lab 2 final (compiled)

5/28/2018 Lab 2 Final (Compiled)

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Lab: 2

Section #: 004

Group #: 5

Experiment #: 2

Date : 3/6/2014

Oscilloscope

Your signature indicates that you have completely read the entire report and agree witheverything here in. Failure to sign will result in a zero for your personal grade unless a formal

exception is filed with your TA.

Please Print and Sign Full Name

Principal investigator: Ryan Samons_________________________________________

Skeptic: Morgan Culver_________________________________________

Researcher Logan Murphy

_________________________________________

TA Justin Woods__________________________________________

Lab Report Score:________________

Role I DC AD RC Q1 Q2 PI PG

Legend:

I introductionDC data and calculationAD analysis and discussion

RC results and conclusion

Q1/Q2 quiz/prelabPI principal investigator points

PG personal grade (average of individual score and Lab Report Score)


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Introduction:

After familiarizing ourselves with equipment during lab one, lab two focuses on learning

how to use and becoming familiar with the oscilloscope. We learned how to look at the data

displayed on the oscilloscopes screen and interpret that data to find other measurements. From

this experiment will verify ohms law, and confirm that there are different ways to calculatevoltages but ohms law works for all the methods and the values calculated are not significantlydifferent between the methods used.

Equipment:

1 Digital Multimeter 91910044 1 Oscilloscope C050155 1 DC power supply C1010444 2 AC power supply (function generator) FG24243,FG24241 1 10-k resistor 5 Banana clip wires 2 BNC cables

Post Lab Meetings:

Monday February 24th

there was a meeting in the lab to finish and finalize the data from

the lab. Morgan and Logan were in attendance. Ryan had a class at the time of the office hours

were the lab was completed therefore he was unfortunately unable to attend. The meeting lasted

from approximately 11:00 am to 11:40 am.

Thursday February 27th

there was a meeting during the lab time. We discussed how we

were going to proceed on the lab and discussed the results and comments given by the TA. This

meeting lasted approximately 30 minutes.

References:

Ellis, Steven L. Laboratory Manual Spring 2013-2014 Appendix Fa - Tektronix_PWS4305 Appendix Fb - Tektronix_PWS4305

Appendix H- Tenma function generator 72-7210 Appendix K - Digital Multimeter Appendix S - Tenma Function Generator72 7210 Manual Appendix JError propagation Appendix CTDS 100B Oscilloscopes users manual Standard Cover Sheet


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Procedure:

The research team began the experiment by reviewing the lab manual and trying to learnthe general procedures of the lab before moving any further.

Next, Ryan Samons and Morgan Culver retrieved the required equipment from the filingcabinet and Logan Murphy recorded the serial numbers of the equipment.

Table 1

The PI Ryan Samons referenced the lab manual for the proper setup of the equipment forthis part of the experiment. By placing cables between the oscilloscope and the DC

power supply we were able to complete the circuit.

These banana clips were ran through the resistor. The Digital Multimeter was then placed where it would read the voltage running through

the system. At this point the DMM Voltage heading of Table 1 was completed by reading

the DMM.

Next the oscilloscope was used to record the scale and divisions of the data given in orderto find the voltage reading on that device.

These steps were repeated for .5V,1V,2V,4V, and 8V. The percent difference were then calculated by Skeptic Morgan Culver and recorded in

Table 1.

The diagram below shows the setup for this part of the experiment.

Table 2

For this part of the experiment the DC power supply was replaced with the functiongenerator in order to find the same measurements using an AC power supply. All group

members helped in switching these devices.

The connection between the oscilloscope and function generator was made using BNC tobanana clip cables.

The TA Mr. Wood was asked by Logan Murphy to check the setup before continuing.


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The DMM readings were taken in the same manner as before, with the DMM beingplaced on top of the banana wires in the experiment in order to accurately record the data.

Next the oscilloscope was used to find the divisions and scale of the data given in orderto calculate the voltage readings for this part of the experiment.

The percent difference was then calculated by the Skeptic Morgan Culver and recordedalong with the other data

The table below shows the setup for this part of the experiment.

