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ELECTRONIC CIRCUIT ANALYSIS

ELECTRONIC CIRCUIT ANALYSIS

ELECTRONIC CIRCUIT ANALYSIS Series-Parallel Circuits Analyse series-parallel resistive circuit using electronic laws and principles.

Circuit: An interconnection of electronic components that provide a closed path for current to flow. Circuit diagram: A schematic representation of the interconnection of electronic components. Electronic components are modelled and represented using symbols. A simple circuit has a voltage source, conductor and load. Other electronic circuit components may be included in a circuit for controlling, protection and monitoring capabilities. Voltage source: Provide the electrical energy (voltage) required to cause the movement of electrons through the electronic circuit. Most common voltage sources are batteries, generators and power supplies. Conductor: a wire that connects source and load or provides a path for current to flow. Load: Device (or circuit) that consumes, uses or absorbs the energy supplied by the power source, eg resistor, inductor, capacitor, etc. The flow of electric current can be described by conventional flow or electron flow . Three basic types of circuit configurations: 1. Series 2. Parallel and 3. Combinational (Series-parallel)

Series Circuit A circuit with only one path for current to flow.

Figure 1

Characteristics: • Current is the same throughout the circuit. • There is a voltage drop across each resistor. • The voltage drop across each resistor depends on the resistances.

ELECTRONIC CIRCUIT ANALYSIS Parallel Circuit A circuit with multiple paths (referred to as branches) for current flow.

Figure 2 Characteristics: • Currents, known as branch currents, depend on the branch resistances. • Voltage is the same across each branch resistor in the circuit. Series-Parallel Circuit

This configuration combines series and parallel circuits into one.

Figure 3

Node/Junction: Any point where two or more circuit components are connected together Ohm’s Law

Describe the relationship between the three electrical quantities – current (I), voltage (V) and resistance (R). “The current (I) that flows in a resistor is directly proportional to the voltage drop (V) across the resistor and inversely proportional to the resistance (R)”. Mathematical expression  

and







therefore

=





ELECTRONIC CIRCUIT ANALYSIS Kirchhoff’s Laws Deals with the conservation of charge and energy within electronic circuits.

Kirchhoff’s Current Law (KCL) Deals with the conservation of charge within electronic circuit. This law is also referred to as the conservation of charge. The law applies to currents in parallel circuits. Parallel circuits are also referred to as current dividers.

“The current flowing towards a junction equals the current flowing away from the junction”.  =  +  + … +  The branch current is determined using the current-divider formula:  = 

   +   

This formula applies only to two resistors in parallel. IX = current flowing in branch x. RX = resistance of branch x RY = resistance of branch y Kirchhoff’s Voltage Law

Deals with the conservation of energy within electronic circuits. This law is also referred to as the conservation of energy.

The law applies to the voltage drops in series circuits. Series circuits are also referred to as voltage dividers. “The voltage applied to a series circuit is equal to the sum of the voltage drops in the circuit”.  =  +  + … +  The voltage drop across each resistor is determined using the voltage-divider formula:     =    +   + … + 

ELECTRONIC CIRCUIT ANALYSIS Consider the following series-parallel circuit shown in figure 4.

Figure 4 Determine 1. All the currents in the circuit. 2. The voltage at node A with respect to ground. The E12 Range and Power Rating

Resistors are available in a number of standard ranges, referred to as E series. E series: E3, E6, E12, E24, E48, E96 and E192. These series are logarithmic and are derived from the resistor tolerances. The calculated resistor value may have to be rounded to an E-series value, which is the value closest to the calculated one. It is advisable to round up to the next higher value. A value smaller than calculated could overload a component such as in current limiting resistors. Use the E12 series (Table 1).

