Introduction to Circuit Analysis Overview In this lesson we will

9 Introduce a very high level view of 9 Introduce voltage and current 9 Several major and common electronic components 9 Examine some of the basic rules of 9 Explore some simple circuits

Getting Started We analyze circuits for several reasons • Understand how they work • Learn how to design from other people’s work • Debug our own designs • Troubleshoot circuit or system that may have failed

Observe these are same reasons we analyze a system in any field Chemistry Mechanical engineering Civil engineering Computing science Physics Any other field of science We learning to solve problems

We’ll start with some of the • Basic terms • Components Then see what we can do with them

The Terms Three of the fundamental items in electronics • Circuit • Current • Voltage

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Electronics is based upon Controlled movement of electric charge From one place to another 9 Path that the charge follows as it moves is called the circuit This path is made up of • Electronic components • Wires connect components together

9 Amount of charge that moves through circuit in specified time Called current From physics we know If we raise stone above earth’s surface against gravity Work stored as potential energy If we have two charges Decrease separation between them Work stored in system as electric potential energy 9 We define electric potential energy - voltage Work required to move a charge From infinity to reference point

Simple analogy for electric circuit Called water analogy Consider closed circuit of pipes as in city water system as in following figure

Water flows From Source of higher pressure Through Pipes To Place of lower pressure

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Current flows From Source of higher potential Through Wires To Place of lower potential Called

Tank in drawing Represents source of higher pressure

Battery in electric circuit Represents equivalent source In circuit called potential or voltage

Pipes in drawing Provide path for water to flow Wires in electric circuit Provide path for current to flow

Water in drawing Represents flow of material through pipes Current in electric circuit Represents flow of charge through wires

The Components Have seen that electric circuit • Closed path • With things connected by

Basic things in electric circuit Fall into two categories 9 Sources 9 Components

Basic Sources Sources provide energy to circuit Enable components to do work Without sources

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Electric circuit would be of little use Without source of water Pipes would serve no purpose

Sources come in two major flavours • Voltage sources Provide voltage – like a battery • Current sources Provide current – like water flowing from a melting glacier

Voltage Source Value of electric potential Called volts or voltage

Voltage labeled by letter V Sometimes lower case v

Electronic symbol for voltage source Represented by Circle Shown in left hand figure Battery Shown in right hand figure Plus sign (+) shows Positive terminal Terminal of higher potential Minus sign (-) shows Negative terminal Terminal of lower potential

Current Source Value of current Called amperes or amps Represents amount of charge moved per time Charge labeled by letter Q Sometimes by lower case q

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Relationship between current charge and time Given as ΔQ i = Δt

Current labeled by letter I Sometimes lower case i

Electronic symbol for current source Represented by Circle containing arrow in adjacent figure Circle is the source Arrow (↑) shows

Direction of current flow Ground Ground refers to reference point in electrical circuit Other voltages within circuit Measured with respect to ground

Ground also known as earth Signal Chassis Earth Ground Ground Ground Several different electronic symbols for ground Illustrated in accompanying figure

Components A First Look To start will consider three basic components 9 9 9 Certainly are many many others Returning to water analogy momentarily

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Resistor Resistor labeled by letter R Value of resistor Called resistance Measured in ohms

Behaviour somewhat like going from ¾” pipe to ½” pipe and back Smaller pipe restricts flow of water Resistor restricts flow of current

Electronic symbol for resistor given in adjacent figure

Relationship between voltage current and resistance Given by following two equations V = RIV i = R Equation on left Fundamental electrical engineering relationship Known as Ohm’s Law

Capacitor Capacitor labeled by letter C Value of capacitor Called capacitance Measured in farads

Somewhat like a cistern Small container for holding water Capacitor stores electric charge

Electronic symbol for capacitor given in adjacent figure

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Relationship between voltage current and capacitance Given by following two equations Given in two forms First set in differential form 1 ΔV V Δ= Q = Ci C ∑ Δt Second integral and derivative form 1 dV V = idt = Ci C ∫ dt

Inductor Inductor labeled by letter L Value of inductor Called inductance Measured in henrys

Somewhat like a cistern on a rooftop Stores energy Inductor stores electric energy

Electronic symbol for capacitor given in adjacent figure

Relationship between voltage current and inductance Given by following two equations Given in two forms First set in differential form Δi i V = L i Δ= V Δt L ∑ Second integral and derivative form di i V = L i = dV dt L ∫

The Next Look Let’s now look at several additional useful components 9 9 LED

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Switches Let’s start with switches is mechanical device Are several types of switches

Switches often classified by Number of poles and the number of throws they have A pole is a lever arm Provides a contact between two electrical terminals A throw is a contact in which the switch can be positioned

Example SPST o DIP – Dual Inline Package – switch Is a single-pole single-throw (SPST) switch Its single arm Makes contact in one position Does not make contact in the other When contact made – closed Current can flow through switch

SPDT ƒ A lock switch The CAP LOCK key in old keyboards Actually locks in o Two-position lever-arm switch

