EN2042102 วงจรไฟฟ าและอ เล กทรอน กส Circuits and Electronics บทท 2 พ นฐานวงจรไฟฟ า สาขาว ชาว ศวกรรมคอมพ วเตอร คณะว ศวกรรมศาสตร มหาว ทยาล ยเทคโนโลย ราชมงคลพระนคร
INTRODUCTION Two types of current are readily available to the consumer today. One is direct current (dc), in which ideally the flow of charge (current) does not change in magnitude (or direction) with time. The other is sinusoidal alternating current (ac), in which the flow of charge is continually changing in magnitude (and direction) with time.
INTRODUCTION FIG. 5.1 Introducing the basic components of an electric circuit.
INTRODUCTION FIG. 5.2 Defining the direction of conventional flow for single-source dc circuits. FIG. 5.3 Defining the polarity resulting from a conventional current I through a resistive element.
SERIES RESISTORS Before the series connection is described, first recognize that every fixed resistor has only two terminals to connect in a configuration it is therefore referred to as a two-terminal device. FIG. 5.4 Series connection of resistors.
SERIES RESISTORS Instrumentation FIG. 5.11 Using an ohmmeter to measure the total resistance of a series circuit.
SERIES CIRCUITS If we now take an 8.4 V dc supply and connect it in series with the series resistors in Fig. 5.4, we have the series circuit in Fig. 5.12. FIG. 5.12 Schematic representation for a dc series circuit.
SERIES CIRCUITS FIG. 5.13 Resistance seen at the terminals of a series circuit.
SERIES CIRCUITS FIG. 5.14 Inserting the polarities across a resistor as determined by the direction of the current.
SERIES CIRCUITS FIG. 5.15 Series circuit to be investigated in Example 5.4. FIG. 5.16 Series circuit to be analyzed in Example 5.5.
SERIES CIRCUITS FIG. 5.17 Circuit in Fig. 5.16 redrawn to permit the use of Eq. (5.2).
SERIES CIRCUITS FIG. 5.18 Series circuit to be analyzed in Example 5.6.
SERIES CIRCUITS Instrumentation FIG. 5.19 Using voltmeters to measure the voltages across the resistors in Fig. 5.12.
SERIES CIRCUITS Instrumentation FIG. 5.20 Measuring the current throughout the series circuit in Fig. 5.12.
POWER DISTRIBUTION IN A SERIES CIRCUIT FIG. 5.21 Power distribution in a series circuit.
POWER DISTRIBUTION IN A SERIES CIRCUIT FIG. 5.22 Series circuit to be investigated in Example 5.7.
VOLTAGE SOURCES IN SERIES FIG. 5.23 Reducing series dc voltage sources to a single source.
KIRCHHOFF S VOLTAGE LAW The law, called Kirchhoff s voltage law (KVL), was developed by Gustav Kirchhoff in the mid-1800s. The law specifies that the algebraic sum of the potential rises and drops around a closed path (or closed loop) is zero. FIG. 5.26 Applying Kirchhoff s voltage law to a series dc circuit.
KIRCHHOFF S VOLTAGE LAW FIG. 5.27 Series circuit to be examined in Example 5.8. FIG. 5.28 Series dc circuit to be analyzed in Example 5.9.
KIRCHHOFF S VOLTAGE LAW FIG. 5.29 Combination of voltage sources to be examined in Example 5.10.
KIRCHHOFF S VOLTAGE LAW FIG. 5.30 Series configuration to be examined in Example 5.11. FIG. 5.31 Applying Kirchhoff s voltage law to a circuit in which the polarities have not been provided for one of the voltages (Example 5.12).
KIRCHHOFF S VOLTAGE LAW FIG. 5.32 Series configuration to be examined in Example 5.13.
VOLTAGE DIVISION IN A SERIES CIRCUIT FIG. 5.33 Revealing how the voltage will divide across series resistive elements.
VOLTAGE DIVISION IN A SERIES CIRCUIT FIG. 5.34 The ratio of the resistive values determines the voltage division of a series dc circuit. FIG. 5.35 The largest of the series resistive elements will capture the major share of the applied voltage.
VOLTAGE DIVISION IN A SERIES CIRCUIT Voltage Divider Rule (VDR) The voltage divider rule (VDR) permits the determination of the voltage across a series resistor without first having to determine the current of the circuit. The rule itself can be derived by analyzing the simple series circuit in Fig. 5.36. FIG. 5.36 Developing the voltage divider rule.
VOLTAGE DIVISION IN A SERIES CIRCUIT Voltage Divider Rule (VDR) FIG. 5.37 Series circuit to be examined using the voltage divider rule in Example 5.15. FIG. 5.38 Series circuit to be investigated in Examples 5.16 and 5.17.
