San Francisco State University. School of Engineering
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1 1 San Francisco State University School of Engineering ENGR 300 ENGR EXPERIMENATION Final Project: MULTI SOURCE CIRCUITS ANALYSIS TECHNIQUES Submitted By: Kuan Keong Austin Yiu Yin Yin Wu March 8, 2005 Instructor: Mutlu Ozer Abstract: Our objective was to determine and compare the current and voltage values of two multisource circuits by measuring the circuit with a multimeter, by Loop, calculation methods and by running a PSPICE program. 1
2 2 Contents Page No. 1. Title page 1 2. Abstract 1 3. Table of contents 2 4. Summary 3 5. Introduction 4 6. Apparatus and test procedure 5 7. Results 7 8. Discussion Conclusions References 14 2
3 3 Summary: 1. Use DMM to measure the voltage source and current source. 2. Carefully measure all the sources, such as resistors, used in this experiment. 3. Built the multisource circuits and measure all the currents and voltages. 4. Calculate all the voltages and currents by using Loop, Nodal and Superposition methods. 5. Simulate the circuit into PSPICE program. 6. Run an analysis for the circuits on PSPICE. 7. Compare measured values and PSPICE values and compute the percentage of error. 3
4 4 Introduction: In this project, we will demonstrate the analysis techniques for multisource circuit by three methods. We start with building multisource circuits and measuring all currents and voltages of these circuits directly from a digital multimeter (DMM); the second method is to measure all the resistors first, and then we will verify the values of currents and voltages by Loop, Nodal and Superposition calculation methods. Finally, we will simulate the multisource circuits into a PSPICE program in order to get the ideal result. We will set up two different circuits and obtain the current and voltage values by the three methods. Last but not least, we will compare our measured results, calculated results and PSPICE results to get the accuracy of this experiment. This experiment is significant since we can evaluate the same values through different techniques. As a result, we can identify each method s accuracy so that we can check the equipment s precision. 4
5 5 Apparatus and Test Procedure: 1. Measuring Method Equipments: (1)D.C. power supply (2)Four resistors of 1kΩ, 330Ω, 470Ω, and 2.2kΩ, respectively (3)Digital multimeter (DMM) (4)Wires and leads (5) Breadboard Breadboard DMM Lead Wire Power supply 4 Watt Resistors Fig. 1 Procedures: 5
6 6 (1) Use a DMM to measure the voltage sources and current source. (2) Use a DMM to measure the resistance of each resistor. (3) Built the first multisource circuit and measure currents and voltages of each resistor. (4) Repeat the same procedure for the second circuit. 2. Calculating Method Equipments: (1)Four resistors of 1kΩ, 330Ω, 470Ω, and 2.2kΩ, respectively (2)Digital multimeter (DMM) Procedures: (1) Measure the resistance of each resistor. (3) Calculate the values of current and voltage for each resistor. 3. Pspice Method Equipments: (1) Computer with PSPICE program Procedures: (1) Simulate the circuit into PSPICE program. (2) Run an analysis for the circuits on PSPICE 6
7 7 Results 1. Measuring Method Table 1 shows the values of four resistors. We obtained the values from the color codes and also from the DMM measurement. We will use the measured values for the follow analysis and calculation. Reference 1. demonstrates more details about reading values from the color band. Table 1 - Resistor Measurements Resistor Color Coded Value(Ohms) Value(Ohms) R1 1K 1.003K R R R4 2.2K Figure 2 is the circuit diagram for circui#1 set-up, and Table 2 are the values measured by a DMM. R1 R V E1 R V E mA 3.476V 7.443mA R mA 0V 0 Fig 2 - Circuit #1 for Measuring Method 7
8 8 Table 2 - Voltages/Current Data for Circuit#1 Component Voltage(V) Current(mA) E E R R R R Figure 3 is the circuit diagram for circui#2 set-up, and Table 3 are the values measured by a DMM V R V E 14.69mA R mA R3 I 10mAdc 10.00mA 15.09mA 0V 0 Fig 3 - Circuit #2 for Measuring Method Table 3 - Voltages/Current Data for Circuit #2 Component Voltage(V) Current(mA) E I R R R Calculating Method We will calculate the circuit s current by using Kirchoff's Rules with loop method. A detail description about using Kirchoff s Rules is show in Reference 2. In this part, circuit#1 s calculation is demonstrated. Figure 4 shows the data we 8
9 9 need for calculation mA R V R mA 12.00V 12Vdc 6.043mA V kohm 3.476V 7.443mA R2 331ohm 7.443mA R kohm 9Vdc 9.000V V mA 467ohm 0V 0 Fig 4 - Circuit #1 for Calculating Method The current across R1 is I1, across R2 & R3 is I3 and across R4 is I2. E1 = 12V E2 = 9V E1 = I1R1 + I3R2 + I3 R3 12V = I1(1003ohm) + I3(331ohm + 467ohm) 12V = I1(1003ohm) + I3(798ohm).(eq. 1) E2 = I2R4 + I3R2 + I3R3 9V = I2(2186ohm) + I3(331ohm) + I3(467ohm) 9V = I2(2186ohm) + I3(798ohm)..(eq. 2) By solving the eq. 1 & 2, we got: I1 = 6.09mA I2 = 1.39mA I3 = 7.48mA Use Ohm s Law, we calculated the voltage for each resistor: V1 = 6.11V V2 = 2.476V 9
