EEE598_F15_ Exam 1_solution_key
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Arizona State University *
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598
Subject
Electrical Engineering
Date
May 20, 2024
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Midterm Exam 1 EEE598 VLSI Analog Filter & Signal Processing Circuits Fall 2015 Arizona State University Instructor: Dr. Hongjiang Song Exam Time: 6:00pm –
7:15pm Tuesday, September 29, 2015 Name: _________________ ID#: _________________ General instruction:
This is a closed book/notes exam. However, you may bring a sheet (8.5x11) of notes and a calculator to this exam. Good luck! Page 1/7 Solution
Problem 1 (Passive LRC filter, transfer function, Bode plots and steady state response) Shown in circuit below is a normalized (i.e. simplified) filter model of a VLSI high-speed I/O circuit. 1.1)
Derive the s-domain transfer function for the filter (10 points). ?
)
(
)
(
)
(
s
V
s
V
s
H
A
B
H(s) = 1/(s^2+0.5s+1.001) Pole ~ -0.25+/j Page 2/7 A B L = 1 C = 1 R = 0.5 C = 1000 Note: there is a typo in sheet. So everyone get 5 points for this question
1.2) Find the zero(s) and pole(s) of the transfer function and plot them in the s-plane below. Sketch the gain and phase responses of the circuit in the graphs given below (15 points). 1.3) For each input signal given below sketch the steady state output V
B
(t) in the same graph with the input. Please indicate your important values in the output signals (i.e. peak and phase or delay) (15 points) Page 3/7 j
s-plane -1 -1 0 0 -2 -2 1 1 Gain (dB) 20 -20 0 180 -180 0 Phase (degree)
10
log
10
log
2 2 V
A
(t) t (sec.) 1 -1 3.14 0 6.28 t (sec.) 1 -1 0.314 0 0.628 t (sec.) 1 -1 31.4 0 62.8 V
A
(t) V
A
(t) 6dB
= 10 |H| ~ 0.1 Phase ~ -180 degree
= 1 |H| = 2 Phase = -90 degree
= 0.1 |H| ~ 1 Phase ~ 0 degree
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Problem 2 (SFG, transfer function and Bode Plots) Shown in figure is a complex filter SFG, where X and Y are the input and the output respectively. (Note: j
2
= -1)
2.1) Derive the s-domain signal functions of this filter (15 points). H(s) = Y(s)/X(s) =? 2.2) Find the pole/zero of the filter. Sketch the gain and phase responses of this filter in the graphs given (15 points). Page 4/7 -1 -1 0 0 -2 -2 1 1 1 -20 180 -180 0 Phase (degree)
2 2 1
s
Y X jY 1 1 -1 |H| j
s-plane Y =(1/s)[X+jY-Y]
Y/X = 1/(s-j+1) Pole = -1+j 0.707 90 -90
Problem 3 (Quick questions) Please circle
the best (only one please!) answer to each question. Don’t
spend too much time on an individual question
. It is OK to select the answer based on reasonable guessing. 3.1 –
3.7 are based on the following inverter based Gm-C circuit shown below. 3.1) What is most likely the way to enhance the linearity of this Gm circuit? (3 points) a)
To let the devices in linear operation mode; b)
To balance the strength of the two MOS transistors (e.g. by letting
p
~
n
); c)
To balance the threshold voltages of the two MOS transistors (e.g. by letting |V
Tp
|= V
Tn
); d)
To use large device sizes. 3.2) Which of the following statements about the Gm value of this circuit is most likely true? (3 points) a)
It is independent of the MOS device sizes; b)
It is proportional to the MOS device sizes
p
and
n’
c)
It is proportional to the square root of MOS device sizes
p
and
n’
d)
It is proportional to the square of MOS device sizes
p
and
n’
3.3) Which of the following is most likely the way to tune this Gm circuit? (3 points) a)
To tune the threshold voltage of the MOS circuit; b)
To tune the device size of the circuit; c)
To tune the common-mode voltage of the circuit; d)
To tune the supply voltage of the circuit. 3.4) What is most likely the voltage gain of the following Gm-C circuit? (3 points) a)
–
N/M b)
–
M/N c)
–
(N/M)
0.5
d)
–
(M/N)
0.5
Vi(t) I
o
(t)
p
n
Vi(t) I
o
(t) gm Mx Nx Vi(t) V
o
(t) Page 5/7
3.5) What is most likely the output impedance of the following Gm-C circuit (where g is the gm value of a single Gm unit and N and M are the members)? (3 points) a)
1/(Ng); b)
1/(Mg) c)
1/(NMg) d)
1/(M
0.5
g) 3.6) What is most likely the s-domain TF of the following Gm-C circuit? (3 points) a)
H(s) = -1/(1+s/
o
) b)
H(s) = -1/(s/
o
) c)
H(s) = -(1+s/
o
) d)
H(s) = -(s/
o
) 3.7) What is most likely the s-domain TF of the following Gm-C circuit? (3 points) a)
H(s) = -1/(1+(s/
o
)/Q+( s/
o
)
2
) b)
H(s) = -1/(s/
o
)
2
c)
H(s) = 1/(1+(s/
o
)/Q+( s/
o
)
2
) d)
H(s) = 1/(1+s/
o
) 3.8) Why active-RC circuit is generally not suitable for high frequency application? (3 points) a)
Limitation on available values of the resistor b)
Limitation on available values of capacitor c)
Variations of resistance and capacitance d)
Limitation of opamp circuit Vi(s) V
o
(s) Mx Nx Vi(t) V
o
(t) V
o
(s) Vi(s) Page 6/7
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3.9) For the Gm-C oscillator given, what is most likely the oscillation frequency? (3 points) a)
= 1/(GmC)
0.5
b)
= Gm/C c)
= (GmC)
0.5
d)
= C/Gm 3.10) For the LC oscillator given, what is most likely the oscillation frequency? (3 points) a)
= 1/(LC)
0.5
b)
= Gm/C c)
= (LC)
0.5
d)
= L/C Page 7/7 Vo Gm C Gm C Vo+ Gm C L Vo-
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