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MT-144
NETWORK ANALYSIS
Mechatronics Engineering
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Instructor:
Gp Capt (R) Muzaffar Ali
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MS Aerospace Systems – Cranfield, UK 1979
BE Avionics – CAE, Karachi University 1974
Pakistan Air Force – 1970 to 2002
MCS, NUST – 2002 to 2009
Mechatronics Engineering Dept. at AU – September 2009 onward
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Course Details:
Textbook: Sergio Franco, Electric Circuits Fundamentals, Oxford
University Press
Reference Books:
1. Irwin, Basic Engineering Circuit Analysis, 9th Edition, Wiley
2. W. H. Hayt et al., Engineering Circuit Analysis, 6th edition,
McGraw-Hill Higher Education, 2002
Course Assessment:
Homework: 5 – 10 %
Quizes: 10 %
Mid Term: 20 %
Labs: 20%
Final: 40 - 45%
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LIKELY TOPICS
Review:
• Basic concepts
• Notations and Symbols
• Voltage and Current Sources
Network Analysis:
• Natural response of 1st order circuits
• 1st order circuits with dependent sources
• Response of 1st order circuits to constant forcing function
• Response of 1st order circuits to non-constant forcing
function
• Complete response of 2nd order circuits,
• AC response
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LIKELY TOPICS…
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Laplace transform and inverse Laplace transform
Solving Circuit differential equations using Laplace
transform
Laplace transform of special signals
Direct transformation of circuits in to s-domain
AC steady state power
Concepts of average power, complex power and power
factor
Frequency response of 1st order circuits
Asymptotic magnitude and phase Bode plots
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A Crude History of Electricity
• 600 BC:
Ancient Greeks rub amber on cat fur to produce
static charge
• Circa 0 AD: Persians in present-day Iraq invent the battery for
unknown (probably medical) purposes
• 1720’s:
Stephen Gray shows that static charges can be
‘conducted’ from point to point
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History (Cont.)
• 1750’s:
Benjamin Franklin’s One Fluid Theory of Electricity
unifies scientific approaches to electricity and forms the
foundation of modern electrical theory
• 1800’s:
Alessandro Volta makes his Voltaic Pile using zinc
and copper disks submersed in an electrolytic solution (acid),
thus re-inventing the battery, 1800 years after the Persians
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History (Cont.)
• 1820’s:
Hans Oerstad discovers electromagnetism with
his famous “compass and current-carrying wire” experiments
– Andre-Marie Ampere defines electric current and
electromagnetism, invents the ammeter
– Georg Ohm delivers his theory of electricity, including what
later became Ohm’s Law
• 1830’s:
intense
Michael Faraday enters the game and things get
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Basic Concepts
We will review the basic concepts and some laws relevant to
the field of electrical engineering: charge, electric field, voltage
current, energy and power.
We will also learn about an electric signal, circuit, circuit
elements and a few of the relevant laws.
These concepts were (assumed to be) covered earlier in the
various courses of physics undertaken by you, here as well as at
the Intermediate college level.
These concepts are critical for developing physical insight into
the operation of the electric circuits, we are about to study.
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Basic Concepts
§ 1.1 UNITS AND NOTATIONS
SI Units. We use the ‘International system of Units’. ,which is
based on the meter as the unit of length, the kilogram as the unit of
mass, the second as the unit of time, the kelvin as the unit of
temperature, the ampere as the unit of current, the candela as the
unit of light intensity.
Please carefully study at home, the table 1.1 at page 2 of your text
book. This table gives summary of various SI Units. Also study
table 1.2 (at page 3) giving magnitude prefixes, which are going to
be confronted frequently, in engineering.
Unit Prefixes. It is usual to use the standard prefixes of table 1.2.
You are required to revise and learn the use of these prefixes.
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Basic Concepts
§ 1.1 UNITS AND NOTATIONS …
Consistent Sets of Units. We say that a system of unit is
consistent if an equation as expressed in the SI system remains
unchanged when expressed in the new system e.g.
Ohm’s law, which relates voltage v, resistance R, and current I
as v = Ri. In SI units this law may be expressed as [V] = [Ω] [A]., we
can write it in consistent sets of units as [V] = [103Ω] [10-3A], and so
on.
It is exactly same way as you have been treating mm, cm,
meters, KM etc , as a measure of length (or distance).
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Basic Concepts
§ 1.2 ELECTRICAL QUANTITIES.
Let us review the basic concepts of charge, electric field,
voltage, current and power. A clear understanding of these
concepts is necessary for developing physical insight into the
operation of electric circuits.
Charge (q). Fundamental quantity of electricity is the electric
charge; measured in Coulombs (C). Charge may be positive or
negative. The most elementary positive charge is that of the proton,
and the most elementary negative charge is that of the electron
One electron has a charge of
- 1.602 x 10-19 C
One hole/ proton has a charge of + 1.602 x 10-19 C
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Basic Concepts
§ 1.2 ELECTRICAL QUANTITIES. …
Potential Energy (w). As a consequence the force exerted by
the electric field (E), a charge (q) posses potential energy. This
energy is denoted by w. It depends upon the magnitude of the
charge as well as the its location in space. It is similar to a mass
exposed to the gravitational earth. (w = mgh, in that case).
