Unformatted text preview: C IN is: R IN = R S
The opencircuit time constant associated with C IN is: τ IN = R IN C IN
The pole associated with node IN is: ω IN = 1 ⁄ τ IN
Node X:
Using Miller theorem, Cgd1 is replaced by C gd 1 ( 1 + 1 ⁄ A M 1 ) between node X and GND.
The total capacitance associated with node X is then: C X = C gd 1 ( 1 + 1 ⁄ A M 1 ) + C db 1 + C L 1 + C gs 2
The total resistance associated with C X is: R X = r o 1  R L 1  R 1
The opencircuit time constant associated with C X is: τ X = R X C X
The pole associated with node X is: ω X = 1 ⁄ τ X
Node OUT:
The total capacitance associated with node X is then: C OUT = C gd 2 + C db 2 + C L 2
The total resistance associated with C OUT is: R OUT = R L 2  R 2
The opencircuit time constant associated with C OUT is: τ OUT = R OUT C OUT
The pole associated with node OUT is: ω OUT = 1 ⁄ τ OUT ECSE334  Prof. Anas Hamoui Midterm  SOLUTION page 6 of 7 ECSE334 Introduction to Microelectronics Winter 2009 e) Assuming a dominant pole exists, estimate:
i) the 3dB frequency, based on the opencircuit timeconstant approximation
ω 3 dB ≅ 1 ⁄ ( τ IN + τ X + τ OUT )
ii) the unitygain frequency
Note: For simplicity, write your expressions using the previouslyderived variables.
ω t ≅ A M ω 3 dB
f) Current sources IBIAS1 and IBIAS2 in Fig. 3 can be realized using, respectively,
current sources Q3Q4 and Q5Q6, as shown in Fig. 4.
Assume that the signal voltage at the gate of Q3 and Q5 in Fig. 4 is zero.
For the expressions found in parts (b)(d) for the circuit in Fig. 3,
which variables must be replaced and by which variables in Fig. 4 must they be replaced,
in order to obtain the corresponding expressions for the circuit in Fig. 4 ?
Q3 Q4 Cdb3 Cgd3 vS RS
Q1 Vbias Q2 vo
Cgd5 Q6 Q5 Cdb5 Fig. 4
Exchange: • RL1 with ro3 (to account for the output resistance of current source IBIAS1)
• RL2 with ro5 (to account for the output resistance of current source IBIAS2)
• CL1 with Cgd3 + Cdb3 (to account for the effect of the internal capacitance of Q3 on the total
capacitance at node X).
• CL2 with Cgd5 + Cdb5 (to account for the effect of the internal capacitance of Q5 on the total
capacitance at node OUT). ECSE334  Prof. Anas Hamoui Midterm  SOLUTION page 7 of 7...
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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.
 Spring '10
 ANASHAMOUI

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