Section #020
Experiment #:1
Date performed: Wednesday, June 17, 2009
Date due: Wednesday, June 24, 2009
The Oscilloscope
Principal investigator:
Skeptic:
____________________________________________________
Researcher
____________________________________________________
TA
Role
___________________________________________________
Kreswell Neely
I
DC
AD
I introduction
DC data and calculation
AD analysis and discussion
RC results and conclusion
Q1/Q2 quiz/prelab
PI principal investigator points
PG personal grade
RC
Q1
Q2
PI
PG
The Oscilloscope
The Oscilloscope | 6/18/2009
PHY 213 – Lab 1
1
UNIVERISTY OF KENTUCKY
2009
Authored by: Tuoxin Cao / Terpsichore Lindeman
The Oscilloscope
PHY 213 – Lab 1
INTRODUCTION ............................................................................................................ 3
EXPERIMENTAL LOG................................................................................................. 4
TABLE 1 ............................................................................................................... 4
METHOD, DATA, AND CALCULATIONS ........................................................................... 5
PART A .................................................................................................................... 5
TABLE 2 ............................................................................................................... 5
PART B .................................................................................................................... 6
DATA ........................................................................................................................ 6
TABLE 3 ............................................................................................................... 6
PART C .................................................................................................................... 8
TABLE 4 ............................................................................................................... 8
DISCUSSION AND ANALYSIS ........................................................................................ 10
ERROR PROPAGATION ............................................................................................... 11
TABLE 5 ................................................................................................................ 13
TABLE 6 ................................................................................................................ 14
PERCENT DIFFERENCE ............................................................................................... 18
PERCENTAGE OF ERROR ............................................................................................. 19
RESULTS AND CONCLUSIONS ...................................................................................... 21
RESULTS ................................................................................................................... 21
RESULTS PART A ...................................................................................................... 21
RESULTS PART B ...................................................................................................... 21
NUMBER LINE PART B ................................................................................................ 22
RESULTS PART C ...................................................................................................... 23
SINE WAVE EMITTING AT 250HZ ................................................................................. 25
NUMBER LINE 4 ......................................................................................................... 26
SQUARE WAVE EMITTING AT 250HZ............................................................................ 26
CONCLUSIONS ............................................................................................................ 27
WORKS CITED ............................................................................................................ 28
APPENDIX ( RAW DATA).............................................................................................. 29
The Oscilloscope | 6/18/2009
Contents
2
Introduction
The aim of this lab is to familiarize one with the oscilloscope which is
critical to subsequent laboratory exercises.
In this experiment, the output of a frequency generator was observed on
the screen of an oscilloscope. Two different types of graphical displays of
voltage, waves, are observed during the course of the experiment. A sine wave
and a square wave graphical representation of voltage were observed. A sine
wave is fluid when observed and (Lenk, 1997) where as a square wave is not
fluid.
This was a three part laboratory exercise. Firstly, the dynamic range was
determined. Secondly, it was observed and determined that the voltage and
specifically the root-mean square voltage is independent of the frequency it is
emitted at. Lastly, the time was determined from observing the frequency as
represented on the oscilloscope at 2 different frequencies but at two different
types of waves, sine wave and square wave. Determining the frequency from
the time measurements collected from the oscilloscope was done, and in turn
from these calculations it was established that wave functions do not affect the
frequency emission value nor the period observed on the oscilloscope.
One of the major advantages of using an oscilloscope is its capabilities (Fogiel,
2002)to provide large quantity of information about the signal that is being
measured as opposed to other devices. When analyzing a current, one can
actually “see” if the shape of the voltages’ frequency is the one expected! The
oscilloscope not only allows us to obtain quantitative but also qualitative
measurements!
Objective
The Oscilloscope | 6/18/2009
Familiarize one with the oscilloscope and help understand its various functions
and applications.
3
Experimental Log
Equipments used for this laboratory are noted below in the table of materials
used.
Table 1
Materials Used
Oscilloscope – TDS 1002 Tektronix PHY213OSC015
Frequency Generator- Tenma 72-7210 FG21318
TI 84 Plus Calculator
Laboratory Manual PHYSICS 213
Steven L. Ellis
Writing materials to record data
The equipment was set up for the experiment prior to arrival at the physics
laboratory. Reading materials are provided including experimental procedure.
The experiment was carried out following the procedure as state in the
laboratory manual, however the cursor on oscilloscope was used to assist read
the information of interest, including the data recorded.
As a two person group, we worked on the data individually as a whole in order
to create the foundations for this report and exchanged documents with each
other on June 18th 2009, and on June 19th 2009, we met at the Young Library
to complete the lab report and combine our outlines and elaborate our findings
ensuring that all components required were present.
The Oscilloscope | 6/18/2009
There were various books that were referenced in order to further understand
the workings of the oscilloscope and in order to help us identify and verify the
finding of this laboratory and to further understand the difference between
both types of waves observed and how those different waves are applicable in
everyday situations or specialized areas of interest.
4
Method, Data, and Calculations
The Raw Data recorded for this experiment is Appendix 1. Though, within this
section this three (3) part laboratory is indentified, realized and depicted, by
describing the purpose of each part of this laboratory, how the data was
collected and briefly introducing the findings of the data collected.
Part A
Method: This part of the experiment was done in order to introduce and
familiarize the generator and oscilloscope. The generator was turned on and
then the oscilloscope was turned on after checking correct connection of input
terminal. Then, various changes in the VOLTS/ DIV and TIME/DIV were made
in order to observe the effects of these various changes. Finally the volts/div
and time/div knobs were adjusted to their smallest values and then to their
largest values. Through the experiment, the frequency generator has been set
to a constant output. Results have been recorded. Below is the table of
findings.
