1. ABE425 Engineering Measurement Systems Circuit Analysis Dr. Tony E. Grift Dept. of Agricultural & Biological Engineering University of Illinois

2. Agenda Fundamental laws of electricity in circuits Kirchoff’s Current Law (KCL) Kirchoff’s Voltage Law (KVL) Basic circuits Series resistance Parallel resistance Voltage divider Current divider Circuit simplification Thevenin equivalent Norton equivalent

3. Fundamental laws of electricity in circuits Kirchoff’s Current Law In a node the algebraic sum of currents equals zero Kirchoff’s Voltage Law In a loop the algebraic sum of voltages equals zero

4. The equivalent resistance of two resistances in series is the sum of the resistances.

5. The equivalent resistance of two resistances in parallel is the product divided by the sum of the resistances.

6. If you have a voltage divider and you want to know the voltage drop across one resistor, you take that resistor itself, you divide by the sum of both resistors and you multiply by the voltage drop across both of them.

7. Let’s see how a voltage divider works. Let’s calculate the current i to get all voltages.

8. Now we can use Ohm’s Law to calculate voltage DROPS.

9. Now we can calculate all the voltages.

10. Let’s verify the voltage DROPS using the Voltage Divider rule.

11. If you have a current divider and you want to know the current through one resistor, you take the opposite resistor, you divide by the sum of both resistors and you multiply by the current into both of them.

12. Thevenin equivalent circuit Thevenin: replace a complicated circuit with a simple voltage source with a series resistance Thevenin Equivalent

13. Thevenin equivalent circuit procedure Step 1: Identify the circuit of which the Thevenin equivalent is to be determined Step 2: Determine the Open Voltage across the terminals of interest Step 3: Turn OFF voltage sources, (short voltage sources, open-circuit all current sources and determine the equivalent series resistance that a voltage source at the load location would see Step 4: Replace the circuit with its equivalent Voltage source and the equivalent series resistance computed in steps 2 and 3

14. Step 1: Identify the circuit of which the Thevenin equivalent is to be determined Thevenin equivalent circuit procedure

15. Step 2: Determine the Open Voltage across the terminals of interest Thevenin equivalent circuit procedure

16. Step 3: Turn OFF voltage sources, (short voltage sources, open-circuit all current sources) and determine the equivalent series resistance that a voltage source at the load location would see Thevenin equivalent circuit procedure

17. Step 4: Replace the circuit with its equivalent Voltage source and the equivalent series resistance computed in steps 2 and 3 Thevenin equivalent circuit procedure

18. 1) Compute the Open Voltage Thevenin equivalent circuit procedure

19. 1A) Contribution of Voltage source Remember that the internal resistance of the current source is infinite! Thevenin equivalent circuit procedure

20. 1B) Contribution of Current source Remember that the internal resistance of the Voltage source is 0! Thevenin equivalent circuit procedure

21. 1B) Contribution of Current source Remember that the internal resistance of the Voltage source is 0! Thevenin equivalent circuit procedure

22. 1C) Add contributions of both sources In linear circuits this is allowed and called superposition Thevenin equivalent circuit procedure

23. 1C) Add contributions of both sources In linear circuits this is allowed and called superposition Thevenin equivalent circuit procedure

24. 2A) Compute the equivalent series resistance that a voltage source at the load location a,b would see Thevenin equivalent circuit procedure

25. 2A) Compute the equivalent series resistance that a voltage source at the load location a,b would see Thevenin equivalent circuit procedure

26. Step 4: Replace the circuit with its equivalent Voltage source and the equivalent series resistance computed in steps 2 and 3 Thevenin equivalent circuit procedure

27. Norton: replace a complicated circuit with a simple current source with a parallel resistance Norton Equivalent Norton equivalent circuit

28. Step 1: Identify the circuit of which the Norton equivalent is to be determined Step 2: Determine the short current across the terminals of interest Step 3: Turn OFF voltage sources, (short voltage sources, open-circuit all current sources and determine the equivalent parallel resistance that a voltage source at the load location would see Step 4: Replace the circuit with its equivalent Current source and the equivalent parallel resistance computed in steps 2 and 3 Norton equivalent circuit procedure

29. 1) Compute the Short Current through load Norton equivalent circuit procedure

30. 1A) Contribution of Voltage source Remember that the internal resistance of the current source is infinite! Norton equivalent circuit procedure

31. 1B) Contribution of Current source Current will take the path of least resistance! Norton equivalent circuit procedure

32. 1C) Contribution of Current source Current will take the path of least resistance! Norton equivalent circuit procedure

33. 1D) Add contributions of both sources In linear circuits this is allowed and called superposition Norton equivalent circuit procedure

34. 1D) Add contributions of both sources In linear circuits this is allowed and called superposition Norton equivalent circuit procedure

35. 2) Compute the equivalent parallel resistance that a current source at the load location would see Norton equivalent circuit procedure

36. 2) Compute the equivalent parallel resistance that a current source at the load location would see Norton equivalent circuit procedure

37. 2) Compute the equivalent parallel resistance that a current source at the load location would see Norton equivalent circuit procedure

38. Compare Thevenin and Norton procedures

39. ABE425 Engineering Measurement Systems Circuit Analysis The End Dept. of Agricultural & Biological Engineering University of Illinois