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```					EME106 Intro to Engineering II                     Spring 2010
Lecture 10: Analysis of Electrical Systems
Today:
Review of Electrical Components
Ohm’s Law Applications
Study of the Line following Robot Circuit.

Tuesday:
Circuit Board Etching

Thursday:
Tour of Union Solutions
Depart: 2:00 p.m.
Return: 3:20 p.m.

Introduction to Electrical Circuit Analysis:

What is Electricity?

Electricity is a controlled flow of electrons
along a some path. Electrons are the
negatively charged particles that are found
orbiting all elementary particles of matter
we know as atoms. Atoms are extremely
small. A single grain of table salt literally
contains 1018 atoms. Electrons even
smaller.

Normally an atom’s electrons are bond to
the atom by the attraction of the negatively
charged electron to the positively charged
nucleus of the atom. However, for some
substances, when the literally billions
upon billions of atoms are packed closely
enough together with specific structure or
lattice, the outer most electrons of the
atom are freed to move between different
atoms with very little effort. Materials in
which this occurs are generally called
“conductors”. The general movement of
these “free” electrons along a prescribed
path of such material is called “electron
flow” or “electricity”.
Being able to harness this extremely minuscule particle along with many
trillions of its twins to act with the same general motion makes electricity a
powerful phenomenon which can be put to many different uses.

What is Charge?
Charge refers to a property of matter which describes a force of repulsion or attraction to
other matter which also has charge. Elementary particles such as electrons are said to be
negatively charged, protons are positively charged, neutrons have no charge. Alike
charged particles repel each other. Oppositely charged particles attract each other.
Controlling these “forces” allow us to interact with and manipulate the response and
action of particles.

Charge is measured in units of coulombs.
A coulomb is defined in terms of the
force one charged object exerts on another.            F                            F
A charge of 1 coulomb exerts a
-
force of 8.988 x109 N on another                                                              -
1 coulomb charge located 1 meter
away from it in air. In comparison
one electron has a charge of -1.6x10-19 C.

1m
When electrons with their charge are coaxed to move in along the same path of
conducting material, this flow of charge is called electric current. We commonly
distinguish two different types of electric current.

Alternating current (AC): the movement
of electric charge back and forth in a
periodic motion (usually sinusoidal).
This is the kind of current used for most
most electrical distribution systems.

Direct current (DC): the movement of
electric charge in only one direction.
This is most commonly associated with
electrical power provided by batteries and
that current used in digital electronic
devices.

Devices such as batteries and generators are able to set up          Voltage + + + + +
flows of electric current. Their ability to set up this flow is
measured as a quantity called electric potential or a quantity
you are more commonly used to calling “voltage”. Voltage is            Current
actually a measure of the electric potential. When a voltage
exists between locations and a conducting material or path is
available between the two locations, an electric current will                                   light
flow.

Studies of electrical flow or “current” and electric potential
or “voltage” show that for many difference conducting
Current
materials, the current flow is directly proportional to the
electric potential. In other words, the larger the electrical
potential, the larger the current flow for a specific conducting
material. This relationship is called Ohm’s Law.                                        Ground

V I R
The proportional constant between “current” and “voltage” is
called resistance and is measured in units of ohms (Ω). The value of resistance depends
upon the material that is used to form the conducting path and the shape and length of the
material path. Different materials have different resistivity. The geometry of the
material path affects the resistance. In general, a longer path has more resistance…while
a path with a larger cross section has less resistance. All material offer some resistance to
flow of current.

What are the best conducting materials?

Silver, Aluminum, Copper, Gold, SuperConductors….
R=100 Ω

Example 1:
A 12 Volt battery is connected across                    +
a 100 ohm resistance.                              12 V                               I
What current flows?                                       -
Solution:

V   12 V
V I R                              I             012 A
.

R 100 

More complicated circuits may include many resistance values. Designing electric
circuits means that we need to be able to predict current flow through different circuits.

Rules for Resistance Networks:
-------------------------------------------------------------------------------------------------
Resistors in series: Req = R1 + R2 + R3 = Σ Ri
R1                    R2               R3                                  REQ

---------------------------------------------------------------------------------------------------
1
1        1 
Resistors in Parallel: Req      =           =  
1   1   1    Ri
R1                 
R1 R2 R3
REQ
R2

R3
----------------------------------------------------------------------------------------------

Example 2:
The following resistance network can be reduced to an equivalent resistance of what
value?
20 Ω
50 Ω          40 Ω                              10 Ω

30 Ω
REQ
Example 2 Solution:
The following resistance network can be reduced to an equivalent resistance of what
value?
20 Ω
50 Ω          40 Ω                           10 Ω

30 Ω
Resistors in parallel:
1              1             1         60
R20||30                                                12 
1   1           1   1         3   2        5
                            
R20 R|30         20 30        60 60

50 Ω             40 Ω    R20||30 = 12 Ω         10 Ω

Resistors in series:

REQ  R50  R40  R20||30  R10  50  40  12  10  112 

REQ
Example 3:
100 Ω
VA
What is the voltage at point A.