Data
Table 2
The Oscilloscope | 6/18/2009
Oscilloscope Screen Readings
5
Smallest Estimate
Largest Estimate
Y- axis – Volts (V)
20 𝑚𝑉 ± 2𝑚𝑉
50𝑉 ± 5 𝑉
X-axis – Time (s)
5 ns ±0.5𝑛𝑠
50 𝑠𝑒𝑐 ± 5 𝑠𝑒𝑐
Calculation: As the indicators on the oscilloscope were separated in sector of
10 unit increments, the uncertainty derived for each value is one tenth of each
division depicted on the oscilloscope. Also from these recordings we are able to
calculate the dynamic range of the oscilloscope using the following formula:
𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑅𝑎𝑛𝑔𝑒 (𝑑𝐵) = log 20
𝑉𝑚𝑎𝑥
𝑉𝑚𝑖𝑛
Part B
Method: This part of laboratory is designed to help one identify if any changes
in the frequency of a signal directly or indirectly affect the signal reading on the
oscilloscope. In this part of the laboratory exercise the function generator was
adjusted as indicated in the laboratory manual to a sine wave of 500Hz by
hand thus patience, and precision of movement were of essence to manually
adjust the frequency. The frequency reading on the generator and the Volts
per division reading on the oscilloscope were recorded. Then peak to peak
distance of the sine wave in Y-axis divisions as volts are represented by the Yaxis and time for the X-axis by the oscilloscope. Volts/div, Y-deflection
readings were recorded from the oscilloscope.
Then, the frequency on the frequency generator was modified, and then,
Volts/div and Y-deflection were recorded once again for the new frequency and
again for the third. Three frequencies: 500Hz, 250Hz, and 100Hz were tested.
From the data recorded, the Peak voltage and the Root-mean squared voltage
were calculated. The results are shown in Table 3 below.
Table 3
TRIAL
Freq
(Hz)
Volts/div
(o’scope)
Y-deflection
𝑽𝒑𝒑
𝑽𝒑
𝑽𝒓𝒎𝒔
(divisions)
(Volts)
(Volts)
(Volts)
1
500
10𝑉
5.8 ± 0.1𝑑𝑖𝑣
58 V±1𝑉
29 V±0.5𝑉
20.5 V±0.35𝑉
2
100
10𝑉
5.8 ± 0.1𝑑𝑖𝑣
58 V±1𝑉
29 V±0.5𝑉
20.5 V±0.35𝑉
3
250
10𝑉
5.8 ± 0.1𝑑𝑖𝑣
58 V±1𝑉
29 V±0.5𝑉
20.5 V±0.35𝑉
The Y-deflection is the number of divisions from peak to peak within one
period. Each division was sub sectioned by 5 units, thus when measuring the
Y-deflection, the divisions was rounded to what seemed to be the closest sub
unit and the uncertainty for each Y-deflection measurement collected was
equal to one tenth of a unit thus:
Calculations
1
𝑂𝑛𝑒 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝑖𝑠 𝑐𝑜𝑚𝑝𝑜𝑠𝑒𝑑 𝑜𝑓 5 𝑠𝑢𝑏𝑢𝑛𝑖𝑡𝑠 𝑎𝑛𝑑 ℎℎℎℎℎℎℎℎℎ 10 𝑜𝑓 5 𝑠𝑢𝑏𝑢𝑛𝑖𝑡𝑠 𝑖𝑠 0.5
𝐻𝑒𝑛𝑐𝑒, 𝑡ℎ𝑒 𝑢𝑛𝑐𝑒𝑟𝑡𝑎𝑖𝑛𝑡𝑦 𝑓𝑜𝑟 𝑡ℎ𝑒 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡𝑠 𝑖𝑠 ± 0.5 𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛𝑠.
The Oscilloscope | 6/18/2009
Data
6
As we know that each division represents 10V and our divisions from peak to
peak of the frequency within one period is 5.8 ± 0.5𝑑𝑖𝑣 thus the voltage peak to
peak is calculated as follows:
𝑉𝑝𝑝 =
𝑉𝑜𝑙𝑡𝑠
× 𝑌 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛
The uncertainty for the peak to peak voltage is calculated below.
𝛥𝑉𝑝𝑝
𝑉𝑝𝑝
=
𝑉𝑜𝑙𝑡𝑠
𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛
𝑉𝑜𝑙𝑡𝑠
𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛
𝛥
+
𝛥𝑌−𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑉𝑝𝑝
𝑌−𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
→
𝛥𝑉𝑝𝑝 = (0 +
±0.1𝑑𝑖𝑣
5.8𝑑𝑖𝑣
) 58𝑉 = ±1𝑉
The peak voltage is half of the peak to peak voltage. Hence:
𝑉𝑝𝑝
𝑉𝑝 =
2
Since peak voltage is equal to half of peak to peak voltage then the uncertainty
𝛥𝑉𝑝𝑝
for 𝛥𝑉𝑝 is half of the uncertainty 2 though traditionally done it is:
𝛥𝑉𝑝𝑝
±1𝑉
𝛥𝑉𝑝 = (
+ 0) 𝑉𝑝 = (
) × 29𝑉 = ±0.5𝑉
𝑉𝑝𝑝
58𝑉
Also the root-mean square voltage was calculated using the formula depicted in
the laboratory manual (Ellis, Summer 2009).
𝑉𝑝
𝑉𝑟𝑚𝑠 =
√2
In turn the root-mean square voltage’s uncertainty is calculated as follows:
𝛥𝑉𝑟𝑚𝑠 =
The Oscilloscope | 6/18/2009
OR
7
𝛥𝑉𝑝
√2
=
= ±0.25𝑚𝑉
√2
= ±0.35𝑉
𝛥𝑉𝑝 𝛥𝑉𝑟𝑚𝑠 𝛥√2 𝑠𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝛥𝑉𝑟𝑚𝑠
𝛥𝑉𝑝
=
+
→
𝛥𝑉𝑟𝑚𝑠 = (
) 𝑉 = ±0.35
𝑉𝑝
𝑉𝑟𝑚𝑠
𝑉𝑝 𝑟𝑚𝑠
√2
Part C
In this part of the laboratory exercise time and frequency for both sine wave
and square wave functions were measured. Adjusting the generator initially at
500 Hz manually and the X-divisions for the sine wave to go through two cycles
and then divided that by two to obtain our actual recorded X-division
measurement. Same procedure at 500Hz for the square wave output were
measured and recorded again both the X-divisions in the same manner. In
turn the frequency was changed to 250Hz and repeated the same procedure as
previously done at 500Hz for both the sine wave and square wave functions.
