EE40 Lecture 14 Josh Hug 7 26 2010 EE40 Summer 2010 Hug 1 Logisticals 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 up EE40 Summer 2010 Hug 2 Lab 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 EE40 Summer 2010 Hug 3 Power 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 10 50 5 10 10 cos 50 cos 50 5 2 20 cos 50 EE40 Summer 2010 Hug 4 Or graphically 10 50 5 10 10 cos 50 cos 50 5 20 cos2 50 EE40 Summer 2010 Hug 5 Average Power 10 50 EE40 Summer 2010 5 Peak Power 20W Min Power 0W Avg Power 10W Hug 6 Capacitor example Find p t 10 50 1 EE40 Summer 2010 Hug 7 Graphically 10 50 1 Peak Power 5 2 Min Power 5 2 Avg Power 0W 5 sin 50 cos 50 EE40 Summer 2010 Hug 8 Is there some easier way of calculating power Like maybe with phasors 10 50 1 0 5 cos 50 2 Phasors are How about EE40 Summer 2010 Hug 9 Is there some easier way of measuring power Phasors are Does EE40 Summer 2010 A B C D Yes matches p t No wrong magnitude No wrong phase No wrong frequency Hug 10 It gets worse For the resistor there is no phasor which represents the power never goes negative EE40 Summer 2010 Hug 11 Average 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 1 T is time for 1 period 0 EE40 Summer 2010 Hug 12 Power 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 1 T is time for 1 period 0 We ll use this definition of average power to derive an expression for average power in terms of phasors EE40 Summer 2010 Hug 13 Average Power Note e g Average of each cosine is zero Average of their product is 10 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 EE40 Summer 2010 Hug 14 Power from Phasors EE40 Summer 2010 Hug 15 Power from Phasors Thus given a voltage phasor and a current phasor the average power absorbed is EE40 Summer 2010 Hug 16 Capacitor Example 10 50 1 0 5 cos 50 2 Phasors are EE40 Summer 2010 Hug 17 Resistor Example 1 2 10 50 5 Find avg power across resistor A 0 Watts B 10 Watts C 20 Watts EE40 Summer 2010 Hug 18 Resistor Example 1 10 50 5 Find avg power from source 1 2 1 100 2 5 20 1 1 17 4 7 0 58 2 EE40 Summer 2010 Hug 19 Reactive 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 EE40 Summer 2010 Hug 20 Capacitor Reactive Power Example 10 50 1 0 5 cos 50 2 Phasors are EE40 Summer 2010 Hug 21 Graphically 10 50 1 Peak Power 5 2 Min Power 5 2 Avg Power 0W Avg Reactive Power 5 2W Like a frictionless car with perfect regenerative brakes starting and stopping again and again and again EE40 Summer 2010 Hug 22 Note 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 EE40 Summer 2010 Hug 23 And that rounds out Unit 2 We ve covered all that needs to be covered on capacitors and inductors so it s time to continue moving on to the next big thing EE40 Summer 2010 Hug 24 Back to Unit 3 Integrated Circuits Last Friday we started talking about integrated circuits Analog integrated circuits Behave mostly like our discrete circuits in lab can reuse old analysis Digital integrated circuits We haven t discussed discrete digital circuits so in order to understand digital ICs we will first have to do a bunch of new definitions EE40 Summer 2010 Hug 25 Digital Representations of Logical Functions Digital signals offer an easy way to perform logical functions using Boolean algebra Example Hot tub controller with the following algorithm Turn on heating element if A Temperature is less than desired T Tset and B The motor is on and C The hot tub key is turned to on OR T Test heater button is pressed EE40 Summer 2010 Hug 26 Hot Tub Controller Example Example Hot tub controller with the following algorithm Turn on heating element if A Temperature is less than desired T Tset and B The motor is on and C The hot tub key is turned to on OR T Test heater button is pressed C 110V EE40 Summer 2010 B T A Heater Hug 27 Hot Tub Controller Example Example Hot tub controller with the following algorithm A Temperature is less than desired T Tset B The motor is on C The hot tub key is turned to on T Test heater button is pressed Or more briefly ON A and B and C or T C 110V EE40 Summer 2010 B T A Heater Hug 28 Boolean Algebra and Truth Tables We ll next formalize some useful mathematical expressions for dealing with logical functions These will be useful in understanding the function of digital circuits EE40 Summer 2010 Hug 29 Boolean Logic Functions Example ON A and B and C or T Boolean logic functions are like algebraic equations Domain of variables is 0 and 1 Operations are AND OR and NOT In contrast to our usual algebra on real numbers Domain of variables is the real numbers Operations are addition multiplication exponentiation etc EE40 Summer 2010 Hug 30 Examples In normal algebra we can have 3 5 8 A B C In Boolean algebra we ll have 1 and 0 0 A and B C EE40 Summer 2010 Hug 31 Have you seen …
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