EGR 2201 Circuit Analysis Professor Nick Reeder Reminders Please turn off cell phones. No food or soft drinks in the classroom. Stow water bottles at floor level. EGR 2201 Unit 1 Basic Concepts

Read Alexander & Sadiku, Chapter 1. Homework #1 and Lab #1 due next week. Quiz next week. What This Course Is About In this course youll learn mathematical techniques for studying electric circuits. Our focus is not on practical circuits that do interesting things.

Youll study those in later courses, using the techniques that you learn in this course. The Math That Well Use Calculator or Math Software Some of the math well do is timeconsuming with a basic calculator. Its faster with a powerful calculator that can solve systems of linear equations and manipulate complex numbers.

Examples: TI-30 or Casio fx-115 Examples: TI-86 or TI-89 You can use any calculator on exams, but no cell phones. Another option: Use MATLAB software, which we will learn how to use. Calculator or Math Software (Contd.)

Be aware of the calculator policy for the Fundamentals of Engineering exam and the Principles and Practice of Engineering exam, administered by the National Council of Examiners for Engineering and Surveying (NCEES). In a few years you may decide to take these exams for professional advancement. What is a Circuit? Our books definition (page 4): An electric circuit is an interconnection of electrical elements. Five electrical elements that well

focus on: Resistors Capacitors Inductors Voltage Sources Current Sources Example Circuit: A Power Supply from a Flat-Screen Television Resistor Inductor Capacitors

Schematic Diagrams To discuss circuits, we draw schematic diagrams that represent those circuits. Schematic diagrams do not show the parts of the circuit as they actually look. Instead, they contain standard symbols that represent electrical elements. Example Schematic Diagram: A Radio Transmitter (from books page 4) Resistor Symbol Inductor Symbol

Capacitor Symbol A Simpler Example Schematic Diagram: Flashlight Switch Light Bulb Battery (Voltage Source) When the switch is open (as drawn), no current flows, so the bulb is dark. When the switch is closed, current flows, and the bulb lights. Another Simple Example: A Voltage Source And Two Resistors

Polarity of a Battery Note that the symbol for a battery is asymmetric. The end with the longer line represents the batterys positive terminal, and the other end represents its negative terminal. Positive terminal + Negative terminal Direction of Current Flow For historical reasons, we say that in our simple circuit current flows out of the

batterys positive terminal and into its negative terminal. Modern science tells us that electrons actually move in the opposite direction, but well follow the standard convention shown above. Element Ratings The schematic diagrams so far have been incomplete. They show what kinds of elements are in the circuit and how those elements are connected to each other. But they do not show numerical ratings

that let us quantify the circuits behavior. Every voltage source has a numerical rating in volts (V). Every resistor has a numerical rating in ohms (). Examples of Voltage Sources What is the rating of these sources? Flashlight battery ____ V Wall outlet ____ V

But the battery is a DC voltage source, while the outlet is an AC voltage source. DC Versus AC In a direct-current (DC) circuit, current flows in one direction only. The textbooks Chapters 1 through 8 cover DC circuits. In an alternating-current (AC) circuit, current periodically reverses direction.

The books Chapters 9 through 11 cover AC circuits. Schematic Symbols for Independent Voltage Sources Several different symbols are commonly used for voltage sources: Type of Voltage Source Generic voltage source (may be DC or AC) DC voltage source AC voltage source

Symbol Used in Our Symbol Used in Textbook Multisim Software V or v? Some authors use uppercase letters for constant quantities, such as V for the voltage of a constant DC voltage source. And they use lowercase letters for time-varying quantities, such as v for the voltage of an AC voltage source. Our textbook mentions this convention on pages 7 and 10, but

usually uses lowercase letters for both constant and time-varying quantities. DC Voltage Sources on Our Trainer Fixed +5 V voltage source No matter which red socket you use, you must also use the GROUND socket. Fixed -5 V voltage source Variable positive voltage source, controlled by the lefthand knob. Well usually use this one. Variable negative voltage source, controlled by the right-hand knob. Using a Digital Multimeter to Measure Voltage