Thus after recording the frequency set manually and recording measurements
of time/period we were also able to calculate the frequency and in turn
compared our calculated frequency with that of which was set at generator.
Below in the table our data is presented.
The procedures to calculate the values of data were done the same way for both
sine wave and square wave trials at all frequencies observed.
Table 4
Trial/
Freq
(Hz)
Function
Time/div
(o’scope)
X-deflection
𝑷𝒆𝒓𝒊𝒐𝒅 𝑻
𝑬𝒙𝒑′ 𝒍 𝑭𝒓𝒆𝒒.
(divisions)
(Seconds)
(Hertz)
% 𝒅𝒊𝒇𝒇.
Sine 1
500
1𝑚𝑠
2 ± 0.1𝑑𝑖𝑣
2.0𝑚𝑠 ± 0.1𝑚𝑠
500 ± 5.0𝐻𝑧
0%
Sine 2
250
2.5𝑚𝑠
1.6 ± 0.25𝑑𝑖𝑣
4.0𝑚𝑠 ± 0.25𝑚𝑠
250 ± 3.9𝐻𝑧
0%
Square 1
500
1𝑚𝑠
2 ± 0.1𝑑𝑖𝑣
2.0𝑚𝑠 ± 0.1𝑚𝑠
500 ± 5.0𝐻𝑧
0%
Square 2
250
2.5𝑚𝑠
1.6 ± 0.25𝑑𝑖𝑣
4.0𝑚𝑠 ± 0.25𝑚𝑠
250 ± 3.9𝐻𝑧
0%
The period in turn was calculated again in the same mannerism as we
calculated the peak to peak voltage.
𝑃𝑒𝑟𝑖𝑜𝑑 (𝑇) =
𝑇𝑖𝑚𝑒
× 𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
𝑑𝑖𝑣
And the uncertainty for the period is visualized below (at frequency 500Hz):
The Oscilloscope | 6/18/2009
The uncertainty for the X-deflection was done in the same manner as in Part B,
as each division had 5 subunits, the uncertainty for the X-deflection is±0.1𝑑𝑖𝑣.
8
𝑇𝑖𝑚𝑒
𝛥𝑇 𝛥 𝑑𝑖𝑣
𝛥𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑇
±0.1𝑑𝑖𝑣
=
+
→
𝛥𝑇 = (0 +
) 2𝑚𝑠𝑒𝑐 = ±0.1𝑚𝑠
𝑇𝑖𝑚𝑒
𝑇
𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
2𝑑𝑖𝑣
1
𝑑𝑖𝑣
The experimental frequency was calculated with the formula stated in the
laboratory manual (Ellis, Summer 2009) using the period obtained from the
calculations above. The formula used to calculate the experimental frequency
is stated below.
𝑓=
1
1
= −3 = 500𝐻𝑧
𝑇 2𝑒
To calculate the uncertainty of the frequency (at 500Hz) we have
𝛥𝑓 𝛥1 𝛥𝛵 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑓
𝛥1 𝛥𝛵 1 ±0.1𝑒 −3 𝑠
=
+
→
𝛥𝑓 = ( + ) =
= ±5.0𝐻𝑧
𝑓
1
𝛵
1
𝛵 𝑇 (2𝑒 −3 𝑠)2
The Oscilloscope | 6/18/2009
The same calculations were executed for both wave functions at both
frequencies observed.
9
Discussion and Analysis
In this laboratory exercise we realized, how to use the oscilloscope and
generator. We were able to “see” a frequency of electricity and from that visual
to actually gain understanding of how a signal is transmitted, analyzed and
interpreted.
Part A of this laboratory exercise was simply to familiarize one with the
functions and operations of both the generator and oscilloscope. During this
part of the exercise we simply attempted to realize the minimum and maximum
reading ranges for both time recorded and the frequency minimum and
maximum voltage output range.
As in any calculation there are uncertainties. In this part of the laboratory
exercise we determined that the maximum voltage output reading division in
frequency of the oscilloscope was 50V per division on the Y-axis/ Y-deflection.
This division in turn was composed of 5 subdivisions each representing 10V.
Thus the uncertainty for measurements in respects to voltage is half of one
subdivision which is ±5V for the maximum reading. Moreover, in the same
mannerism the minimum output range was calculated. Thus for a minimum
voltage output reading on this oscilloscope was determined at 20mV, which in
turn is composed of 5 sub-divisions of 4mV, which in turn concludes that the
uncertainty is half of one subdivision which equates to ±2mV.
In turn from these calculations we expect the following ranges of output on the
oscilloscope:
Voltage readings:
20𝑚𝑉 ± 2𝑚𝑉 ≥ 𝑋 ≤ 50𝑉 ± 5𝑉
Time readings:
The Oscilloscope | 6/18/2009
5𝑛𝑠 ± 0.5𝑛𝑠 ≥ 𝑋 ≤ 50𝑠 ± 5𝑠
10
Error Propagation
Once armed with the knowledge of range output expectation we moved forward
the second part of this three part laboratory exercise. In this exercise we were
to change the frequency settings on the generator and observe any changes in
respects to voltage output on the oscilloscope. At first instance we set the
generator at a frequency of 500 Hz, which was difficult as the generator dial to
adjust the frequency was very sensitive and was time consuming to adjust to
the desired frequency. Once the frequency was set, we collected data from the
oscilloscope. As the oscilloscope itself provides various data, we collected only
the data indicated in the laboratory manual (Ellis, Summer 2009).
Furthermore, the Voltage/division measurements were identified and recorded
and the Y-deflection measurements as indicated throughout this part of the
exercise as indicated in the laboratory manual (Ellis, Summer 2009).
As the Voltage/divisions measurements were factored we must take into
account that no internal “clock” is perfect (Tenma, p. 10). Referencing the
generator’s manufacturer’s manual we are able to identify any uncertainties in
the generator’s output to the oscilloscope.
The first and foremost dependent variable is the temperature. As the
temperature is something that was not taken into account when performing
this laboratory exercise, it will be considered a systematic error as it is an
unidentifiable value, and though due to the laboratory regulations the
temperature is to remain constant an x temperature. Thus the data provided
on the documentation from the manufacturer is quoted at a stable temperature
of ±23.5ºC which will be considered a fact or minimal factor in our error
The Oscilloscope | 6/18/2009
As per the manual the uncertainty for the output of the frequency to the
oscilloscope is ±0.03% +1. That means that the total frequency as an output is
about ± 0.03% +1, thus a frequency as it was in this lab exercise of 500 Hz the
accuracy of this measurement is off by ±0.03% (0.15Hz) +1Hz.
