1. Pusan National University power PNU 세계로 미래로 Electric Circuits Fall, 2014 Chapter 6 Series-Parallel Circuits

2. Advanced Broadcasting & Communications Lab. 1 power PNU 세계로 미래로 6.1 Introduction This chapter will cover circuits that combine series and parallel features. A series-parallel circuit is a circuit that contains both series and parallel circuit topologies.

3. Advanced Broadcasting & Communications Lab. 2 power PNU 세계로 미래로 6.2 Series-Parallel Circuits Analysis of a series-parallel circuit involves using a combination of the following principle Combination of resistors in series. Combination of resistors in parallel KVL KCL Ohm’s law Voltage division principle Current division principle

4. Advanced Broadcasting & Communications Lab. 3 power PNU 세계로 미래로 6.2 Series-Parallel Circuits Analysis Analysis always begins with identification of any regions that are purely series or parallel. These can be reduced to equivalent resistances and the circuit reexamined. At this point new series or parallel segments may be identified and treated in the same manner. If a circuit cannot be fully reduced by this method alone, then one can turn to using KVL and KCL, or Ohm’s law. Additionally, voltage or current division may also be useful when the circuit presents such configurations.

5. Advanced Broadcasting & Communications Lab. 4 power PNU 세계로 미래로 6.2 Series-Parallel Circuits Example and Problem Example 6.1 Find current and power. Practice Problem 6.1 Find current and power

6. Advanced Broadcasting & Communications Lab. 5 power PNU 세계로 미래로 6.2 Series-Parallel Circuits Example and Problem Example 6.2 Find R eq. Practice Problem 6.2 Find R eq.

7. Advanced Broadcasting & Communications Lab. 6 power PNU 세계로 미래로 6.2 Series-Parallel Circuits Example and Problem Example 6.3 Find R ab. Practice Problem 6.3 Find R ab.

8. Advanced Broadcasting & Communications Lab. 7 power PNU 세계로 미래로 6.2 Series-Parallel Circuits Example and Problem Example 6.4 Find G eq. Practice Problem 6.4 Calculate G eq.

9. Advanced Broadcasting & Communications Lab. 8 power PNU 세계로 미래로 6.2 Series-Parallel Circuits Example and Problem Example 6.5 Find voltage. Practice Problem 6.5 Calculate voltage.

10. Advanced Broadcasting & Communications Lab. 9 power PNU 세계로 미래로 6.2 Series-Parallel Circuits Example and Problem Example 6.6 Find V ab. Practice Problem 6.6 Determine I.

11. Advanced Broadcasting & Communications Lab. 10 power PNU 세계로 미래로 6.3 Ladder Networks A ladder network is a special series-parallel circuit. An example is shown below. It is often referred to as a ladder because of its shape.

12. Advanced Broadcasting & Communications Lab. 11 power PNU 세계로 미래로 6.3 Ladder Networks DACs Ladder networks are used in digital to analog converters (DACs) A special ladder used in DACs is called a R/2R ladder An example is shown below.

13. Advanced Broadcasting & Communications Lab. 12 power PNU 세계로 미래로 6.3 Ladder Networks DACs II The ladder shown works by the input of a parallel digital signal (represented by the switches in this case) The most significant bit (MSB) has the greatest effect on the output voltage. The least significant bit (LSB) has the least impact on the output, and represents the smallest change in output voltage possible. A ladder network is analyzed just like other series-parallel circuits. Except that the analysis usually starts by working backwards. This can be seen in an example:

14. Advanced Broadcasting & Communications Lab. 13 power PNU 세계로 미래로 6.3 Ladder Networks Example and Problem Example 6.7 Find V O. Practice Problem 6.7 R/2R ladder Find I x.

15. Advanced Broadcasting & Communications Lab. 14 power PNU 세계로 미래로 6.4 Dependent Sources Up to this point we have analyzed circuits only with independent sources. These sources are unaffected by anything going on elsewhere in the circuit. Dependent sources on the other hand, have outputs that, as the name suggests, depend on something elsewhere in the circuit. A dependent source is either a voltage or current whose value is proportional to some other voltage or current in the circuit.

16. Advanced Broadcasting & Communications Lab. 15 power PNU 세계로 미래로 6.4 Dependent Sources Dependent Sources II There are four types of dependent sources: 1. A voltage-controlled voltage source 2. A voltage-controlled current source 3. A current-controlled voltage source 4. A current-controlled current source).

