Avishai Wool, lecture 1 - 1 Introduction to Information Security Lecture 1.
Lecture 1
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Lecture 1
•Course Overview–System modeling, analysis and design
•Basic Circuit Parameters•Passive Sign Convention•Related educational module:
– Section 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
Test results from designed system
may result in model modifications and
re-design
Comparison of model results and test data may result in model
modifications
General Modeling Approaches
Modeling Approach
Physical Criteria Types of Governing Equations
Lumped Parameters
Parameters change slowly relative to component response time
Ordinary differential equations
Modeling Approach
Physical Criteria Types of Governing Equations
Lumped Parameters
Parameters change slowly relative to component response time
Ordinary differential equations
Distributed Parameters
Parameters change rapidly relative to component response time
Partial differential equations
Modeling Approach
Physical Criteria Types of Governing Equations
Lumped Parameters
Parameters change slowly relative to component response time
Ordinary differential equations
Distributed Parameters
Parameters change rapidly relative to component response time
Partial differential equations
Linear Relationships between dependent variables are linear
Linear differential equations
Modeling Approach
Physical Criteria Types of Governing Equations
Lumped Parameters
Parameters change slowly relative to component response time
Ordinary differential equations
Distributed Parameters
Parameters change rapidly relative to component response time
Partial differential equations
Linear Relationships between dependent variables are linear
Linear differential equations
Nonlinear Relationships between dependent variables are non-linear
Nonlinear differential equations
Modeling Approach
Physical Criteria Types of Governing Equations
Lumped Parameters
Parameters change slowly relative to component response time
Ordinary differential equations
Distributed Parameters
Parameters change rapidly relative to component response time
Partial differential equations
Linear Relationships between dependent variables are linear
Linear differential equations
Nonlinear Relationships between dependent variables are non-linear
Nonlinear differential equations
Time-varying System physical parameters change with time
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
Basic Circuit Parameters
• Charge (q) is the basic quantity in circuit analysis• Units are Coulombs (C) 1 Coulomb -6.241018
electrons
• Current (i) is the rate of change of charge with time:
• Units are Amperes (A) dt
dqi
A ,mperesA Second
Coulombs
Basic Circuit Parameters – continued
• Voltage (v) is the change in energy of a unit charge at two different points:
• Units are Volts (V) V ,Volts Coulomb
Joules
dq
dWv
Basic Circuit Parameters – continued
• Power (P) is the time rate of change of energy:
• Units are Watts (W)
ivdt
dq
dq
dW
dt
dWP
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 tovoltage for passive circuitelements
• Positive current enters thenode 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: