E E 1205 Circuit Analysis

Lecture 1 - Introduction to Electrical Engineering

Overview of Electrical Engineering• Electrical engineers design

systems with two main objectives: to…– Gather, store, process,

transport or present information

– Distribute, and convert energy between different forms

• Electrical systems can be divided into seven major classifications.

7 Linked Classifications of Electrical Systems

• Communications Systems• Computer Systems• Control Systems• Electromagnetics• Electronics• Power Systems• Signal Processing Systems

Communications Systems• Telephony

– Analog and Digital– Switched Channels

• Radio– Broadcast AM, FM, & SW– Two-Way

• Television

Computer Systems

• Programmable Microcircuits

• High-speed switching of logic circuits

• Used for– Computation– Control

Control Systems

• Automated• Adaptable• Faster Operation than

Manual• More Reliable than Manual• Modern high-performance

aircraft rely on automated control systems

Electromagnetics

• Antennas for Sending & Receiving Information– Cell Phones– Satellite Dishes

• Magnetrons for generation of Microwave Energy

• Induction Heating for Industrial processes

Electronics

• Material Properties• Devices• Circuits• Used for Detecting,

Amplifying and Switching Electrical Signals

Power Systems

• Large networks connected by low frequency a-c transmission lines

• Small networks in aircraft and spacecraft

• Electromechanical Energy Conversion

• Power Electronics– High frequency switching converters– High efficiency, high power density

Signal Processing Systems• Transform and manipulate

signals and the information they contain

• Image processing– Data from weather satellites– MRI scans of the human

body• Noise reduction• Encryption

Circuit Theory

• Mathematical modeling of physical phenomena

• Circuit theory is a special case of electromagnetic field theory– General EM theory is more

complex than circuit theory– General EM theory requires

more complex mathematics

Three Basic Assumptions of Circuit Theory

• Electric effects happen instantaneously throughout a system

• Net Charge on every component in the system is zero

• No magnetic coupling between components

cf

Effect of Frequency

Frequency Wavelength Usage

0 Hz (DC) Infinite Basic Power

60 Hz 5000 km Power

400 Hz 750 km Aircraft Power

1000 Hz 300 km Acoustic

1000 kHz 300 m AM Radio

500 MHz 60 cm Television

2.45 GHz 122.4 mm Microwave Oven

20 GHz 15 mm K-band Radar

Problem Solving

• Identify what is given and what is to be found.

• Sketch a circuit diagram or other visual model

• Think of several solution methods and a way of choosing between them

• Calculate a solution

Problem Solving (continued)• Use your creativity

– If your efforts are not converging to a solution, you may want to rethink your assumptions.

• Test your solution– Is your answer reasonable?– Does your answer validate

your assumptions?

International System of Units

– Frequency hertz (Hz) s-1 – Force newton (N) kg·m/s2

– Energy or work joule (J) N·m– Power watt (W)

J/s– Electric charge coulomb

A·s– Electric potential volt (V) W/A– Electric resistance ohm ()

V/A– Electric conductance siemens (S)

A/V

International System of Units (continued)

– Electric capacitance farad (F)C/V

– Magnetic flux weber (Wb)V·s

– Inductance henry (H) Wb/A

Standardized Prefixes

• atto a 10-18

• femto f 10-15

• pico p 10-12

• nanon 10-9

• micro 10-6

• milli m 10-3

• centic 10-2

• deci d 10-1

• dekada 10• hecto h

102

• kilo k 103

• mega M106

• giga G 109

• tera T 1012

• peta P 1015

• exa E1018

Circuit Analysis: An Overview• A circuit model is used to

connect our visualization to our analysis of a physical system

• The elements of our circuit model are ideal circuit components.

• The behavior of output parameters is governed by physical/mathematical laws for the elements of the circuit model.

Voltage and Current

• Voltage is the energy per unit of charge.

• Current is the rate of flow of charge.

dwv

dq

dqidt

Voltage and Current (continued)• The relationship between

voltage and current in a circuit element defines that circuit element.

• Both voltage and current have associated polarities.

• These polarities determine the direction of power flow.

Ideal Basic Circuit Element

• Three attributes of an ideal circuit element:– There are only two terminals– Described mathematically in terms of

current and/or voltage– Cannot be subdivided into smaller

components

+v-

i1

2

Voltage Polarity Definitions

• Positive v– voltage drop from 1 to 2 or– voltage rise from 2 to 1

• Negative v– voltage drop from 2 to 1 or– voltage rise from 1 to 2

+v-

i1

2

Current Polarity Definitions

• Positive i– Positive charge flowing from 1 to 2– Negative charge flowing from 2 to 1

• Negative i– Positive charge flowing from 2 to 1– negative charge flowing from 1 to 2

+v-

i1

2

Passive Sign Convention

• Whenever the reference direction for the current in an element is in the direction of the reference voltage drop, use a positive sign in any expression that relates voltage to current. Otherwise, use a negative sign.

+v-

i1

2

Power and Energy

• Power associated with a circuit element is consumed by that circuit element when the value of power is positive.

• Conversely, power is generated, or produced by the element if the value consumed is negative.

dw dw dqp vi

dt dq dt

Expression of Power

+v-

i1

2

+v-

i1

2

-v+

i1

2

-v+

i1

2

p vi

p vi

p vi

p vi