Switch the *?!!# thing off! Clickers at the ready …

1. Switch the *?!!# thing off! Clickers at the ready … e Alan Murray – University of Edinburgh

2. Introductory comments • Minor re-jig of content in 2011 • Exams from past mostly relevant! • Focus on practical • Major practical exercise • Practical dictates order of lecture content • “My” section is slightly disjointed • Course Organiser: Prof Markus Mueller Alan Murray – University of Edinburgh

3. Resources • These powerpoints(Learn) • Notes under slides • Tutorials • EE1 “toybox” Alan Murray – University of Edinburgh

4. Syllabus : Alan Murray • Potential divider. Resistors and capacitors • RC circuit introduction. • RC circuits charge-discharge • Inductors and RL circuits, charge-discharge • Nodal analysis introduction • Nodal analysis examples • Op-Amps, introduction • Op-Amp circuits • Op-Amp worked examples • Real Op-Amps (limitations) • Diodes – “cartoon” version • Filters (introduction only) Alan Murray – University of Edinburgh

5. Resistors and Capacitors -Introduction Alan Murray

6. Agenda • Potential dividers • Voltage and current sources • Resistors and capacitors Alan Murray – University of Edinburgh

7. Height =1.8m 0.4xHeight 2m The potential divider: AnalogyHow high is the book? Solution Alan Murray – University of Edinburgh

8. The potential divider: RealityHow high is the voltage? 1kΩ Solution 9V Voltage =? 2kΩ 1.5V 0V Alan Murray – University of Edinburgh

9. Vtop Rtop Vmid Rbottom Vbottom Potential dividers • Voltage at the mid-point depends upon a resistor RATIO • Do not forget the voltage at the bottom DC simulation AC simulation Alan Murray – University of Edinburgh

10. A I I I In parallel (V1=V2): In series (I1=I2): A R1 R1 R2 R2 V2 V1 B B Adding resistors Alan Murray – University of Edinburgh

11. V1 R1 R1 R2 R2 I V2 Adding resistors In series (I1=I2): In parallel (V1=V2): B A A B Alan Murray – University of Edinburgh

12. For example (Tutorial) Series Parallel Alan Murray – University of Edinburgh

13. R VR=9V 9V IR VR 9V Aside …Voltage sources • A perfect voltage source will make VR=9V ALWAYS • A real voltage source may not manage this • Battery? • Bench supply? • They are “imperfect” ∞ Alan Murray – University of Edinburgh

14. IR VR 9V Aside … Voltage sources • Real battery • Nonzero internal resistance • Some voltage “lost” across Rint • Lower load resistor? • More current • More loss over Rint Rint RL VR<9V 9V Alan Murray – University of Edinburgh

15. IR R 1A IR 1A VR Aside … Current sources • A perfect current source will make IR=1A ALWAYS • A real current source may not manage this • Bench supply? • MOSFET • Op-Amp circuit? • They are “imperfect” ∞ Alan Murray – University of Edinburgh

16. Capacitors Alan Murray – University of Edinburgh

17. Small volume(“charge”) Large volume(“charge”) SameWater level(“Voltage”) Analogy – capacitor Current source Current source Large Capacitor Small Capacitor Alan Murray – University of Edinburgh

18. Analogy – capacitor/resistor Water current Switch Resistor Voltage source Pressure Difference Water level Capacitor Alan Murray – University of Edinburgh

19. Analogy – capacitor/resistor Water current Time Water level Time Pressure Difference Time Alan Murray – University of Edinburgh

20. Analogy – capacitor/resistor Larger “capacitor” = more to fill Water current Animation Time Water level Time Pressure Difference Time Alan Murray – University of Edinburgh

21. Analogy – capacitor/resistor Larger “resistor” = less current = slower flow Water current Animation Time Water level Time Pressure Difference Time Alan Murray – University of Edinburgh

22. I V +Q V Charge -Q I Q Large capacitance Small resistance Small capacitance Large resistance V V Resistor and capacitor“comparison” Ohm’s Law Definition of capacitance Alan Murray – University of Edinburgh

23. + + + + + + + + + + + - - - - - - - - - - - Capacitor, Q=CV C=Area x dielectric constantseparation Opposite charges attract Plates larger – more charge, bigger capacitance Plates closer together – stronger force, more charge/area, bigger capacitance Dielectric constant – charges in the dielectric join in to increase the force Alan Murray – University of Edinburgh

