1Lecture 2, Slide 1EECS40, Fall 2003 Prof. KingAnnouncements• Lectures will be in 4 LeConte– beginning Friday 8/29• Additional discussion TA– Dennis Chang (Sections 101, 105)– Office hours: Mo 2-3 PM; Th 5-6 PM• Lab sections begin Tuesday 9/2– Read Experiment #1 online– Download Pre-Lab #1 and complete it beforegoing to the lab (140 Cory)• Discussion sections begin Tuesday 9/2Lecture 2, Slide 2EECS40, Fall 2003 Prof. KingLecture #2OUTLINE• Introduction to circuit analysis• Electrical quantities–Charge– Current– Voltage–Power• The ideal basic circuit element• Sign conventionsReadingChapter 12Lecture 2, Slide 3EECS40, Fall 2003 Prof. KingElectrical System Design Process1. Identify system performance requirementsÆ design specifications2. Conceive of approachÆ design concept3. Develop an electric circuit model(mathematical model that approximates the behaviorof an actual electrical system)… using ideal circuit components(mathematical models of actual electrical components)4. Build and test a physical prototypeLecture 2, Slide 4EECS40, Fall 2003 Prof. KingCircuit Analysis• Circuit analysis is used to predict the behavior of the electric circuit, and plays a key role in the design process.– Comparison between desired behavior (design specifications) and predicted behavior (from circuit analysis) leads to refinements in design• In order to analyze an electric circuit, we need to know the behavior of each ideal circuit element (in terms of its voltage and current) and the constraints imposed by interconnecting the various elements.3Lecture 2, Slide 5EECS40, Fall 2003 Prof. KingMacroscopically, most matter is electrically neutral most of the time.Exceptions: clouds in a thunderstorm, people on carpets in dry weather, plates of a charged capacitor, etc.Microscopically, matter is full of electric charges.• Electric charge exists in discrete quantities, integralmultiples of the electronic charge 1.6 x 10-19coulombs• Electrical effects are due to separation of charge Æ electric force (voltage) charges in motion Æ electric flow (current)Electric ChargeLecture 2, Slide 6EECS40, Fall 2003 Prof. KingQuartz, SiO2Solids in which all electrons are tightly bound to atoms are insulators.Solids in which the outermost atomic electrons are free to move around are metals.Metals typically have ~1 “free electron” per atom (~5 ×1022free electrons per cubic cm)Electrons in semiconductors are not tightly bound and can be easily “promoted” to a free state.Classification of MaterialsinsulatorsmetalssemiconductorsSi, GaAs Al, Cudielectric materialsexcellent conductors4Lecture 2, Slide 7EECS40, Fall 2003 Prof. KingElectric CurrentDefinition: rate of positive charge flowSymbol: iUnits: Coulombs per second ≡ Amperes (A)i = dq/dtwhere q = charge (in Coulombs), t = time (in seconds)Note: Current has polarity.Lecture 2, Slide 8EECS40, Fall 2003 Prof. King1. 105positively charged particles (each with charge 1.6×10-19 C) flow to the right (+x direction) every nanosecond2. 105electrons flow to the right (+x direction) every microsecondElectric Current Examples5Lecture 2, Slide 9EECS40, Fall 2003 Prof. King2 cm10 cm1 cmC2C1XExample 1:Suppose we force a current of 1 A to flow from C1 to C2:• Electron flow is in -x direction:Current Densitysec 1025.6/106.1sec/11819electronselectronCC×−=×−−Semiconductor with 1018“free electrons” per cm3Wire attached to endDefinition: rate of positive charge flow per unit areaSymbol: JUnits: A / cm2Lecture 2, Slide 10EECS40, Fall 2003 Prof. KingExample 2:Typical dimensions of integrated circuit components are in the range of 1 µm. What is the current density in a wire with 1 µm² area carrying 5 mA?The current density in the semiconductor isCurrent Density Example (cont’d)6Lecture 2, Slide 11EECS40, Fall 2003 Prof. KingElectric Potential (Voltage)• Definition: energy per unit charge• Symbol: v• Units: Volts (V)v = dw/dqwhere w = energy (in Joules), q = charge (in Coulombs)Note: Potential is always referenced to some point.Subscript convention:vabmeans the potential at aminus the potential at b.abvab≡ va-vbLecture 2, Slide 12EECS40, Fall 2003 Prof. KingElectric Power• Definition: transfer of energy per unit time• Symbol: p• Units: Joules per second ≡ Watts (W)p = dw/dt = (dw/dq)(dq/dt) = vi• Concept:As a positive charge q moves through a drop in voltage v, it loses energy energy change = qv rate is proportional to # charges/sec7Lecture 2, Slide 13EECS40, Fall 2003 Prof. KingThe Ideal Basic Circuit ElementAttributes:• Two terminals (points of connection)• Mathematically described in terms of current and/or voltage• Cannot be subdivided into other elements+v_i• Polarity reference for voltage can beindicated by plus and minus signs• Reference direction for the currentis indicated by an arrowLecture 2, Slide 14EECS40, Fall 2003 Prof. King- v +A problem like “Find the current” or “Find the voltage” is always accompanied by a definition of the direction: In this case, if the current turns out to be 1 mA flowing to the left, we would say i = -1 mA.In order to perform circuit analysis to determine the voltages and currents in an electric circuit, you need to specify reference directions. There is no need to guess the reference direction so that the answers come out positive, however.A Note about Reference Directionsi8Lecture 2, Slide 15EECS40, Fall 2003 Prof. KingSuppose you have an unlabelled battery and you measure its voltage with a digital voltmeter (DVM). It will tell you the magnitude and sign of the voltage.With this circuit, you are measuring vab. The DVM indicates −1.401, so vais lower than vbby 1.401 V. Which is the positive battery terminal?−1.401DVM+abNote that we have used the “ground” symbol ( ) for the reference node on the DVM. Often it is labeled “C” for “common.”Sign Convention ExampleLecture 2, Slide 16EECS40, Fall 2003 Prof. KingFind vab, vca, vcbNote that the labeling convention has nothing to do with whether or not v is positive or negative.−+−+2 V−1 V−+−+vbdvcdabdcAnother Example9Lecture 2, Slide 17EECS40, Fall 2003 Prof. KingSign Convention for Power• If p > 0, power is being delivered to the box. • If p < 0, power is being extracted from the box.+v_iPassive sign convention_v+ip = vi+v_i_v+ip = -viLecture 2, Slide 18EECS40, Fall 2003 Prof. KingSummary• Current = rate of charge flow• Voltage = energy per
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