Table 3

The next part of the experiment focused on using the function generator and seeing theeffect the shape of the wave and the frequency strength had on the voltage given off.

The same setup from table 2 was used in this part of the experiment also. Mr. Wood was asked by Morgan Culver to check the setup before preceding. First the data was recorded for all of the sine, triangle, and square waves at the 400Hz

values, then the 4000Hz value, and the 40000Hz value.

The divisions and scale factor data were gathered by Ryan Samons and Logan Murphyfrom the screen of the Oscilloscope itself. The divisions were the number of lines in

between the two points needed.

All the data was then recorded by the Skeptic Morgan Culver. The table below shows the setup for this part of the experiment.

Table 4


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The last part of the experiment involved 2 function generators. The two function generators were connected to the oscilloscope. One in channel one and

the other in channel two.

Mr. Wood was asked by Ryan Samons to check the setup before preceding.

Both were turned on and the frequency values set to about equal, one double the other,and one triple the other, with the data being recorded along the way.

The data recorded were the number of loops along the Lissajous pattern. After findingthe display button we were able to find the proper display to show the data in this form.

The number of loops were counted in the horizontal and vertical directions. The diagram below shows the setup for this part of the experiment.

Data and Calculations:

Table 1

The DC power supply was used in this part of the experiment changing the voltage asdesired anywhere from .5V to 8V. The device was connected directly to the Oscilloscope and

the reading came out to be in Volts as well. Below is the data collected.

Power

Supply

DMM

Voltage Oscilloscope

%

Difference

Divisions Scale DC Voltage

.5V .5V 2.5 200mV .5V 0

1.00V 1V 2 500mV 1V 0

2.00V 2V 2 1V 2V 0

4.00V 4V 2 2V 4V 0

8.00V 8V 1.6 5V 8V 0

Although the percent difference equation does not apply here because the data was

exactly the same the equation for percent difference will be used throughout the experiment and

thus will be referenced in this section.


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Equation 1

Below is a sample equation for Equation 1. Since the values from the table above all give

the % to be zero, the sample calculation will be if the values were 4V and 4.2V.

This next equation applies to all the numbers underneath the oscilloscope heading in the

charts throughout the experiment. In order to find the DC voltage you must multiply the scale by

the divisions.

Equation 2 Sample equation using the row of the .5V.

Table 2

This part of the lab used the function generator to produce current using a sine wave and

was measured both with the DMM and the oscilloscope. Before comparing the data the DMMvoltage reading had to be converted to the peak voltage readings and the divisions and Scale had

to be found on the oscilloscope. The data for this part of the experiment is shown below.

Function

Generator

Oscilloscope

Digital Multimeter V(rms) Digital Multimeter V(pp) %differeDivisions Scale V(pp)

min 0 db 5 .1V .5V .1738V .491V 1.81

mid 0 db 6.4 1V 6.4V 2.21V 6.25V 2.37

max 0 db 4.6 5V 23V 7.68V 21.73V 5.68

mid -20 db 6.4 .1V .64V .22V .62V 3.17

max -20 db 4.6 .5V 2.3V .795V 2.25V 2.2

There a few equations needed for the completion of the table above. The first is the conversion

of the Digital Multimeter V(rms) into the V(pp). This equation is listed below.

Equation 3


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Sample equation for equation 2 will be used at the mid 0 db row of calculations above.

The percent difference for this part of the experiment was found using Equation 1from

earlier in the experiment. The V(pp) underneath the oscilloscope was calculated by simply

multiplying the divisions and the scale together. Also under the oscilloscope in the table there is

a divisions and scale column. Using Equation 2you find the values for the next column in the

table.

Equation 4

Table 3In this part of the experiment the function generator was used to find the changes sine,

triangular, and square waves affected the frequency readings. The table below shows the data

gathered from this section of the lab.

Table 3Wave

form

type

Function

generato

r

frequenc

y

Amplitude Peak-to-Peak

Amplitude

Period Frequ

ency

F

(HZ)

% di

in fr

Div Scale

factor

r (V)

Volt

s

Div Scale

factor

r (V)

Volts Div Scale

factor

r (ms)

Sec.

