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

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Lecture 1

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Lecture 1

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-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

Course Goals

  • Introduction to modeling, analysis and design of electrical circuits

  • We will often use a systems-level approach:


What are modeling analysis and design

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, and design – overview


General modeling approaches

General Modeling Approaches


Circuits i modeling approach

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


Lecture 1

  • Slinky demo

    • Linear

    • Nonlinear

    • Lumped

    • Distributed


Basic circuit parameters

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:

    • Units are Amperes (A) 


Basic circuit parameters continued

Basic Circuit Parameters – continued

  • Voltage (v) is the change in energy of a unit charge at two different points:

    • Units are Volts (V) 


Basic circuit parameters continued1

Basic Circuit Parameters – continued

  • Power (P) is the time rate of change of energy:

    • Units are Watts (W)


Passive circuit elements

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

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

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

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

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

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

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

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


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