24. VR VC Capacitor/Resistor Q=3C R +Q 3V C=1F Time -Q VC Q=3C Time VR C initially DISCHARGED Time Alan Murray – University of Edinburgh

25. I = const V V time Charging capacitors –current source • Q = CV • I = constant = rate of change of Q • I = dQ/dt = C dV/dt • dV/dt = I/C = constant • dV/dt is constant for constant current High current Low current Alan Murray – University of Edinburgh

26. R I C VC RC: how does the maths work? VS VS=VR+VC IC=IS=IR VR=RIR QC=CVC IC=dQC dt IC= CdVC dt Alan Murray – University of Edinburgh

27. Vfinish – Vstart= = “journey” 1 RC charge (and discharge) – demonstration of the formula. Start with (1-et/RC) Add Vstart “Stretch” … ie x(Vfinish - Vstart) Vfinish Vstart + (Vfinish - Vstart)x(1-et/RC) …  Vstart + (1-et/RC) – right shape and start Vstart (1-et/RC) – right shape Time Alan Murray – University of Edinburgh

28. VC Vfinish Vstart I Istart R I C VC time time Resistor charging capacitor VR Challenge? Find Vstart, Vfinish, Istart , Ifinish Some examples follow … Alan Murray – University of Edinburgh

29. This is worth remembering … Alan Murray – University of Edinburgh

30. Exercise … check this givesthe same answer finish start start time time Resistor charging capacitor R=1Ω VCstart=0V VC =3V Vfinish 3V VC C=2F VR=3V-VC Vstart =0V I Istart =3A Alan Murray – University of Edinburgh

31. Check – differentiate VC Same answer J Alan Murray – University of Edinburgh

32. RC larger – longer time constant Exercise for you … check this givesthe same answer Resistor discharging capacitor R=5Ω Vstart=6V VC Vstart 1V 6V VC C=4F Vfinish time VR time Istart Simulation Simulation (tol) Alan Murray – University of Edinburgh

33. VC (a) VC VC (b) VC (c) (d) Clicker Question i R=10Ω ii 2V VC C=1F I= -0.5A Capacitor initially discharged Switch from (i) to (ii) and then backto (i) again Solution Alan Murray – University of Edinburgh

34. Clicker Question R=10Ω VCstart VCfinish Istart Ifinish Work through it here! 2V 2V 0A 0A a 10V 2V VC C=1F I 10V 10V 0.2A 1A b 8V 8V 1.2A 1.2A c 12V 12V 0.8A 0.8A d Alan Murray – University of Edinburgh

35. Worked example Vcomp=8V 3 seconds R Vin C Capacitor is initially discharged. Choose R and C to make the comparator signal after 3 seconds 10V Alan Murray – University of Edinburgh

36. Worked example How logs work RC=1.86 (ideal) Choose R=1.2kΩ, C=1.5mF RC=1.8 VC(3)=8.1V, or 8V at 2.9sec (not 3) This may or may not be good enough … Depends upon the application. And then, of course, R = R±5%, C=C ±5% … Alan Murray – University of Edinburgh

37. A A C2 C1 C1 C2 B B Adding Capacitors In parallel: In series: Alan Murray – University of Edinburgh

38. Example from Tutorial again Series Parallel Alan Murray – University of Edinburgh

39. This is the capacitor’s “resistance” (actually “reactance”) High for low frequency Low for high frequency Forward look – capacitors and AC signals Simulation (DC) Simulation (DC) Compare with V=RI Simulation (AC) Simulation (AC) Alan Murray – University of Edinburgh

40. 3V supply Digital Chip Post Script – “decoupling” Digital signals = sharp edges Sharp edges = large currents for short periods Large current = loss of voltage over the internal impedance of Vsupply This causes Vsupply to “bounce” in sympathy with digital signals Solution? Place a “current storage” device (ie a reservoir of charge) close to the chip Capacitor to the rescue … Vsupply Alan Murray – University of Edinburgh

41. 3V supply Post Script – “decoupling” Add a capacitor to decouple the power supply to ground Large current required to create a sharp edge? Comes from Cdecouple, not from 3V supply 3V supply must simply keep Cdecouple “topped up”. Analogy – food! Q(lots of) Cdecouple Currentrequired Digital Chip Alan Murray – University of Edinburgh

42. Summary • Potential dividers – how to analyse • Try to remember the equation • Don’t forget the potential at the bottom! • Capacitors =- charge/discharge • Simple way to concoct the equation and graph Alan Murray – University of Edinburgh