EE80T – Modern Electronic Technology and How it Works
Winter 2009
HOMEWORK #2
Due in class Tuesday January 27, 2009
1.
(Proposal) This is an exercise to produce an experimental proposal, please
carefully follow the directions in the problem. This should be a neatly typed
document such as you would give your supervisor or someone who might be
funding your research or development project. Typically you need to write up a
proposal to get projects funded within a company, by a research funding agency
or a venture capitalist backing your new start-up company.
Most of you have probably seen the television ad in which a toy bunny powered
by an Energizer-brand battery keeps on going…and going… long after a similar
toy power by the Duracell “coppertop” battery has stopped working. The problem
here is to design a sensible experiment (or several different experiments, if you
get motivated) to determine whether the Energizer battery really delivers better
performance than the Duracell. Feel free to ask anybody associated with your
course for further information - this is the kind of problem for which it is good to
be able to discuss your ideas with others. Output: Please write up your proposal
for the testing to establish whether the TV ad tells the truth about these batteries.
You can use the “proposal” template in the text (page 71). DO NOT WRITE
MORE THAN ONE PAGE ON THIS. Hand written submissions will be deemed
“unprofessional” and will not be graded. Be imaginative. Here are some questions
to consider (answer):
a) What does “better performance” really mean to you as a potential battery
customer? Longest functioning?
b) How would you factor purchase prices of the two different batteries into
the evaluation? Are there any other “figures of merit” you could imagine
to permit comparison of batteries?
c) Since you probably don’t have a battery-powered bunny toy, what
electrical “load” will you use in the evaluation? How realistic is it?
d) How long would your actual testing take in order to produce meaningful
results? If the duration is longer than you’d like to spend sitting in the
testing lab, how would you be able to get results and still do other things
with your life?
e) Cost (always important!): How much would your proposed evaluation
method cost?
2. Efficiency of Light Bulbs – This problem requires you to evaluate the power and
efficiency of incandescent (regular) light bulbs vs. compact fluorescent light
bulbs. A regular incandescent light bulb has an average working life span of
1,500 hours, consumes 100 watts, and emits 1,500 lumens. A comparably bright
compact fluorescent light bulb has an average working life span of 15,000 hours,
consumes 23 watts, and also emits 1,500 lumens. Lumen is the SI unit of
luminous flux, a measure of the perceived power of light emitted. You can think
of it as the amount of light your light bulb emits. The cost of the regular
incandescent light bulb is $3.00 per bulb, and the cost of the fluorescent light
bulb is $9.00 per bulb. PG & E baseline electric rates are around $0.12 per
kilowatt hour.
a) How many equivalent incandescent light bulbs would you expect to use over
the life span of one fluorescent light bulb?
b) How many kilowatt hours does one fluorescent light bulb consume in its life
span? How many kilowatt hours does the equivalent number of regular
incandescent light bulbs consume over the same period of time?
c) Find the total cost of using incandescent vs. fluorescent light bulbs for the life
span of one fluorescent light bulb. This includes the cost of the light bulbs and
the cost of the total energy used.
d) Calculate the lumens per watt for the incandescent and fluorescent light bulb.
e) Based on the answers from a) to d), which light bulb is better in terms of cost
and amount of light emitted per watt or efficiency?
3. Lithium vs. Nickel-Metal Hydride Battery - In a battery, electrical energy is
produced through reaction among the chemicals contained inside the battery
housing. From the time it is placed into service until just before the end of its
useful life, a battery delivers a nearly constant voltage, and its load-bearing
ability is described in “ampere-hours”. Ampere-hours is the product of the
current the battery can deliver at its rated voltage times the number of hours of
useful service life. So a one ampere hour battery could deliver 1 Amp for one
hour or ½ an Amp for two hours. Below are actual specification for common
batteries.
A. How much electrical energy (Joules) could be delivered by a 2.85-amperehour, 1.5-volt alkaline battery?
B. How much electrical energy could be delivered by a 1.2-ampere-hour, 1.2volt rechargeable, Nickle Metal Hydride (NiMh) battery from a single
charge?
C. How much electrical energy could you get from a single charge from a 3.6V
0.8 Amp-Hour rechargeable Li-ion battery
D. Assume that the Li-ion battery costs $4.00 each and will last through 400
recharge cycles, the NiMh battery costs $2.00 and is good for 500 recharge
cycles while the Alkaline batteries costs $1.00 each and you throw them
away when the are discharged. How much energy per dollar are you able to
supply to you electronic device for each type of battery over it’s lifetime?
