EGR 214 Lab Experiment 7

 

Theveninís Theorem

 

Lee C. Groeneweg

&

Steve Adamczyk

 

Date: February 25, 1998

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Objective:

 

 

Materials:

1 Ė Heath Circuit Design Trainer (CDT)

1 Ė Digital Multimeter (DMM)

3 Ė ľ W resistors with values to be selected in lab

1 Ė Multi-turn potentiometer ("pot") with value to be selected in lab

Miscellaneous leads and connectors

 

 

 

 

 

 

 

In this lab the circuit to be considered for analysis will be resistive with a single independent voltage source. For a circuit with "output " terminals designated a and b, the Thevenin equivalent will replace the circuit at these terminals as shown in Figure 1.

 

In this lab we will determine the Thevenin equivalent circuit using both analytical and experimental methods. Analytically, the Thevenin equivalent circuit can be found as follows:

  1. Find the open circuit voltage at the terminals a and b.
  2. De-activate (that is, de-energize) all independent sources (but not the controlled sources) in the circuit. Independent sources are replaced with shorts and independent current sources are replaced with opens to deactivate them.
  3. With all independent sources deactivated, "look back" into terminals a and b and calculate the equivalent resistance, RT.
  4. The Theveninís equivalent circuit is then an independent voltage source with a voltage equal to the open circuit voltage in series with the Theveninís equivalent resistance.

 

We apply the above steps for the circuit shown in Figure 1. The open circuit voltage can be found by applying the voltage divider rule:

 

Voc = Vs * R2 / (R1+R2)

 

The Theveninís equivalent impedance can be found by deactivating the source and looking back into terminals a and b as shown in Figure 2. The Theveninís equivalent resistance can then be calculated by simply adding the resistance of R3 to the resistance of the parallel combination of R1 and R2. Part of this experiment is to verify that the two parameter Theveninís equivalent circuit is indeed equivalent to the original circuit.

 

 

 

In the first procedure we were to measure the values of the resistors used in this lab. These values are located in Table 1.

 

Resistor

Resistance

R #1

2002 W

R # 2

 

3545 W

R #3

4252 W

Table 1. Resistor values used in this experiment.

 

In the second procedure we were asked to calculate the theoretical values of VNl

and RT for the circuit in Figure 1. The formula used to calculate the value of VNL and R T are as follows:

VNL = Vs * R2 / (R1+R2) & RT =R3 +R1 // R2

In the third procedure we were asked to find a suitable resistive load RL for our circuit. That means to determine a value for RL such that the current flow through RL from terminal a to b causes the voltage from terminal a to b to drop to around one-half of the no-load value.

The fourth procedure required us to set up the circuit of Figure 1 using the resistor values we have selected. We were to set the value of V to the value we had selected.

In the fifth procedure we were to measure and record VNL. Apply the load RL we had selected to the terminals of our circuit and determine D V and D i. We were then to calculate the Theveninís resistance. RT = D V/D I. These values are found in Table 2.

 

VNL (calculated) = 3.2037 V

VNL (measured) = 3.204V

RT (theory) = 5531.446 W

RT (calculated) = 5555.446 W

D V = 1.6 Volts

D I = .288 mA

Table 2. Voltage and Resistance values calculated and measured.

 

Procedure Six asked us to compare the calculated theoretical and measured values of VNL and RT for our circuit.

Procedure Seven asked us to replace the actual circuit used in the previous three steps with the Thevenin equivalent circuit. We were to use a multi-turn "pot" for RT . These values are found in Table 3.

 

 

 

 

 

 

 

 

VT = VNL

VL

RT

3.201 Volts

1.609 Volts

5555.40 W

Table 3. Voltage and Resistance values when using the "pot"

 

In the eighth procedure we were to load the Thevenin equivalent circuit with the same load RL used in step 5 and compare the values of D V measured in step 5 with the values measured here.

In the final procedure we were asked to find the Thevenin equivalent of:

 

    1. DMM when it is set as a voltmeter with V scale = 20 V.
    2. DMM when it is set as an ammeter with I scale = 20 mA.
    3. DMM when it is set as an ohmmeter with R scale = 20 kW .

 

These results are explained in the conclusion.

In this experiment we learned to use Theveninís equivalent circuit theorem as applied to an actual circuit. We first set up a circuit with three known resistors and a voltage source. From this circuit we calculated the open circuit voltage, Voc and the Thevenin equivalent resistance, RT . Measuring VNL and RT with the DMM revealed values matching those calculated. Using the potentiometer to create the Thevenin equivalent circuit showed us that the same values could be obtained when the circuit was given the same load.

The last procedure of this experiment involved measuring the VNL and RT of a DMM set to measure voltage, current and resistance. We found that the RT is very large when measuring voltage or resistance and the voltage is zero when the DMM is set as a voltmeter or ammeter.

This lab experiment gave us hands on experience using Theveninís Theorem to analyze a real circuit and showed us the limits of the DMM.