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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:

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

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 -6.241018 electrons

- Current (i) is the rate of change of charge with time:
- Units are Amperes (A)

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 – continued

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

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