+           I
50 V                            100 Ω            100 Ω
-
Solution:

Start by replacing system with an equivalent resistance network.

100 Ω
100 Ω                                                                     REQ = 150 Ω

100 Ω

1                          1                    100
REQ  R100                 100                         100         150 
1    1                1   1                         2
                    
R100 R100             100 100

then the circuit can be simplified as, where the overall current may be found using
Ohm’s Law, V  I R .
REQ =150 Ω

V   50 V
I             0333 A
.
R 150                                             +
I
50 V
-

then the voltage drops from 50 V to VA as
the 0.333 A current passes through the 100 Ω resistor.

V  IR                                                              100 Ω
VA
50V  VA  ( 0333 A )( 100  )
.
VA  50  333  167 V
.     .                                 +                I
50 V                                   I     R100||100=50 Ω
-
Common Circuit Components:
There are many electrical components, but the vast majority of them will include such
components as

Resistors                             Capacitors                     Inductors or Coils
Batteries                             Diodes                         Bulbs
Transistors                           Switches                       Integrated Circuit Chips
Crystals                              LEDs                           Fuses
Motors                                Voltage regulators             Relays

Systems of real electrical components are modeled as electrical circuit diagrams:
R1                R         C  2          2

+                       C1
vo(t)                                                            R3
L1
-                                        R4

where each component can be modeled mathematically for its behavior.

Resistor:                         Capacitor:                  Inductor or Coil:
1                                 dI
Principle:        VA  VB  IR                       VA  VB   Idt                VA  VB  L
C                                 dt
VA                               VA                             VA

I               C
I                   R                                                 I                L

VB
VB
Resistors:
Resistors are electrical components which dissipate electrical energy as heat. Important
ratings for a resistor are it Resistance (in Ohms) and its Power rating (in Watts)

Resistors use a color code to identify the resistance of component. The most common
type of resistors used are 1/4 watt metal or metal oxide film resistors. This is what you
see on many printed circuit board assembly.

The gold or silver bar represents a tolerance level
of the resistor. The other three color bars give you
the resistance value.

To find the resistance of the one shown here
(bars from left to right: Orange, White, Red, Gold)
can be found as

Color Bar:         Value:
st
1 Digit:   Orange              3
2nd Digit:   White              9
Multiplier:    Red              102
Accuracy:      Gold             5%

from the Handbook of tables for Applied Engineering Science by Bolz and Tuve
Capacitors:
Capacitors are electrical components that store charge. Capacitors are commonly used for
applications which require:
a) filtering applications
b) voltage stabilization
c) voltage spike suppression
d) rapid release of energy and current
e) oscillation circuitry
Capacitors can be used as power storage devices
which don't generally hold a lot of energy, they
then can charge and discharge very quickly and
can be recharged an almost unlimited number of
times. They are small, light weight, and
inexpensive and usually have a disk or barrel
shape. Important characteristics to consider when
selecting a capacitor include type ( electrolytic,
tantalum, ceramic have slightly different ),
capacitance (in farads), maximum voltage, and
directionality (unidirectional or bidirectional).

If you were to attempt to measure
the ability of a capacitor to build up
a stored charge, it is proportional
to the charge already held by the
capacitor. Which means the time
response of the voltage across the
capacitor follows an exponential
time response function.

What this means, is it takes time to
charge a capacitor, but an empty
capacitor charges faster than one which
is already partially charged. It doesn’t
happen instantaneously.

As an example, when the switch in the circuit below is closed, the output voltage V across the
capacitor, builds up as shown by the graph below. RC is called the time constant.

Potential
difference (V)
R
Vo – Vo/e
+
C           V
VO
-
RC            2RC            3RC    Time (t)
There are a variety of different types of capacitors. The large barrel-shaped electrolytic
capacitors usually have the rating labeled on the case. Smaller capacitors including both
tantalum and ceramic capacitors more commonly use a three digit code to indicate their
size. The larger capacitor give both the capacitance and the maximum voltage rating.

from the website http://www.electronics-tutorials.ws/capacitor/
Diodes and LEDs:
A diode is a semiconductor component which allows current to pass through it in only
one direction.

