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Lecture 1
•Course Overview
–System modeling, analysis and design
•Basic Circuit Parameters
•Passive Sign Convention
•Related educational materials:
–
Chapter 1.1
Pre-requisite and Co-requisite requirements
• Pre-requisites (recommended)
• Basic exposure to electricity and magnetism
• Two semesters of Calculus
• Co-requisites (recommended)
• Differential equations
• Pre- and Co-requisite requirements are rather weak
• Superficial introductions to necessary topics provided at
the appropriate points during this course
Course Goals
• Introduction to modeling, analysis and design of
electrical circuits
• We will often use a systems-level approach:
= f{u(t)}
What are modeling, analysis and design?
• We model the system by determining the
mathematical relationship between the input and
the output
• System analysis often refers to determining the
output from a system, for some given input
• System design involves creating a system to provide
some desired output
Modeling, analysis, and design – overview
Modeling
Analysis
Design
Implement
Comparison of model
results and test data
may result in model
modifications
Test results from
designed system
may result in model
modifications and
re-design
General Modeling Approaches
Modeling
Modeling
Modeling
Approach
Approach
Approach
Lumped
Lumped
Lumped
Parameters
Parameters
Parameters
Distributed
Distributed
Parameters
Parameters
Linear
Linear
Nonlinear
Time-varying
Physical Criteria
Criteria
Physical
Physical
Parameters change
relative
change slowly
slowly relative
Parameters
Parameters
tocomponent
component response
response time
time
to
component
to
change rapidly
rapidly
Parameters change
Parameters
response
relative to
to component
component response
relative
time
time
Relationships between
between dependent
dependent
Relationships
variables are
are linear
linear
variables
Relationships between dependent
variables are non-linear
System physical parameters
change with time
Types of Governing
Equations
Ordinary differential
Ordinary
equations
equations
Partial differential
equations
Linear differential equations
Nonlinear differential
equations
Differential equations whose
coefficients vary with time
Circuits I modeling approach
• We will restrict our attention to lumped parameter
models of linear, time-invariant systems
• Governing equations will be linear, constant-coefficient,
ordinary differential equations
• Slinky demo
–
–
–
–
Linear
Nonlinear
Lumped
Distributed
Basic Circuit Parameters
• Charge (q) is the basic quantity in circuit analysis
• Units are Coulombs (C)  1 Coulomb  -6.241018
electrons
• Current (i) is the rate of change of charge with time:
dq
i
dt
Coulombs
• Units are Amperes (A) 
 Amperes , A
Second
Basic Circuit Parameters – continued
• Voltage (v) is the change in energy of a unit charge
at two different points:
dW
v
dq
Joules
 Volts , V
• Units are Volts (V) 
Coulomb
Basic Circuit Parameters – continued
• Power (P) is the time rate of change of energy:
dW dW dq
P


 v i
dt
dq dt
• Units are Watts (W)
Passive Circuit Elements
• For a passive circuit element, the total energy
delivered to the circuit element by the rest of the
circuit is non-negative
• The element can store energy, but it cannot create energy
• Active circuit elements can supply energy to the
circuit from external sources
Passive Sign Convention
• We will assume the sign
of the current relative to
voltage for passive circuit
elements
• Positive current enters the
node at the higher voltage
• Sign must be known for active circuit elements
Passive Sign Convention – continued
• You can assume (arbitrarily) either the voltage
polarity or the current direction
• This assumption dictates the assumed direction of the
other parameter
• These assumptions provide reference voltage
polarities and current directions
• Subsequent analysis is performed based on this
assumption; a negative result simply means that
the assumed voltage polarity or current direction
was incorrect
Passive Sign Convention – Example 1
• Provide the appropriate sign convention for the missing
parameter on the passive elements represented by grey boxes.
Passive Sign Conventions – Hints
• It is generally counter-productive to attempt to
determine the “correct” voltage polarities and current
directions before analyzing the circuit
• Just arbitrarily choose either the assumed voltage
polarity or current direction for each passive circuit
element
• This choice dictates the sign of the other parameter
• Perform analysis using assumed signs
• Negative signs mean that the assumption was incorrect
Passive Sign Convention – Example 2
• Assign reference voltage and current directions for the passive
elements represented by shaded boxes in the circuit below:
Passive Sign Convention – Example 3
• Assign reference voltage and current directions for the passive
elements represented by shaded boxes in the circuit below:
Passive Sign Convention – Example 4
• For the circuit below, the sign convention shown is chosen
• After analyzing the circuit, it is determined that I1 = -3mA, I2 =
3mA, V1 = -1.5V, and V2 = 2.5V. Re-draw the circuit showing the
actual voltages and currents and their directions