EE2210 Lecture 1:
Introduction and
Lumped Circuit Abstraction
Dorf’s
Ch1.1~1.5
Ch2.1~2.5
Ch3.2
Ping-Hsuan Hsieh (謝秉璇)
Delta Building R908
EXT 42590
phsieh@ee.nthu.edu.tw
What is Engineering?
 Purposeful use of science
– Electrical engineering is one of many engineering fields
– Electrical engineering is the purposeful use of Maxwell’s Equations
(or abstractions) for electromagnetic phenomena
 Maxwell’s Equations
Gauss’s Law
Faraday’s Law
Ampere’s Law
Continuity Equation
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What is EE2210 about?
 Gainful employment of Maxwell’s equations
 From electrons to digital gates and Op-Amps
– Nature as observed in experiments
– Physical laws or ‘abstractions’
● Maxwell’s equations
● Ohm’s Law
– Lumped circuit abstraction
– Simple amplifier abstraction
● Electronics (EE2255)
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Analog and Digital Abstraction
Analog
Digital
Operational amplifier
Filters
Analog subsystems
Modulators
Oscillators
RF amplifiers
Power supplies
Digital abstraction
Combinational logic
Clocked digital abstraction
Instruction set abstraction
Programming languages
Software systems
AIC-I (EE3235)
AIC-II (EE4280)
Introduction to IC Design (EE4290)
Power Electronics (EE4830)
Power System I (EE4710)
Logic Design (EE2280)
Intro. to Programming (EE2310)
Data Structures (EE2410)
Microprocessor Systems (EE2401)
Computer Architecture (EE3450)
Embedded System Laboratory (EE2405)
Special Topic on Implementation (EE3900)
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Lumped Circuit Abstraction
 The big jump from physics to EE
 Consider
I ??
V
 Suppose we wish to answer the question:
– What is the current flowing through the bulb?
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We could do it the Hard Way
 Apply Maxwell’s equations
Differential Form
Integral Form
Gauss’s Law
Faraday’s Law
Ampere’s Law
Continuity Equation
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Instead, there is an Easy Way…
 First, let us build some insight:
Analogy
– I ask you:
– You may quickly ask me:
– I tell you:
– You respond:
What is the acceleration?
Done!!
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Instead, there is an Easy Way…
 First, let us build some insight:
Analogy
 In doing so, you ignored:
– The object’s shape
– Its temperature
– Its color
– Point of force application
– …
 Point-mass discretization
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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
– It’s temperature, shape, orientation, etc.
 We can replace the bulb with a
discrete resistor
– For the purpose of calculating the current
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The Easy Way…
 We replace the bulb with a
discrete resistor
– For the purpose of calculating the current
 In EE, we do things the easy way…
– R represents the only property of interest!
– Like with point-mass:
replace objects with their mass to find
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Element V-I Relationship
 R represents the only property of interest!
 R relates element V and I
called element v-i relationship
 R is a lumped element abstraction for the bulb
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Lumped Element
 Lumped circuit element described by its v-i relation
Resistor
Voltage source
 Power is the time rate of expending or absorbing energy
– Power consumed by element
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Is R a lumped element abstraction for the bulb?
 Although we will take the easy way of using lumped abstraction
for the rest of this course, we must make sure (at least for the
first time) that our abstraction is reasonable.
 Ensure that V and I are uniquely defined for the element
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Current I must be uniquely defined
 True when
 True only when
 From Maxwell’s equation
only if
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Voltage V must be defined
 V is uniquely defined only when
for any closed loop outside the element, so
 From Maxwell’s equation
only if
 Furthermore, the signal speeds of interest should be way lower
than speed of light
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Lumped Matter Discipline (LMD)
 Self imposed constraints:
– Choose lumped element boundaries so that the rate of change of magnetic
flux linked by any closed loop outside an element must be zero for all time.
through any closed path outside the element
– Choose lumped element boundaries so that there is no total time varying
charge within the element for all time.
where q is the total charge inside the element
– Operate in the regime in which signal timescales of interest are much larger
than propagation delay of electromagnetic waves across the lumped
elements.
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So, what does LMD buy us?
 Replace the differential equations with simple algebra using
lumped circuit abstraction (LCA)
 For example
 What can we say about voltages in a loop
under the lumped matter discipline?
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What can we say about voltages in a loop under LMD?
 Kirchhoff’s Voltage Law (KVL):
The sum of the voltages in a loop is 0.
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What can we say about currents at a node under LMD?
 Consider node a
 Kirchhoff’s Current Law (KCL):
The sum of the currents into a node is 0
– This is simply the conservation of charges.
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KVL and KCL Summary
 Kirchhoff’s Voltage Law (KVL):
 Kirchhoff’s Current Law (KCL):
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Summary
 Lumped Matter Discipline (LMD)
outside elements
inside elements
– Also, signal speeds of interest should be way lower than speed of light
 Lumped circuit abstraction
– Element described by its v-i relation
– Power consumed by element is
 Maxwell’s equations simplify to algebraic KVL & KCL under LMD
– Kirchhoff’s Voltage Law (KVL):
for loop
– Kirchhoff’s Current Law (KCL):
for node
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