Well use a digital multimeter, like the Fluke 45 shown, to measure voltage. Note that the meter has a red lead and a black lead. See next slide . Meters Red and Black Leads When you measure a voltage, the order of the red and black leads determines whether the value is displayed as positive or negative. Meter will display 5.00 V Meter will display 5.00 V

Resistance Resistance is opposition to the flow of electrons. Resistances unit of measure is the ohm (). A perfect conductor would have zero resistance and a perfect insulator would have infinite resistance. A resistor is a device manufactured to have a specific amount of resistance. Resistor Ratings

The resistors in our labs range in value from 10 to 10,000,000 . Instead of having the value printed in numbers on the case, our resistors are marked with a four-band color code to indicate the value. Resistor Color Code The first three color bands specify the resistances nominal value. Digit Color

0 Black 1 Brown 2 Red 3 Orange 4 Yellow

5 Green 6 Blue 7 Violet 8 Gray 9 White

Resistor Color Code (Contd.) The fourth band (tolerance band) gives the percent variation from the nominal value that the actual resistance may have. Tolerance Color 5% Gold 10%

Silver 20% None Many websites have color-code charts and calculators, such as this one. Tolerance Calculations To find a resistors tolerance in ohms, multiply its nominal value by the percentage tolerance. Example: For a 220 resistor with 5% tolerance, the tolerance in ohms is 220 0.05 = 11 .

Then Tolerance Calculations (Contd.) To find the minimum value that a resistor can have, subtract its tolerance in ohms from its nominal value. In example above, the nominal value was

220 and the tolerance was 11 . So the minimum value is 220 11 = 209 . To find the maximum value that a resistor can have, add its tolerance in ohms to its nominal value. In example above, the maximum value is 220 + 11 = 231 . Using a Digital Multimeter to Measure Resistance Digital multimeters can measure resistance as well as voltage. When measuring a resistors resistance, the resistor must be out of circuit: definitely no power applied

and disconnected from other elements. Selecting the Measurement Type on the Digital Multimeter DC Voltage AC Voltage DC Current AC Current Resistance Plugging the Meters Leads into the Jacks Red lead here

to measure voltage or resistance. Black lead always in this jack. Red lead here to measure current. Same Circuit Layout, but Different Element Ratings These two circuits will perform differently. In particular, the different element ratings will result in: Different

current values Different voltage values Current Current is the flow of electric charge through a circuit. We use the symbol I or i to represent current. Currents unit of measure is the ampere, or amp (A). For example, To

say that a current is 2.5 amperes, we write i = 2.5 A Voltage Voltage is a measure of how forcefully charge is being pushed through a circuit. We use the symbol V or v to represent voltage. Voltages unit of measure is the volt

(V). For example, To say that a voltage is 5 volts, we write v=5V Summary of Some Electrical Quantities, Units, and Symbols Quantity Symbol SI Unit Symbol for the Unit Current

I or i ampere A Voltage V or v volt Resistance R ohm V

Plumbing Analogy It may help to think of a circuit as being like a plumbing system, with water flowing through pipes. On this analogy, voltage is like the water pressure in a pipe. Its value will be different at different points in the circuit. Current is like the volumetric flow rate through a pipe. See Wikipedia article on Hydraulic analogy.

Plumbing Analogy in Our Simple Circuit A wire is like a water pipe. The amount of electricity per second flowing through a wire is the current, which is measured in amperes. The voltage (pressure) at this point is greater than the voltage at this point. A voltage source is like a water pump. Its voltage rating (in volts) tells you how strong it is. Resistors are like partial blockages in the pipe. They restrict the amount of current that flows through the circuit.

The Goal of Circuit Analysis This courses main goal: to learn how, given the schematic diagram of a circuit, to compute the voltages and currents in the circuit. For some circuits, such as this one, the math is simple (basic algebra). More complicated circuits require more powerful math (trig, complex numbers, calculus, differential equations).