17. Advanced Broadcasting & Communications Lab. 16 power PNU 세계로 미래로 6.4 Dependent Sources Dependent Sources III These sources are never inputs to a circuit. They instead are used to model active electronic circuit elements, such as an operational amplifier. The element controlling the source does not need to be close (in the circuit topology) to the source.

18. Advanced Broadcasting & Communications Lab. 17 power PNU 세계로 미래로 6.4 Dependent Sources Example and Problem Example 6.8 Determine V x. Practice Problem 6.9 Find V x.

19. Advanced Broadcasting & Communications Lab. 18 power PNU 세계로 미래로 6.5 Loading Effects We would like to think that the act of taking a measurement has no impact on what we measure. In ideal circumstances that would be true, but in reality, we must be aware of the effect attaching a measuring instrument to a circuit has. This effect on the circuit is called loading.

20. Advanced Broadcasting & Communications Lab. 19 power PNU 세계로 미래로 6.5 Loading Effects Voltmeter Loading Voltmeters ideally have infinite resistance, but in reality they have resistances typically in the range of 10’s of MΩ. Connecting the voltmeter to a circuit element puts this resistance in parallel with it.

21. Advanced Broadcasting & Communications Lab. 20 power PNU 세계로 미래로 6.5 Loading Effects Ammeter Loading An ideal ammeter has zero resistance. Ammeters are inserted in series with the branch to be measured. Connecting an ammeter in series adds resistance to the branch.

22. Advanced Broadcasting & Communications Lab. 21 power PNU 세계로 미래로 6.5 Loading Effects Calculating Error The percentage error introduced by adding the instrument into the circuit can be calculated as: Where the ideal value is what we would get if no instrument had been added. Generally, an error of less than 5% is acceptable.

23. Advanced Broadcasting & Communications Lab. 22 power PNU 세계로 미래로 6.5 Loading Effects Example and Problem Example 6.10 Calculate loading effects. Practice Problem 6.10 Calculate percentage error

24. Advanced Broadcasting & Communications Lab. 23 power PNU 세계로 미래로 5.7 Wheatstone Bridge Although an ohmmeter provides the simplest way to measure resistance, more accurate measurements may be obtained by using a Wheatstone bridge. The Wheatstone bridge is best suited for measuring resistances in the range of 1Ω to 1MΩ. The bridge uses three known values for resistance to measure an unknown.

25. Advanced Broadcasting & Communications Lab. 24 power PNU 세계로 미래로 5.7 Wheatstone Bridge Wheatstone Bridge II The unknown resistor is R x. That plus R 3 make up a voltage divider. R 1 and R 2 make up another divider. A galvanometer which is very sensitive to current flow is placed between the dividers.

26. Advanced Broadcasting & Communications Lab. 25 power PNU 세계로 미래로 5.7 Wheatstone Bridge Wheatstone Bridge II The unknown resistor is R x. That plus R 3 make up a voltage divider. R 1 and R 2 make up another divider. A galvanometer which is very sensitive to current flow is placed between the dividers. If the bridge is “out of balance”, then the voltages on the two dividers are not the same and the galvanometer does not read zero.

27. Advanced Broadcasting & Communications Lab. 26 power PNU 세계로 미래로 5.7 Wheatstone Bridge Wheatstone Bridge III When the bridge is balanced, the voltages on the two dividers is the same: From this we can see that the unknown resistance is:

28. Advanced Broadcasting & Communications Lab. 27 power PNU 세계로 미래로 5.7 Wheatstone Bridge Unbalanced Mode The bridge can also be operated when unbalanced. This is often employed for resistive sensors, where the degree of unbalance indicates the value of the quantity being measured. The bridge may also be used to measure capacitance and inductance.

29. Advanced Broadcasting & Communications Lab. 28 power PNU 세계로 미래로 5.7 Wheatstone Bridge Example and Problem Example 6.14 Determine R x. Practice Problem 6.14 What is the value of the unknown R?

30. Advanced Broadcasting & Communications Lab. 29 power PNU 세계로 미래로 Homework Read Text Chapter 7. Methods of Analysis, pp 141-176 Prepare Presentation Solve Problems 6.3, 6.10, 6.28, 6.35, 6.41, 6.44, 6.59 Computer Analysis 6.49