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by: Christelle Zulauf


Christelle Zulauf
GPA 3.63

Sean Washburn

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About this Document

Sean Washburn
Class Notes
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This 3 page Class Notes was uploaded by Christelle Zulauf on Sunday October 25, 2015. The Class Notes belongs to PHYS 351 at University of North Carolina - Chapel Hill taught by Sean Washburn in Fall. Since its upload, it has received 33 views. For similar materials see /class/228724/phys-351-university-of-north-carolina-chapel-hill in Physics 2 at University of North Carolina - Chapel Hill.




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Date Created: 10/25/15
Operational Amplifiers Boxes full of transistors resistors all in one package Voltage amplifiers Hu controlled by Feedback Hu for designed circuit function and signal manipulation Instrumentation amplifiers boxes full of op amps resistors Phys 351 Fall 2008 Lecture 11 1 ldeal Amplifier Special three port network that AMPLIFIES the voltage on the inputs Typically values of A gt 105 noninverting input inverting input Vout AV Vs V Feedback Control 7777777777777777777777 391 v i 0 H p Ava and l Vout ADV A0Vin vout i I luut AU i Vm 1 EVAU which for large A0 leaves the total circuit gain independent of A0 V07 i Vm Amplify Without fear if you control with negative feedback Phys 351 Fall 2008 Lecture 11 2 Detailed analysis of amplifier circuit R2 R1 Viquot iAV39 Vout V V V V KIL 11 12 Lko R R Z 1 But you already know Vow AV V A V So Q0 RZAARlRl Phys 351 Fall 2008 Lem 3 Golden rules are a roximations pp VDJr Gain is 10 so 10 V input drives Vnut V7 V I to the so VD VD or VD V out i No matter What VD S Vnut S VD VD So to keep Vnut off of the rails requires IV V7 lt0000010 Very high input impedance so Usually Znut is small enough to ignore in a circuit so outth current compliance is in nite this is obviously bogus if you push the limits Golden Rules for OpAmps These ruleslies are good approximations in most fedback schemes unless you Work hard to violate them Phys 3511a112008 Lecture 11 5 AndforAreally big H V077 i z amp Vt AR1 R1R2 AR R1 Phys 351 Fall 2008 Lem 4 Simple examples Voltage follower VD Since V5 V7 require Vout Vir Vin Vm RZ Invem39ng amp Rl V5 V7 0 so V7 Virtual Ground Vm V Vin 1R1 and Vent 0 1R2 so m V NanInvemng amp Vm Vin V IR1 VentCR1 R2R1gt so R1 R2 7 Lecture ll 6 Phys 3511a112008 Analog computations Summing voltage K L V su rfR7 R1 R3R then V V v2 V3 Subtracting vollogss Tup ML 017 VR 7 il 7 V VmuyRi R sn v 7 Viki vkakl Rf Rr Vi V 1 buttum KlL V2 7 VQR 7 i2 7 VRi V SUVFVzR RHRr 2 Rr Rr sincev V write as can VmIL VrVrWrRi Phys 35115 nus Lacuna ii 7 Analog calculus Why stop at algebra R since erR 7 1 7 dQdt 7 7Cdedt V V Van 7 71RcfdtVu ie an integrator Rm prevents uncontrolled charging by allowing slow lCRh discharge g Or use a reset switch R Here Cdedt 7 1 7 7 erk so Vm7 7Rcdvdt V ie a differentiator Also has instabilities that we ll correct in the lab rm u s Phys 351 mi nus R Analog computation R 2 R Rr R 7 R ophisticated analog computation is available in sim le elements Multiplicationdivision additionsu differentiation and integration units can be assembledto solvearly linear diff eq Each DE comprises a string of terms output voltages added in series around a KVL loop muiuur 39 39 39 39 39 pal licuml ululiun Fundamental elementm servo ontrol circuits Phys nus Lacuna ii 9 Example analog computation 1 Suppose want solution to y t 2y t 3yt 7 xt where xt is provided Formal solution is easy on paper but suppose this yt is needed to control a mac ine i e you need the solution output as a voltage to input on the machine 1 rearrange y t 7 xt 7 2y t 7 3yt 2 use combination summerintegrator which gives Vm 7 ifdwm t andRC1R2C13 R3c712 so RC picking c 7 lpE sets 1 Rs Y 039 5 RR2 R3 7 1M9 0 33MQ OSMQ R c and constructy t x0 71 1 sun u m Phys 351 mi nus Example analog computation H 3 integrate one more time RC 7 l to get yt which is desired output stage to build signal for y t Y t X0 23 3Y0 Phys 351 mi nus Nonlinear feedback elements Not so good analog computation Diode equation Km 7 1D eV Vv 1 R Insert onto the feedback loop forces Vm 7 7ng6 Vm IR IDR2VW W7 71 andthen Va7Vrlt1uRIr7luVm so Can be used in the usual way to multiply signals together but Dif culty Exponential dependences blow up very fast so be careful with how much voltage rangeyou allow in the calculati on Phys 35 minus LN 2


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