measurement and instrumentation lab 1

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Mompati Letsweletse 201100183 eeb 316 lab report

FACULTY OF ENGINEERING AND TECHNOLOGY

DEPARTMENT OF ELETRILICAL AND ELECTRONICS ENGINEERING

EEB 316: ELECTRILICAL MEASUREMENT AND INSTRUMENTATIONLABORATORY 1: THE OSCILLOSCOPE AND FUNCTION GENERATOR

MOMPATI LETSWELETSE

ID NO: 201100183

LAB PARTNER: KEVIN DINTWA

ID NO: 200501164

GROUP A

DATE OF EXPERIMENT: 22-06-2013

DATE OF SUBMISSION: 13-09-2013STEADY STATE RESPONSE FOR RCNETWORKS


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OBJECTIVES

To understand the operation of the oscilloscope To understand the operation of the signal generator To verify the input-output relation of the first order element

INTRODUCTION

ABSTRACT

the main purpose of the experiment was to get student to learn how to use the oscilloscope

together with the function generator and it was very important because student got to learn how to

operate the two instruments. The other objective was to verify the input-output relation of a first

order element by using the RC circuit systems whose input-output relationship is afirst order

Differential equation.The above circuit was used in the experiments as analysis. The functional

generator was used to give the input AC with the frequency varied from 340hz to 3800hz.The inputand output signals were displayed in the the oscilloscope hence comparison was made between the

phase(output voltage and input voltage). Here is some brief explanation of how the oscilloscope and

function generator work in general. From performing this experiment very well students learn a lot

of engineering skills apart from the fact that they got to know the basic function of an oscilloscope

and functions generator some other engineering principles such as reading the phase shift and

presenting well the data gathered.

OSCILLOSCOPE

An oscilloscope is a type of electronic test instrument that allows observation of constantly varying

signal voltage, usually as a two dimensional graph of one or more electrical potential difference

using the vertical or y axis plotted and displayed to voltages this way. Signals are often periodic and

repeat constantly so that multiplies samples of a signal which is actually varying with time are

displayed as a steady picture. Oscilloscope are used to observe the exact wave shape of an electrical

signal, they are calibrated so that voltage and time can be read as well as possible by the eye. This

allows the measurement of peak to peak voltage of a waveform, the frequency of periodic signals

the time between pulses

In a nutshell when a signal is injected in an oscilloscope, the input signal will be used to change the

position of the beam in the y direction. The trace left behind can be used to measure the voltage of

the input signal (off-the y axis) and the duration of frequency and read of x-axis. In this experiment

the oscilloscope was used to display input voltage and output voltage for comparison of phase shifts

THE FUNCTION GENERATOR

A function generator is a piece of electronic test equipment used to generate different types of

electrical waveforms over a wide range of frequencies waveforms produced by the function

generator are sine, square, triangular and sawtooth shape. Basically it is used to test the response of

a circuit to common inputs signals .The electrical leads from the device are attached to the ground

and signal input terminal of the device under test. After being powered the output signal needs to

be configured to the desired shape. In this experiment the function generator will be used to provide

the voltage to the circuit with the oscilloscope to find waves that will be displayed in the oscilloscope


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THEORY

An RC circuit is made of different combinations of capacitors and resistors. This kind of

circuit has certain frequency response1 and thus can be used to reduce the amplitude of

signals of certain input frequencies leaving others almost unaffected. In other words RC

circuits built in different ways can allow to pass, say, low(high) frequencies cutting off

high(low) frequencies (this kind of RC circuit is called low-pass(high-pass) filter) or they can

allow to pass signals with a certain frequency range (so called band-pass filters2).

