Series-Parallel Circuits

Transcription

1 Series-Parallel Circuits

2 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

3 SERIES-PARALLEL NETWORKS FIG. 7.1 Series-parallel dc network. 5/26/2016 EEE 141 3

4 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

5 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 /26/2016 EEE 141 5

6 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

7 FIG. 7.7 Inserting an ammeter and a voltmeter to measure I 4 and V 2, respectively. 5/26/2016 EEE 141 7

8 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

9 BLOCK DIAGRAM APPROACH FIG. 7.8 Introducing the block diagram approach. FIG. 7.9 Block diagram format of Fig 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

10 FIG Example 7.3. FIG Reduced equivalent of Fig /26/2016 EEE

11 FIG Example /26/2016 EEE

12 Example 7.4 (Continued) FIG Reduced equivalent Circuit 5/26/2016 EEE

13 FIG 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 Block diagram of Fig /26/2016 EEE

14 FIG Example 7.5. FIG Alternative block diagram for the first parallel branch in Fig /26/2016 EEE

15 FIG Example 7.6. FIG Block diagram for Fig FIG Reduced form of Fig /26/2016 EEE

16 FIG Example 7.6. FIG Reduced form of Fig /26/2016 EEE

17 FIG Example 7.7. FIG Network in Fig redrawn. 5/26/2016 EEE

18 FIG Example /26/2016 EEE

19 FIG Example /26/2016 EEE

20 FIG Example /26/2016 EEE

21 FIG Example /26/2016 EEE

22 FIG Complex network for Example /26/2016 EEE

23 LADDER NETWORKS FIG 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

24 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 Working back to the source to determine R T for the network in Fig /26/2016 EEE

25 Solving Ladder Networks: Method 1 FIG Calculating R T and I s. FIG Working back toward I 6. 5/26/2016 EEE

26 Solving Ladder Networks: Method 1 FIG Calculating I 6. 5/26/2016 EEE

27 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 An alternative approach for ladder networks. 5/26/2016 EEE

28 Solving Ladder Networks: Method 2 FIG An alternative approach for ladder networks. 5/26/2016 EEE

29 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

30 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

31 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

32 POTENTIOMETER LOADING FIG 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

33 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

34 FIG Example 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

35 COMPUTER ANALYSIS PSpice FIG Using PSpice to verify the results of Example /26/2016 EEE

36 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