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Theveninís Theorem and Maximum Power Transfer

 

Introduction

A two terminal network resistive network can be replaced by a voltage source in series with an equivalent resistor. The value of the source voltage equals the open circuit voltage of the two terminals under consideration. The value of the equivalent resistor equals the resistance measured between the open terminals when all the sources of the circuit are deactivated (voltage source shorted and current source opened). This is termed as the Theveninís theorem. The voltage source is called Theveninís voltage (VTH) and the equivalent resistor, the Theveninís resistance (RTH).

The maximum power output to a variable output resistance occurs when the value of the outputresistance equals the Theveninís resistance.

 

Figure 1: Maximum power output condition

The value of the maximum output power or transferred power is given as,

 

Objectives

1. To construct Theveninís equivalent using Workbench.

2. To verify the equivalent obtained in step 1 using hardwired components.

3. To determine maximum power transfer condition experimentally.

Step 1: Construct the circuit given in Figure 2 on Multisim Electronics Workbench.

Step 2: Remove the load resistor RL and connect a multimeter (or voltmeter) to read the open circuit voltage between A and B. Simulate and record the voltage. This is VTH for this circuit between A and B.

Step 3: Remove the 10-V source. Replace it by a short circuit.

Step 4: Remove the 5-V source. Replace it by a short circuit.

Step 5: Connect a mutimeter in the resistance measurement mode between A and B. Run the simulation and record the value of the resistor. This is RTH in Figure 1.

Table 1: Simulation results for Theveninís voltage and resistance

  VTH   RTH  
Simulated Measurements   7.6758V 6.7092kOhm

 

Step 6: In the circuit of Figure 2 connect a variable resistor (RL) between A and B.

 

 

Step 7: Vary RL between 2.5 kOhm to 10.5 kOhm in steps of 1 kOhm . Measure voltage between A and B (VL) in each case. Enter your results in Table 2.

 

 

Table 2: Measured results for maximum power transfer

RL(kOhm )   2.5   3.5   4.5   5.5   6.5   7.5   8.5   9.5   10.5  
VL   2.080 2.625 3.073 3.447 3.765 4.037 4.274 4.481 4.664
PL   0.43 0.49 0.525 0.54 0.545 0.543 0.538 0.528 0.518

 

Step 8: Plot RL vs. PL

 

Questions:

1) At what value of RL the maximum value of PL occurs in the graph?

At RL=6.5kOhm the value of PL is maximum



 

2) How does this value of RL compare with RTH you obtained through Workbench?

 

3) Draw the Nortonís equivalent of the circuit in Figure 1.

 

4) Suppose you did not know the Theveninís equivalent circuit, what procedure would you follow in the laboratory to get the Nortonís equivalent?


Date: 2015-02-03; view: 1120


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