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(ELEC304)Midterm_2002Fall.pdf
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The Hong Kong University of Science and Technology
Department of Electrical and Electronic Engineering

ELEC304 Midterm Exam 24th Oct. 2002
Name:
Student Number:

Time: 15:00-16:30 (1.5-hour closed book examination) Do all the problems in the answer book and the provided graph paper
Q1. Consider the following circuit.

Find


Vo ()
s
()
(a) The transfer function Hs = (5 Marks)

Vi ()
s
(b)
The pole and zero frequencies in terms of circuit parameters (5 Marks) 1000

(c)
The phase at = (5 Marks)


C .(R1 +R2 )
Q2. An amplifier with feedback is shown in the figure. Find (a) Type of feedback (5 Marks) (b) Closed-loop voltage gain socl vvA = (10 Marks) (c) Closed-loop input resistance Rincl (10 Marks) (d) Closed-loop output resistance Rocl (10 Marks) Notes: (1) Answer in symbolic form (2) No simplification is required (3) Include ro in all your answers (4) Show all evaluation steps (5) No mark will be given without evaluation steps vs RD1 Rincl RS VDD vo
Written By: Alex K. N. Leung p. 1


Q3. A two-stage amplifier with feedback is shown below. It is noted that ZF and ZL are impedances.

v
o
(a) Evaluate the closed-loop voltage gain in symbolic form (You need to show all steps
v
s
and include ro in your result). (15 Marks)
(b) As shown in the figure below, ZF and ZL are the impedances of CF and CL, respectively. VDD

By using the result of part (a), prove that the transfer function is given by
As () gg .( // r .r // r )

vs r )(
om1 m5 o2 o4 o5 o6
()=
svs () 1 +sC .g .(r // r )( .r // r )+s2C .(C +C )( .r // r )( .r // r 6 )
Fm5 o2 o4 o5 o6 FF Lo2 o4 o5 o
based on the assumptions (1) C .g .r // r )( // r >>C .( 4 )
(.r ) r // r
Fm5 o2 o4 o5 o6 Fo2 o
(2) CF .gm5 .(ro2 // ro4 .ro5 // ro6 )>> CF +CL )( o5 o6 )
)( (.r // r
(15 Marks)
(c) Given that the transfer function in part (b) can be further approximated as As v () gg .( // r )( r ) A
os m1 m5 ro2 o4 .ro5 // o6 o
()= =
vs
s () . CL .. s .. s .
[+sCF .gm5 .(o2 // ro4 )( o5 // ro6 )..1+s .......+ ..1 r .r ]. 1+ ..1
g pp
. m5 .. 1 .. 2 . Find Ao, p1 and p2 in terms of circuit parameters in the transfer function. (5 Marks)
(d)
Given that gm1 =10A /V , gm5 =100A /V , ro2 =ro4 =ro5 =ro6 =2M., CF =10 pF

and CL =10 pF , plot the Bode plot (both magnitude plot and phase plot) on the graph provided. (10 Marks)

(e)
Find the gain-bandwidth product. (5 Marks)



Q1. Answer
1
R +
2
Hs Vo ()s sC 1+sCR2
(a) ()= = 1 =
V () 1+sC .(R +R2 )
s
i 1
R +R +
12
sC
11
(b) p = and z =
C .(R +R2 ) CR
12 1000R
1+j . 2
1+j.CR2 . 1000 . R1 +R2
(c) () = .H .j .=
Hj.
1+j.C(R1 +R2 ) ..C(R1 +R2 )..1+j1000
.1000R ..1000R .
.12 .1 .12 o
Thus, Phase = tan .. tan (1000)=tan .. 90
... ...
R +RR +R
. 12 .. 12 .

Q2. Answer
(a) Series-Shunt Feedback
(b), (c) and (d)

RS RS

open! vf

vo
RS
short! open! RLf = RS
Rf = 0 f = vf/