Importance of learning of this type of circuits is determined but their wide area of

applications: radio receivers, audio systems (e.g. low pass audio filter is used preselect low

frequencies before amplification in a subwoofer) and even AC generators. Frequency

dependent characteristics of RC the combined resistors and capacitors is due to the ability of

a capacitor to store charge.In this laboratory activity the response of RC circuits to

alternating voltage at different frequencies was investigated through the circuit as a function

of the frequency applied voltage .The concept of phase shift was also studied. At lowfrequencies. The capacitive reactance dominates over the resistance so the signal voltage is

dropped off mostly across the capacitance. It is as though the capacitor is offering more

effective resistance than the resistor. In the extreme case, at zero frequency, the reactance

is infinite, the current is zero, and all the voltage is across the capacitor while at high

frequencies, the capacitive reactance becomes negligible most of the Signal voltage is across

the resistor. At infinite frequency, the capacitive reactance is zero, and it is as though there

is no capacitor in the circuit, or the capacitor is shorted out. The phase angle also behaves

similarly. At low frequencies, the phase shift becomes closer to /2, as it should for a pure

capacitance with no resistance in the circuit. At high frequencies, the phase shift approaches

zero, and the circuit behaves like a purely resistive circuit. These statements are generally

summed up by saying that the capacitor acts like a block for low frequencies, but like a short

for high frequencies

The ratio of the voltages is equal to the transfer function magnitude |H(jw)|, that is:

| The phase magnitude was measured by using the difference between the input and the

output wave divided by the period of the input voltage and multiplied by 3600

that is by

using the equation

Were by is the distance between the input voltage and output voltage. In thisexperiment, the output voltage is expected to lead the input voltage because the energy the

energy storage element is a capacitor hence producing a negative phase shift.

figure 3:showing the phase shift


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EQUIPMENTS

1. Oscilloscope

2. Function Generator3. R=1 k ohm4. C=0.47 micro Farads5. Breadboard6. Small wires

PROCEDURE:

The circuit was connected as shown in figure 1 and the input signal on CH1 and the output on CH2was displayed on the oscilloscope and the input and output voltage was measured across the

capacitor using the two channels of the oscilloscope. This was done for frequency range from 34 to

34000hz

A sinusoidal input with amplitude of 5V peak to peak was selected and displayed on channel 1 andthe output signal on channel 2 of the oscilloscope

The frequency of the input signal was varied and the output changes were observed Obtained results were presented in the form of a table for the given frequency values The oscilloscope controls were set in the following manner

Time/div was set to a mid range value

TV Sep control was set off and Trigger select to AC

Input attenuator (volts/Div) control was set to (2V/cm)

Variable Time base and variable gain controls were sat to their cal position

The input coupling switches were set to DC

Intensity controls was set to mid-range to get a better view of the signal

The Y position controls for channel 1 and X position control were set to mid range

EXPERIMENTAL CIRCUIT DIAGRAM


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RESULTS

Theoretical

Table (a)

Freq

(Hz)

w

(rad/s)

Vo/Vi Vo/Vi

(dB)

Phase shift[]

34 213.63 1 0.000 -5.7

68 427.26 0.98 -0.175 -11.4

102 640.88 0.96 -0.355 -16.8

136 854.51 0.93 -0.630 -21.9

170 1068.14 0.89 -1.012 -26.7

204 1281.77 0.85 -1.411 -31.0

238 1495.40 0.82 -1.734 -35.1

272 1709.03 0.78 -2.158 -38.8

306 1922.65 0.74 -2.615 -42.1

340 2136.28 0.71 -2.975 -45.0680 4272.57 0.44 -7.131 -63.5

1020 6408.85 0.315 -10.034 -71.6

1360 8545.13 0.242 -12.324 -76.0

1700 10681.42 0.195 -14.199 -78.7

2040 12817.70 0.164 -15.703 -80.6

2380 14953.98 0.141 -17.016 -81.9

2720 17090.26 0.124 -18.132 -82.9

3060 19226.55 0.110 -19.172 -83.7

3400 21362.83 0.0991 -20.079 -84.3

6800 42725.66 0.0498 -26.055 -87.1

13600 85451.32 0.0249 -32.076 -88.5

20400 128176.98 0.0166 -35.598 -89.0

27200 170902.64 0.0124 -38.131 -89.3

34000 213628.30 0.00996 -40.035 -89.4


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-50

-40

-30

-20

-10

0

1 10 100 1000 10000 100000

Vo/Vi

(dB)