Large and Small Numbers We must often deal with very large or very small numbers. Example: a resistor might have a resistance of 680,000 and a current of 0.000145 A. Its not convenient to use so many zeroes when writing or discussing numbers. Instead we use SI prefixes (or engineering prefixes), which are abbreviations for certain powers of 10. Table 1.2

1,000,000,000,000 1,000,000,000 1,000,000 1,000 We rarely use these. 1 / 1,000 1 / 1,000,000 1 / 1,000,000,000 1 / 1,000,000,000,000 Engineering Prefix Game You must memorize these prefixes. To

practice, play my Metric Prefix matching game at http ://nreeder.com/flashgames.htm. You must also be able to convert between numbers written with engineering prefixes and numbers written in everyday (floating-point) notation. To practice, play my Engineering- Notation game. Using Engineering Prefixes

Whenever you have a number thats greater than 1000 or less than 1, you should use these prefixes. Examples: Instead of writing 680,000 , write 680 k (pronounced 680 kilohms). Instead of writing 0.000145 A, write 145 A (pronounced 145 microamps). Calculators Exponent Key

Scientific calculators have an exponent key (usually labeled EE, EXP, or E) that lets you easily enter numbers with engineering prefixes. Examples: To enter 680 k, press 680 EE 3. To enter 145 , press 145 EE 6. Calculators Engineering Mode Most scientific calculators also have an engineering mode, which forces the answer always to be displayed with one of the engineering powers of 10.

Learn how to use this feature of your calculator. It will save you from making mistakes. Measuring Voltage A voltmeter is an instrument designed to measure voltage (also called potential difference). Voltage measurements are always made across elements.

To measure a voltage in a circuit, you dont need to disconnect any Measuring the voltage across R1. elements. Positive or Negative Voltage? When you measure a voltage, the displayed value may be positive or negative. In the drawing, the meters + lead is connected to point a and its a lead to point b.

To indicate this, we would say that were b measuring vab. If we swapped the leads, wed be measuring vba. These two voltages, vab and vba, have the same magnitude but different signs. Example: If vab = 1.60 V, then vba must be 1.60 V. Voltage Drops and Rises

If vab = 1.60 V, we say that theres a voltage drop of 1.60 V from point a to point b. Equivalently, we say that theres a voltage rise of 1.60 V from point b to point a. a b Though it may seem confusing, we could also say that theres a voltage rise of 1.60 V from point a to

point b, or that theres a voltage drop of 1.60 V from point b to point a. Measuring Current An ammeter is an instrument designed to measure current. To measure the current at a point, you must break the circuit at that point and insert the ammeter in such a way that the current flows through the ammeter. Measuring current. Positive or Negative Current?

When you measure a current, the displayed value may be positive or negative. Note that in the drawing, the meters + lead is connected to the battery and its lead to R1. The displayed value is the current flowing into the + lead and out of the lead. Positive or Negative Current? (Contd.)

As with voltage measurements, swapping the leads would give the same magnitude but opposite sign. Example: If the meter displays 34.0 mA when connected as shown, then it would display 34.0 mA if you swapped the leads. We could express this by saying either that a current of 34.0 mA flows from V1 to R1 (clockwise), or that a current of 34.0 mA flows from R1 to V1 (counter-clockwise).

Measuring Resistance An ohmmeter is an instrument designed to measure resistance. To measure an elements resistance, you must remove the element from the circuit. Measuring R1s resistance. When measuring resistance, the meter will never display a negative value.

Multimeter A multimeter can measure voltage, current, or resistance, depending on the setting of a selector switch. A multimeter must not be set to measure current when it is connected as a voltmeter, or set to measure voltage when it is connected as an ammeter. Multimeter Challenge Game You must learn how to use a

multimeter. To learn the basics, play my Multimeter Challenge game at http ://nreeder.com/flashgames.htm. Some Quantities and Their Units Three that we have discussed: Quantity Symbol SI Unit Symbol for the Unit

Current I or i ampere A Voltage V or v volt Resistance R ohm

V Four new ones: Quantity Symbol SI Unit Symbol for the Unit Charge Q or q coulomb C

Time t second s Energy W or w joule J Power P or p

watt W Charge All electrical phenomena are based on the movement or separation of electric charge. We dont often measure charge directly, but sometimes we need to calculate it. The symbol for charge is Q or q.