Just as in the gravitational case it is often convenient to choose
sea level as the zero level of potential energy. In the electrical case
it has been agreed to regard earth as the zero level of potential
energy for charges.
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Basic Concepts
§ 1.2 ELECTRICAL QUANTITIES. …
Voltage (v). The rate at which the potential energy varies with
charge is denoted as v and is called electrical potential,
V ≡ dw / dq
….. (1.5)
This electrical potential could also be viewed as potential
energy per unit charge, or potential energy density.
But we are most interested in the potential difference or
voltage and not the earlier discussed potential.
The physical interpretation of equation (1.5) is as follows: if a
charge dq gives up an amount of energy dw in going from one point
to another in space, then we define the voltage between those
points as v = dw / dq.
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Basic Concepts
§ 1.2 ELECTRICAL QUANTITIES. …
Relation Between Electric Field and Potential. By
establishing a potential difference, a battery generates an electric
field. Field and potential are related by the important law of physics,
E = – grad v
….(1.7a)
E = - [ dv/dx i + dv/dy j + dv/ dz K ] Pl check the correctness
through your mathematics book.
If we orientate the battery terminals such that the field is same
as that of the x-axis, then we get a simplified expression for the
above relation:
E =- dv/ dx
….. (1.7b)
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Basic Concepts
§ 1.2 ELECTRICAL QUANTITIES. …
Electric Current (i). If charges are free to move, exposing
them to an electric field will force them to drift either along or
opposite to E, depending on charge polarity. The resulting stream
of charges is called Current.
The electric current measures the rate of change in Charge per
unit time; unit of measurements is Amperes (C/s)
By definition:
i ≡ dq/dt
…. (1.13)
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Basic Concepts
• Charge (q) – fundamental property of atomic structures;
measured in Coulombs (C)
– One electron has a charge of - 1.602 x 10-19 C
– One holes has a charge of + 1.602 x 10-19 C
• Electric Current (i) – measures the rate of change in Charge;
unit is Amperes (C/s)
– Relationship:
i = dq/dt
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Physics - Continued
• Voltage (v) – The Electromotive Force (emf) required to move
Charge around a circuit. Indicative of the Electric Field. Also
called Potential Difference; measured in Volts (J/C or N-m/C)
– Relationship to charge:
v = dw/dq
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Physics – Continued Some More
• Power (p) – Rate of change in work (the expending of energy in
time); measured in Watts (J/s)
p = dw/dt = dw/dq * dq/dt = vi
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Electric Conventions:
• Current Convention:
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Electric Conventions (Cont.)
• Voltage Rise/Drop Convention
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Electric Conventions (Cont.)
• Source/Load Convention
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Fundamental Laws
• Ohm’s Law: V = I*R
• Kirchoff’s Laws:
– Voltage: Sum the voltages around a loop to
Zero
– Current: Sum the currents around a node to
Zero
• Power Equation: P = V*I
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Maximum Power Transfer
• Power Transfer is maximized when load impedance equals
source impedance
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Laboratory Equipment
• Oscilloscope
– 1 M-Ohm Impedance
– “Shunt” Device
– Measures Voltages
– Always measure voltages with respect to scope ground
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Laboratory Equipment (Cont.)
• Multimeter
– Measures Voltage, Current, Resistance, etc.
– “Shunt” Device for Voltage (High Impedance)
– “Series” Device for Current (Low Impedance)
– Acts as a DC source when measuring Resistance
– NEVER measure resistance on an Energized Circuit
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SAFETY
• CONTACT WITH ELECTRIC CURRENT CAN CAUSE DEATH
• As little as 100 milliamperes (0.1 Amp) of electric current
can kill, if it travels across the heart
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SAFETY (Cont.)
• Follow Instructions, Ask for Clarification
• Know where Safety Equipment is Located - Fire
Extinguishers, Telephones, Fire Blankets, Eye Wash
Stations, etc.
• Always Assume an Electric Circuit is Hot (Energized) and
Dangerous and Act Accordingly
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SAFETY (Cont.)
• Keep Work Areas Clean and Uncluttered
• Double Check Circuit Wiring before Energizing
• Never Work Alone
• Wire with One Hand - Minimizes exposure to the
Heart
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SAFETY CONCLUSIONS
Always understand the Laboratory Procedures before
touching anything.
Always assume that electric circuits are potentially live and
dangerous.
Make sure there are adequate life saving resources available
and know how to use them.
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Resistor Color Code
Blk BR Red Or Yel Gr Blu Vi Gry Wht
0 1
2 3 4 5 6 7 8
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First Band – “Tens” Column
Second Band – “Ones” Column
Third Band – Power of 10
Fourth Band – Tolerance:
Gold = 5% , Silver = 10%
Fifth Band – Ignore for now
In this example: 10 x 102 =1000 Ohms +/- 5%
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