Frequency (Hz)

Vo/Vi

(dB) AGAINST FREQUENCY

-100

-80

-60

-40

-20

0

1 10 100 1000 10000 100000

phases

hift[]

frequency Hz

phase shift against frequency


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PRACTICAl RESULTS

Table b

Note also that:

dB=20Log10M(vo/vi)

SAMPLE CALCULATIONS FOR 340Hz

DB=20log10M (vo/vi)

(DB)=2Olog(

)=-2.853

=2=2 =21362.8(rad/s)

Phase shift

-0.1/6.45* 360 = --5.6degrees

Freq

(Hz)

w

(rad/s)

Vi(p-

p)

Vo(p-p)

Vo/Vi Vo/Vi

(dB)

x

[ms]

T

[ms]

Phase

shift[]

34 213.63 5 5.00 1.00 0.000 0.10 6.45 -5.668 427.26 5 4.90 0.98 -0.175 0.15 4.50 -12.0

102 640.88 5 4.80 0.96 -0.355 0.50 10.3 -17.5

136 854.51 5 4.70 0.94 -0.537 0.45 7.45 -21.7

170 1068.14 5 4.40 0.88 -1.110 0.45 6.00 -27.0

204 1281.77 5 4.20 0.84 -1.514 0.45 5.00 -32.4

238 1495.40 5 4.10 0.82 -1.724 0.40 4.10 -35.1

272 1709.03 5 4.00 0.80 -1.938 0.50 6.50 -27.7

306 1922.65 5 3.70 0.74 -2.615 0.50 6.00 -30.0

340 2136.28 5 3.60 0.72 -2.853 0.45 3.75 -43.2

680 4272.57 5 2.30 0.46 -6.745 0.60 3.50 -61.7

1020 6408.85 5 1.70 0.34 -9.370 0.40 2.00 -72.01360 8545.13 5 1.30 0.26 -11.700 0.35 1.60 -78.8

1700 10681.42 5 1.00 0.20 -13.979 0.32 1.50 -76.8

2040 12817.70 5 0.90 0.18 -14.895 0.20 0.89 -80.9

2380 14953.98 5 0.70 0.14 -17.077 0.20 0.80 -90.0

2720 17090.26 5 0.60 0.12 -18.416 0.20 0.90 -80.0

3060 19226.55 5 0.60 0.12 -18.416 0.15 0.70 -77.0

3400 21362.83 5 0.50 0.10 -20.000 0.50 2.0 -90.0

6800 42725.66 5 0.26 0.052 -25.680 0.40 1.50 -96.0

13600 85451.32 5 0.13 0.026 -31.701 0.20 0.80 -90.0

20400 128176.98 5 0.09 0.018 -34.895 0.10 0.50 -72.0

27200 170902.64 5 0.064 0.0128 -37.856 0.40 1.70 -84.7

34000 213628.30 5 0.052 0.0104 -39.660 0.40 1.60 -90.0


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-45

-40

-35

-30

-25

-20

-15

-10

-5

0

1 10 100 1000 10000 100000

VO

/VI(

DB)

Frequecy(Hz)

vi/vo(DB AGAINST FREQUECY

-120

-100

-80

-60

-40

-20

0

1 10 100 1000 10000 100000

phases

hift(0)

frequencyHz

phase shift against frequency


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ANALYSIS OF RESULTS

From the result obtained from the experiment it can be seen that inverse proportion between the

Transfer function and Frequency i.e. transfer function, G(s) (Vo / Vi), decreases as the frequency

increases. This strongly agrees with the hypothesis since Vo / Vi = Xc / ( Xc + R1) implies that when Vi is

kept constant and the capacitance as well as the resistance of the capacitor and resistor respectively,are fixed then the only variable that can change is the Output voltage, Vo.

Xc =1/jwC 2 f

As frequency increases, Xc decreases as illustrated above and for that reason Vo also decreases

resulting in a decreasing transfer function.