Common uses of diodes are in
a) overvoltage protection circuits
b) AC voltage rectification circuits
c) high voltage gain circuits

Diodes are identified by a system which uses
numbers and letters to identify different types of
semiconductor devices. This is the same system
used for identification of transistors and many
other semiconductor components. The first
number in the system indicates the number of
junctions in the semiconductor device and is a
number, one less than the number of active
elements. A 1 designates a diode; 2 designates a
transistor, and 3 designates a tetrode (a four-element transistor). The letter "N" following
the first number indicates a semiconductor. The 2- or 3-digit number following the letter
"N" is a serialized identification number.

A diode is a directional device. Diodes distinguish one end of the diode from the other
(anode from cathode). Manufacturers generally code the cathode end of the diode with a
"k," "+," "cath," a color dot or band, or by an unusual shape (raised edge or taper). In
some cases, standard color code bands are placed on the cathode end of the diode. This
serves two purposes: (1) it identifies the cathode end of the diode, and (2) it also serves to
identify the diode by number. Light emitting diodes (LED) usually distinguish the
negative lead (anode) by a flattened part of the LED’s base. Length of the LED legs will
usually have the longer leg as the cathode, but not always, so check its polarity.

Be careful when placing diodes in a circuit. In some circuits, incorrect orientation
of the diode can result in a short circuit condition and can cause damage to
components. In the case of LEDs, they should always be used in conjunction with a
current limiting resistor.
Transistors:
Transistors are semiconductor devices which primarily serve one of two main functions.
In the majority of applications they will function as an electrically controlled switch. In
other applications they may be used for current or voltage amplification. We will only be
considering their use in switching applications.

There are several different types of transistors but we will only disucss one type here.
BJTs are Bipolar Junction Transistors and come in two flavors: PNP and NPN. Both
flavors of BJT have three input lets called the Emitter, Base, and Collector. In each case,
the transistor acts like a switch when there exists adequate current flow through the base.
The main difference between the two flavors is the direction of the current flow with
respect to the base.

NPN transistors turn on when sufficient current flows into the base (usually achieved by
applying a positive voltage to the base). When this is the case, the path from the
Collector to the Emitter behaves as if it is a conducting circuit. If the current flow into the
base is below a specified current level, then the path from the Collector to the Emitter is
blocked, and no current flows.

PNP transistors works when current flows out of the base (which is usually achieved by
holding the voltage level of the base close to ground). When this happens current is
allowed to flow from the Emitter to the Collector as if it were an shorted circuit circuit.

PNP               NPN
Typical circuit applications of NPN and PNP switching circuits are shown below .

R1                                                    R1
C                                                            E
On                                                   Off                 B
B
-                                                     -              On                          C
Off                     E
NPN                                          R2        PNP

The main concept is when you supply a small current flow to the base, you can induce a
larger current flow through the Collector. For switching, the current flow is effectively
saturated. The resistances R1 and R2 are used in conjunction with the transistor gain to
limit the current through the load and transistor. Proper selection of these resistances can
make the transistor function as an amplifier instead of a switch.
Line Following Robot Circuit:
A complete circuit of the line-following controller is given below. You should examine this circuit and attempt to identify the different
electrical components that are present.
+9 VDC

R1
EME 106: Intro to Engineeirng II
Lecture 11: Homework

1) For the Resistance shown, calculate the voltages at TP1 and TP2.
R1=2 kΩ        R2 = 10 kΩ (evenly split) R3 = 7.5 kΩ                                                  TP1        TP2
R4 = 7.2 kΩ R5 = 4.3 kΩ                    R6 = 4.1 kΩ                                                      R2
R3     R4                    R5   R6
9V     9V   9V

2) For the LM393 Linear Comparitor IC:                    R7            R8
Pins 2,3,5 and 6 are the inputs                                                             TP1    TP2
Pins 1 and 7 are the outputs
Fill in the truth table for this chip.
(consult your Data sheets on Lecture 10)

A Inputs    A out          B inputs   B out
Bout B- B+
A- < A+                    B- < B+                                             LM393
A- = A+                    B- = B+                                           Aout A- A+

A- > A+                    B- > B+

3) What is the purpose of Resistors R7 and R8?
If typical current to the LED is 10 to 20 mA and they have a
voltage drop across the LED of 1.8 V, what size should the resistors be for a 9 V input?                                       Input
(what this means is the chosen resistor should allow a current flow of
10 to 20 mA for a voltage drop of 7.2 volts.)                                          Output
to Motor

4) Will the transistor turn On when the Input goes High or Low?
Does turning transistor On or Off turn the motor On or Off?
Explain how you know these answers.

```
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