10 10 V3 = 3.49V V4 = 3.05V 3. Pspice Method PSpice is the very reliable software to check the load, voltage and current in the circuit. After we measured the certain resistance of the resistor, we put the value in PSpice to measured the voltage and current for than. In this part, we follow the direction of How to use PSpice by Larry Klingenberg; Reference 3. demonstrates more detail and source about this method. Figure 5 is the circuit diagram for circui#1 set-up, and Table 4 are the values measured by a DMM mA R V R mA 12.00V 12Vdc 6.043mA V k 3.476V 7.443mA R mA R k 9Vdc 9.000V V mA 467 0V 0 Fig 5 - Circuit #1 for Pspice Method Table 4 - Voltages/Current Data obtained from Pspice for Circuit #2 R1 R2 R3 R4 V V V V V I ma ma ma 1.4 ma Figure 6 is the circuit diagram for circui#2 set-up, and Table 3 are the values measured by a DMM. 10
11 mA R V 1.003k 20.00V 20Vdc V mA R mA R3 467 I1 10mAdc 10.00mA 15.09mA 0V 0 Fig 6 - Circuit #2 for Pspice Method Table 5 - Voltages/Current Data obtained from Pspice for Circuit #2 R1 R2 R3 V V V V I ma ma ma 11
12 12 Discussion Table 6 and Table 7 are comparisons of the circuit values of the Measure, Calculation and Pspice methods of the two circuits. The result of each method is very closed to the other two. Table 6 Comparison of three methods for Circuit#1 Component Voltage(V) Calculated Voltage(V) Pspice Voltage(V) Current(mA) Calculated Current(mA) Pspice Current(mA) E N/A N/A N/A E N/A N/A N/A R R R R Table 7 Comparison of three methods for Circuit#2 Component Voltage(V) Calculated Voltage(V) Pspice Voltage(V) Current(mA) Calculated Current(mA) Pspice Current(mA) E N/A N/A N/A I N/A 9.96 N/A N/A R R R
13 13 Conclusion The answers from the calculation agree with the results from the circuit analysis program PSPICE and measurements. Therefore, we can conclude that the Measuring Method by using a DMM, the Calculation Method by using the Kirchoff s rules, and the Pspice Method are all accurate and they the results they obtain are equivalent to the other two. Also, this project can help us to specify which method may be more convenient to use than the other two. Since all the answers are closed to the other two, we know that they are all proper. However, the Pspice method is the easiest one to use, and we can get the results fast without any measuring equipment. Furthermore, we believe that it s better to study the Calculation Method so that we will also be able to understand the concept of how to get the results from the Pspice. 13
14 14 Reference Reference 1 On Line Source for Resistor Color Band: Resistor Color Band Resistors are color coded for easy reading. Imagine how many blind technicians there would be otherwise. To determine the value of a given resistor look for the gold or silver tolerance band and rotate the resistor as in the photo above. (Tolerance band always set to the right). Look at the 1st color band and determine its color. This may be difficult on small or oddly colored resistors. Now look at the chart and match the "1st & 2nd color band" color to the "Digit it represents". Write this number down. Common Resistor 1st. & 2nd Color Band Resistor Color Code Chart Digit it Represents -----Multiplier----- BLACK 0 X1 BROWN 1 X10 RED 2 X100 ORANGE 3 X1,000 or 1K YELLOW 4 X10,000 or 10K GREEN 5 X100,000 or 100K BLUE 6 X1,000,000 or 1M VIOLET 7 Silver is divide by
15 15 GRAY 8 Gold is divide by 10 WHITE Now look at the 2nd color band and match that color to the same chart. Write this number next to the 1st Digit. The Last color band is the number you will multiply the result by. Match the 3rd color band with the chart under multiplier. This is the number you will multiple the other 2 numbers by. Write it next to the other 2 numbers with a multiplication sign before it. Example: 2 2 x 1,000. To pull it all together now, simply multiply the first 2 numbers (1st number in the tens column and 2nd in the ones column) by the Multiplier. Reference 2 On Line Source for Kirchoff s Rules: Calculate the circuits by Kirchoff's Rules with loop method: Introduction how to use Kirchoff s rules: Before talking about what a multi-loop circuit is, it is helpful to define two terms, junction and branch. A junction is a point where at least three circuit paths meet. A branch is a path connecting two junctions. In the circuit below, there are two junctions, labeled a and b. There are three branches: these are the three paths from a to b. Multi-loop circuits In a circuit involving one battery and a number of resistors in series and/or parallel, the resistors can generally be reduced to a single equivalent resistor. With more than one battery, the situation is trickier. If all the batteries are part of one branch they can be combined into a single equivalent battery. Generally, the batteries will be 15
16 16 part of different branches, and another method has to be used to analyze the circuit to find the current in each branch. Circuits like this are known as multi-loop circuits. Finding the current in all branches of a multi-loop circuit (or the emf of a battery or the value of a resistor) is done by following guidelines known as Kirchoff's rules. These guidelines also apply to very simple circuits. Kirchoff's first rule: the junction rule. The sum of the currents coming in to a junction is equal to the sum leaving the junction. (Basically this is conservation of charge) Kirchoff's second rule: the loop rule. The sum of all the potential differences around a complete loop is equal to zero. (Conservation of energy) There are two different methods for analyzing circuits. The standard method in physics, which is the one followed by the textbook, is the branch current method. There is another method, the loop current method, but we won't worry about that one. Reference 3 On Line Source for Pspice: 16
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