1. today: dc circuits mostly current & resistance

4. not so funny now. just wait...

8. battery = pump voltage = pressure current = flow resistor = constriction capacitor = diaphragm / flexible reservoir diode = check valve inductor = paddle wheel

12. real V source = ideal V source + R

13. actual circuit has a parasitic r R in series with output (“steals” V)

14. real current sources R in parallel with output (“steals” I)

15. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center series resistors: conservation of energy - + R2R2 I I ∆V∆V R1R1 acb R eq ∆V∆V ac - +

16. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center voltage divider R2R2 R1R1 V in V out V out = R2R2 R 1 +R 2 V in signal in signal out R1R1 R2R2 volume

17. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center parallel resistors: conservation of charge current divider I - + R1R1 ∆V∆V R2R2 ab I1I1 I2I2 ∆V 1 =∆V 2= ∆V - + R eq ∆V∆V R eq R 1 R 2 111 = +

18. rank the currents

19. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center more complex arrangements

20. measuring voltage

21. real voltmeters

22. measuring current

23. a simple ammeter

24. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center dc Circuits, part II same thing, just more of it

25. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Thévenin equivalents any combination of R’s and V’s is equivalent to a SINGLE R and V (Norton equivalent: a single I source in parallel with R) V th = V (open circuit) R th = V (open circuit) I (closed circuit) disconnect from red dots = open circuit voltage short red dots, current there is closed-circuit current. This image: Horowitz & Hill, The art of electronics

26. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center series resistors: conservation of energy - + R2R2 I I ∆V∆V R1R1 acb R eq ∆V∆V ac - + source voltage = sum of voltages on resistors

27. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center parallel resistors: conservation of charge current divider I - + R1R1 ∆V∆V R2R2 ab I1I1 I2I2 ∆V 1 =∆V 2= ∆V - + R eq ∆V∆V R eq R 1 R 2 111 = + source current = sum of currents in resistors

28. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center so what? V R real sources = ideal sources + R real meter = ideal meter with R V I R what about ammeter?

29. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center V source loading V r source extra series resistance R load ∆V load = V - Ir for r ≪ R load, ∆V load ≈ V V source wants R high one solution: large resistor in parallel with load I

30. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center IpIp I source loading source extra parallel resistance R load I source wants R low sourcing currents at high R load is hard I r I load I load = I r r+R for R load ≪ r, I load ≈ I

31. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center measuring the meter R load I V r real meter R eq I V ideal meter ∆V load = IR eq = R 1+R/r I R load ≪ r, ∆V load ≈ IR

32. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center summary voltmeter wants R low! can use a buffer/follower... later I source wants R low transformer pre-amp consider sourcing V V source wants R high large series + parallel resistors present large R

33. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing current R wires R thing I V This is what a hand meter does. Why is it no good? V meter = I(R thing + 2R wires )

34. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing current, properly No problem. You just need four wires. R wires R thin g I V R thing ≪ R internal or add buffer

35. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing voltage R wires R thing VsVs Still have to measure voltage on device the wires still use up some of V What about current? V

36. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Sourcing voltage better R = ∆V / I Note we need 4 wires again current meter - not hard still problems? R wires R thing VsVs V Ι Ι = R precise V RsRs

37. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center source/meter resistances voltmeter wants R low but V source wants R high need buffer/amp on V meter resistor in parallel with source if V source is problem, R is too low consider sourcing I

38. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center what if I want to measure a *really* high R? R wires R thing VsVs V Ι = R s ≪ R thing RpRp Ι = V source voltage R p has same voltage as R thing R s has same current have done >10 10 Ohm

39. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center what if I want to measure a *really* low R? R wires R thin g I V this works just fine... so long as your V meter is good or you can tolerate large I v. good amp / part of a bridge

40. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center what if I want to measure a small change in R? V R1R1 R3R3 R2R2 R x +dR VsVs balance bridge to V=0 detect small changes from null make R 1 -R 3 about the same trimming resistor on R 2 = dR R 2 = ≈ R 3

41. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center Rules for analyzing more complicated circuits

42. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

43. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center

44. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center + + +

45. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center capacitors frequency-dependent resistor I and V are 90 o out of phase can’t dissipate power, ideally

46. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center combinations of capacitors

47. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center capacitors with stuff inside Q0Q0 + - C0C0 ∆V0∆V0 Q0Q0 + - Dielectric C0C0 ∆V∆V

48. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center rc circuits R C S V ∝ e -τ/RC V E

49. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center RC differentiator C V in (t)V out (t) R for small RC, }

50. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center RC integrator C V in (t)V out (t) R for large RC (V ≪ V in ) }

51. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center so what? filtering of signals unintentional capacitive coupling see from waveform shape more later

52. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center ac resistive circuits nothing earth-shattering happens except P is lower than you expect

53. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center ac capacitive circuits I and V 90 o out of phase average power is ZERO frequency response? insulating at dc conducting at high f voltage “lags” current

54. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center filters C R V in V out low-pass C V in V out R high-pass

55. THE UNIVERSITY OF ALABAMA CENTER FOR MATERIALS FOR INFORMATION TECHNOLOGY An NSF Science and Engineering Center familiar? low-pass filter C R V in V out C V in V out R high-pass filter differentiatorintegrator frequency domain ⇕ time domain

58. audio crossovers

61. dB/decade...

62. +-+- +V cc -V cc 100k photo- diode +V cc 741 741 pinout output Today: amplify photodiode signal