11
Also, according to the manufacturer’s manual the external output accuracy
values between the areas of range we are examining which is 5Hz to 999Hz (as
all our measurements were within that range) the stated accuracy for the
division measurements is ± our time base error calculated + 3 counts/subunits
(Tenma) and for the voltage time division readings is 20mV is the sensitivity
error for the 𝑉𝑟𝑚𝑠 input to the generator from the power source.
These are to be considered systematic errors. Hence these deviations will not
be taken into consideration during our calculations as more variables including
resistance temperature (mentioned above) should be taken into account as well
as these in order to conclude the most accurate results, but due to the fact of
limited electronic physical theory on the other variables needed to be taken into
account in conjunction with these they will be evaded though mentioned as
they are noteworthy.
In Part B of this laboratory exercise, we were to identify if there are any
changes in peak-to-peak voltage, peak voltage and the root-squared mean
voltage when the frequency is the only variable toggled with.
The uncertainty as described in the data and calculations previously, was
determined as 1/10th of the division measurement, which in turn is sectioned
into 5 subdivision, which in turn would equate to ½ a subdivision. Thus for 5.8
divisions as a Y-deflection measurement at 500Hz, we have an uncertainty of
±0.5 divisions.
In turn as stated the Volts/division was maintained at 10V and the frequency
was altered. In order to understand if there was any difference it was
determined that we measure 1/5 of the original frequency and if the results
were to deflect a decrease or increase by 5≥ x ≥ 5 . Thus the frequency of
100Hz was set and again measurements of the Y-deflection were collected. In
The Oscilloscope | 6/18/2009
Thus, with a lot of patience and accuracy the generator was set to three
different frequencies, 500 Hz, 100 Hz and 250 Hz. The frequencies were not
selected at random. The initial frequency of 500 Hz was set as instructed in
the laboratory manual and the volts/div were set at 10V as per the laboratory
manual (Ellis, Summer 2009) and in turn the volts/div setting of 10V per
division were maintained in order to isolate and have only one variable, the
frequency setting. In turn with the frequency set recorded, and the volts/div
set, we manually counted by eye to hand coordination the Y-deflection as
instructed in the laboratory manual (Ellis, Summer 2009), though due to fear
of inaccuracy we made use of the cursor available for us to use on the
oscilloscope. At this instance, we counted how many divisions (squares of the
graph) spanned from the minimum peak of the frequency along the Y-axis
below the +X-axis to the peak of the frequency along the Y-axis above the
+X-axis. As the frequency recorded by hand to eye coordination depicted
rounding off, we then used the cursor which in turn gave a result of 3
significant figures at least which in turn was rounded to the neared
subdivision. Thus for Trial 1, at a frequency of 500Hz, the cursor read 5.84923,
thus the Y-deflection was recorded as 5.8 divisions.
12
turn we decided to set the last trial frequency to half of that of the initial one,
so that if any changes would occur they should be in ration to ½ increase or
decrease as by general mathematical statistical laws would imply if data was
dependent on the variable.
As shown in Table 3 and restated below we see that indeed there was no
change in our Y-deflection calculations.
Table 5
TRIAL
Freq (Hz)
Volts/div (o’scope)
Y-deflection
(divisions)
1
500
10𝑉
5.8 ± 0.1𝑑𝑖𝑣
2
100
10𝑉
5.8 ± 0.1𝑑𝑖𝑣
3
250
10𝑉
5.8 ± 0.1𝑑𝑖𝑣
Next with this data we were to calculate the 𝑉𝑝𝑝 , 𝑉𝑝 , 𝑉𝑟𝑚𝑠 .
For Trial 1 we have:
𝑉𝑝𝑝 =
𝑉𝑜𝑙𝑡𝑠
× 𝑌 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛
The uncertainty for the peak to peak voltage is calculated below.
𝛥𝑉𝑝𝑝
The Oscilloscope | 6/18/2009
𝑉𝑝𝑝
13
=
𝑉𝑜𝑙𝑡𝑠
𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛
𝑉𝑜𝑙𝑡𝑠
𝑑𝑖𝑣𝑖𝑠𝑖𝑜𝑛
𝛥
+
𝛥𝑌−𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑉𝑝𝑝
𝑌−𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
→
𝛥𝑉𝑝𝑝 = (0 +
±0.1𝑑𝑖𝑣
5.8𝑑𝑖𝑣
) 58𝑉 = ±1𝑉
The peak voltage is half of the peak to peak voltage. Hence:
𝑉𝑝𝑝
𝑉𝑝 =
2
Since peak voltage is equal to half of peak to peak voltage then the uncertainty
𝛥𝑉𝑝𝑝
for 𝛥𝑉𝑝 is half of the uncertainty 2 though traditionally done it is:
𝛥𝑉𝑝𝑝
±1𝑉
𝛥𝑉𝑝 = (
+ 0) 𝑉𝑝 = (
) × 29 = ±0.5𝑉
𝑉𝑝𝑝
58
Also the root-mean square voltage was calculated using the formula depicted in
the laboratory manual (Ellis, Summer 2009).
𝑉𝑝
𝑉𝑟𝑚𝑠 =
√2
In turn the root-mean square voltage’s uncertainty is calculated as follows:
𝛥𝑉𝑟𝑚𝑠 =
OR
𝛥𝑉𝑝
√2
=
= ±0.25𝑚𝑉
√2
= ±0.35𝑉
𝛥𝑉𝑝 𝛥𝑉𝑟𝑚𝑠 𝛥√2 𝑠𝑜𝑙𝑣𝑒 𝑓𝑜𝑟 𝛥𝑉𝑟𝑚𝑠
𝛥𝑉𝑝
=
+
→
𝛥𝑉𝑟𝑚𝑠 = (
) 𝑉 = ±0.35𝑉
𝑉𝑝
𝑉𝑟𝑚𝑠
𝑉𝑝 𝑟𝑚𝑠
√2
Trial 2 at 100 Hz and Trial 3 at 250 Hz – produced the same exact results.