Sine 400 Hz 3.2 .1 .32 6.4 .1 .64 2.46 1 .00246 406.5 1.61

Sine 4000 Hz 3.3 .1 .33 6.6 .1 .66 2.6 .1 .00026 3846.15 3.921

Sine 40000 Hz 3.1 .1 .31 6.2 .1 .62 2.5 .01 .000025 40000 0

Triangl

e

400 Hz 3.7 .1 .37 7.4 .1 .74 2.48 1 .00248 403.22 .8

Triangl

e

4000 Hz 3.65 .1 .365 7.5 .1 .75 2.6 .1 .00026 3846.15 3.92

Triangl

e

40000 Hz 3.75 .1 .375 7.5 .1 .75 2.6 .01 .000026 38461.5 3.92

Square 400 Hz 2.75 .2 .55 5.5 .2 1.1 2.46 1 .00246 406.5 1.611Square 4000 Hz 2.7 .2 .54 5.4 .2 1.08 2.5 .1 .00025 4000 0

Square 40000 Hz 2.25 .2 .45 5.5 .2 1.1 2.5 .01 .000025 40000 0

The percent difference is found in this table by once again using Equation 1. The two

volts categories under amplitude and peak to peak were calculated by taking the divisions and

multiplying them by the scale factor. Another equation used in this chart is Equation 2. This is


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used by multiplying the divisions and scales in order to get the values. This just leaves the

calculated frequency. Calculating frequency has the following equation.

Equation 5

The sample calculation for this equation will be using the information in the square

40000Hz row. Table 4

The last part of the experiment involved using two function generators changing the

frequency of one of them and creating Lissajous Pattern. We had to set up the oscilloscope in

the XY mode and looked at the ratio of vertical loops to horizontal loops. The chart below was

created after looking at different ratios of frequencies given off by the function generator.

Frequency ratio Number of Vertical

Loops

Number of Horizontal

Loops

Ratio

1/1 1 1 1/1

1 2

1/3 1 3 1/3

The picture below shows the oscilloscope at the time when both function generators were

set at 400Hz. As you can see there is one vertical and one horizontal loop.


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The next picture shows the oscilloscope when one of the function generators is at double

the frequency of the other. As you can see there is two horizontal loops and one vertical loop.

The last ratio tested was when one function generator was 3 times the other. As you can

see there is three horizontal loops and one vertical loop.


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Discussion and Analysis

Throughout this entire experiment there were errors in the measurements taken. Some of

these were measurable while others were more random and unmeasurable. Each piece of data

collected will have a certain measurable or unmeasurable amount of error. This error is a result

from the error in the equipment used during the experiment as well as random human error.These errors can be analyzed by breaking them down into four different sections, ranking them,

and then further discussing systematic versus random error. The first sources of error occurred in

part two of this experiment.

Part 2: Measurement of DC Voltage with the Oscilloscope

The error in this section of the lab will affect the data values collected in Data Table 1.

Each piece of equipment used in this section will have a certain amount of error. These pieces of

equipment include the digital multi-meter, power supply, and the oscilloscope. The oscilloscope

will have sub errors that must be propagated such as the error in divisions, scale, and DC voltage.

The systematic error for the power supply can be found using the following equation, where: Vpsis the error in the power supply output measured in volts

: Vpsis the voltage setting on the power supply

: [2] is the number added to the smallest significant digit of the voltage of the power

supply.

Below is a sample equation of the error for the Power Supply using the voltage at 0V.

By using this equation, the error regarding the power supply can be found for each individual

measurement taken. These errors can be found in Errors in Table 1.

The systematic error in the digital multi-meter can also be found using a similar equation show

below,

where: V is the digital multi-meter voltage measurement.

:is the total error in the power supply: [1] is the number added to the smallest significant digit


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Because the digital multi-meter is measuring the power supply voltage, the error in the

digital multi-meter will also include the error in the power supply as seen above. Below is a

sample equation of the error for the DMM device using the voltage at 0V.