Please give answers in Joules per Dollar (J / $). This tells you which battery
gives you better “bang-for-the- buck.”
So now when you go to buy a new battery for your car at least you know how to
decide whether that expensive Sears Diehard or the cheapo no-name battery is the
better deal., assuming, that is, that you can get the right data from the
manufacturer…
4. Shake Flashlights and Energy Storage with Capacitors – the “no-battery
solution”. A shake flashlight is a flashlight contains a generator which changes
the mechanical energy from the shaking of the flashlight into electrical energy
which powers the flashlight itself. Besides the generator, it also contains a large
capacitor that holds the electrical charge and hence electrical energy. The
capacitor discharges a current that flows across the bulb and powers on the
flashlight. Below is a picture of a shake flashlight.
This flashlight contains a 1 Farad capacitor that can be charged to a maximum
voltage of 5.5 Volts DC. As you shake the flashlight a magnet (silver thing
above) is moved back and forth through the coil. The changing magnetic field in
the coil generates an electric field that makes current flow in the wire. This
generator converts mechanical energy to AC current as the magnet goes back and
forth. Then a special circuit converts the AC to DC and with vigorous shaking
produces produces roughly 10 mA of DC current up to a maximum voltage of 5.5
V . The schematic below is a simplified diagram of the shake flashlight. The 100
Ω resistor represents the light emitting diode, which requires current flow to emit
light.
Generator
AC‐DC
Converter
Vo = 5.5V
C = 1F
R = 100Ω
a) How long will it take to charge the 1 Farad capacitor up to 5.5 Volts
assuming 10 mA charging current, the switch is open and the capacitor
is initially discharged?
b) After the capacitor charges up to 5.5 Volts, the switch closes and the
charge stored on the capacitor will begin to discharge through the resistor.
How long will it take to discharge the capacitor to 1/e of it’s initial
voltage? In other words find the time constant associated with the
resistor and capacitor. Does this seem like a reasonable design to you?
That is does it run long enough to be useful given the time you need to
shake it to charge it up?
5. Average Voltage, Pulse-Width Modulation, and DC Motors - Consider the plot
below of Voltage as a function of time.
a) What is the average voltage of the periodic waveform shown?
b) What is the peak-to-peak voltage?
c) What is the repetition rate T?
d) What is the duty cycle TON/T?
e) The rotation speed of DC motors depends on the average applied voltage,
if a waveform like that pictured below is used to drive the motor then this
is proportional to the total fraction of the time the pulse is on, otherwise
expressed as the duty cycle. Assuming that the peak voltage is fixed at
10 V what fraction of the maximum speed will the motor turn if the
waveform below is applied? This is a common and efficient way to
control the speed of a motor and is known by the name “pulse width
modulation” or just as PWM control. The same principle is used in light
dimmers to adjust the brightness of incandescent lamps.
12
10
Voltage [volts]
8
6
4
2
0
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70
Time [sec]
6. Sinusoidal AC Voltage - Sinusoidal AC quantities are calculated in many
different and useful ways. One of the more useful and perhaps confusing among
them is the RMS value. The RMS value is useful because it allows you to treat
calculation of AC current, power dissipation, and so on as if they were simple DC
calculations. This simplification makes the understanding of RMS values well
worth the effort.
For the following example of an AM radio signal, plotted as the electrical signal
voltage (in microvolts, 1 µV = 10-6 Volts), as a function of time (seconds).
Careful the scale below is given in terms of seconds time 10-3. This is a realistic
representation of a typical received signal from your antenna. Answer the
following questions.
a)
b)
c)
d)
e)
f)
Find the amplitude of AC voltage.
Find the peak-to-peak voltage (VP-P ).
Find the period (T) of AC voltage.
Find the frequency (Hz) of AC voltage.
What is the average value of this voltage over time?
What is the RMS value of this AC voltage?
200
150
100
Voltage [uV]
50
0
-50
-100
-150
-200
0
0.5
1
1 .5
2
Tim e [s ec ]
2.5
3
3.5
4
x 10
-3
7. More Root Mean Square Voltage - A periodic AC voltage signal V(t) is
described by the expression below.
V(t) = 200 * cos(2π ∗1000 ∗ t)
a)
b)
c)
d)
(Volts)
Find the frequency of the AC voltage in Hertz.
Calculate the peak-to-peak Voltage of the signal
Calculate RMS value of the AC voltage.