VOLTAGE DIVISION IN A SERIES CIRCUIT Voltage Divider Rule (VDR) FIG. 5.39 Voltage divider action for Example 5.18. FIG. 5.40 Designing a voltage divider circuit (Example 5.19).
INTERCHANGING SERIES ELEMENTS The elements of a series circuit can be interchanged without affecting the total resistance, current, or power to each element. FIG. 5.41 Series dc circuit with elements to be interchanged. FIG. 5.42 Circuit in Fig. 5.41 with R 2 and R 3 interchanged.
INTERCHANGING SERIES ELEMENTS FIG. 5.43 Example 5.20.
INTERCHANGING SERIES ELEMENTS FIG. 5.44 Redrawing the circuit in Fig. 5.43.
NOTATION Voltage Sources and Ground Except for a few special cases, electrical and electronic systems are grounded for reference and safety purposes. The symbol for the ground connection appears in Fig. 5.45 with its defined potential level zero volts. FIG. 5.45 Ground potential.
NOTATION Voltage Sources and Ground FIG. 5.46 Three ways to sketch the same series dc circuit.
NOTATION Double-Subscript Notation The fact that voltage is an across variable and exists between two points has resulted in a double-subscript notation that defines the first subscript as the higher potential. FIG. 5.50 Defining the sign for double-subscript notation.
NOTATION Double-Subscript Notation The double-subscript notation V ab specifies point a as the higher potential. If this is not the case, a negative sign must be associated with the magnitude of V ab. In other words, the voltage V ab is the voltage at point a with respect to (w.r.t.) point b.
NOTATION Single-Subscript Notation If point b of the notation V ab is specified as ground potential (zero volts), then a single-subscript notation can be used that provides the voltage at a point with respect to ground. FIG. 5.51 Defining the use of single-subscript notation for voltage levels.
NOTATION General Comments A particularly useful relationship can now be established that has extensive applications in the analysis of electronic circuits. For the above notational standards, the following relationship exists:
NOTATION General Comments FIG. 5.52 Example 5.21. FIG. 5.53 Example 5.22.
NOTATION General Comments FIG. 5.56 Example 5.24. FIG. 5.57 Determining V b using the defined voltage levels.
PROTOBOARDS (BREADBOARDS) At some point in the design of any electrical/electronic system, a prototype must be built and tested. One of the most effective ways to build a testing model is to use the protoboard (in the past most commonly called a breadboard) in Fig. 5.75. FIG. 5.75 Protoboard with areas of conductivity defined using two different approaches.
PROTOBOARDS (BREADBOARDS) FIG. 5.76 Two setups for the network in Fig. 5.12 on a protoboard with yellow leads added to each configuration to measure voltage V 3 with a voltmeter.
Parallel dc Circuits
PARALLEL RESISTORS The term parallel is used so often to describe a physical arrangement between two elements that most individuals are aware of its general characteristics. In general, two elements, branches, or circuits are in parallel if they have two points in common.
PARALLEL RESISTORS FIG. 6.2 Schematic representations of three parallel resistors.
PARALLEL RESISTORS FIG. 6.3 Parallel combination of resistors.
PARALLEL RESISTORS FIG. 6.6 Network to be investigated in Example 6.3.
PARALLEL RESISTORS Instrumentation FIG. 6.17 Using an ohmmeter to measure the total resistance of a parallel network.
PARALLEL CIRCUITS A parallel circuit can now be established by connecting a supply across a set of parallel resistors as shown in Fig. 6.18. The positive terminal of the supply is directly connected to the top of each resistor, while the negative terminal is connected to the bottom of each resistor. FIG. 6.18 Parallel network.
PARALLEL CIRCUITS In general, the voltage is always the same across parallel elements. Therefore, remember that if two elements are in parallel, the voltage across them must be the same. However, if the voltage across two neighboring elements is the same, the two elements may or may not be in parallel.
PARALLEL CIRCUITS FIG. 6.19 Replacing the parallel resistors in Fig. 6.18 with the equivalent total resistance. FIG. 6.20 Mechanical analogy for Fig. 6.18.
PARALLEL CIRCUITS For single-source parallel networks, the source current (Is) is always equal to the sum of the individual branch currents. FIG. 6.21 Demonstrating the duality that exists between series and parallel circuits.
PARALLEL CIRCUITS FIG. 6.22 Parallel network for Example 6.12. FIG. 6.23 Parallel network for Example 6.13.
PARALLEL CIRCUITS FIG. 6.24 Parallel network for Example 6.14.
PARALLEL CIRCUITS Instrumentation FIG. 6.25 Measuring the voltages of a parallel dc network.
PARALLEL CIRCUITS Instrumentation FIG. 6.26 Measuring the source current of a parallel network.
PARALLEL CIRCUITS Instrumentation FIG. 6.27 Measuring the current through resistor R 1.
