Exercise 1: Thevenin to Norton Conversion

Transcription

1 Exercise 1: Thevenin to Norton Conversion EXERCISE OBJECTIVE When you have completed this exercise, you will be able to convert a voltage source to a current source. You will verify your results by comparing calculated and measured data. DISCUSSION You can simplify a network by applying Thevenin s theorem. Thevenization of a network results in an equivalent constant voltage source. The voltage source in the Thevenin equivalent circuit (V TH ) works through the Thevenin resistance (R TH ) to generate a load voltage (V RL ) and current (I RL ) identical to that generated by the network. To convert the Thevenin voltage source to a constant current source, you must apply a conversion method. N of the current source equal to R TH of the Thevenin equivalent circuit. 226 Festo Didactic P0

2 The next step is to apply Ohm s law to determine I N of the current source. I N equals V TH /R TH of the Thevenin equivalent circuit. PROCEDURE In this procedure, the Thevenin equivalent circuit is derived from the network illustrated. Locate the THEVENIN/NORTON CONVERSION circuit block, and connect the circuit shown. Adjust the positive variable supply to 7.95 Vdc. What is the open circuit (no-load) output voltage of the Thevenin equivalent circuit? V O(NL) = (Recall Value 1) Vdc Festo Didactic P0 227

3 Use a two-post connector to add R L to your circuit. What is the load voltage? V RL = (Recall Value 2) Vdc Why are the unloaded (V O(NL) ) and loaded (V O(L) ) circuit output voltages different? a. The load forms a voltage divider with R TH. b. TH when the load is removed. c. The load causes a voltage drop across R TH. d. All of the above What does the output voltage of a Thevenin equivalent circuit equal if its output terminals are shorted together? a. V TH b. V RTH c. V RL d. None of the above 228 Festo Didactic P0

4 Move the R L two-post connector to place a short circuit across the output terminals of the Thevenin equivalent circuit. Based on your readings, does V TH equal V RTH, and does the Thevenin output terminal equal 0? a. yes b. no Based on a Thevenin open-load output terminal voltage of Vdc (Step 2, Recall Value 1), what is the Norton equivalent circuit current? I N = V TH /R TH I N = ma (Recall Value 3) N and R L are connected into your circuit. Festo Didactic P0 229

5 Measure the voltage across parallel resistors R N and R L. Use Ohm s law to determine the value of I N. I N = ma (Recall Value 4) Remove R L from your constant current circuit. Does the value of I N change? a. yes b. no Are these circuits equivalent in terms of their effect on the load resistor? a. yes b. no 230 Festo Didactic P0

6 CONCLUSION The Thevenin and Norton equivalent circuits of a network generate the same load voltage and load current as the network circuit does. When the output terminals of a Thevenin voltage source circuit are shorted, the constant current equals the Thevenin voltage divided by the Thevenin resistance (I N = V TH /R TH ). In the conversion process between Thevenin and Norton circuits, R N equals R TH. The output voltage of a voltage source is zero when the output terminals are shorted. REVIEW QUESTIONS 1. The open circuit (no-load) current of a Norton current source (I N ) equals a. the maximum current of a Thevenin equivalent circuit. b. V TH /R TH. c. All of the above d. None of the above 2. In a Thevenin equivalent circuit, R TH is Therefore, a. the series resistance of the Norton equivalent circuit is b. the shunt resistance of the Norton equivalent circuit is c. the series/parallel resistance of the Norton equivalent circuit is d. None of the above Festo Didactic P0 231

7 3. When a Thevenin equivalent circuit is converted to its Norton equivalent, the current direction of I N a. does not matter. b. should be opposite to the direction of the current caused by V TH. c. depends on how the load is connected to the circuit output terminals. d. should be the same as the direction of current caused by V TH. 4. If the load is removed from the output terminals of a Thevenin equivalent circuit, the circuit output voltage a. increases to V TH. b. does not change. c. decreases. d. reduces to zero. 5. If the output voltage of a Thevenin equivalent circuit is 0 V, the a. load is open. b. load current is properly connected. c. load is shorted. d. 232 Festo Didactic P0