vo CL2 Fig. 3b d) Write an expression for the high-frequency poles associated with nodes IN, X, and OUT. Hint: Apply Miller’s theorem, then find the open-circuit time constants. Note: For simplicity, write your expressions using the previously-derived variables, together with the MOSFET small-signal parameters. The above circuit diagram (Fig. 3b) can be used to determine the high-frequency poles of the amplifier. Node IN: Using Miller theorem, Cgd1 is replaced by C gd 1 ( 1 + A M 1 ) between node IN and GND. The total capacitance associated with node IN is then: C IN = C gs 1 + C gd 1 ( 1 + A M 1 ) The total resistance associated with...
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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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