POWER DISTRIBUTION IN A PARALLEL CIRCUIT FIG. 6.28 Power flow in a dc parallel network.
POWER DISTRIBUTION IN A PARALLEL CIRCUIT FIG. 6.29 Parallel network for Example 6.15.
KIRCHHOFF S CURRENT LAW In the previous chapter, Kirchhoff s voltage law was introduced, providing a very important relationship among the voltages of a closed path. Kirchhoff is also credited with developing the following equally important relationship between the currents of a network, called Kirchhoff s current law (KCL): The algebraic sum of the currents entering and leaving a junction (or region) of a network is zero.
KIRCHHOFF S CURRENT LAW FIG. 6.30 Introducing Kirchhoff s current law.
KIRCHHOFF S CURRENT LAW FIG. 6.31 (a) Demonstrating Kirchhoff s current law; (b) the water analogy for the junction in (a).
KIRCHHOFF S CURRENT LAW In technology, the term node is commonly used to refer to a junction of two or more branches. FIG. 6.32 Two-node configuration for Example 6.16.
KIRCHHOFF S CURRENT LAW FIG. 6.33 Four-node configuration for Example 6.17.
KIRCHHOFF S CURRENT LAW FIG. 6.34 Network for Example 6.18.
KIRCHHOFF S CURRENT LAW FIG. 6.35 Parallel network for Example 6.19.
KIRCHHOFF S CURRENT LAW FIG. 6.36 Redrawn network in Fig. 6.35. FIG. 6.37 Integrated circuit for Example 6.20.
CURRENT DIVIDER RULE For series circuits we have the powerful voltage divider rule for finding the voltage across a resistor in a series circuit. We now introduce the equally powerful current divider rule (CDR) for finding the current through a resistor in a parallel circuit.
CURRENT DIVIDER RULE In general: For two parallel elements of equal value, the current will divide equally. For parallel elements with different values, the smaller the resistance, the greater is the share of input current. For parallel elements of different values, the current will split with a ratio equal to the inverse of their resistance values.
CURRENT DIVIDER RULE FIG. 6.38 Discussing the manner in which the current will split between three parallel branches of different resistive value. FIG. 6.39 Parallel network for Example 6.21.
CURRENT DIVIDER RULE FIG. 6.41 Using the current divider rule to calculate current I1 in Example 6.22.
CURRENT DIVIDER RULE Special Case: Two Parallel Resistors FIG. 6.42 Deriving the current divider rule for the special case of only two parallel resistors.
CURRENT DIVIDER RULE Special Case: Two Parallel Resistors FIG. 6.43 Using the current divider rule to determine current I 2 in Example 6.23. FIG. 6.44 A design-type problem for two parallel resistors (Example 6.24).
VOLTAGE SOURCES IN PARALLEL FIG. 6.46 Demonstrating the effect of placing two ideal supplies of the same voltage in parallel.
OPEN AND SHORT CIRCUITS FIG. 6.50 Defining a short circuit. FIG. 6.48 Defining an open circuit.
OPEN AND SHORT CIRCUITS FIG. 6.49 Examples of open circuits.
OPEN AND SHORT CIRCUITS FIG. 6.52 Examples of short circuits.
OPEN AND SHORT CIRCUITS FIG. 6.56 Networks for Example 6.27.
OPEN AND SHORT CIRCUITS FIG. 6.57 Solutions to Example 6.27.
OPEN AND SHORT CIRCUITS FIG. 6.58 Network for Example 6.28. FIG. 6.59 Network in Fig. 6.58 with R 2 replaced by a jumper.
SUMMARY TABLE TABLE 6.1 Summary table.
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.
SERIES-PARALLEL NETWORKS FIG. 7.1 Series-parallel dc network.
REDUCE AND RETURN APPROACH 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.
REDUCE AND RETURN APPROACH 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.
REDUCE AND RETURN APPROACH FIG. 7.7 Inserting an ammeter and a voltmeter to measure I 4 and V 2, respectively.
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
BLOCK DIAGRAM APPROACH FIG. 7.8 Introducing the block diagram approach. FIG. 7.9 Block diagram format of Fig. 7.3.
BLOCK DIAGRAM APPROACH FIG. 7.10 Example 7.3. FIG. 7.11 Reduced equivalent of Fig. 7.10.
BLOCK DIAGRAM APPROACH FIG. 7.12 Example 7.4.
BLOCK DIAGRAM APPROACH FIG. 7.13 Reduced equivalent of Fig. 7.12.
APPLICATIONS Boosting a Car Battery FIG. 7.55 Boosting a car battery.
APPLICATIONS Electronic 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.
APPLICATIONS Electronic Circuits FIG. 7.58 The dc bias levels of a transistor amplifier.