Ahmad Salmanogli
Room: NC08
salmanogli@cankaya.edu.tr
Introduction
Short Review on Physics
Organization
Prerequisite: physics II
Books:
1. Introductory Circuit Analysis, Robert L. Boylestad, Prentice Hall PTR, 2000,
2003, 2007, 2010;
2. AC and DC Network Theory, A. J. Pointon, H. M. Howarth, Springer Netherlands,
1991;
3. Electrical Circuit Theory and Technology, Bird, John, Elsevier Newnes, 2003;
Assessment:
Final Exam: 50%
Midterm (one exam): 30%
Lab: 20%
Work in Class (Bonus): 10%
Basic bibliography:
1. Introductory Circuit Analysis, Robert L. Boylestad, Prentice Hall PTR, 2000, 2003,
2007, 2010;
2. AC and DC Network Theory, A. J. Pointon, H. M. Howarth, Springer Netherlands,
1991;
3. Electrical Circuit Theory and Technology, Bird, John, Elsevier Newnes, 2003;
Additional bibliography:
1. Circuits Systems with Matlab and PSpice, Won Y. Yang, Seung C. Lee, Wiley, Asia,
2007.
2. Linear and Nonlinear Circuits, L.O. Chua, C.A. Desoer, E.S. Kuh , McGraw-Hill
Inc., 1987.
3. Analog and digital filters: design and realization, H. Y.,-F. Lam , Prentice_Hall, Inc.,
Englewood Cliffs, New Jersey, 1979.
4. Classical Circuit Theory, Omar Wing, Springer US, 2009
Course description
1. Basic laws in circuit theory: voltage and current Kirchoff's laws. Real
circuit and its mathematical model, Thevenin and Norton theorem.
2. Linear and non-linear passive components and active elements of analog
circuits. The basic principles, theorems and methods in the analysis of
resistive circuits.
3. Circuits with harmonic currents in steady state - Method of complex
numbers, phasor diagrams. Coupled and resonant circuits.
4. Transients, analysis in time and frequency domain
5. The concept of transfer function, amplitude and phase characteristics.
6. Basic concepts of circuits stability.
Electric Circuit
• An electric circuit is an interconnection of electrical
elements.
• A circuit consists of a mesh of loops
Represented as branches
and nodes in an undirected
graph.
Circuit components reside
in the branches
Connectivity resides in the
nodes and nodes represent
wires
Charge q = ne
Basic SI unit, measured in Coulombs (C)
“e” charge of electron and “n” is the number
Counts the number of electrons (or positive charges)
present.
Charge of single electron is 1.602*10-19 C
One Coulomb = 6.24*1018 electrons.
Charge is always multiple of electron charge
Charge cannot be created or destroyed, only
transferred.
Current
The movement of charge.
We always note the direction of the equivalent positive
charges, even if the moving charges are negative.
It is the time derivative of charge passing through a
circuit branch
dq
i
dt
Unit is Ampere (A), is one Coulomb/second
Customarily represented by i (AC) or I (DC).
Voltage
a difference in electric potential
always taken between two points.
It is a line integral of the force exerted by an electric
field on a unit charge.
v E f dx Ef electric field
Customarily represented by u (AC) or U (DC) or v and
V alternativelly.
The SI unit is the Volt [V].
Power
Power is the product of voltage by current.
It is the time derivative of energy delivered to or
extracted from a circuit branch.
dE
P
dt
Customarily represented by P or S or W.
The SI unit is the Watt [W].
AC vs. DC circuits
• Direct Current (DC) is a
current that remains constant
with time
• A common source of DC is a
battery.
• A current that varies sinusoidally
with time is called Alternating
Current (AC)
Basic circuit elements - resistor
Resistors are circuit elements that resist the flow of current. When this
is done a voltage appears across the resistor's two wires.
A pure resistor turns electrical energy into heat. Devices similar to
resistors turn this energy into light, motion, heat, and other forms of
energy.
Resistors don't care which leg is connected to positive or negative. We note
the current flow opposite to the voltage. This is called the an "positive charge”
sign convention. Some circuit theory books assume "electron flow" flow sign
convention.