Thus we are able to conclude that the 𝑉𝑝𝑝 , 𝑉𝑝 , 𝑉𝑟𝑚𝑠 are independent of the
frequency at a signal of 10V.
The next part of this laboratory exercise was to examine changes in time in
reference to change in wave functions and in turn to calculate theexperimental
frequency based on the time measurements collected.
Thus square waves and sine waves were compared, set at two different
frequencies on the generator and in turn the experimental frequency was
calculated from the measurements of time retrieved from the oscilloscope.
These time measurements are: the Time per divisions measurements per
frequency and wave function and X-deflection (as the X-axis depicts time as
opposed to Y-axis which depicts voltage).
The data collected is depicted on Table 4,
Freq (Hz)
Time/div (o’scope)
Function
X-deflection
(divisions)
Sine 1
500
1𝑚𝑠
2 ± 0.1𝑑𝑖𝑣
Sine 2
250
2.5𝑚𝑠
1.6 ± 0.25𝑑𝑖𝑣
Square 1
500
1𝑚𝑠
2 ± 0.1𝑑𝑖𝑣
Square 2
250
2.5𝑚𝑠
1.6 ± 0.25𝑑𝑖𝑣
The Oscilloscope | 6/18/2009
Table 6
Trial/
14
Once again the X-deflection was counted manually along the +X-axis direction
but at this instance as the laboratory manual requested for two cycles and in
turn divide that by two. Once again the Time/division was recorded in
milliseconds, and no uncertainty value was calculated as the uncertainties for
the time/division measurements fall within our systematic errors as mentioned
earlier in this section of the report. The X-deflection uncertainty in turn was
calculated in the same manner as that of the Y-deflection.
Sine wave at 500Hz
The period in turn was calculated again in the same mannerism as we
calculated the peak to peak voltage.
𝑃𝑒𝑟𝑖𝑜𝑑 (𝑇) =
𝑇𝑖𝑚𝑒
× 𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 = 2𝑚𝑠
𝑑𝑖𝑣
And the uncertainty for the period is visualized below (at frequency 250Hz):
𝑇𝑖𝑚𝑒
𝛥𝑇 𝛥 𝑑𝑖𝑣
𝛥𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑇
±0.1𝑑𝑖𝑣
=
+
→
𝛥𝑇 = (0 +
) 2𝑚𝑠𝑒𝑐 = ±0.5𝑚𝑠
𝑇𝑖𝑚𝑒
𝑇
𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
2.0𝑑𝑖𝑣
1
𝑑𝑖𝑣
The experimental frequency was calculated with the formula stated in the
laboratory manual (Ellis, Summer 2009) using the period obtained from the
calculations above. The formula used to calculate the experimental frequency
is stated below.
𝑓=
1
1
= −3 = 500𝐻𝑧
𝑇 2𝑒
The Oscilloscope | 6/18/2009
To calculate the uncertainty of the frequency (at 500Hz) we have
15
𝛥𝑓 𝛥1 𝛥𝛵 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑓
𝛥1 𝛥𝛵 1 ±0.1𝑒 −3 𝑠
=
+
→
𝛥𝑓 = ( + ) =
= ±5.0𝐻𝑧
𝑓
1
𝛵
1
𝛵 𝑇 (2𝑒 −3 𝑠)2
Sine wave at 250 Hz
𝑃𝑒𝑟𝑖𝑜𝑑 (𝑇) =
𝑇𝑖𝑚𝑒
× 𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 = 4𝑚𝑠
𝑑𝑖𝑣
And the uncertainty for the period is visualized below:
𝑇𝑖𝑚𝑒
𝛥𝑇 𝛥 𝑑𝑖𝑣
𝛥𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑇
±0.25𝑑𝑖𝑣
=
+
→
𝛥𝑇 = (0 +
) 4𝑚𝑠 = ±0.25𝑚𝑠
𝑇𝑖𝑚𝑒
𝑇
𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
1.6𝑑𝑖𝑣
1
𝑑𝑖𝑣
The experimental frequency was calculated with the formula stated in the
laboratory manual (Ellis, Summer 2009) using the period obtained from the
calculations above. The formula used to calculate the experimental frequency
is stated below.
𝑓=
1
1
= −3 = 250𝐻𝑧
𝑇 4𝑒
To calculate the uncertainty of the frequency we have
𝛥𝑓 𝛥1 𝛥𝛵 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑓
𝛥1 𝛥𝛵 1 ±0.25𝑒 −3 𝑠
=
+
→
𝛥𝑓 = ( + ) =
= ±3.9𝐻𝑧
(4𝑒 −3 𝑠)2
𝑓
1
𝛵
1
𝛵 𝑇
Square Wave at 500 Hz
The period in turn was calculated again in the same mannerism as we
calculated the peak to peak voltage.
𝑃𝑒𝑟𝑖𝑜𝑑 (𝑇) =
𝑇𝑖𝑚𝑒
× 𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 = 2𝑚𝑠
𝑑𝑖𝑣
And the uncertainty for the period is visualized below (at frequency 250Hz):
The experimental frequency was calculated with the formula stated in the
laboratory manual (Ellis, Summer 2009) using the period obtained from the
calculations above. The formula used to calculate the experimental frequency
is stated below.