If V(t) is applied to a 10Ω load, for example a vacuum cleaner, what is the
RMS current, peak current, and average power dissipated?
8. Inductors and Radios – Almost all wireless devices use a combination of
inductors to select its frequency of operation. Often times, the quality of
transmission and reception in wireless systems are limited by the quality of the
inductors. The quality factor Q of inductors can determine how many
neighboring interferers you will pick when trying to receive a message. The Q of
an inductor is determined by how much parasitic resistance is in the inductor.
This parasitic resistance of an inductor is due to the resistance of the wires in the
winded coil. The parasitic resistance of an inductor can be modeled as a resistor
in series with an ideal inductor. The schematic below illustrates an inductor with
its parasitic series resistor attached to an ideal current source in parallel with a
resistor. The resistor Rp represents the parasitic resistance of the inductor.
Rp = 100?
Vs= 12 V
+
-
R1 =10k?
L = 50 µH
a) In the figure above, the switch has been closed for a long time. Find the
voltage established across the resistor R1 and the current through the
inductor L.
b) In the figure above, after a steady-state current is achieved, the switch is
opened. Calculate the time constant after the switch is suddenly opened.
Hint: the voltage source is no longer in the picture and the parasitic
resistor Rp and the regular resistor R1 is now connected in series.
9. AC Power Transformers – Most of you know that the voltage coming out of the
wall sockets in your homes in the US are at nominally 110 Volts (this actually
fluctuates over the course of the day). However, the voltage level that comes out
of the sockets of homes in Europe, Asia, and many other parts of the world are at
220 Volts. If you purchased an appliance in the US and would like it to function
overseas, you will need an additional transformer that converts 220 Volts to 110
Volts if you don’t want to fry your equipment. The schematic below illustrates
the equivalent circuit.
N:1
Vs = 220V
+
-
.
.
Vp
110 Volt
US Made
Appliance
If we would like to keep our appliance working while overseas where the voltage
delivered to wall socket is at 220 Volts, what is the turns ratio of the transformer
that we need to purchase so the voltage delivered across our appliance is at 110
Volts. In other words, find the turns ratio N on the side that plugs into the wall
socket in relation to the appliance side so that Vp, the voltage delivered to the
appliance is at 110 Volts. The other thing you need are all sort of funny plugs that
fit the receptacles which are also different from country to country, these are
usually also included in the travel kits you can buy.
10. Electromagnetism and the Earth – When you take a magnetic compass outside,
the end marked “N”always point to the North Pole due to the magnetic field of
the earth. Of course, magnetic fields are generated by moving charges called
currents. This must imply that there are currents in the earth that produce such
magnetic fields. In this exercise, we will explore the concept of magnetic fields
and there relationship to currents. Using this knowledge, you will find the
direction of the current flow in the earth.
a) Please indicate the direction of the magnetic field by drawing a
to
indicate that the magnetic field is coming out of the paper towards you
and a
to indicate that the magnetic field is going into the paper away
from you. Close to the short section wire with the current flowing as
indicated by the arrow in the schematic below indicate the direction of
the the magnetic field on either side. Really this piece of wire must be
part of a larger circuit as current can only flow in loops. We have just
zoomed in on a little piece of the wire…
I
b) From the exercise above, one can surmise that magnetic field loops are
formed around current. Given that there is a constant current flowing in
a loop as illustrated below, please draw the magnetic field lines that
surround the current loop given the direction of the current flow as
indicated.
I
c) When you pick up a compass, the end of the needle marked with the “N”
(the north magnetic pole of the magnetized compass needle) always
points to the geographic North poles of the earth. The schematic below
illustrates the North and South geographic poles. Please draw the
magnetic field lines including arrows showing the direction of the field
around the earth. Next indicate using the same arrow convention that we
used for the magnetic filed above the direction of the current flow on
either side of the earths axis of rotation. Finally is this current flowing in
the same direction that the earth is rotating or in the opposite direction,
indicate these directions using by drawing and labeling arrows on the
drawings below. (Hint, face north and observe which direction the sun
moves after it rises to figure out which way we rotate.)
Axis of Rotation
N
N
S
Side View of the Earth
Top View of the Earth
Reading Questions
11. Name the inventor who challenged Alexander Graham Bell in court for the
invention of the talking machine “telephone”.
12. What was the name of the first man to die in the electric chair?
13. Name the reactive gas element that General Electric first used in the development
of halogen lights.