Eng. Mohammed Alhissy
Problems on Water Flow in Pipes
Problem (1)
Water flows through a 20-cm horizontal PVC pipe at 20oC (as shown in figure 1). The length of the pipe is
50m. Calculate the discharge rate (Q) ?
Solution:
P1 V 12
P2 V 2 2
Z1
Z 2 hL
2g
Amplifier without feedback
Amplifier without feedback has small phase margin, which make it becomes
unstable easily. However, with feedback network, the phase margin can be
improved. We saw that for a resistor feedback network, we can add a capacitor to
i
The first part of the lab is determining the relationship between input and
output signal. From here, students will apply the concept of state variable to derive
the description for state-space. Students will then observe the output for different
type of
infinite-impulse- response filters
learn how to design digital IIR filter. In particular, students will focus on the concept
of digital infinite-impulse- response filters by digital conversion of analog filters. The
method starts off with the frequency ch
Human Body Model
Human Body Model and ESC schematic
Figure 11: Input voltage is 100 V
Figure 12: Input voltage is 750 V
Figure 13: Input voltage is 3000 V
Figure 14: Input voltage is 8000 V
1
Comments:
For high voltages, the input voltages to the internal
AC Analysis
Comparison:
The -3dB corner frequency occurred when the voltage is 350 mV at 1626 Hz.
The calculated value in pre-lab was 1592 Hz, which was very close to the
simulations result.
1
Transient Analysis
However, throughout the lab, everything ma
Analog filters
Design basic analog filters using Butterworth and Chebyshev approach. Students
will start out by designing a simple low-pass filter. Then the derivation of high-pass,
band-pass, and band-stop filter can be made using the transformations.
1.
Boolean Equation
For most part of the lab, students are going to implement a Boolean function
using basic elements like inverter, 3-input NAND, and 3-input NOR. The final design
has to meet the area limit and pin constraint. Same as previous lab, the sche
Nyquist stability criterion
the root locus and Nyquist stability criterion. Students will observe how the use of
feedback influences the stability and the bandwidth of an amplifier. Students will
analyze the root locus and verify the Nyquist stability cri
Part 1: Layout of an inverter using pcells
Figure 6: Layout of an inverter using pcells
Figure 7: LVS result
Part 2: Layout of circuits to implement Boolean functions
Part 2.1: 3-input NAND/NOR Gate
Figure 8: Schematic view 3-NAND
Figure 9: Symbol
1
Figur
Feedback effects on stability
In this lab, students will learn about feedback effects on stability. Basically, students
will observe how the use of feedback influences the stability of an amplifier and
what can be done to improve its performance.
1. Uncom
Square-Law Model
Students will be comparing the square law model with BSIM to conclude at
what conditions they are similar and what conditions they are different. In addition,
students will observe the relationship between lambda and transistors length, a
DRC feature
The design rules must be followed so there are no violations in the design. DRC
feature will be used to check for any error regarding design rule. Finally, students
will compare the layout with schematic using LVS. This helps to ensure that th
Verilog ModelSim
Finally, students will create another inverter simulation, but with Verilog
code using ModelSim. This is very common software for designing and testing
digital circuits.
Part 2.0-2.2: Creation of a Schematic
The circuit consists of the ce
Digital FIR filter design
using method of windowing. This method starts off with the
frequency characteristics of the desired digital filter, computes the
corresponding impulse response, and trims this impulse response using
a finite-support window. Stude
Discrete approximation
Frequency characteristic of infinite impulse response discrete-time system. We will
test using different sampling time. Most importantly,
Problem 1
1
2
3
we will see the effect of different discrete approximation methods have on the
4. Design bandpass filter using Kaiser window
Figure 6: filter parameter
Figure 7: Frequency response
In this lab, we learned how to design digital FIR filter using windowing method. We
observed that the higher the order of filter, the better frequency re
Comparison with BSIM Model
Comparison between Square and BSIM
Ids (uA) when (Vds = 4 V and Vgs = 2 V)
Square Law
Model
265.20
BSIM model
265.19
Percentage
difference
0.004 %
Comment: Near the operating point, the difference between Square Law
model and B
The Trapezoidal Approximation
k+1
y [ ()T ] y [k ]
k+1
k+1
x [ ()T ] x [k ]
k+1
x [ ()T ] x [k ]
( y [ () T ]+ y [ k ] )=
( 50 T +1 ) y [ k + 1 ] + ( 50 T 1 ) y [ k ] =( 550T +1 ) x [ k +1 ] + ( 550T 1 ) x [ k ]
z ( 550 T +1 ) +( 550T 1)
H t ( z )=
z ( 50
State Variable
In this lab, we are going to explore two different ways to model a system. The
first one is using differential equation. The second one is using the state space
representation.
System (a)
Differential equation
v v out 1
= v 0 ut ( t ) dt
R
initial settings for Virtuoso
students will create initial settings for Virtuoso. Students will use Unix commands
to create system files and directory for the course. Then, students will get familiar
with Cadence Custom IC tool including Command Interpret
Simulink
In this lab, we are going to use Simulink to model a RLC circuit and spring mass
system. The goal is to use the differential equations to describe the systems.
Overview: Simulink provides a block diagram environment for simulation. It has a
graph
Zero-Order-Hold discretization and Aliasing
In problem 1, we concluded that the larger sampling time yields slower discrete
systems response. On the other hand, when the sampling time is small, the
response is quicker. In problem 2, we used zero-order-hol
The Euler Approximation
1. Differential equation
dy
dx
+100 y= +1100 x
dt
dt
2. Equation at time kT
d
y ( kT )+100 y ( kT )= x ( kT ) +1100 x (kT )
dt
3. Difference equation
y [ k+ 1 ] + ( 100 T 1 ) y [ k ] =x [ k +1 ] + ( 1100T 1 ) x [kT ]
4. Transfer fu
A second problem
y [ k ] =c [ k ] + i [ k ] + f [ k ]
c [ k ] =ay [ k1 ]
i [ k ] =b ( c [ k ] c [ k1 ] )
y [ k ] =ay [ k1 ] +b ( c [ k ] c [ k 1 ] ) + f [ k ]
ay [ k1 ] +b( ay [ k 1 ] ay [ k 2 ] + f [k ])
1
2
Y [ z ] =z a (1+ b ) Y ( z )z abY ( z ) + F (
ROC unstable
We observed that smaller sampling time increases the closeness of
approximation. When T = 0.01 s, it seems that both systems worked fine. Using
Euler approximation, we want the pole to be inside the unit circle so that the ROC
also includes i
Computing the Laplace transform of the integrator
H ( s )= u ( t ) et dt
1
s
0
Region of convergence:
H ( s )= et dt=
( s )= >0
Deriving the integro-differential equation RLC circuit
i ( t )=i C (t ) +i R ( t )+ i L ( t )
t
Cdv ( t ) v ( t ) 1
i ( t )=
+
Empty Matrix
We learned how to use Mablab to quickly identify poles and zeros of the system as
well as obtaining different types of signal response. Then, we build block diagram to
actually test the systems and to observe its behavior. We used the fact th
This can be done by finding the poles and zeros of the transfer function. The second
part requires students to make a block diagram for the system to validate the
theoretical bode plot. This can be done by manually measuring the magnitude and
phase shift
Test System
Test system behavior exploiting Laplace analysis. The goal is to observe the
relationship between Laplace transform, frequency domain, and time domain
feature of the response.
1. Verification
pole =
-100
zero =
0
Z=
-100
P=
-100
K=
1
Figure 3: