Lab #4 Thevenin s Theorem

Transcription

1 In this experiment you will become familiar with one of the most important theorems in circuit analysis, Thevenin s Theorem. Thevenin s Theorem can be used for two purposes: 1. To calculate the current through (or voltage across) a component in any circuit, or 2. To develop a constant voltage equivalent circuit which may be used to simplify the analysis of a complex circuit. Any linear one-port network can be replaced with a single voltage source in series with a single resistor (see Figure 1 below). The voltage source is called the Thevenin equivalent voltage, and the resistor is called the Thevenin equivalent resistance. What this means is that a single voltage source and series resistor will behave identically to the actual part of the circuit it is replacing. In this experiment, you will use Thevenin s theorem to solve a complex DC circuit. Figure 1 A network replaced with its Thevenin equivalent circuit 4-1

2 The steps used for Thevenin s Theorem are listed below: Step 1 Remove the resistor (R) through which you wish to calculate the current or across which you want to know the voltage. Label these terminals (where the resistor was removed) a and b. Calculate the voltage across these open terminals. This is called the open circuit voltage or the Thevenin equivalent voltage, V. + V íã Step 2 From the open terminals, ( a and b ) calculate the resistance looking back from the open terminals with all voltage sources removed and replaced by their internal resistances (if R Internal = 0, replace the voltage source with a short). This resistance is R. R Now we have the components we need to create the Thevenin equivalent circuit as shown below using the Thevenin equivalent voltage and resistance values calculated above connected in series with the load resistor as shown below. 4-2

3 Step 3 The current (through R) you wish to calculate will be: I R V = R + R and the voltage across R will be: V R = I () R V = R () R + R where: V is from Thevenin equivalent voltage obtained in Step 1, R is the Thevenin equivalent voltage obtained in Step 2, and R is the value of the resistor removed in Step 1. Instructional Objectives 4.1) To work through the procedural steps involved in Thevenin s theorem. 4.2) To verify the values obtained by measuring them using the digital multimeter. 4.3) To construct a Thevenin equivalent circuit. Procedure a) Connect the circuit in Figure 2. We will use Thevenin s theorem to find the current through R3. Figure 2 b) Measure the current through R3 and the voltage across R3. Record them: IR3 = (meas) VR3 = (meas) c) You will now use Thevenin s Theorem to calculate the current through R3, by following the steps outlined in the introduction. SHOW ALL WORK in the space provided. Record the results for each step in the space provided. 4-3

4 Referring to Figure 3, which is Figure 2 with R3 removed, calculate V in Figure 3, showing all work. Figure 3 V = (calc) d) Verify the actual Thevenin equivalent voltage by measurement: Construct the circuit in Figure 3, and measure and record V. V = (meas) 4-4

5 e) Construct the circuit in Figure 4, which is the circuit in Figure 2 with R3 removed and the 12 V source replaced by a short circuit (a dead voltage source). Calculate R in Figure 4, showing all work. Figure 4 R = (calc) f) Verify your R calculation by measurement. Connect Figure 4, and measure and record the equivalent resistance (R ) measured between terminals a and b. R = (meas) g) Draw below the Thevenin equivalent circuit, using your calculated values for V and R. This diagram is Figure

6 h) Calculate IR3 using the Thevenin equivalent circuit (the V and R you found above). V I = R + R i) Compare the current measured in step 1b (original circuit) and the current calculated in step 3 above (which used Thevenin s Theorem). If they are not reasonably close, find the reason for the discrepancy). j) Build the circuit of Figure 5. Obtain a resistor for R as close as possible to its calculated value (or use a potentiometer or a decade box, whose value you can set equal to R ). k) Measure the current through R3 and the voltage across R3 in the circuit of Figure 5. Record them: IR3 = (meas) VR3 = (meas) l) Compare these measured results with the results of part b (the original circuit). If the results are not close, find the reason for the discrepancy. 3 Post Lab Questions 1. What is meant by the word "equivalent" in Thevenin Equivalent circuits? 2. What is the practical value of Thevenin Equivalent circuits? Give several practical applications in which Thevenin Equivalent circuits are used. 3. For the following circuit, use Thevenin s theorem to find the current through R. Show the Thevenin equivalent circuit you used and the values of R th and V th you obtained. 4-6

7 Name: Section: Pre-Lab #5: Digital Oscilloscope Figure 5.0: Oscilloscope Screen for Problem The oscilloscope screen displayed in Figure 5.0 has the following properties: V/div setting = 1V/div S/div setting = 1mS/div a) What is the frequency of the signal? b) What is the trigger level setting on the oscilloscope? c) What is the slope setting on the oscilloscope? d) Recalling trigonometry, the equation of a wave of this nature is given as v(t) = V max sin(ωt) + V dc. Therefore, what is the equation of the above wave? 2. What does a 10:1 oscilloscope probe do? 4-7