ENGR 12Engineering Circuits

Tom Rebold

Lecture 1A: Basic Concepts

Today Why this stuff matters What is voltage and current

physics vs common sense Ideal Circuit Element

And some real ones: Resistors, Capacitors, Inductors

Power and Energy Voltage and Current Sources

Later This Week…

Ohms Law Network Topology Kirchoff’s Circuit Laws

Circuit Theory is a Pre-requisite for

Analog and digital circuits Amplifiers, Power System, Integrated Circuits

Communication systems design Filters, Modulation theory, Signal Processing

Computer architectures Control of electro-mechanical systems

Feedback, stability analysis

Solid State

Devices Transistors Diodes (LED’s, Laser diodes) Photodetectors

Miniaturization of electrical devices Integration of many devices on a single chip

Digital Logic Based on logic gates, truth tables, and

combinational and sequential logic circuit design

Uses Boolean algebra and Karnaugh maps to develop

minimized

logic circuits.

Power Systems

Generation of electrical energy Storage of electrical energy Distribution of electrical energy Rotating machinery-generators, motors

Communications/Signal Processing Transmission of information electrically and

optically Modification of signals

enhancement compression noise reduction filtering

Controls

Changing system inputs to obtain desired outputs

Feedback Stability

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Introduction to Electric CircuitsIntroduction to Electric Circuits

Here we are going to remind what are:

•Voltage

•Current

•Current flow

•Voltage Sources

•Voltmeter (Multimeter)

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What is Voltage?

V = “Electrical pressure” - measured in volts.

H2O

High Pressure Low Pressure

Figure 1.1

13

A battery in an electrical circuit plays the same role as a pump in a water system.

14

What Produces Voltage?

V = “Electrical pressure”

A Battery

Electric Power Plant

Lab Power Supply

Nerve Cell

1.5 V

9 V

13,500 V13,500 V

A few Volts

Solar Cell

A few millivoltswhen activated bya synapse

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Other Symbols Used for Other Symbols Used for Specific Voltage Sources Specific Voltage Sources

+_

+

_

Battery

~

Time-varyingsource

Solar Cell

. Generator (power plant)

These are all…

Voltage Sources Figure 1.2

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A Typical Voltage SourceA Typical Voltage Source

Lab Power Supply

Remember: A voltage is measured between two points

This supply goes upto 10 V

The red (+) and black (-) terminals emulate the twoends of a battery.

The voltage is adjustablevia this knob

The white terminal is The white terminal is connected to earth groundconnected to earth groundvia the third prong of the via the third prong of the power cordpower cord

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I COM V

volts

We can measure voltage between two points with a metermeter

Measuring VoltagesMeasuring Voltages

• Connect the V of the meter to power supply red

• Connect COM (common) of the meter to power supply black

• Read the Voltage white

+2.62

•Set the meter to read Voltage

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The power supply is changed to 3.2 V. What does the meter read?

Exercise

I COM V

What’s the answer?

–3.2 V

Answer: –3.2 V

Find out

19

What is “Ground”

“Ground” refers to the reference terminal to which all other voltages are measured

+_V1 +_V2 +_V3

Point of Reference

Figure 1.3

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Most people choose the earth as the reference ground when a connection to it is available.

A ground connection to earth is often made via the third prong of a power cord.

The earth is really just one big ground node.

+_V2

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+_V1 +_V2 +_V3

Ground Symbol

V4 +_

Positive relative to ground

Negative relative to ground

Figure 1.4

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Voltage Relative to Ground

+

The red terminal is positive with respect to “ground”

The white terminal is connected to earth ground

Connect the black terminal to ground

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The black terminal is negative with respect to ground.

Negative Polarity Relative to

Ground

+

24

What is Current?

• Current is the flow of charge from a voltage source• 1 Ampere (“Amp”) = Flow of 1 Coulomb/sec

+++

25

How Does Current Flow?

Current can only flow through conductors

+++

Metal wires (conductors)

Currentflow

26

When Does Current NOT Flow?

+++

Plastic material (insulators)

Current cannot flow through insulators

No currentflow

27

Note that Air is an Insulator

+++Air

Current cannot flow through insulators

No current flow

That’s why a battery doesn’t discharge if left on its own.

28

What is Current?

• Electricity flows when electrons travel through a conductor.

• Only some materials have free electrons inside.

Conductors: YES!

Insulators:

NO!

No free electrons = No current

• We call this flow “current.”

silver copper gold aluminium iron steel brass bronze mercury graphite dirty water concrete

glass rubber oil asphalt fiberglass porcelain ceramic quartz (dry) cotton (dry) paper (dry) wood plastic air diamond pure water

29

CurrenCurrentt

Current is the amount of electric charge (coulombs) flowing past a specific point in a conductor over an interval of one second. 

1 ampere = 1 coulomb/second

Electron flow is from a lower potential (voltage) to a higher potential (voltage).

-ee e+

Wire

e

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Current For historical reasons, current is

conventionally thought to flow from the positive to the negative potential in a circuit.

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Formal Definition of Current Flow

• Rate of flow of “positive” charge

1 Ampere = 1 Coulomb of electrons flowing by per second in the wire

• Measured in Coulombs per second of charge

• (It’s really the electrons flowing in the opposite direction)

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- --

--

-- -

--

-- - -

--

-- - -

--

--

electron motion

positive current direction

Sign Convention for Current Flow

• Electrons carry negative charge

• Positive current flow is in opposite direction

Textbook Definitions Charge: bipolar (+/-), basic unit 1.6e-19 C

Effects from separation (volt) and flow (current)

Voltage: the energy needed to separate +/-charges by a certain distance Not unlike the energy needed to lift an object in a

gravity field V = dw/dq = delta energy / delta charge

W is in Joules, q is in coulombs Unit: 1 V = 1 Joule/ Coulomb

Current: rate of flow of electrical charges I = dq/dt = delta charge /delta time

q is in Coulombs, t in seconds Unit: 1 Amp is a flow of 1 Coulomb / sec

The Ideal Circuit Element

Could be battery, resistor, capacitor, etc. Defined by a mathematical model Polarity is arbitrary

We choose the “passive sign convention” Voltage “drop” from terminal 1 to 2 Positive charge flowing from term 1 to 2

1

2

+

v

-

i

Power and Energy

Often more useful quantities in understanding a circuit How many kilowatt-hours did you use last month? Many circuits have power limits

Beyond which, you “fry” the circuit!

Power is the time rate of expending or absorbing energy p = dw/dt Unit: 1 W = 1Joule / second

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Power Flow

+V

i

P = V iIf the physical current is positive Power flows into the element)

The current variable i is defined as positive into the (+) terminal of the element

The current variable i is defined as positive into the (+) terminal of the element

+_ +V

iP = V i

Here the physical current is negativePower flows out of the source

“Passive” sign convention

Voltage and Current Sources

Ideal Voltage Source Maintains voltage regardless of current

Ideal Current Source Maintains current regardless of voltage

+

-vs

is

Dependent (Controlled) Sources Controlled by a voltage or current elsewhere

in the circuit Voltage controlled voltage source Voltage controlled current source Current controlled voltage source Current controlled current source

vs =kvx

+

-

Example 1.1

Which

interconections

are valid/invalid?

Example 1.2 p 13 valid/invalid?? Which interconections are valid/invalid?

Summary

Circuits are foundational for many of the most exciting engineering topics

Voltage is like water pressure, current is like water flow

“Ideal Element” follows “Passive Sign Convention”

Ideal Sources can provide

constant voltage or current, or

can depend on some other part of circuit

1

2

+

v

-

i