Example Midterm Exam ABE425
NAME:_____________________________
1 (3)
What is a Lissajous figure and what is its purpose?
2 (3)
Name the three components of a typical measurement system



3 (4) Given that the Laplace Transform of a Unit Step function is L1t  
1
and that the
s
 df t  
L
  s * F s  , explain why the Laplace Transform of an impulse (Dirac Delta function) is
 dt 
unity (1).
Example Midterm Exam ABE425
4 (3) Explain the difference between accuracy and precision.
5 (3) Explain what the Virtual Ground Principle (VGP) is and what it is used for.
6 (4) Explain in general what a loading error is and give two examples


Example Midterm Exam ABE425
7 (20) A sensor has a maximum voltage output of 50Volt. You need to bring this voltage down
to a maximum of 5 Volt. Resistor R1  1k and you only have 1 Watt resistors.

Compute the resistor R2 needed for this attenuation factor.

When you turn on the power, after a short while you smell something burning. Analyze
which resistor is burning up and why.
Example Midterm Exam ABE425
8) (15) The transient response U o t  of a dynamic system to a Unit Step function is shown as,
U o t   1  e
t

, where t is time, and  is a time constant.

What is the response of this system to an impulse (Dirac delta)?

How can you determine the time constant from the figure? Show your method in the
figure itself.
Example Midterm Exam ABE425
9 (20) You have an AC signal that has a frequency of 15 Hz. Unfortunately it also has a
superimposed high noise component caused by net interference of 60 Hz.
U IN
UC  UO
You are designing a first order passive low pass filter as shown that suppresses the noise
component by -6 dB @ 60 Hz by doing the following steps:
If you need to convert the frequency f in Hz to  in rad/s, use   2f
1. Derive the transfer function of the passive low pass filter circuit
2. Compute the value of the time constant  in seconds
3. Assuming you have a Capacitor with a value of 1 nF, compute an appropriate resistor.
4. Compute the amplification factor for DC signals in dB.
Example Midterm Exam ABE425
10 (10) You have a resistor, you apply 110V DC and the measured current is 1 Ampere which
gives the Power of 110 Watt.
Now you switch the power supply to AC (wall outlet) and you adjust the sinusoidal voltage until
you get again 110W.
1. What is the Amplitude of this AC Voltage?
2. Does it matter what the frequency of the AC Voltage is?
11 (15) OpAmps are very useful devices as buffers (aka Voltage Followers). Draw the schematic
of a buffer using an OpAmp and describe what this configuration does.
Example Midterm Exam ABE425
Formula sheet ABE 425: YOU WILL NOT GET THIS ON THE EXAM
Kirchoff’s Voltage Law:
The sum of all the voltage differences around a complete loop is equal to zero.
Kirchoff’s Current Law:
The sum of the currents coming in to a junction is equal to the sum leaving the junction.
Ohm’s Law
U  i*R
(1.)
1
jC
(2.)
Z L  jL
(3.)
Impedance of a Capacitor
ZC 
Impedance of an Inductor
Power in a resistance
P  I2 *R 
Ordinary Least Squares estimator
U2
R
(4.)
ˆ   AT A  AT y
1
(5.)
Definition of Laplace Transform
L  f t  
t 
 f t  e
t 0
 st
dt
(6.)