EXP. 1.2 - DC CIRCUITS - THEVENIN EQUIVALENT CIRCUIT

Before you come to class

1. Read carefully the Horowitz/Bill references for this experiment.

2. Read carefully these experiment inssssttions.

Introduction

Linear circuits are those that contain only linear elements. Active

elements are those having a source of power within them, as opposed to

passive elements that contain no sources of power. Common linear pas­

sive elements are resistors, capacitors and inductors. The common

flashlight battery or a regulated power supply are linear active ele­

ments. Circuits containing linear elements can be put into simpler form

for numerical circuit analysis by using well-known theorems for series

and parallel passive elements, and by using Thevenin's theorem and/or

Norton's theorem for active circuits. Electronic power supplies and

function generators are examples of linear active circuits.

In this experiment, we shall study the function generator as an ex­

ample of an active circuit.

A linear active circuit (assumed to have only 2 terminals) is defined

as any circuit whose terminal voltage, V, is a linear function of the

current, I, that flows out of one terminal and into the other. The cir­

cuit may be either a DC, or an AC, circuit. In the next experiment we

study AC circuits in detail. The function generator delivers AC voltage

and current (at fairly low power), but it has been designed not to dis­

play any internal capacitive or inductive effects in its output charac­

teristics, usually found in AC circuits.

Thevenin's Theorem

A simple circuit consisting of a constant amplitude voltage, of magni-

tude VTh (the Thevenin voltage), in series with a resistance RTh (the

Thevenin resistance) is the electrical equivalent of any linear active

circuit, provided that:

Voc = the open circuit terminal voltage (output current I

the short circuit terminal current (terminal voltage V

0)

[This current is also called the Norton current in the Norton theorem.]

RTh = /Voc / Iscl = the magnitude of the (-) slope of the V-I graph.

R(Thevenin) Vout

v

LOAD;Slope = m = L1V/L1I=~

10

Current (I)

Figure: Thevenin equivalent circuit and Voltage (V) vs. Current (I) graph.

EXP. 1.2 Thevenin equivalent circuit for function generator

1. Connect the signal generator output to one DO channel input, using a

coaxial cable with dual banana plug terminals. Be sure to connect

the GROUND (cable shield) banana plugs to the COMMON output terminal

of the function generator, and to the GROUND input of the DO.

2. Display a I-kHz sine waveform on the DO. Use 1 V/DIV, on the DO. Use

AC input so that the function generator OFFSET control can be ig-

nored. Display a large number of cycles to permit easy peak-to-peak

voltage measurements.

3. Set up a suitable table for measured, and for calculated, data. Re­

cord ALL pertinent data - name, date, station, equipment informa­

tion, etc., and measured data.

4. Adj ust the function generator for an 8. 0 V peak-to-peak vol tage.

This is your value of Voc. (The DO input resistance is 1M ohm, which

draws negligible current, for our purposes.) Keep the 8.0 V peak-to­

peak output fixed as the frequency is varied during the complete

course of this experiment, by making adjustments of the frequency

generator output.

5. Set the decade resistor to 2,000 ohm. Do not at any time decrease

the decade box resistance below 100 ohm. Then connect it to the

function generator, using a second dual banana plug coaxial cable.

This places the resistor in series wi th the Thevenin equivalent

vol tage and the Thevenin resistance of the function generator. It

keeps the DO as a voltage measuring device, measuring the terminal

voltage of the function generator.

6. Adjust the decade resistor to a value that makes V = 4.0 V, equal to

one-half of the open-circuit voltage. Justify in mathematical form

that this value of the decade resistor equals the Thevenin resis­

tance. [This measurement method is a quick way to measure the Theve­

nin resistance provided that the circuit is capable of delivering

the current that is required at this load resistance.]

7. To prove that the function generator is a LINEAR device, take data

for a terminal voltage-versus-current graph.

7.1 Suggestion: Take data for peak-to-peak voltages equal to 7.0 to 1.0

volts, in steps of 0.5 V adjusting the decade (load) resistance RLoM

to give each of these values. Use the data to calculate respective

currents I with I=V/RLoM •

7.2 Plot the voltage-current graph, current on the horizontal axis. By

drawing two estimated l-standard deviation separated slopes on your

data, calculate the slope for this graph and the error on the slope.

Determine the Thevenin resistance from the slope.

7.3 Include the Thevenin circuit with your data.

8. Write a summary of your experiment. See end of this section for

guidelines.

Final comment: This experiment shows you the important fact that the

output voltage amplitude of your function generator depends upon how

much current your circuit draws from the generator. For DC circuits, the

current will change only when the load resistance is changed. For AC

circuits, the load impedance often depends upon frequency, and so fre­

quency changes, alone, will cause the function generator output current

and output voltage to change. You are, therefore, cautioned to monitor

the function generator output voltage in all experiments.