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Lecture 1 - PowerPoint PPT Presentation

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

Course Overview

System modeling, analysis and design

Basic Circuit Parameters

Passive Sign Convention

Related educational module:

Section 1.1

• 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

• Introduction to modeling, analysis and design of electrical circuits

• We will often use a systems-level approach:

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

• We will restrict our attention to lumped parameter models of linear, time-invariant systems

• Governing equations will be linear, constant-coefficient, ordinary differential equations

• 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) 

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

• Units are Volts (V) 

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

• Units are Watts (W)

• 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

• 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

• 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

• Provide the appropriate sign convention for the missing parameter on the passive elements represented by grey boxes.

• 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

• Assign reference voltage and current directions for the passive elements represented by shaded boxes in the circuit below:

• Assign reference voltage and current directions for the passive elements represented by shaded boxes in the circuit below:

• 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