The error in the oscilloscope will also affect the measurements found in Data Table 1.

The error regarding this piece of equipment is more complex than the previous two. The total

error in the DC voltage measurements taken has three different components. The first two are the

error in the number of divisions and the error in the scale factor. The error in the divisions was

given as0.1 because it is designated as half of the smallest possible measurement. The error inthe scale factor will be as 0.3% of the scale factor. In order to find the total error in DCmeasurement, these two values are multiplied together. Because of this, the total error must be

propagated using the following equation:

This equation can be simplified, however, to an even simpler equation show below. The

partial derivative of the voltage with respect to the divisions is just S. The partial derivative of

the voltage with respect to the scale will be D. These can be substituted into the equation and

then it be further simplified,

where:V is the error in the voltage

: S is the scale factor

: D is the error in the divisions: D is the number of divisions

: S is the error in the scale

Similar to the digital multi-meter, the error in the oscilloscope will also inherit the error

in the power supply. Because of this, the total error in the voltage measured by the oscilloscope

can be found using the equation below. Below is a sample calculation where S is .2V with an uncertainty of .006, a division of 2.5 and

an uncertainty of .1, and the error in the power supply is .045V.


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Error in Table 1

Power Supply

Setting

Error inPower

Supply

Voltage

Error inDMM

Voltage

Reading

Oscilloscope

Error in

Divisions

Error in

Scale

Error in DC

Voltage

0.50V .045 .07 .1 .0006 .065

1.00V .07 .11 .1 .0015 .12

2.00V .12 .19 .1 .003 .22

4.00V .22 .35 .1 .006 .42

8.00V .42 .67 .1 .015 .92

Part 3: Comparison of AC voltages measured with either the oscilloscope or DMM

The errors regarding the section of the lab will be similar to those seen in part 2 of the

lab. The oscilloscope and digital multi-meter were used and will have the same measurable error.

The error for measurements taken using the digital multi-meter will be slightly different,

however, because now it is being used to measure the root mean square voltage and peak to peak

voltage of AC voltages. A new piece of equipment was introduced in this section of the lab as

well. For this part the function generator was used as well and it will have a measurable amount

of error. All systematic error that will affect the measurements taken can be found in Errors in

Table 2.

The error in the digital multi-meter will have two different measurable errors due to the two

different ways it was used in this section of the lab. The first error that can be calculated in the

error in root mean square measurements. This error can be found using the simple equation, where: Vrmsis the total error in the measurement


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: Vrmsis the original measurement

: [2] is the number added to the smallest significant figure.

Below is a sample calculation where the peak to peak voltage is .1738V.

The other measurable error for the digital multi-meter is the error in measuring peak to peak

voltage. This error can be found using a simple process. Because the peak to peak voltage is

found by multiplying the root mean square measurement by 22, the error in peak to peakvoltage is simply:

=* 2Below is a sample calculation with Vrmsis .=.0037* 2=.0105The measurements taken using the oscilloscope will also have a certain amount of measurable

error. These can be found by solving the following equation for peak to peak voltage.

In this equation the variables represent the same values that they did for the error in the

oscilloscope measurement in the previous section. A sample calculation using this equation can

be seen below where the function generator is set to min 0 db, the scale is .1V, the uncertainty in

divisions is .1, the number of divisions is 5 and the uncertainty in the scale is .0003V.


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Error in Table 2

Function

Generator

Oscilloscope Error in

DMM Vrms

Error in

DMM VppError in

Divisions

Error in

Scale

Error in Vpp

Min 0 db .1 .0003 .01 .01Mid 0 db .1 .003 .1 .0642 .18Max 0 db .1 .015 .5 .1736 .491

Mid -20 db

.1 .0003 .01 .0244 .069

Max -20 db .1 .0015 .05 .0179 .051Part 4: Measurement AC voltage for Different Waveforms

This section of the lab will have similar errors as in the previous section along with new

errors regarding the error in time and frequency. The error in the divisions and scale factor will

be the same as in part 3 on the lab. These can be found in Error in Table 2. The error in seconds

can be found using a similar equation used to find the error in DC voltage in part 2 of the lab.

