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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

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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

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Course Goals Introduction to modeling, analysis and design of electrical circuits We will often use a systems-level approach:

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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

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Modeling, analysis, and design – overview

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General Modeling Approaches

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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

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Slinky demo – Linear – Nonlinear – Lumped – Distributed

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Basic Circuit Parameters Charge (q) is the basic quantity in circuit analysis Units are Coulombs (C) 1 Coulomb -6.24 10 18 electrons Current (i) is the rate of change of charge with time: Units are Amperes (A)

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Basic Circuit Parameters – continued Voltage (v) is the change in energy of a unit charge at two different points: Units are Volts (V)

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Basic Circuit Parameters – continued Power (P) is the time rate of change of energy: Units are Watts (W)

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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

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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

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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

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Passive Sign Convention – Example 1 Provide the appropriate sign convention for the missing parameter on the passive elements represented by grey boxes.

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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

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Passive Sign Convention – Example 2 Assign reference voltage and current directions for the passive elements represented by shaded boxes in the circuit below:

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Passive Sign Convention – Example 3 Assign reference voltage and current directions for the passive elements represented by shaded boxes in the circuit below:

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Passive Sign Convention – Example 4 For the circuit below, the sign convention shown is chosen After analyzing the circuit, it is determined that I 1 = -3mA, I 2 = 3mA, V 1 = -1.5V, and V 2 = 2.5V. Re-draw the circuit showing the actual voltages and currents and their directions

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