Basic circuit elements - resistor
Resistance is measured in terms of units called "Ohms" (volts per ampere), which is
commonly abbreviated with the Greek letter Ω ("Omega"). Ohms are also used to
measure the quantities of impedance and reactance. The variable most commonly used
to represent resistance is "r" or "R". Resistance is defined as:
where ρ is the resistivity of the material, L is the length of the resistor, and A is the
cross-sectional area of the resistor.
Conductance is the inverse of resistance. Conductance has units of "Siemens" (S). The
associated variable is "G":
1
G
r
The relation between voltage and current: V = r*I
Basic circuit elements - inductor
Inductance is the property whereby an inductor exhibits opposition to the
change of current flowing through it, measured in henrys (H).
Where µ is the permeability of the dielectric material
Basic circuit elements – inductor (2)
The dependence between the current and the voltage
of the inductor is described by the equations:
The power stored by an inductor:
An inductor acts like a short circuit to dc (di/dt = 0) and its
current cannot change abruptly.
Basic circuit elements - capacitor
A capacitor is a passive element designed to store energy in its electric field.
A capacitor consists of two conducting
plates separated by an insulator (or
dielectric).
Capacitance C is the ratio of the charge q on one plate of a capacitor
to the voltage difference v between the two plates, measured in farads
(F).
Where ε is the permittivity of the dielectric material between the plates, A is the
surface area of each plate, d is the distance between the plates.
Basic circuit elements – capacitor (2)
The dependence between the charge and voltage is:
Then current –voltage relationship of the capacitor is
described by the equations:
The power stored by an inductor:
A capacitor is an open circuit to dc (dv/dt = 0). And its voltage cannot change
abruptly (depends on integral of i).
Circuit Elements Ideal
Independent Voltage Source
provides a specified voltage or current that is completely independent
of other circuit variables
The voltage at the nodes is strictly defined by voltage of the source, the
current flow depends on the other elements in the circuit
The ideal voltage source is only a mathematical model.
Generally we can divide the voltage sources into three groups:
• Batteries
• Generators
• Supplies
Circuit Elements Ideal
independent current source
The current flow in the branch is strictly defined by current
of the source, the voltage at the nodes of the source
depends on the other elements in the circuit
The symbols used for AC current sources (similarly as for
voltage sources) are the same as for the DC current sources,
but described with noncapital letters (e.g. j(t)).
The ideal current source similarly to ideal
voltage source is only a mathematical model.
Circuit Elements – dependent
sources
Ohms Law
The potential difference (voltage) across an ideal conductor is proportional
to the current through it.
For the DC
For the AC
where: U - voltage I - current R – resistance, Z- inductance
Kirchhoff’s Circuit Laws
Kirchhoff’s circuit laws were first described in 1845 by
Gustav Kirchhoff. They consist from two equalities for
the lumped element model of electrical circuits. They
describe the current and voltage behaviour in the
circuit.
Kirchhoff’s First Law - Kirchhoff’s
Current Law (KCL)
The algebraic sum of currents in a network of conductors meeting at a node is
zero.
It can be described by the equation:
The currents flowing into the node (I1, I6) we describe as positive, the
currents flowing out the node (I2, I3, I4, I5) we describe as negative.
Kirchhoff’s Second Law -
Kirchhoff’s Voltage Law (KVL)
The algebraic sum of the potential rises and drops
around a closed loop or path is zero.
where Ui describes both the potential
drops at the elements and the
voltages generated by sources.
To use the KVL one need to set up a rotation in the circuit. Potentials with direction
of the circuit have a positive sign, voltage opposite to the direction of circulation of
the circuit have a negative sign.
Series Connection
All components are connected end-to-end.
Voltage drops add to total voltage.
Due to all components goes the same (equal) current.
Impedance (or simply resistance in DC) add to total impedance
(resistance).
Parallel Connection
All components are conected between the same two sets of electrically
common points.
Currents add to total current.
Voltage drop on the components are the same.
Conductances (inverse of resistance) add to total conductance.
or
Series-Parallel Connection
Typical circuits have some series
connected components in some parts
of the circuit and parallel in others.
Then it is impossible to apply a single
set of rules to the all circuit. Instead, it
is possible to identify which parts of
that circuit are series and which parts
are parallel, then selectively apply
series and parallel rules.