𝑓=
1
1
= −3 = 500𝐻𝑧
𝑇 2𝑒
To calculate the uncertainty of the frequency (at 500Hz) we have
The Oscilloscope | 6/18/2009
𝑇𝑖𝑚𝑒
𝛥𝑇 𝛥 𝑑𝑖𝑣
𝛥𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑇
±0.1𝑑𝑖𝑣
=
+
→
𝛥𝑇 = (0 +
) 2𝑚𝑠𝑒𝑐 = ±0.5𝑚𝑠
𝑇𝑖𝑚𝑒
𝑇
𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
2.0𝑑𝑖𝑣
1
𝑑𝑖𝑣
16
𝛥𝑓 𝛥1 𝛥𝛵 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑓
𝛥1 𝛥𝛵 1 ±0.1𝑒 −3 𝑠
=
+
→
𝛥𝑓 = ( + ) =
= ±5.0𝐻𝑧
𝑓
1
𝛵
1
𝛵 𝑇 (2𝑒 −3 𝑠)2
Square Wave at 250 Hz
𝑃𝑒𝑟𝑖𝑜𝑑 (𝑇) =
𝑇𝑖𝑚𝑒
× 𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 = 4𝑚𝑠
𝑑𝑖𝑣
And the uncertainty for the period is visualized below:
𝑇𝑖𝑚𝑒
𝛥𝑇 𝛥 𝑑𝑖𝑣
𝛥𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑇
±0.25𝑑𝑖𝑣
=
+
→
𝛥𝑇 = (0 +
) 4𝑚𝑠 = ±0.25𝑚𝑠
𝑇𝑖𝑚𝑒
𝑇
𝑋 − 𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛
1.6𝑑𝑖𝑣
1
𝑑𝑖𝑣
The experimental frequency was calculated with the formula stated in the
laboratory manual (Ellis, Summer 2009) using the period obtained from the
calculations above. The formula used to calculate the experimental frequency
is stated below.
𝑓=
1
1
= −3 = 250𝐻𝑧
𝑇 4𝑒
To calculate the uncertainty of the frequency we have
The Oscilloscope | 6/18/2009
𝛥𝑓 𝛥1 𝛥𝛵 𝑠𝑜𝑙𝑣𝑖𝑛𝑔 𝑓𝑜𝑟 𝛥𝑓
𝛥1 𝛥𝛵 1 ±0.25𝑒 −3 𝑠
=
+
→
𝛥𝑓 = ( + ) =
= ±3.9𝐻𝑧
(4𝑒 −3 𝑠)2
𝑓
1
𝛵
1
𝛵 𝑇
17
Percent Difference
As per our laboratory manual (Ellis, Summer 2009) we are to determine any
differences between our set frequency and calculated experiemental frequency.
In order to calculate this we do as follows.
Sine wave at 500Hz
%𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
500𝐻𝑧(𝑠𝑒𝑡) − 500𝐻𝑧 (𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑)
× 100% = 0(𝑧𝑒𝑟𝑜)
0.5(500𝐻𝑧 𝑠𝑒𝑡 − 500𝐻𝑧 𝐶𝑎𝑙𝑢𝑙𝑎𝑡𝑒𝑑)
Hence, the frequency manually set in turn has no difference with that of the
experimental frequency calculated.
Sine wave at 250Hz
%𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
250𝐻𝑧(𝑠𝑒𝑡) − 250𝐻𝑧 (𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑)
× 100% = 0(𝑧𝑒𝑟𝑜)
0.5(500𝐻𝑧 𝑠𝑒𝑡 − 500𝐻𝑧 𝐶𝑎𝑙𝑢𝑙𝑎𝑡𝑒𝑑)
Evidently the frequency manually set in turn has no difference with that of the
experimental frequency calculated.
Square wave at 500Hz
%𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
500𝐻𝑧(𝑠𝑒𝑡) − 500𝐻𝑧 (𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑)
× 100% = 0(𝑧𝑒𝑟𝑜)
0.5(500𝐻𝑧 𝑠𝑒𝑡 − 500𝐻𝑧 𝐶𝑎𝑙𝑢𝑙𝑎𝑡𝑒𝑑)
Clearly. the frequency manually set in turn has no difference with that of the
experimental frequency calculated and also coincides with that of the sine wave
function at the same frequency, leading one to hypothesize that the wave
function has no effect on the frequency emitted.
%𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 =
250𝐻𝑧(𝑠𝑒𝑡) − 250𝐻𝑧 (𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑)
× 100% = 0(𝑧𝑒𝑟𝑜)
0.5(250𝐻𝑧 𝑠𝑒𝑡 − 250𝐻𝑧 𝐶𝑎𝑙𝑢𝑙𝑎𝑡𝑒𝑑)
Evidently, the frequency manually set in turn has no difference with that of the
experimental frequency calculated and in turn insinuates, when compared with
the sine wave function emission at 250Hz depicts a substantial observation
that the frequency omitted is independent of the wave function.
The Oscilloscope | 6/18/2009
Square wave at 250Hz
18
Percentage of Error
Moreover, by calculating the error percentage between the actual (set)
frequency emitted to the experimental frequency calculated taking into account
both extremities of uncertainties as stated in Table 4 and as stated in the user
manual for the generator (Tenma) the results below show identical error
percentages for both the maximum and minimum extremities of their values
including the uncertainties. Due to the conclusion, previously that the wave
function is not a significant it will not be taken into account as the frequency
both actual and experimental is independent of the wave function.
Hence at a frequency of 500Hz the actual uncertainty is stated as
±0.03%+1Hz= ±1.15Hz (Tenma) and from Table 4 at a frequency of 500Hz we
have an uncertainty of ±5Hz.
The maximum extremity values at 500 Hz are portrayed below showing their
error difference.
%𝑒𝑟𝑟𝑜𝑟 = |
(501.15 − 505)
| × 100% = 0.77%
501.15
The minimum extremity values at 500 Hz in turn, are portrayed below showing
their error difference.
%𝑒𝑟𝑟𝑜𝑟 = |
(498.85 − 495)
| × 100% = 0.77%
498.85
The Oscilloscope | 6/18/2009
Clearly, they are both the same difference and since all calculations are correct
one would expect them to be such.
19
Furthermore examining the error percentage at a frequency emitting at 250Hz
it is observed that there is an increased error percentage.
The maximum extremity values at emission of 250 Hz are portrayed below
showing their error difference.
A frequency emitting at 250 Hz the actual uncertainty is stated as
±0.03%+1Hz= ±1.15Hz (Tenma, p. 10) as stated in the user manual of the
generator in relation to output which is the same as at an emission at 500Hz,
as this uncertainty is stated for any frequency output between 50Hz to 500 Hz
and from Table 4 at a frequency of 250 Hz we have an uncertainty of ±3.9Hz.
The maximum extremity values at 250 Hz are portrayed below showing their
error difference.
%𝑒𝑟𝑟𝑜𝑟 = |
(251.15 − 253.9)
| × 100% = 1.1%
251.15
The minimum extremity values at 250 Hz in turn, are portrayed below showing
their error difference.
