Experiment #6. Thevenin Equivalent Circuits and Power Transfer

Transcription

1 Experiment #6 Thevenin Equivalent Circuits and Power Transfer Objective: In this lab you will confirm the equivalence between a complicated resistor circuit and its Thevenin equivalent. You will also learn about matching loads to maximize power transfer. * Equipment list : 1. MB Board and components 2. Multimeter 3. Xplorer handset 4. Resistors various values between 100Ω and 5 kω. I.) Thevenin Equivalent (85 points): Construct the circuit shown in figure 1. Use R1=R4= 10 kω and R2=R3=1kΩ. Various values of resistance will be used for R load. To connect the different loads use the multipurpose socket in the component s board. In this experiment, we will consider the Thevenin equivalent for the circuit composed of R1, R2, R3, R4 and the 9V source. R load is the load and is not part of the circuit to be replaced with a Thevenin equivalent circuit. By the way, this configuration is called a bridge circuit. Install a 100Ω resistor for R load, then measure the voltage between the points a and b and measure the current I load which passes through R load. To perform these measurements use the Xplorer handset unit. How should the amp meter be connected?. How should the voltmeter be connected?.. Page 1 of 5 10/03/14

2 Change the value of R load and complete the table below. Note that R Load = Ω is accomplished by leaving an open circuit between point a and b. The current through the infinite load resistance will be 0 ma as already entered for you in the table. For the case of R load = 0Ω, put a wire between points a and b for a short circuit. In this case, the voltage between a and b will be 0 V as shown in the table. Table(1) R load (Ω) I load (ma) V ab (volts) infinite (open circuit = OC) 0 V OC : 0 (short circuit = SC) I SC : 0 Using MATLAB plot the data from the table above on a graph of V ab (y-axis) vs. I load (x-axis) for all values of Rload and attach the plot to this report. What type of curve fits the data? What is the slope of the plot (include the right units)? Now disconnect R load and the power supply from your circuit. Replace the branch of the circuit that had contained the power supply, Vs, with a short circuit. Using the ohm meter measure the resistance between the points a and b. R(ab) =.. How does this value of resistance compare numerically to the slope of the plot in step 5? Now try to decide how to select values for the components of the Thevenin equivalent circuit shown in Figure 1, so that the equivalent circuit will produce the same effect as the original circuit. That is, the two circuits should produce the same values of V ab and I load for any of the given load resistors. Think about this problem for a few minutes before continuing. Page 2 of 5 10/03/14

3 Do you have all the data to sketch the Thevenin s equivalent circuit? You only need to determine the two unknown values, R Th and V Th, to establish the Thevenin equivalent circuit in Figure 1. Think through the following questions: Referring to table 1, what is the value of V ab when no load resistor is connected between points a and b, i.e. when R load = Ω? Now considering the original circuit in Figure 1, how is V Th related to this value of V ab when no load resistor is connected between points a and b, i.e. when the load is open circuited? You ve just used one of the data points from table 1, the open circuit point, to figure out one of the unknown values of the Thevenin equivalent circuit, V Th. Now let s use another data point to figure out the other unknown value, R Th. Determining R Th turns out to be simplest if we now consider the short circuit data point. Again looking at Figure 1, how much current will flow between points a and b if we short circuit them, i.e. if R load = 0 Ω? Solve this relationship for R Th and use numerical values for the short circuit current from Table 1 to determine the value of R Th. Record your values for the Thevenin equivalent circuit elements below: V Th =.. R Th =.. Draw the schematic of your Thevenin equivalent for the original circuit. It should be in the form of one resistor (R Th ) and a voltage source (V Th ). Locate the points a and b in your new schematic. Page 3 of 5 10/03/14

4 Connect the circuit using component values you have calculated and reconnect R load between the points a and b. Your new circuit should look like the circuit in figure above. To adjust the value of the equivalent Thevenin voltage, use a variable DC power supply and connect to the board of the MB circuit board using alligator clips. Measure the voltage between the points a and b and measure the current I load which passes through R load utilizing the same set up as you used with the original circuit. Record the values of the current I load and the voltage V ab for different load resistors and fill the following table. Table(2) R load (Ω) I load (ma) V ab (volts) infinite (open circuit = OC) 0 V OC : 0 (short circuit = SC) I SC : 0 Now using MATLAB plot the data from the table above on a graph of V ab (y-axis) vs. I load (xaxis) for all the values of Rload and attach the plot to this report. It is best if you can plot this data and the data from your data of the original circuit on the same axes, i.e. two curves on the same graph. Don t forget to use a legend or another method to indicate which curve is which. How do the two set of data from compare? Are the two circuits equivalent? Comment on the differences. (Required) Page 4 of 5 10/03/14

5 II.) Load Matching for Maximum Power Transfer (15 points) : Using the data from Table 2, calculate the power delivered to the load resistor for each value of Rload, and enter the data below. Table(3) R load (Ω) P L (mw) infinite 0 Now plot this data from the Table 3 on a graph of P L (y-axis) vs. R load (x-axis). From your plot, what value of R load gets the most power?. Rload, max power= How is this value of load resistance related to the resistance values in the original circuit or the Thevenin equivalent circuit? If you wanted to make a single type of measurement for each resistance value to verify the power transfer was maximized, what could you measure? Hint: Don t just think about electrical measurements only. Page 5 of 5 10/03/14