At frequencies 340 and 3400 Hz, it has been noticed that the Vo/ Vi decreased by a larger margin to

the next frequency. The capacitive reactance dominated over the resistance so the signal voltage

was dropped off mostly across the capacitance merely due to the fact that the capacitor offered

more effective resistance than the resistor. At zero frequency, the reactance was infinite, the currentis zero, and all the voltage is across the capacitor while at high frequencies, the capacitive reactance

seemed to be negligible most of the Signal voltage was across the resistor. At infinite frequency, the

capacitive reactance was zero, and if there capacitor was not present in the circuit, was shorted out.

The phase angle also behaves similarly. At low frequencies, the phase shift became closer to /2, as

it was for a pure capacitance with no resistance in the circuit.

DISCUSSION

The objectives of the experiment were successfully achieved according to the results obtained which

were presented in a table and graph format. The results obtained were the expected one even

though there are some anomalous results. This awkward are due to errors encountered during the

experiment. Here are some of the errors encountered during the experiment

When making a measurement with an oscilloscope: the calibration error and the reading error. The

total error of any reading is found by combining the calibration and reading errors. Similarly the

error when setting up a waveform on a signal generator will be due to the calibration error (5%) and

a setting error, the latter is related to the scale andwidth of the cursor.compare the parameters of

a signal produced by asignal generator and that measured by an oscilloscope. In this case both the

voltage and frequency (with errors) as set on the signal generator should be compared with the

values determined by the oscilloscope. The other reason for the difference in practical and

theoretical values could be due to aging of the apparatus used, the resistors and capacitors when

measured could not give their exact values marked on them. There is also an element of parallax

error, but this was minimized as much as possible to get the exact values displayed.

Care was taken to ensure correct values were obtained, check if the circuit was connected correctly

& that controls of oscilloscope and the function generator were used properly.

Based on the concept of the transfer functions, one can get a clear understanding of the results.

Because this experiment proved theory, it would help to explain, why the transfer function

decreases as the frequency increases.

The method of measurement used is useful and relevant in that it allows students a physical

contact with apparatus used and this would go a long way in helping them get the necessary skills

of operating them.


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M ti L t l t 201100183 b 316 l b t

RECOMMENDATION

This experiment can be improved to help students apply their theory into practice byensuring that each student is assigned to his/her own workstation, and does the experiment

alone to ensure maximum gaining of engineering concepts and principles avoid a situations

where some students just become passengers during the experiment thereby hindering

them from understanding and relate theory with the practical and even get the knowledge

of using the apparatus hands on.

The other improvement is that student should have a clear lecture before the experimentfor them to appreciate how they should handle the experiment also to avoid spending hours

figuring how to build circuit

Also the equipments should be replaced because of aging especially the oscilloscopesbecause they make it very difficult for the student to read displayed signals

CONCLUSION

The objectives of this experiment have been almost met. It has been discovered that the

oscilloscope, when used with the function generator is a very important device in electrical

and electronic engineering. The controls and operation of the oscilloscope and the function

generator have been learnt and understood. From the experiment, it has been shown that

the ratio of the output voltage to the input voltage varies according to the frequency. while

the output voltage was kept constant, the decibel was directly proportional to the output

voltage. The phase shift increased with a decrease in the output voltage.

REFERENCES

[1] J. Abel and D. Berbers, Signal Processing Techniques for Digital Audio Effects,

http://ccrma.stanford.edu/courses/424/, 2005.

[2] A. Farina, Simultaneous measurement of impulse response and distortion with a swept-sine

Technique, Audio Engineering Society Convention, vol. Preprint 5093, Feb. 2000. 6.

[3] Tektronix XYZs of Oscilloscopes.

Online: http://www.tek.com/Measurement/App_Notes/XYZs/03W_8605_2.pdf.

Last accessed: August 29th 2013S

[4] Osilloscope Wikipedia.Online: http://en.wikipedia.org/wiki/Oscilloscope#X-Y_mode

Last accessed: September 7th 2013

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