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Circuit Theory I Basic Concepts Assistant Professor Suna BOLAT
Eastern Mediterranean University
Electric and electronic department
AnantAgarwaland Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare(http://ocw.mit.edu/), Massachusetts Institute of Technology
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Electrical engineering
What is engineering?
The application of scientific, economic, social, and practical knowledge in order to design, build, maintain, and improve structures, machines, devices, systems, materials and processes (Source: wikipedia).
Purposeful use of science (cite: Steve Sentura).
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What is this course about?
Circuit theory
• Gainful employment of Maxwell’s equations...
• From electrons to digitial gates and op-amps.
• Make it simple though!
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Six basic SI units and one derived unit relevant to this course...
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SI prefixes
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From the facts of nature to build interesting systems...
Nature as observed in experiments
tables of data from the measurements&observations
Physics laws
Maxwell’s equations, Ohm’s Law abstraction for tables of data
Simple amplifier abstraction
Lumped Circuit abstraction
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Simple amplifier
Operational amplifier
Digital abstraction
Filters Combinational logic
Analog system components: modulators, oscillators, RF amps, Power supplies
Clocked digital
Instruction set
Programming languages
Software systems, operating systems, browsers
+
+
Toasters, sonar, stereos, space shuttle, doomsday devices
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Electrical charge
• Charge is a characteristic of a unit of matter that expresses the extent to which it has more or fewer electrons than protons.
• Measured in coulombs [C]
• 1 C of charge requires 6.24 x 1018 electrons.
• 1 electron charge e = −1.602 x 10−19 C .
• Law of Conservation of Charge: Charge can only be transferred. Cannot be created/destroyed.
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Electrical current
• Electric currents are flows of electric charge.
• Suppose a collection of charges is moving perpendicular to a surface of area A
• The electric current is defined to be the rate at which charges flow across any cross-sectional area. If an amount of charge ΔQ passes through a surface in a time interval Δt, then the average current Iavg
is given by
𝑰𝒂𝒗𝒆 =∆𝑸
∆𝒕
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Electrical current
• The SI unit of current is the ampere (A), with 1 A = 1 coulomb/sec.
• Common currents range from mega-amperes in lightning to nano-amperes in your nerves.
• In the limit t0 the instantaneous current I may be defined as
𝑰𝒂𝒗𝒆 =
𝒅𝒒
𝒅𝒕
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Direct current (DC)
• Direct current (dc) is
the unidirectional flow of electric charge
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Alternating current (AC)
• In alternating current (ac), the flow of electric charge periodically reverses direction
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Problems:
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Problems
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Voltage and potential
• Electrostatic Potential Energy:
the work that I have to do to bring a charge to a point P
unit: joules
• Electric potential, V:
Energy required to move a unit charge through an element
unit: volt
q1
q2
P
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Voltage and potential
• Electric Potential, V:
Electrical location of a point according to a reference.
unit: volt
• Voltage, U:
Energy required to move a unit charge through an element
unit: volt 2
1
V2 V1
V21 = V2 - V1
reference Vr
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Potential, V:
Electrical location of a point according to a reference.
unit: volt
Potential
2
1
+V2 + V1
- V3
reference Vr
3
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Voltage
Voltage, vab: potential difference
unit: volt
Reference, Vr
V1
V2
V21 = V2 - V1
𝑣𝑎𝑏 =𝑑𝑤
𝑑𝑞
v : voltage in volts (V) w : Energy in joules (J) q : charge in coulombs (C)
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Voltage
• Voltage pushes charge in one direction.
• We use polarity (+ and −) on batteries to indicate which direction the charge is being pushed.
• dc voltage is represented by V and ac voltage is represented by υ.
Two equivalent representation of the same voltage: (a) point a is 9 V above point b, (b) point b is −9 V above point a.
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Alternating voltage
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1.5
-1
-0.5
0
0.5
1
1.5
Umax
Voltage, U(t)
Time, t
Period, T = 1/f
Ue = effective value = Umax/2
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Direct voltage
constant
DIRECT VOLTAGE
IMPULSE VOLTAGE
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Lumped circuit abstraction
Consider this circuit:
Suppose we wish to answer this question:
What is the current through the bulb?
Big jump from physics to circuit theory!!!
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Apply Maxwell’s equations...
It is hard
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Instead there is an easy way...
• First let’s build some insight:
• I ask you: what is the acceleration?
• You should ask me: what is the mass?
• I tell you: m
• You respond: 𝑎 =𝐹
𝑚
–Done!
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• In doing so, we ignored
• The shape of the object
• Its temperature
• Its color
• Point of force application
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The easy way...
• Consider the filament of the light bulb.
• We do not care about
– How current flows inside the filament
– Its temeperature, shape, orientation, etc.
Then we can replace the bulb with a «discrete resistor» for the purpose of calculating the current.
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The easy way...
• R represents the only property of interest!
• Like with the point-mass: replace objects with their mass m to find a.
𝐼 =𝑉
𝑅
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The easy way...
• R represents the only property of interest!
• R relates element V and I
is called element v-i relationship.
𝐼 =𝑉
𝑅
𝐼 =𝑉
𝑅
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R is a lumped element abstraction for the bulb.
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R is a lumped element abstraction for the bulb
• Although we take the easy way using lumped abstractions for the rest of this course, we must make sure (at least the first time) that our abstraction is reasonable.
• In this case, ensure V and I are defined for the element.
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What does it buy us?
• Replace differential equations with simple algebra using lumped circuit abstraction.
under some constraints...
(you will learn them later, keep those in mind...)
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Power and Energy
• Power is the rate of expending and absorbing energy, measured in watts (W).
𝑝 =𝑑𝑤
𝑑𝑡= 𝑣. 𝑖
p : Power in watts (W) v : Voltage in volts (V) w : Energy in joules (J) t : Time in seconds (s) i : current in amperes (A)
• Circuit elements that absorb power has positive value of p.
• Circuit elements that supply (produce) power has negative value of p.
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Power and Energy
• Energy is the capacity to do work, measured in joules (J).
• If current and voltage are constant (dc), the power is constant. The energy is: 𝑤 = 𝑝 𝑑𝑡 = 𝑝(𝑡 − 𝑡0)
𝑡
𝑡0
• In adddition to joules, Watt-hour can also be used to measure energy.
1 Wh = 3,600 J
• Law of conservation of energy. Total power in a circuit at any instant is must be zero.
𝑤 = 𝑝 𝑑𝑡 𝑡
𝑡0
= ±𝑣. 𝑖 𝑑𝑡𝑡
𝑡0
p : Power in watts (W) v : Voltage in volts (V) w : Energy in joules (J) t : Time in seconds (s) i : current in amperes (A)
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Problems
Ex. 1.4:
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Problems
Ex. 1.5:
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Problems
Ex. 1.5:
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Problems
Ex. 1.5:
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Passive sign convention
Ex. 1.7: Sign convention is applied.
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Circuit elements
• Ideal independent sources: provides a specified voltage or current that is completely independent of other circuit variables
• Ideal Independent Voltage Source:
(a)Independent voltage source (constant / time varying)
(b) Independent voltage source (battery).
• Ideal Independent Current Source:
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Circuit elements
• Ideal Dependent Sources: controlled by other voltage or current
(a) dependent voltage source
(b) dependent current source