%𝑒𝑟𝑟𝑜𝑟 = |
(248.85 − 246.10)
| × 100% = 1.1%
248.85
The Oscilloscope | 6/18/2009
Wave behavior as stated and known in general physics states that the lower a
frequency experiences fewer periods per set time frame as opposed to a higher
frequency. This in turn increases chances for distortion and error as the
smaller frequency has a larger wave length per period increasing chances of
transmission error and reading errors as particles of a wave are able to
“escape” the wave pathway. (Serway, 2008) Thus, as expected the percentage
of error at an emission of 250 Hz is greater than that of a frequency emitted at
500 Hz.
20
Results and Conclusions
As observed the purpose of this laboratory was to familiarize oneself with the
operation of the oscilloscope and comprehension of the output of the
oscilloscope in order to understand the relationships between frequency, time
and voltage and to be able to identify these relationships as either dependent or
non-dependent.
This was a three part laboratory exercise in which is extremely well presented
and easy to understand. The oscilloscope is capable of providing information
about a “signal” it receives and computes. Notably, the oscilloscope is not only
a piece of equipment that quantifies data it also, shows the signal’s qualitative
values.
At first instance capabilities is observed, finding the minimum and maximum
reading values of the oscilloscope using in Part A of this laboratory exercise.
Secondly, part B tests if the change in the frequency of the generator would
affect the voltage reading, at peak to peak, peak and root-mean square. Lastly,
the frequency of the wave function of the signal to the oscilloscope is changed
to realize if there is any impact on the results of frequency calculated based on
time and compared experimental results to the set errors and differentiation
stated by the manufacturer. Presented below in detail and graphical or
number line representation, results are analyzed in order to conclude our
observations with validation.
The Oscilloscope | 6/18/2009
Results
21
Results Part A
In Part A of the laboratory exercises the maximum and minimum values of the
oscilloscope is observed. This in turn assists in realizing the dynamic range of
the oscilloscope. As see in Table 2, the voltage minimum is 20 𝑚𝑉 ± 2𝑚𝑉 and
the voltage maximum is 50𝑉 ± 5 𝑉 and in turn the minimum time is 5 ns ±0.5𝑛𝑠
and the maximum time is 50 𝑠𝑒𝑐 ± 5 𝑠𝑒𝑐.
This allows us to see what margin of voltages and time we should be expecting
when using the oscilloscope.
Results Part B
This part of the laboratory exercise was to familiarize ourselves on the
relationships between the components observing. From the data in Table 3
that even though the frequency was changed, in respects to measuring
alternating current voltages at different frequencies, that the voltage values at
all frequencies remained the same. One is able to conclude that the voltage
signal depicted via the oscilloscope is independent of the frequency.
Also, the number line below indicates the same result: changing frequency
from 500Hz to 100Hz then to 250Hz does not affect Vrms. This result is
observed through that three number lines are completely overlapping with each
other including error. Vrms was 20.5V±0.5𝑉, for all three measurements. This
result indicates not only the voltage signal output is independent of frequency.
To visualize this graphically one can refer to the graph below were at all three
frequencies, the 𝑉𝑝𝑝 , 𝑉𝑝 , 𝑉𝑟𝑚𝑠 are the same.
Below the number line depicts the above. Evidently there is exact overlap and
exact results.
𝑉𝑟𝑚𝑠 500 𝐻𝑧
Number Line Part B
𝑉𝑟𝑚𝑠 100𝐻𝑧
𝑉𝑟𝑚𝑠 250 𝐻𝑧
20.1V
20.2V
20.3V
20.4V
20.5 V 20.6V
20.7V
20.8V
20.9V
30.0V
The Oscilloscope | 6/18/2009
20.0V
22
Results Part C
The purpose of Part C of this laboratory exercise was to further our
knowledge about oscilloscope and the relationships between the frequency (Hz)
and the Period T(s). Period (T) was determined by multiply Time/div and Xdeflect (See Calculation Part C). Period T is calculated for both 500Hz output
and 250Hz output. From the results stated at Table 4, change in Period T was
observed when Frequency output was changed. At frequency output equals to
500Hz, the period T was 2.00ms±0.1ms, and then at frequency output equals
to 250Hz, the period T 4.00ms±0.25ms was observed. As the frequency output
was cut to half, Period T was doubled. From this result, the relationship of
frequency f and Period T can be concluded as fT=1. In other word, frequency (f)
and Period (T) is inverse proportion to each other.
In this case, we examined not only the relationship between period and
frequency; we also examined to see if a different type of frequency function
would produce different results in calculations. We compared the sine wave
frequency function with the square wave frequency function in order to do so.
This was done by examining the time to frequency measurements at 500 Hz
and 250 Hz at both wave functions. From our results stated at Table 4, the
result of the time to frequency measurements are independent of the wave
function as same Period T was observed between two different type of function
at a constant frequency. When comparing sine wave function to square wave
function results of the same frequency set (i.e. 500Hz) we see that again there
is no difference in any measurements taken and produced by calculations.
Thus, we are able to conclude that indeed, the wave function does not result in
alteration of the Period T calculated or recorded by the oscilloscope when the
frequency is kept constant.
The Oscilloscope | 6/18/2009
t-Test: Two-Sample Assuming Unequal Variances
23
Mean
Variance
Observations
Hypothesized Mean Difference
Df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Sine Wave
334Hz
82668
3
0%
4
0
0.5
2.131846782
1
2.776445105
Square Wave
334Hz
82668
3
Above a simple two-sample t-test was performed between the results collected
for the Sine wave and Square wave functions both at a set frequency by the
generator of 500 Hz. We see that the P value shows that there is NO significant
difference between the two in the laboratory exercise. The t-test was repeated
for the two wave functions at a set frequency of 250 Hz on the generator and
produced identical results in respects to significance. Thus it is valid to
conclude that based on the data collected that the wave function plays no
significant role in altering the experimental frequencies.
In order to realize the errors of the frequency emitted by the generator to the
oscilloscope and establish the uncertainties that are calculated are valid the
experimental frequency is compared with the actual frequency.