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Considered a single-pole double-throw (SPDT) switches The single arm is making contact in either position

DPST – DPDT Several other configurations Illustrated in next diagram

Can use switch to generate input Connect the switch as shown in following figure Observe that we have a pull-up resistor shown Such a resistor is used to ensure Never have an open input Nothing connected to circuit input when switch open

Vcc

10K

circuit input

Switch Closed - Logic 0 Switch Open - Logic 1

Figure 10 DIP Switch with Pull-Up Resistor

LED Now look device we can use to show circuit output LED is an acronym for a Light-Emitting . - 9 of 15 -

Is a semiconductor device that emits light (much like a light bulb) when Voltage applied at the anode (+) is larger than Voltage applied at the (-) Under such conditions, a current will flow from the anode to the cathode

Vcc Can regulate amount of current flowing through device 330 ohms By connecting a current-limiting resistor in series Value used is usually 330 ohm + LED and resistor shown in figure - Driving an LED

Getting to Work Let’s now see how we can put sources and components together

We need some basic rules first In accompanying drawing we have 1. Two pieces of wire connected together Small black dot symbolizes connection Called node

2. Two currents i1 and i2

i1 going into node and i2 going out

3. First rule i1 and i2 must be equal Current cannot disappear going into the node or be created by node

Second rule extends the first and so on 1. Three pieces of wire connected together

2. Two currents i1 and i2

i1 going into node and i2 and i3 going out

3. Second rule i1 must equal i2 + i3 Current still cannot disappear going into the node or be created by node

Third rule 1. Voltage measured from high to low potential 2. High considered positive and low considered negative 3. Interpreted as drop in voltage thus (-)

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Fourth rule coming up shortly

Let’s now take a look at components

Components and Circuits As we noted earlier Circuit made up of wires and components

Let’s start with simple circuit We have resister and two wires

We show current i1 Coming in to circuit at terminal A

Going through resistor R1 Leaving the circuit on terminal B

Let’s believe in a little bit of magic for now

Let’s not worry about where i1 comes from nor where it goes

From Ohm’s law we have

•= IRV 111 That is

Voltage drop V1 across resistor Given by value of resistor multiplied by current through it While not shown Assume bottom side of resistor is (-)

Now let’s add some more parts In the circuit we have

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1. Wire connected between A and left hand side of R1

2. Right hand side of R1 connected to wire which is connected in turn to top of R2.

3. Bottom of R2 connected to wire which is connected in turn to B. 4. The two are connected in series with each other. Following the path from A through two resistors we have

•= IRV 111 Then

•= IRV 111 Total from A to B

+VV 21 Finally •+•=+ IRIRVV 121121 ()•+= IRR 121 From this circuit we can see several things 1. We see that two resistors connected in series add Can generalize to n resistors Thus For n resistors connected in series −1n = RR eq ∑ i =0i 2. Voltage drops across two resistors added

Fourth rule 1. Voltage drops in series add

Let’s now take our first circuit and extend it a bit From our earlier work we know Cannot consume or create current going into or out of node Therefore we know that

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+= IIi 321 V V 1 += 1 R1 R2 ()•+ VRR = 121 RR 21

RR 21 V1 = • i1 ()+ RR 21

The two resistors are connected in parallel We see from the equation above Their equivalent resistance given by

RR 21 Req = ()+ RR 21

As we did for resistors in series Can extend relationship to many resistors Numerator Will be product of all the resistors Denominator Will be sum of all the resistors

Sources Let’s revisit sources briefly – we’ll begin with voltage sources Voltage Series Let’s start with two voltage sources connected in series What happens if we connect two different voltage sources in parallel

For the following circuit

+ +

+ V1 + V - V Veq + V2 - - - -

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For our case There is no voltage drop across the wires So starting from the (-) terminal on the left hand side 1. We have a voltage rise (- to +) of V volts 2. Turning the corner we have a voltage drop of V1 3. Followed by a second voltage drop of V2 to take us back to where we started We now have

V - V1 - V2 = 0

Thus we see

V = V1 - V2

The values of the two voltage sources added together Let’s try a different configuration Now we have

For this circuit we have

V + V1 + V2 = 0

Thus we see

V = - ( V1 + V2 )

For this circuit we have

V - V1 + V2 = 0

Thus we see V = ( V1 - V2 )

For this circuit we have

V + V1 - V2 = 0

Thus we see V = V - V 2 1

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Current Parallel Let’s start with two current sources connected in parallel What happens if we connect two different current sources in series

For the following circuit

We know that current cant vanish or be created at a node So

I = I1 + I2 We see then that Current sources in parallel add as voltage sources did in series

Summary and Review of Objectives At this time you should have a general understanding of Voltage and current Voltage and current sources How they behave when connected in series or parallel The basic electronic components Resistors, , Switches, LEDs Simple circuits with Voltage sources Current sources Resistors connected in series or parallel Ohm’s law

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