Series-Parallel Circuits
INTRODUCTION A series-parallel configuration is one that is formed by a combination of series and parallel elements. A complex configuration is one in which none of the elements are in series or parallel. 5/26/2016 EEE 141 2
SERIES-PARALLEL NETWORKS FIG. 7.1 Series-parallel dc network. 5/26/2016 EEE 141 3
REDUCE AND RETURN APPROACH The reduce and return approach enables you to reduce the network to its simplest form across the source and then determine the source current. In the return phase, you use the resulting source current to work back to the desired unknown. 5/26/2016 EEE 141 4
FIG. 7.3 Series-parallel network for Example 7.1. FIG. 7.4 Substituting the parallel equivalent resistance for resistors R 2 and R 3 in Fig. 7.3. 5/26/2016 EEE 141 5
FIG. 7.5 Series-parallel network for Example 7.2. FIG. 7.6 Schematic representation of the network in Fig. 7.5 after substituting the equivalent resistance R for the parallel combination of R 2 and R 3. 5/26/2016 EEE 141 6
FIG. 7.7 Inserting an ammeter and a voltmeter to measure I 4 and V 2, respectively. 5/26/2016 EEE 141 7
BLOCK DIAGRAM APPROACH FIG. 7.8 Introducing the block diagram approach. Occasionally, the reduce and return approach is not as obvious, and you may need to look at groups of elements rather than the individual components. Once the grouping of elements reveals the most direct approach, you can examine the impact of the individual components in each group. This grouping of elements is called the block diagram approach 5/26/2016 EEE 141 8
BLOCK DIAGRAM APPROACH FIG. 7.8 Introducing the block diagram approach. FIG. 7.9 Block diagram format of Fig. 7.3. If each block in Fig. 7.8 were a single resistive element, the network in Fig. 7.9 would result. Blocks B and C are in parallel, and their combination is in series with block A. 5/26/2016 EEE 141 9
FIG. 7.10 Example 7.3. FIG. 7.11 Reduced equivalent of Fig. 7.10. 5/26/2016 EEE 141 10
FIG. 7.12 Example 7.4. 5/26/2016 EEE 141 11
Example 7.4 (Continued) FIG. 7.13 Reduced equivalent Circuit 5/26/2016 EEE 141 12
FIG. 7.14 Example 7.5. In this case, particular unknowns are requested instead of a complete solution. It would, therefore, be a waste of time to find all the currents and voltages of the network. The method used should concentrate on obtaining only the unknowns requested. FIG. 7.15 Block diagram of Fig. 7.14. 5/26/2016 EEE 141 13
FIG. 7.14 Example 7.5. FIG. 7.16 Alternative block diagram for the first parallel branch in Fig. 7.14. 5/26/2016 EEE 141 14
FIG. 7.17 Example 7.6. FIG. 7.18 Block diagram for Fig. 7.17. FIG. 7.19 Reduced form of Fig. 7.17. 5/26/2016 EEE 141 15
FIG. 7.17 Example 7.6. FIG. 7.19 Reduced form of Fig. 7.17. 5/26/2016 EEE 141 16
FIG. 7.20 Example 7.7. FIG. 7.21 Network in Fig. 7.20 redrawn. 5/26/2016 EEE 141 17
FIG. 7.22 Example 7.8. 5/26/2016 EEE 141 18
FIG. 7.24 Example 7.9. 5/26/2016 EEE 141 19
FIG. 7.26 Example 7.10. 5/26/2016 EEE 141 20
FIG. 7.29 Example 7.11. 5/26/2016 EEE 141 21
FIG. 7.31 Complex network for Example 7.11. 5/26/2016 EEE 141 22
LADDER NETWORKS FIG. 7.32 A three-section ladder network. The reason for the terminology ladder network is obvious for its repetitive structure. Basically two approaches are used to solve networks of this type. 5/26/2016 EEE 141 23
Solving Ladder Networks: Method 1 Calculate the total resistance and resulting source current, and then work back through the ladder until the desired current or voltage is obtained. FIG. 7.33 Working back to the source to determine R T for the network in Fig. 7.32. 5/26/2016 EEE 141 24
Solving Ladder Networks: Method 1 FIG. 7.34 Calculating R T and I s. FIG. 7.35 Working back toward I 6. 5/26/2016 EEE 141 25
Solving Ladder Networks: Method 1 FIG. 7.36 Calculating I 6. 5/26/2016 EEE 141 26
Solving Ladder Networks: Method 2 Assign a letter symbol to the last branch current and work back through the network to the source, maintaining this assigned current or other current of interest. The desired current can then be found directly. FIG. 7.37 An alternative approach for ladder networks. 5/26/2016 EEE 141 27
Solving Ladder Networks: Method 2 FIG. 7.37 An alternative approach for ladder networks. 5/26/2016 EEE 141 28
VOLTAGE DIVIDER SUPPLY Through a voltage divider network, a number of different terminal voltages can be made available from a single supply. FIG.7.38 Voltage divider supply (No-Load Condition). 5/26/2016 EEE 141 29
LOADING The term load is used to refer to the application of an element, network, or system to a supply that draws current from the supply. In other words, the loading down of a system is the process of introducing elements that will draw current from the system. The heavier the current, the greater is the loading effect. For a voltage divider supply to be effective, the applied resistive loads should be significantly larger than the resistors in the voltage divider network. 5/26/2016 EEE 141 30
Effect of Applying Small Resistive Loads on a Voltage Divider Supply If the load resistors are changed to the 1 kω level, the terminal voltages will all be relatively close to the no-load values. 5/26/2016 EEE 141 31
POTENTIOMETER LOADING FIG. 7.41 Unloaded potentiometer. For an unloaded potentiometer, the output voltage is determined by the voltage divider rule. Too often it is assumed that the voltage across a load is determined solely by the potentiometer and the effect of the load can be ignored. This is definitely not the case. 5/26/2016 EEE 141 32
POTENTIOMETER LOADING When a load is applied, the output voltage V L is now a function of the magnitude of the load applied. To have good control of the output voltage V L, the following relationship must be satisfied: 5/26/2016 EEE 141 33
FIG. 7.45 Example 7.13. The ideal and loaded voltage levels are so close that the design can be considered a good one for the applied loads. 5/26/2016 EEE 141 34
COMPUTER ANALYSIS PSpice FIG. 7.59 Using PSpice to verify the results of Example 7.12. 5/26/2016 EEE 141 35
Homework 4 Use the 12 th Edition of the textbook Problems from chapter 7 exercise: 2, 7, 8, 12, 14, 16, 18, 20, 22, 26, 27, 28, 29, 30, 34 EEE141 36