The Oscilloscope | 6/18/2009
Actual Frequency in this case is defined as the frequency manually set on the
generator and the uncertainty in the frequency’s transmission is the
uncertainty that the manufacturer of the generator has stated, as previously
mention in the laboratory report, which in turn has been established my
numerous trials and errors, taking into account all variables that are to be
considered when using the generator to transmit a frequency. This uncertainty
stated in the manufacturer’s manual (Tenma) is ±0.03%+1Hz. This uncertainty
is accepted for all frequencies within the range of 50 Hz and 500 Hz.
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Below are plotted representations in order to assist in identifying if and how
accurate our experimental frequency and experimental frequency’s
uncertainties are.
Actual Frequency 500 Hz ±0.03%+1Hz =500 Hz ±1.15Hz
Experimental Frequency 500 Hz ±5 Hz
Number Line 1
Experimental Frequency
Calculated from Time
Sine Wave emitting at 500Hz
475 Hz
480 Hz
485 Hz 490 Hz
Frequency of Generator
495 Hz 500 Hz 505 Hz 510 Hz 515 Hz
520 Hz 525 Hz
Actual Frequency 250 Hz ±0.03%+1Hz =250 Hz ±1.15Hz
Experimental Frequency 250 Hz ± 3.9 Hz
Number Line 2
Frequency of Generator
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Sine Wave emitting at 250Hz
25
225 Hz
230 Hz
235 Hz 240 Hz
245 Hz 250 Hz 255 Hz
Experimental Frequency
Calculated from Time
260 Hz 265 Hz 270 Hz 275 Hz
Actual Frequency 500 Hz ±0.03%+1Hz =500 Hz ±1.15Hz
Experimental Frequency 500 Hz ±5 Hz
Number Line 3
Experimental Frequency
Calculated from Time
Square Wave emitting at 500Hz
475 Hz
480 Hz
485 Hz 490 Hz
Frequency of Generator
495 Hz 500 Hz 505 Hz 510 Hz 515 Hz
520 Hz 525 Hz
Actual Frequency 250 Hz ±0.03%+1Hz =250 Hz ±1.15Hz
Experimental Frequency 250 Hz ± 3.9 Hz
Number Line 4
Frequency of Generator
Square Wave emitting at 250Hz
Experimental Frequency
Calculated from Time
230 Hz
235 Hz 240 Hz
245 Hz 250 Hz 255 Hz
260 Hz 265 Hz 270 Hz 275 Hz
The Oscilloscope | 6/18/2009
225 Hz
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Conclusions
Firstly, in conclusion, from both the t-test performed and from the above
number lines and from the data collected shown on Table 4, if is confirmed
that indeed the wave function is not a factor that influences time or frequency.
When observing the four number lines above it is evident at first instance that
the experimental frequency concurs with that of the actual frequency and in
turn due to the overlap in all four number lines, that depict concise yet
exaggerated uncertainties the laboratory exercise is considered to be a success.
However, in all four number lines, the uncertainty range is greater than that of
the actual range. This is something that would be expected as previously
mentioned in the Error Propagation section of this report within the discussion
and analysis section.
The Oscilloscope | 6/18/2009
The manufacturer’s manual on the generator, states many variables and
uncertainties ranging from input of power source, to distortion of wave, to
conversion of signal for transmission and wire uncertainties for internal “clock”
functions and temperature settings suggested for ideal usage which is 23.5ºC.
All of the varied uncertainties stated in the manual are areas of electronic
physics that are not intended for this laboratory exercise. Thus, these
uncertainties are considered to be systematic as they are constant
uncertainties with fluctuations or non within their stated limits. There is a
possibility of a random error occurrence, though as the results are satisfying
and no trial indicated results deviating from the minimum trials executed
already it is minimal thus not taken into consideration.
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Hence, the exaggerated uncertainty range is to be expected and reasonable and
is due to these uncertainties that were not indentified individually as they are
all systematic errors, which include but are not limited to, the room
temperature, the input error of voltage into the generator from the power
source (estimated 20mV), the conversion internal clock which presents a
distortion of <2% at a frequency of 0Hz to 999Hz, and in turn the uncertainty
of output to the oscilloscope which had been previously identified as
±0.03%+1Hz. Though, it is noteworthy to take into account that the
uncertainties in input by the oscilloscope, the wiring health, the oscilloscopes
internal clock for signal interpretation are also to be considered systematic
errors. These errors were evident during the execution of the laboratory
exercise, as the oscilloscope as previously mentioned is able to provide a lot of
information about a signal and one of which is determining the frequency
which even though was set for 500Hz was stated as 500.044 Hz, or 500.32 Hz
and many times fluctuating within the tenth to hundredths band.
Concluding, this laboratory exercise validates the following:
a) The oscilloscope used is has many functions that allow one to interpret
qualitative and quantitative measurements of a frequency as it provides a
lot of information on an incoming signal that it receives.
b) That a signal’s magnitude is independent to the frequency and thus the
voltage signal will quantitively remain constant though it does not entail
in constant quality of the signal (Fogiel, 2002).
c) The wave function has no effect on the time or frequency of the signal
and this a signal transmitted in sine wave and square wave format will in
turn have the same frequency.
d) The uncertainties stated in the manufacturers manual for the generator
were validated and within the span of our experimental values.
The calculations executed throughout this laboratory exercise were
satisfactory and successful due to precision and matriculate direction
taken from the laboratory manual. All safety was considered throughout
the exercise.
Concluding this laboratory exercise was a success.
Works Cited
Ellis, S. L. (Summer 2009). Laboratory Manual for Physics 213. University of Kentucky .
Fogiel, M. (2002). Basic Electricity. Research & Education Association U S Naval Personnel, US Naval Personnel Staff.
Lenk, J. D. (1997). Simplified Design of Voltage/Frequency Converters. Elsevier Science.
Manual, T. (n.d.). www.pa.uky.edu~ellis. Retrieved from Dr. Ellis' Website.
Tenma. (n.d.). 72 7210 Tenma Function Generator. Retrieved from Ternma: www.tenma.com
The Oscilloscope | 6/18/2009
Tooley, M. H. (2002). Electronic circuits. Butterworth-Heinemann.
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The Oscilloscope | 6/18/2009
Appendix ( Raw Data)
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