ELECTRONIC CIRCUIT ANALYSIS Table 1: E12 series (Fill in the resistance values) 1R0 Ω

10 Ω

100 Ω

1R2 Ω

12 Ω

120 Ω

1R5 Ω

15 Ω

150 Ω

1R8 Ω

18 Ω

180 Ω

2R2 Ω

22 Ω

220 Ω

2R7 Ω

27 Ω

270 Ω

3R3 Ω

33 Ω

330 Ω

3R9 Ω

39 Ω

390 Ω

4R7 Ω

47 Ω

470 Ω

5R6 Ω

56 Ω

560 Ω

6R8 Ω

68 Ω

680 Ω

8R2 Ω

82 Ω

820 Ω

1k0 Ω

10 kΩ

100 kΩ

1 MΩ

10 MΩ

Resistor Power Rating It is also referred to as resistors wattage rating. This is the amount of heat that a resistive element can dissipate for an indefinite period of time without degrading its performance. The power rating of a resistor indicates how much power a resistor can handle before it becomes too hot and burns. The power rating of a resistor is measured in watts, ⅛W, ¼W, ½W, and 1W, are typical. Circuit Measurements

Three (basic) electrical quantities of a circuit that can be measured are voltage ( V), current ( I) and resistance (R). A digital multi-meter (DMM) is (commonly) used to measure these quantities.

ELECTRONIC CIRCUIT ANALYSIS Voltage Measurement The measuring instrument (DMM) is connected across the resistor.

Figure 5 Current Measurement

The measuring instrument (DMM) is connected in the conduction path.

Figure 6 Resistance Measurement

Disconnect the resistor.

Figure 7 The measuring instrument is connected across a disconnected electrical component.

Figure 8

ELECTRONIC CIRCUIT ANALYSIS The Loading Effect Consider a DMM connected to measure a voltage drop across a resistor as shown in figure 9.

Figure 9 DMMs have an internal resistance, denoted RM. The internal resistance appears in parallel with the resistor (figure 10).

Figure 10 Hence, the voltage drop across the resistor R3 will be determined by R3 ||RM (figure 11).

Figure 11 The higher the resistance of the resistor across which the voltage is measured, the more the reduction in voltage. Hence, the more the loading effect. That is, the higher the resistance…The more the loading effect. The loading effect of the DMM will be minimal if the internal resistance is much larger than the resistance of the resistor. Ideally, the voltmeter resistance should be infinite, but practically, DMMs have a resistance of 10 MΩ

ELECTRONIC CIRCUIT ANALYSIS Determine and briefly explain how the voltmeter affects the voltage in figure 12. Ignore the internal resistance of voltmeter V1 and assume that voltmeter V2 has an internal resistance of 10 MΩ.

Figure 12 Superimposed Voltages

Both AC and DC voltage sources may be connected in an electronic circuit (figure 13).

Figure 13 In this case, both AC and DC must be taken into consideration when determining the output voltage or the voltage drop across the (load) resistor. AC (Alternating Current): The type of current which (continuously and (un)periodically) changes direction. DC (Direct Current): The type of current which flows consistently in one direction.

ELECTRONIC CIRCUIT ANALYSIS Table 2: Graphic Representation AC

DC

Note: Not all AC are represented in sinusoidal form. Others could be triangular, Square, etc.

The output waveform (for figure 13) illustrated in figure 14 is the algebraic sum of AC and DC with AC ‘riding’ on the DC level.

Figure 14

Thus, the maximum and minimum peak voltages of the AC voltage are altered from their original values.  =  +    



  !   

If VDC > Vac , the ac voltage signal never crosses the zero axis. Therefore, it isnon-alternating.

ELECTRONIC CIRCUIT ANALYSIS

Figure 15 Note: The AC notation uses lowercase subscript and DC uses uppercase subscript.

Sketch a correctly labelled voltage waveform as seen across RL in figure 16.

Figure 16

Circuit Troubleshooting

ELECTRONIC CIRCUIT ANALYSIS Troubleshooting involves identifying and isolating an electrical fault (failure). A digital multimeter (or oscilloscope) may be used to perform the troubleshooting exercise. The most common faults in resistive circuits are open and short circuits. These faults negatively affect (or degrade) the performance of the circuit. For a short circuit, the voltage drop across a resistor is zero. For an open circuit, the voltage drop across a resistor is equal to the source voltage.

Determine whether or not there is a fault in the circuit based on the reading of DMMs. If any, identify the failing component (s) and the type (s) of the fault.

Figure 17...