The main difference in the equation below is that this equation is tailored to seconds instead of

volts,

where: S is the seconds

: D is the error in the divisions

: D is the number of divisions

: S is the error in the seconds

A sample calculation can be seen below where the scale factor is .001s, the error in the divisionsis .1, the number of divisions is 2.46, and


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The error in frequency can also be calculated using a similar equation. The main difference isnow the derivative of frequency is taken with respect to the divisions and the scale.

Because seconds is equal to the divisions multiplied by the scale, this equation can be

rewritten by replacing the two partial derivatives. The equation for error in frequency is

now:

A sample calculation using this equation is shown below where the number of divisions in 2.46,

the scale is .001, the error in divisions in .1, and the error in the scale is 3.0E-6.

There will also be a measurable error in volts in amplitude for this section of the lab. This error

can be calculated using the equation below.


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This equation is the same one used to calculate the total error in voltage in part 2 of the lab. A

sample equation can be seen below.

The error in peak to peak amplitude can be found using the same equation seen in part 3 of the

lab. =* 2A sample calculation regarding this section of the lab can be seen below.

=* 2=.01* 2Vpp=.028

Error in Table 3Waveform

type

Function

generator

frequency

Amplitude Peak-to-Peak

Amplitude

Period Error

Frequ

y

F (HZError

in Div

Error

in

Scalefactor

r (V)

Error

in

Volts

Error

in Div

Error

in

Scalefactor

r (V)

Error

in

Volts

Error

in Div

Error

in

Scalefactor

r (ms)

Error in

Sec.

Sine 400 Hz .1 .0003 .01 .1 .0003 .028 .1 .003 .0001 16.77Sine 4000 Hz .1 .0003 .01 .1 .0003 .028 .1 .0003 .00001 167.7Sine 40000 Hz .1 .0003 .01 .1 .0003 .028 .1 .0000

3

.000001 1677

Triangle 400 Hz .1 .0003 .01 .1 .0003 .028 .1 .003 .0001 16.77


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Triangle 4000 Hz .1 .0003 .01 .1 .0003 .028 .1 .0003 .00001 167.7Triangle 40000 Hz .1 .0003 .01 .1 .0003 .028 .1 .0000

3

.000001 1677

Square 400 Hz .1 .0006 .02 .1 .0006 .057 .1 .003 .0001 16.77Square 4000 Hz

.1 .0006 .02

.1 .0006 .057

.1 .0003 .00001 167.7

Square 40000 Hz .1 .0006 .02 .1 .0006 .057 .1 .00003 .000001 1677Random vs. Systematic Errors

The systematic errors in this experiment are the ones that can be calculated and

mathematically accounted for. The random errors in this experiment are those that cant such ashuman errors. One example of a random human error seen in this experiment that the function

generator would never stay at a set value for frequency. Because it would randomly change, it

cannot be accounted for mathematically. There are also unknown human errors in this lab that

will affect the results. The majority of the error seen in this lab can be broken down into the twocategories.

Error Types

1. Random errors. These are errors that you cannot account for exactly but you know theyexist throughout the experiment.

The function generator fluctuated in its Hz given off. The function generator didnt have a knob to stop at exactly the MID. The research team had faulty cables that may have affected the results. Other unknown sources of error not calculable.

2. Systamatic errors. These are errors that we know occur and have specific equations inorder to find the exact value for the error.

The error in the power supply including that for root mean square and peak topeak.

The error in the digital multi-meter. The error in the oscilloscope readings including the scale and divisions. The error in frequency. The error in time.


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Results and Conclusions

The purpose of this lab was to become familiar with using the oscilloscope. One

advantage that the oscilloscope has when compared to the DMM we learned to use in Lab 1, is

that the oscilloscope displays a graph of the voltage as a function of time. This allows us to view

how the voltage changes over a longer period of time vs. the DMM which shows the voltage

using the root-mean-squared method. One advantage the DMM has is that it can show a more

precise measurement of the voltage at the instant it is measuring.

