Series-Parallel Circuits · Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] VOLTAGE …

Copyright ©2011 by Pearson Education, Inc.

publishing as Pearson [imprint]Introductory Circuit Analysis, 12/e

Boylestad

Chapter 7

Series-Parallel

Circuits

Introductory Circuit Analysis, 12/e

Boylestad


publishing as Pearson [imprint]

OBJECTIVES

• Learn about the unique characteristics of series-parallel configurations and how to solve for the voltage, current, or power to any individual element or combination of elements.

• Become familiar with the voltage divider supply and the conditions needed to use it effectively.

• Learn how to use a potentiometer to control the voltage across any given load.


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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.


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SERIES-PARALLEL NETWORKS

FIG. 7.1 Series-parallel dc network.


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REDUCE AND RETURN APPROACH

FIG. 7.2 Introducing the reduce

and return approach.


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FIG. 7.3 Series-parallel network for

Example 7.1.FIG. 7.4 Substituting the parallel

equivalent resistance for resistors R2

and R3 in Fig. 7.3.


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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 R2 and R3.


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FIG. 7.7 Inserting an ammeter and a voltmeter to measure I4 and V2,

respectively.


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BLOCK DIAGRAM APPROACH

• 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


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FIG. 7.8 Introducing the block diagram

approach.FIG. 7.9 Block diagram format of

Fig. 7.3.


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FIG. 7.10 Example 7.3.

FIG. 7.11 Reduced equivalent of

Fig. 7.10.


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FIG. 7.13 Reduced equivalent of Fig. 7.12.


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DESCRIPTIVE EXAMPLES

FIG. 7.14 Example 7.5.FIG. 7.15 Block diagram of Fig. 7.14.


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FIG. 7.16 Alternative block diagram for

the first parallel branch in Fig. 7.14.


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FIG. 7.18 Block diagram for

Fig. 7.17.FIG. 7.19 Reduced form of

Fig. 7.17.


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FIG. 7.21 Network in Fig. 7.20 redrawn.


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FIG. 7.25 Determining VC for

the network in Fig. 7.24.


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FIG. 7.28 An alternative approach to Example 7.10.


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FIG. 7.30 Network in Fig. 7.29 redrawn

to better define a path toward the

desired unknowns.


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FIG. 7.31 Complex network for Example 7.11.


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LADDER NETWORKS

• A three-section ladder network appears in Fig. 7.32.

• The reason for the terminology is quite obvious for the repetitive structure.

• Basically two approaches are used to solve networks of this type.

FIG. 7.32 Ladder network.


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LADDER NETWORKS

FIG. 7.33 Working back to the source to determine RT for the network in Fig. 7.32.


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LADDER NETWORKS

FIG. 7.34 Calculating RT and Is. FIG. 7.35 Working back toward I6.


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LADDER NETWORKS

FIG. 7.36 Calculating I6.


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LADDER NETWORKS

FIG. 7.37 An alternative approach for ladder networks.


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VOLTAGE DIVIDER SUPPLY

(UNLOADED AND LOADED)

• When the term loaded is used to describe

voltage divider supply, it refers 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.


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(UNLOADED AND LOADED)No-Load Conditions

• Through a voltage

divider network

such as that in Fig.

7.38, a number of

different terminal

voltages can be

made available

from a single

supply.

FIG.7.38 Voltage divider supply.


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(UNLOADED AND LOADED)No-Load Conditions

• In general, for a voltage divider

supply to be effective, the applied

resistive loads should be

significantly larger than the

resistors appearing in the voltage

divider network.


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Loaded Conditions

FIG. 7.39 Voltage divider supply with loads equal to the average value of the

resistive elements that make up the supply.


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Loaded Conditions

FIG. 7.40 Voltage divider supply for Example 7.12.


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POTENTIOMETER LOADING

• For the unloaded potentiometer in Fig. 7.41, the output voltage is determined by the voltage divider rule, with RT in the figure representing the total resistance of the potentiometer.

FIG. 7.41 Unloaded

potentiometer.


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FIG. 7.42 Loaded potentiometer.


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• In general, when hooking up a load

to a potentiometer, be sure that the

load resistance far exceeds the

maximum terminal resistance of

the potentiometer if good control

of the output voltage is desired.


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FIG. 7.43 Loaded potentiometer with

RL << RT.

FIG. 7.44 Loaded potentiometer with

RL >> RT.


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AMMETER, VOLTMETER, AND

OHMMETER DESIGN

FIG. 7.46 Iron-vane movement.


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OHMMETER DESIGN

FIG. 7.47 Iron-vane movement; (a)

photo, (b) symbol and ratings.

FIG. 7.48 Basic ammeter.


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OHMMETER DESIGN

FIG. 7.49 Multirange ammeter.


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OHMMETER DESIGN

FIG. 7.50 Basic voltmeter.


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OHMMETER DESIGNThe Voltmeter

• A variation in the additional circuitry permits the use of the iron-vane movement in the design of a voltmeter.

• The 1 mA, 43 Ω movement can also be rated as a 43 mV (1 mA x 43 Ω), 43 movement, indicating that the maximum voltage that the movement can measure independently is 43 mV.

• The millivolt rating is sometimes referred to as the voltage sensitivity (VS).


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OHMMETER DESIGNThe Voltmeter

FIG. 7.51 Multirange voltmeter.


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OHMMETER DESIGNThe Ohmmeter

• In general, ohmmeters are designed

to measure resistance in the low,

middle, or high range.

• The most common is the series

ohmmeter, designed to read

resistance levels in the midrange.


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FIG. 7.52 Series ohmmeter.


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FIG. 7.53 Nanovoltmeter.


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• The megohmmeter (often called a

megger) is an instrument for measuring

very high resistance values.

• Its primary function is to test the insulation

found in power transmission systems,

electrical machinery, transformers, and so

on.

To measure the high-resistance values, a

high dc voltage is established by a hand-

driven generator.


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FIG. 7.54 Megohmmeter.


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APPLICATIONSBoosting a Car Battery

FIG. 7.55 Boosting a car battery.


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FIG. 7.56 Current levels at starting.


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FIG. 7.57 Current levels if the booster battery is improperly connected.


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APPLICATIONSElectronic Circuits

• The operation of most electronic systems

requires a distribution of dc voltages

throughout the design.

• Although a full explanation of why the dc

level is required (since it is an ac signal to

be amplified) will have to wait for the

introductory courses in electronic circuits,

the dc analysis will proceed in much the

same manner as described in this chapter.


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APPLICATIONSElectronic Circuits

FIG. 7.58 The dc bias levels of a transistor amplifier.


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COMPUTER ANALYSISPSpice

FIG. 7.59 Using PSpice to verify the results of Example

7.12.

Documents

Series-Parallel Circuits · Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] VOLTAGE …