EE40 Lecture 3 Josh Hug 6 25 2010 Users are reporting a drop in signal strength when the phone is held BBC If you ever experience this on your iPhone 4 avoid gripping it in the lower left corner in a way that covers both sides of the black strip in the metal band or simply use one of many available cases Apple EE40 Summer 2010 Hug 1 Logistical Notes Office Hours Room reservation has been put in but no word from the people yet I ve got someone looking into it HW1 due today at 5 PM in the box in 240 Cory No i Clicker today couldn t get hardware today EE40 Summer 2010 Hug 2 Nodal Analysis Example R1 R5 V 1 R2 R3 I1 R4 V2 Using the basic method 5 unknowns 2 KCL equations 3 KVL equations EE40 Summer 2010 Hug 3 Nodal Analysis Example R1 a c V 1 R2 R3 I1 R5 V2 R4 b One equation one unknown With Node Voltage 1 2 1 0 5 4 1 5 4 1 5 2 1 1 1 EE40 Summer 2010 Hug 4 Nodal Analysis Example R1 a c V R2 1 R3 I1 R5 V2 R4 b 5 4 1 5 2 1 1 1 5 2 1 1 1 5 4 1 4 1 1 5 5 1 1 2 EE40 Summer 2010 4 5 1 4 5 It s fine to leave your answer in terms of conductances on HW and exams Hug 5 Dependent Sources In practice we ll want to use controllable sources Called dependent sources since their output is dependent on something external to the source itself vs independent vs x dependent In theory a dependent source could be a function of anything in the universe Intensity of light incident on the source Number of fish within 3 miles EE40 Summer 2010 Hug 6 Dependent Sources Since we re building electrical circuits dependent sources have been developed which are functions of other electrical quantities 10 5V 40 100 3 40 3 40 3 4 100 0 12 100 100 EE40 Summer 2010 Hug 7 Dependent Sources Dependent sources allow us to decouple the controller from the controlled Acceleration of the engine affect by gas pedal Gas pedal not affected by engine acceleration This is in contrast to our circuits so far where everything is connected EE40 Summer 2010 Hug 8 Dependent Sources With Feedback Dependent sources can be coupled to their controller This is useful for when the controller needs feedback from the thing being controlled Can be a little tricky to analyze EE40 Summer 2010 Hug 9 Node Voltage With Dependent Source 100 4 1 0 100 20 100 1 100 There are two ways to proceed Direct substitution almost always better Indirect substitution tough part of the reading 100 100V EE40 Summer 2010 20 4 1 Hug 10 Direct Substitution Method for Dependent Sources 100 4 1 0 100 20 100 1 100 100 100 4 0 100 20 100 100 5 4 400 0 10 500 EE40 Summer 2010 50 Hug 11 Node Voltage With Dependent Source 100 4 1 0 100 20 100 1 100 There are two ways to proceed Direct substitution almost always better Indirect substitution tough part of the reading 100 100V 20 4 1 EE40 Summer 2010 Hug 12 Indirect Substitution Method for Dependent Sources 100 100 4 00 1 100 20 100 20 100 Node voltage vs dummy source 100V 4I 1 20 Node voltage vs controlling current Real source vs dummy source 1 4 EE40 Summer 2010 100 1 100 100 100 100 6 4 100 2 Hug 13 Summary So Far Dependent sources model controllable electrical sources Node voltage can be used with dependent sources Controlling input can be seemingly difficult to deal with e g Direct Substitution Replace controlling input with expression in terms of The node voltages you re trying to solve for Known currents if controlling input driven by current source Indirect Substitution Treat dependent source as a new variable and solve better in rare cases EE40 Summer 2010 Hug 14 Useful Resistive Circuits Wheatstone Bridge Used for measuring unknown resistances Strain Gauge Used for measuring weight EE40 Summer 2010 Hug 15 Wheatstone Bridge Named for Charles Wheatstone Used for measuring resistance of an unknown resistor R Parts Known resistors R1 and R2 Adjustable resistor R3 Unknown resistance Rx V R2 1 R3 Rx Basic concept If then no current will flow in the middle branch EE40 Summer 2010 Invented 1833 by Samuel Christie Hit the charts when remixed by Wheatstone in 1843 Hug 16 Finding the value of Rx Adjust R3 until there is no current in the detector Then Rx R2 R1 R3 Derivation KCL i1 i3 and i2 ix R1 V R2 KVL i3R3 ixRx and i1R1 i2R2 i1R3 i2Rx R3 Rx R3 R1 EE40 Summer 2010 Rx R2 Hug 17 Strain Gauge Intuition Resistance is a function of wire length and area Weight stretches a wire changing its shape Can theoretically get weight of a load by seeing how resistance varies when a load is added EE40 Summer 2010 Hug 18 Resistivity Wire resistance is resistivity measured in m Can think of as how tightly molecular lattice holds on to electrons Material Copper Copper 8 1 68x10 1 68x10 8 Aluminum Aluminum 8 2 82x10 2 82x10 8 Nichrome Nichrome 6 1 1x10 1 1x10 6 Glass 10 1010 EE40 Summer 2010 Hug 19 Wire Gauge Gauge Diameter mm Area mm2 10 2 58 5 26 14 1 62 2 08 16 1 29 1 31 Resistance of 30m 16 gauge extension cord 30 m 8 1 68 10 6 2 1 31 10 0 384 If carrying 10 amps how much power dissipated 2 38 4 EE40 Summer 2010 Hug 20 Basic Principle Pull on resistor L L0 L A A0 A V LA constant Length wins the battle to control resistance R R0 R Define strain 0 0 0 0 Where the Gauge Factor relates to 0 EE40 Summer 2010 how length area change GF 2 Hug 21 Using Strain to Measure Weight 0 We ll attempt to design a circuit which can measure Convert into a voltage 0 Our Circuit We ll leave it to the mechanical engineers to map back to load Vx Microcontroller EE40 Summer 2010 Hug 22 Using Strain to Measure Weight 0 Our Circuit Vx Microcontroller vx ADC vx to delRr0 vx delRr0 weight EE40 Summer 2010 eps2weight eps calc eps delRr0 eps Hug 23 One Possible Design Here Rx is a variable resistor where Rx is dependent on strain As strain varies so will vx EE40 Summer 2010 Hug 24 One Possible Design vx is what Controller sees 1 0 0 0 h Controller calculates from known quantities Vx Vs R0 Rref GF and then weight from EE40 Summer 2010 Hug 25 Better Circuits This will work but for As source voltage varies e g battery gets old calibration changes zero drift EE40 Summer 2010 Hug 26 Improvement 1 Half Bridge Works but requires balanced sources EE40 Summer 2010 Hug 27 Improvement 2 Full Bridge Want Use voltage divider 0 0 0 …
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