Charges unit of measure is the coulomb (C). For example, To indicate a charge of 450 microcoulombs, we write q = 450 C Basic Facts About Charge There are two kinds of charge, which we call positive and negative. Opposite charges attract. Like charges repel. The smallest known charge is the charge on a proton or an electron,

1.602 10-19 C. Most practical charges that we deal with are much larger than thisfor example, nanocoulombs (nC) or microcoulombs (C). Formal Definition of Current Weve seen that current can informally be thought of as being like the flow rate of water through a plumbing system. More formally, current is defined as the rate of change of charge per time: dq

i dt One ampere is equal to one coulomb per second (1 A = 1 C/s). Differentiation and Integration Recall that differentiation and integration are inverse operations. Therefore, any relationship between two quantities that can be expressed in terms of derivatives can also be expressed in terms of integrals.

Charge and Current We saw above that current is the derivative with respect to time of charge: Therefore charge is the integral with respect to time of current: In typical problems, we know the initial charge at time t0 and wish to find the charge q (t ) at later time t. In such cases we use the definite integral:

dq i dt q i dt t i dt q (t0 ) t0 Calculus or Algebra? As weve seen, the equations relating charge and current contain derivatives and integrals: dq i dt

q i dt Some problems involving current and charge therefore require calculus. (For example, Problems 1.2 and 1.3 in the textbook.) But for many problemsin particular, problems in which current is constantthese equations simplify to algebraic equations: q i t q i t Energy

Energy is perhaps the most fundamental physical concept, underlying all areas of physics. We dont often measure energy directly, but sometimes we need to calculate it. The symbol for energy is W or w. Energys unit of measure is the joule (J). For example, To indicate an energy of 780 nanojoules, we write w = 780 nJ Formal Definition of Voltage

Weve seen that voltage can informally be thought of as being like water pressure in a plumbing system. More formally, the voltage between two points is defined as the amount of energy needed to move a unit charge from one point to the other: dw v dq One volt is equal to one joule per coulomb (1 V = 1 J/C).

Power Supplies energy Absorb energy At any time, some elements in a circuit supply energy, and some elements absorb energy. An elements power is the rate at which that element supplies or absorbs energy. The symbol for power is P or p: dw p dt

Powers unit of measure is the watt (W). One watt is equal to one joule per second (1 W = 1 J/s). Energy and Power We saw above that power is the derivative with respect to time of energy: Therefore energy is the integral with respect to time of power:

In typical problems, we know the initial energy at time t0 and wish to find the energy w(t ) at later time t. In such cases we use the definite integral: dw p dt w p dt t p dt w(t0 ) t0 Calculus or Algebra? As weve seen, the equations relating energy and

power contain derivatives and integrals: dw p dt w p dt Some problems involving power and energy therefore require calculus. But for many problemsin particular, problems in which power is constantthese equations simplify to algebraic equations: w p t

w p t Positive or Negative Power? By convention, we assign a positive sign to a power value if the element is absorbing energy, and we assign a negative sign if the element is supplying energy. For example, To say that an element is absorbing 50 milliwatts, we would write p = 50 mW To say that an element is supplying 250 milliwatts, we would write

p = 250 mW Kilowatt-hours Weve seen that in the SI system of units, energy is measured in joules (J) and power is measured in watts (W), with 1J=1W1s But the electrical power industry uses different units: the kilowatt (kW) for power and the kilowatt-hour (kWh) for energy. 1 kWh = 1 kW 1 hour The Power Law

We now have the following definitions: dw p dt dw v dq dq i dt The chain rule of calculus tells us that : dw dw dq

dt dq dt Therefore we can write: p vi In words, an elements power is equal to its voltage times its current. The Passive Sign Convention To get the correct sign (+ or ) on the power value when we use the power law (p=vi), we must be careful with the signs of v and i. Well always follow the passive sign convention,

which says that for i we use the current flowing into (not out of) the elements positive terminal. Conservation Supplies energy of Energy Any circuit must obey the law of conservation of energy. Therefore the algebraic sum of the powers in a circuit must equal 0. Absorb energy Recall that an energy suppliers power is

negative, while an energy absorbers power is positive. Example: In the circuit shown, if we know that the voltage sources power is 100 mW, and R1s power is 75 mW, then what must R2s power be? Review: Some Quantities and Their Units Quantity Symbol SI Unit Symbol for the Unit Current

I or i ampere A Voltage V or v volt Resistance R ohm V

Charge Q or q coulomb C Time t second s Energy

W or w joule J Power P or p watt W Active Elements Circuit elements can be classified as

active or passive, depending on whether they are capable of generating electric energy. Active elements can generate electric energy. Examples: Voltage sources Current sources Passive Elements Passive elements cannot generate electric energy. Examples: Resistors

Capacitors Inductors An important difference among these is that capacitors and inductors can store energy for later use. But resistors cannot store energy: they always dissipate energy as heat. Ideal Sources The most important active elements are voltage sources and current sources.