During the first part of the lab, we measured the DC voltage. The error has been

calculated and organized in the Error in Table 1 table. Below is a sample comparison of the

DMM vs. Oscilloscope measurements for the power supply setting of 2 volts.

Number Line 1:

We can see from the number line that the DMM and Oscilloscope voltage overlap (they

were stacked to aid viewing). This shows that these instruments can be trusted to produce an

accurate value for the voltage.

Now the AC voltage is measured. The AC voltage is provided by the function generator.

Below is a number line that compares the oscilloscope, and the DMM measurements for the

voltage. The number line is based on the 400 Hz and 0 db setting for the function generator. The

errors are taken from the Error in Table 2 table from the skeptic.

Number Line 2:

0 0.5 1 1.5 2 2.5

DMM vs Oscilloscope (2 V)

DMM 2 0.19V

Oscilloscope 2 0.22V

0.475 0.48 0.485 0.49 0.495 0.5 0.505 0.51 0.515

DMM vs Oscilloscope (Min 0 db)

DMM 0.491 0.01V

Oscilloscope 0.5 0.01


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Here we can see that the DMM and the Oscilloscope measurements for voltage overlap.

The percent difference between the two measurements was 1.81%. This, plus the overlapping

error bars, shows that the oscilloscope and the DMM can be used to accurately determine the

voltage. We can conclude because these values overlap, as well as the overlap from Number

Line 1, that the adjusting of the DC power supply and the Function generator using only the front

control knobs can yield a precise output from either unit.

This next section compares the different frequencies of the function generator and that of

the oscilloscope. The uncertainty in the frequency could be calculated by defining the uncertainty

to be that of the error of the inverse of the period. The first number line in this section will be

that of the sin at 400 Hz. The frequency measured by the oscilloscope is the one to trust in this

situation because setting the frequency on the function generator is difficult because of the

sensitivity of the knob on the front of the unit. It is also important to note that one should try to

fit the entire period onto the screen of the oscilloscope to allow for a more accurate

measurement. If the entire period was not on the screen, it would be difficult to determine where

the period began and ended. The errors came from the Error in Table 3 table in from the skeptic.

Below is the comparison for the sin wave at 400 Hz vs. the function generator at 400 Hz.

Number Line 3:

We can see that the error bounds on the oscilloscope's measurements overlapped the

frequency of the function generator. This shows that the oscilloscope can produce an accurate

measurement for the frequency from the function generator; however, it may not be a precise

measurement.


380 390 400 410 420 430

Function Generator vs Oscilloscope (sin 400 Hz)

Function Generator 400Hz

Oscilloscope 406.5 16.77Hz


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Number Line 4:

Because the oscilloscope's measurement and errors overlapped, we can draw the same

conclusion as we did from number line 4, that is, that the oscilloscope can return an accurate

measurement of the frequency. One thing to notice is that the measured frequency of 3846.15 Hz

is lower than the frequency of 4000 Hz we were supposed to compare the oscilloscope to. This is

probably due to a random error or a mistake in setting the function generator's frequency. The

random errors and systematic errors were discussed in the Skeptic's portion of this paper.


Number Line 5:

We can see again that the oscilloscope's measurement and errors overlap the frequency of

the function generator. Based on this, we can again conclude that the oscilloscope will produce

an accurate measurement of the frequency.

Conclusion:

In this lab, we learned how to use the oscilloscope and accompanying software, althoughnot required, to determine voltage and frequency. We learned about using the oscilloscope to

measure AC and DC voltages. We learned how to measure the period and frequency of a signal

using the oscilloscope, and we learned how to make a Lissajous figure using two AC voltage

input signals. This lab also introduced us to the oscilloscope, which allows us to make a more in-

depth analysis of electrical signals for future labs.

3600 3700 3800 3900 4000 4100



Oscilloscope 3846.15

167.7Hz

38000 39000 40000 41000 42000



Oscilloscope 40000 16.77

Hz

lab 2 final (compiled)

Documents

lab manual

lab report score5282018

lab time

data fromthe lab

bnc cablespost lab meetings

appendix fa tektronix

required equipment

pi ryan samons