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# EE70 Review

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1. EE70 Review

2. Electrical Current

3. Circuit Elements An electrical circuit consists of circuit elements such as voltage sources, resistances, inductances and capacitances that are connected in closed paths by conductors

4. Reference Directions The voltage vab has a reference polarity that is positive at point a and negative at point b.

5. Reference Directions

6. Reference Directions “uphill: battery” “downhill: resistor” Energy is transferred when charge flows through an element having a voltage across it.

7. Power and Energy Watts Joules

8. Reference Direction Current is flowing in the passive configuration • If current flows in the passive configuration the power is given by p = vi • If the current flows opposite to the passive configuration, the power is given by p = -vi

9. Dependent Sources

10. Resistors and Ohm’s Law a b The units of resistance are Volts/Amp which are called “ohms”. The symbol for ohms is omega: 

11. Resistance Related to Physical Parameters  is the resistivity of the material used to fabricate the resistor. The units of resitivity are ohm-meters (-m)

12. Power dissipation in a resistor

13. The net current entering a node is zero Alternatively, the sum of the currents entering a node equals the sum of the currents leaving a node Kircohoff’s Current Law (KCL)

14. Kircohoff’s Current Law (KCL)

15. Series Connection

16. The algebraic sum of the voltages equals zero for any closed path (loop) in an electrical circuit. Kircohoff’s Voltage Law (KVL)

17. Kircohoff’s Voltage Law (KVL)

18. Parallel Connection KVL through A and B: -va+vb = 0  va = vb KVL through A and C: -va - vc = 0  va = -vc

19. Equivalent Series Resistance

20. Equivalent Parallel Resistance

21. Circuit Analysis using Series/Parallel Equivalents • Begin by locating a combination of resistances that are in series or parallel. Often the place to start is farthest from the source. • Redraw the circuit with the equivalent resistance for the combination found in step 1.

22. Voltage Division Of the total voltage, the fraction that appears across a given resistance in a series circuit is the ratio of the given resistance to the total series resistance.

23. Current Division For two resistances in parallel, the fraction of the total current flowing in a resistance is the ratio of the other resistance to the sum of the two resistances.

24. Node Voltage Analysis

25. Node Voltage Analysis

26. Mesh Current Analysis

27. Mesh Current Analysis

28. Thévenin Equivalent Circuits

29. Thévenin Equivalent Circuits

30. Thévenin Equivalent Circuits

31. Thévenin Equivalent Circuits

32. Thévenin Equivalent Circuits

33. Norton Equivalent Circuits

34. Norton Equivalent Circuits

35. Source Transformations

36. Maximum Power Transfer

37. Superposition Principle The superposition principle states that the total response is the sum of the responses to each of the independent sources acting individually. In equation form, this is

38. Superposition Principle

39. Superposition Principle Current source open circuit

40. Superposition Principle Voltage source short circuit Req

41. Voltage-Amplifier Model The input resistance Ri is the equivalent resistance see when looking into the input terminals of the amplifier. Ro is the output resistance. Avoc is the open circuit voltage gain.

42. Voltage Gain Ideally, an amplifier produces an output signal with identical waveshape as the input signal, but with a larger amplitude.

43. Current Gain

44. Power Gain

45. Operational Amplifier

46. Summing Point Constraint Operational amplifiers are almost always used with negative feedback, in which part of the output signal is returned to the input in opposition to the source signal.

47. Summing Point Constraint In a negative feedback system, the ideal op-amp output voltage attains the value needed to force the differential input voltage and input current to zero. We call this fact the summing-point constraint.

48. Summing Point Constraint • Verify that negative feedback is present. • Assume that the differential input voltage and the input current of the op amp are forced to zero. (This is the summing-point constraint.) • Apply standard circuit-analysis principles, such as Kirchhoff’s laws and Ohm’s law, to solve for the quantities of interest.

49. The Basic Inverter

50. Applying the Summing Point Constraint