In each case the word ideal means that these are simplified models that ignore some of the effects present in real sources. Ideal Independent Voltage Source An ideal independent voltage source maintains a specified terminal voltage no matter what the rest of the circuit looks like. Weve discussed these previously. The books Figure 1.11 shows two symbols for ideal independent

voltage sources. Ideal Independent Current Source An ideal independent current source supplies a specified current no matter what the rest of the circuit looks like. The arrow identifies it as a current source and shows the direction of positive current flow.

Ideal Dependent Voltage Source An ideal dependent voltage source maintains a terminal voltage whose value depends on a voltage or current somewhere else in the circuit. The diamond-shaped body tells us that its a dependent source. The +/- inside tells us that its a voltage source, and shows the voltage polarity.

Ideal Dependent Current Source An ideal dependent current source supplies a current whose value depends on a voltage or current somewhere else in the circuit. The diamond-shaped body tells us that its a dependent source. The arrow inside tells us that its a current source and shows the direction of current flow.

Summary of Symbols for Ideal Sources Ideal independent voltage source Ideal independent current source Ideal dependent voltage source Ideal dependent

current source Four Kinds of Ideal Dependent Sources Dependent sources are also called controlled sources. An ideal dependent sources value depends on a voltage or current somewhere else in the circuit, giving rise to four kinds: A voltage-controlled voltage source. A current-controlled voltage source. A voltage-controlled current source. A current-controlled current source.

Text next to the symbol will tell exactly which kind it is. Examples of Symbols for Controlled (Dependent) Sources 5v Voltagecontrolled voltage source 5i Currentcontrolled voltage source

5v Voltagecontrolled current source 5i Currentcontrolled current source Example of a Controlled Source in a Schematic Diagram If i in this circuit is equal to 2.5 A, then the dependent voltage sources value is 25 V.

Circuit Analysis with Simulation Software Starting in Chapter 3, our textbook discusses computer software named PSpice, which lets you simulate circuits. Sinclairs computers dont have PSpice installed, but we have a similar program named Multisim. Both are based on open-source code named SPICE (Simulation Program with Integrated Circuit Emphasis), which was first written at the University of California, Berkeley in the 1970s. Starting Multisim on Our Computers

Start Menu All Programs National Instruments Circuit Design Suite 14.1 Multisim 14.1 Where to Find Some Components in Multisim DC Independent Voltage Source Group=Sources > Family=POWER_SOURCES > DC_POWER

Ground Group=Sources > Family=POWER_SOURCES > GROUND DC Independent Current Source Group=Sources > Family=SIGNAL_CURRENT_SOURCES > DC_CURRENT Resistor Group=Basic > Family=RESISTOR Where to Find Some Measuring Instruments in Multisim Voltmeter Group=Indicators > Family=VOLTMETER > VOLTMETER_H

Shown is a horizontal voltmeter. Also available is a vertical version, as well as versions with the leads reversed. Ammeter Group=Indicators > Family=AMMETER > AMMETER_H Shown is a horizontal ammeter. Also available is a vertical version, as well as versions with the leads reversed. Making Sure Your Printouts Fit on One Page When you print a Multisim circuit, Multisim has a nasty habit of spreading the circuit across several pages. This wastes paper and makes your diagram hard to read.

To prevent this, before you print, do File > Print Options > Print sheet setup and then click Fit to page. Multisim Resources Tutorial: Inside the program, click Help > Getting Started. National Instruments Multisim website:

Main site: http://www.ni.com/multisim/ Student version: http://www.ni.com/multisim/student-edition/ Free 30-day trial: http://www.ni.com/multisim/try/