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Berkeley ELENG 40 - Lecture Notes

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Slide 1LogisticalsLabPower in AC CircuitsOr graphicallyAverage PowerCapacitor exampleGraphicallyIs there some easier way of calculating power?Is there some easier way of measuring power?It gets worseAverage PowerPower in terms of phasorsAverage PowerPower from PhasorsPower from PhasorsCapacitor ExampleResistor ExampleResistor ExampleReactive PowerCapacitor Reactive Power ExampleGraphicallyNote on Reactive PowerAnd that rounds out Unit 2Back to Unit 3 – Integrated CircuitsDigital Representations of Logical FunctionsHot Tub Controller ExampleHot Tub Controller ExampleBoolean Algebra and Truth TablesBoolean Logic FunctionsExamplesHave you seen boolean algebra before?Formal DefinitionsFormal DefinitionsFormal DefinitionsBoolean Algebra and Truth TablesBoolean AlgebraSimplification ExampleLogic SimplificationQuick Arithmetic-as-Logic ExampleLogic GatesLogic Functions, Symbols, & NotationMulti Input GatesLogic GatesHot Tub Controller ExampleHot Tub Controller ExampleHow does this all relate to circuits?The “Static Discipline”Many Possible Ways to Realize Logic GatesSwitches as GatesRelays, Tubes, and Transistors as SwitchesElectromechanical RelayElectromechnical Relay SummaryVacuum TubeVacuum Tube DemoVacuum Tube SummaryField Effect TransistorField Effect TransistorField Effect TransistorField Effect Transistor SummaryMOSFET ModelMOSFET ModelS Model of the MOSFETBuilding a NAND gate using MOSFETsThat’s it for today1EE40 Summer 2010HugEE40Lecture 14 Josh Hug7/26/20102EE40 Summer 2010HugLogisticals•Midterm Wednesday–Study guide online–Study room on Monday•Cory 531, 2:00–Cooper, Tony, and I will be there 3:00-5:10–Study room on Tuesday•Cory 521, 2:30 and on•Completed homeworks that have not been picked up have been moved into the lab cabinet•If you have custom Project 2 parts, I’ve emailed you with details about how to pick them up3EE40 Summer 2010HugLab•Lab will be open on Tuesday if you want to work on Project 2 or the Booster Lab or something else–Not required to start Project 2 tomorrow•No lab on Wednesday (won’t be open)4EE40 Summer 2010HugPower in AC Circuits•One last thing to discuss for Unit 2 is power in AC circuits•Let’s start by considering the power dissipated in a resistor:+-1 0��� (50�)5 Ω�(�)=¿�(�)�(�)¿10 cos(50�)×105cos ⁡(50 �)¿20 cos2(50�)5EE40 Summer 2010HugOr graphically+-1 0��� (50�)5 Ω�(�)=¿�(�)�(�)¿10 cos(50�)×105cos ⁡(50 �)¿20 cos2(50�)6EE40 Summer 2010HugAverage Power+-1 0��� (50�)5 ΩPeakPower:MinPower:AvgPower:20W0W10W7EE40 Summer 2010HugCapacitor example• +-1 0��� (50�)1��Findp(t)8EE40 Summer 2010HugGraphically+-1 0��� (50�)1���(�)=− 5 sin(50 �)cos ⁡(50 �)PeakPower:MinPower:AvgPower:5/2 �0W−5 /2 �9EE40 Summer 2010HugIs there some easier way of calculating power?•Like maybe with… phasors?•Phasors are:•How about ?• +-1 0��� (50�)1���(�)=0.5 cos(50 �+�2)10EE40 Summer 2010HugIs there some easier way of measuring power?•Phasors are:•Does ?• A. Yes,matchesp(t)B. No,wrongmagnitudeC. No,wrongphaseD. No,wrongfrequency11EE40 Summer 2010HugIt gets worse•For the resistor, there is no phasor which represents the power (never goes negative)12EE40 Summer 2010HugAverage Power•Tracking the time function of power with some sort of phasor-like quantity is annoying–Frequency changes–Sometimes have an offset (e.g. with resistor)•Often, the thing we care about is the average power, useful for e.g.–Battery drain–Heat dissipation•Useful to define a measure of “average” other than the handwavy thing we did before•Average power given periodic power is:´�=∫0�1��(�)��Tistimefor1period13EE40 Summer 2010HugPower in terms of phasors•We’ve seen that we cannot use phasors to find an expression for p(t)•Average power given periodic power is:•We’ll use this definition of average power to derive an expression for average power in terms of phasors´�=∫0�1��(�)��Tistimefor1period14EE40 Summer 2010HugAverage Power•Note: –e.g. •Average of each cosine is •Average of their product is•Our goal will be to get the average power from phasors and •We’ll utilize –* denotes complex conjugate–See extra slides for proof of this identity• zero1015EE40 Summer 2010HugPower from Phasors •16EE40 Summer 2010HugPower from Phasors•Thus, given a voltage phasor and a current phasor , the average power absorbed is•17EE40 Summer 2010HugCapacitor Example•Phasors are: • +-1 0��� (50�)1���(�)=− 0.5 cos(50 �+�2)18EE40 Summer 2010HugResistor Example• +-1 0��� (50�)5 ΩFindavgpoweracrossresistor�(�)=12��[^�^�∗]A. 0WattsB. 10WattsC. 20Watts19EE40 Summer 2010HugResistor Example• +-1 0��� (50�)5 Ω1��Findavgpowerfromsource¿12��[1.17 −4.7 �]¿0.58 �¿12��[^�^�∗���∗]¿12��[1005+20 �]20EE40 Summer 2010HugReactive Power•So if power dissipated is , then what is ?•Imaginary part is called “reactive power”•Physical intuition is that it’s power that you put into an element with memory, but which the element eventually gives back •21EE40 Summer 2010HugCapacitor Reactive Power Example•Phasors are:• +-1 0��� (50�)1���(�)=− 0.5 cos(50 �+�2)22EE40 Summer 2010HugGraphically+-1 0��� (50�)1��PeakPower:MinPower:AvgPower:5/2 �0W−5 /2 �AvgReactivePower:-5/2WLike a frictionless car with perfect regenerative brakes, starting and stopping again and again and again23EE40 Summer 2010HugNote on Reactive Power•“Providing” reactive power and “consuming” reactive power are physically the same thing•Usually we say capacitors “provide” reactive power, which comes from our definition, whereas inductors “consume” reactive power?•As you’ll see on HW7, capacitors and inductors can be chosen to get rid of reactive power•24EE40 Summer 2010HugAnd that rounds out Unit 2•We’ve covered all that needs to be covered on capacitors and inductors, so


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Berkeley ELENG 40 - Lecture Notes

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