首页 低价平台

服务介绍

代写程序 代写论文 编程辅导
代写案例 论文案例 联系方式 诚邀英才 代写选择指南
程序辅导案例 > Program >

程序代写案例-ECE 264A-Assignment 3

欢迎使用51辅导，51作业君孵化低价透明的学长辅导平台，服务保持优质，平均费用压低50%以上！ 51fudao.top
ECE 264A: Analog Integrated Circuits and Systems I Ian Galton
January 24, 2022 EBU1 5606
Homework Assignment 3
Due: 5 pm, January 31, 2022 r>

The problems on the following four pages are ECE264A midterm exams from 2007, 2008, 2009,
and 2014, respectively. Each exam was given as a closed-book, in-class exam with a time limit
of 1 hour and 20 minutes. It is suggested that you study for the upcoming ECE264A midterm ex-
am prior to working on the problems. Then try to do the problems under conditions that simulate
the exam conditions (i.e., without using books or class notes and with the goal of completing
each set of exam problems within an hour and 20 minutes.)

ECE 264A CMOS Analog Integrated Circuits and Systems Midterm Exam, February 13, 2007
The problems below relate to the following amplifier circuit. While solving them you may
assume that

(i) capacitances C1 and C2 are sufficiently large that the small-signal transistor model
capacitances may be neglected,
(ii) both transistors are in saturation,
(iii) both the current sources are ideal, and
(v) for all values of i and j. 1/
ids m
r
j
g

Vin
M1
VoutIBIAS 2 C2
R2
R1
M2
IBIAS 1
C1



1) Derive a block diagram of the circuit with input vin(s), output vout(s), and nodes
corresponding to vgs1(s) and vds1(s).

2) Derive an expression for Av(s) = vout(s)/vin(s) using Mason’s Gain Formula. You need not
reduce your final answer to its simplest form.

3) Derive an expression for the output resistance of the circuit using Blackaman’s Impedance
Relation. For this problem only, you may neglect capacitors C1 and C2 as well the transistor
model capacitances.

4) Suppose R1 = 3kΩ, R2 = 9kΩ, gm1 = 10−3Ω−1, gm2 = 10−4Ω−1, rds1 =100 kΩ, rds2 = 200kΩ, C1 =
50fF, and C2 = 3pF. Calculate the DC gain and approximate 3dB bandwidth of the amplifier.


2
ECE 264A CMOS Analog Integrated Circuits and Systems Midterm Exam, February 5, 2008
2
All of the problems relate to the following amplifier circuit. In solving the problems, you may
assume that

(i) VB1, VB2, VB3, and VREF, represent constant voltage sources with zero small signal
impedance to ground,
(ii)
3 4m m
g g= and
3 4mb mb
g g= ,
(iii) 1/
i jds m
r g for all values of i and j, and
(iv) all transistors are in saturation.



1. (35 points) Derive and draw a block diagram corresponding to the small-signal model
representation of the amplifier NEGLECTING ALL CAPACITANCES. The block
diagram should have inv as an input, outv as an output, and should also include 1dsv and
6ds
v as additional nodes.

2. (30 points) Use the block diagram and Mason’s Gain Formula to derive an expression for
the DC gain of the amplifier, i.e., find ( )( ) 0
out
in
v j
v j
ω
ω ω=
.

3. (35 points) With the assumption that
3ds
r and
5ds
r can be neglected, derive expressions for
the dominant and two non-dominant poles of the amplifier (hint: the solution need not be
algebra intensive).
ECE 264A CMOS Analog Integrated Circuits and Systems Midterm Exam, February 10, 2009
2
This problem relates to the following amplifier circuit. In solving each part, you may assume
that

(i) Capacitances CC and CL are sufficiently large that the small-signal transistor model
capacitances may be neglected,
(ii) both transistors are in saturation, and
(iii) the two bias current sources are ideal.




a) (30 points) Derive a block diagram of the circuit with input vin(s), output vout(s), and nodes
corresponding to vgs1(s) and vds1(s).

b) (30 points) Derive an expression for Av(s) = vout(s)/vin(s) using Mason’s Gain Formula. You
need not factor or otherwise simplify your answer. However, in addition to ensuring the
units of your expression are correct, apply one or more simple “sanity checks” to determine
whether your expression has any obvious errors.

c) (30 points) Use the block diagram you derived in Part b) to find an expression for
vgs1(s)/vin(s) and use the result to find an expression for the input impedance of the circuit as
seen by the input source, i.e.,
( ) ( )
( )
in
in
in
v sz s
i s
=
Alternatively, you may derive the input impedance via any other valid method, but doing so
will probably require additional time. Either way you need not factor or otherwise simplify
your answer.

d) (10 points) Suppose R1 = 2 kΩ, R2 = 8 kΩ, gm1 = 2·10−3 Ω−1, rds1 = 200 kΩ, gm2 = 10−4 Ω−1,
and rds2 = 1 MΩ. Calculate values for Av(0) and zin(0). Do these values make sense given
the structure of the circuit?

ECE 264A CMOS Analog Integrated Circuits and Systems First Midterm Exam, February 11, 2014
2
The problems below relate to the following buffer circuit (sometimes called a super source
follower):

Va
VDD
RL
Vi
I
Zout
M1
VDD
M2
CL
+
−


You may assume:
(i) the transistors are both in saturation
(ii) the current source between VDD and the drain of M1 has infinite impedance
(iii) the buffer circuit has a dominant pole
Do not neglect rds1 and rds2.
1. (25 points) Use Mason’s Gain Formula to derive the DC gain of the circuit, i.e.,
0
( )
( )
a
i s
v s
v s
.
(Hint: make your KCL analysis easier by recognizing that id1(s) = is1(s) = 0 when s = 0)

2. (25 points) Use Blackman’s Impedance Relation to derive an expression for the output
resistance of the amplifier (i.e., Zout(s) for s = 0, which does not include the RL or any
capacitances).

3. (25 points) Repeat Problem 2 using Mason’s Gain Formula, i.e., use Mason’s Gain Formula
to find an expression for the output resistance of the amplifier.

4. (25 points) Derive an expression for the 3 dB bandwidth of the circuit. To simplify the
problem, you may neglect Cgd2 in the SSM of M2 and Cbd1 in the SSM of M1. Additionally,
you can assume 1 21/ , 1/ , and ds k m ds k m ds k Lr g r g r R for k = 1 and 2 for this part of the
exam.


欢迎咨询51作业君
51作业君

Email:51zuoyejun

@gmail.com

添加客服微信: abby12468