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i need you to write a lab report with following structure abstract ,introduction,Procedure and method,Analysis, result &dissection and conclusioni am international student so please everything meed to be sample not that advance word. most importantly use your own work do not plagiarismeverything need to be normal and sample read the lab and check everything before you bid thank youi will post the lab manual and the picture of result
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BME 206
Sophomore Laboratory
First Order Systems II
Frequency Domain Bode Plot Analysis
Issued: Tuesday, April 10, 2018
Due: Tuesday April 17, 2018
The goal of this study is to determine whether or not a frequency domain analysis
successfully predicts the gain and phase response of first order resistor capacitor (RC) low
pass and high pass filters.
I. Introduction
One of the unique properties of linear time invariant (LTI) systems is that when they are driven
with a sinusoidal input having a given frequency, a sinusoidal output with the same frequency is
produced. The output amplitude and phase, however, are altered with respect to the input in a
frequency dependent manner. This study examines the frequency response of two first order
resistor capacitor (RC) circuits; a low pass filter and a high pass filter. The amplitude and phase
of the output voltage produced in response to input sinusoids of different frequencies are
examined on a logarithmic frequency scale. Based on theoretical predictions of the gain and
phase shifts, this study will conclude whether or not theory can successfully predict first order
RC circuit measurements.
II. Theory
Figure 1 illustrates the central concept of this study. If the input voltage is of the form Vi(s) =
Aiest the output will be of the form Vo(s) = Aoest. In general s = j ?+? has both real and imaginary
parts. The system transfer function is defined as
V ?s ? Ai
,
(1)
H ?s ? ? 0
?
Vi ?s ? Ai
where Ai and Ao are complex numbers. Once the system transfer function is defined, it is
possible to consider only imaginary components of the complex frequency, i.e., s = j?. From
Eulers relation
(2)
exp ? j? ? ? cos?? ? ? j sin?? ? ,
sinusoidal terms that do not decay or grow are obtained.
1
(a)
Aiest
(b)
H(s)
Aoest
Aiej?t
H(j?)
Aoej?t
Fig. 1. Transfer function, H(s), and frequency response, H(j?), of a linear time invariant (LTI)
system. (a) A complex exponential input, Vi(s) = Aiest, gives rise a complex exponential output,
Vo(s) = Aoest. In general, s = j??? has both real, ?, and imaginary, j ?, components. The input
and output voltages are scaled by the complex numbers Ai and Ao, respectively. (b) By
considering only the imaginary part, s = j?, the study can be restricted to the class of sinusoidal
signals that do not decay or grow. The transfer function, H(s), restricted to purely imaginary
frequencies, s= j ?, is known as the frequency response H(j?).
In the special case of a first order RL or RC circuit, the system response can be defined using
complex impedances. Kirchhoffs current and voltage laws give us the voltage divider law
V ?s ?
Z2
.
(3)
H ?s ? ? o
?
Vi ?s ? Z1 ? Z 2
Recall that for a resistor R, inductor L, and a capacitor, C, the complex impedances are given by
ZR ? R ,
1
,
Zc ?
sC
and
(4)
(5)
Z L ? sL ,
(6)
respectively.
Z1
Vi
Z2
AC
Vo
Fig. 2. Complex impedance circuit. The relationship between the input and output can be found
using the voltage divider law Vo/Vi = Z2/(Z1+Z2), where Vi is the input voltage and Vo is the
output voltage.
2
The decibel (dB) scale is often used for describing the output amplitude changes relative to the
input amplitude. For voltage signals, the gain is defined on a decibel scale using the relation
? V0 ?
?.
(7)
Gain(dB) ? 20 log 10 ??
?
V
? i ?
Notice that each 10 fold increase in the amplitude produces 20 dB of gain. Similarly, decreasing
the output by a factor of 10 is equivalent to -20 dB of gain.
Figure 3 illustrates how to determine the gain and phase of the system frequency response when
in the input and output voltages are displayed on the same oscilloscope trace. The gain follows
from Eq. 7 using the measured amplitudes of the in input, |V i|, and the output, |Vo|. The phase
angle, ??, is calculated using
?? ? ??t ? 2?f?t .
(8)
Voltage, V
(Volts)
(Voltage)
Time, t
(s)
|Ai|
|Ao|
?t
Fig. 3. System response gain and phase. The amplitude of the input signal, |Ai|, and the output
signal, |Ao|, define the system gain using the relation Gain = 20 log10(|Ao|/|Ai|) dB. The phase
difference is found by determining the time interval, ?t, between adjacent zero crossings. If the
two sinusoids have a radian frequency ?, the phase difference between the two is ???? ??t =
2?f?t, where f is the frequency in Hertz. Note that in the case shown here, the output is lagging
the input, therefore the phase difference is negative.
3
III. Experimental Measurements and Intermediate Calculations
Using a breadboard (R.S.R. Electronics DS05012A), function waveform generator (Agilent
33220A), oscilloscope (Agilent DS05012A), 1.5 k? resistor, and 0.1 ?F capacitor, construct the
low and high pass filters as shown in Figs. 4 and 5.
A. Low Pass Filter
Apply a 1 V amplitude, or 2 Vp-p, sinusoidal input to the circuit as shown in Fig. 4. Measure the
output voltage amplitude and time lag as a function of frequency. Use a table similar to Table 1
to record your data and calculate the gain in dB and phase angle.
R = 1.5 k?
|Vi| = 1 V
C = 0.1 ?F
AC
Vo
Fig. 4. First order RC low pass filter system with 1 V amplitude sinusoid input voltage. The
output voltage is measured across the capacitor.
Frequency, f
(Hz)
Table 1 Case 1 circuit data and calculations
Gain Ratio
Gain
|Vo|/|Vi|
20Log
Lag ?t, (s)
10(|Vo|/|Vi|)
(dB)
10.0
31.6
100
316
1,000
3,160
10,000
31,600
100,000
*To convert to degrees multiply by 180/?.
4
Phase Angle
???2?f?t
B. High Pass Filter
Apply a 1 V, or 2 Vp-p, sinusoidal input to the circuit as shown in Fig. 5. Measure the output
voltage amplitude and time lag as a function of frequency. Use a table similar to Table 2 to
record your data and calculate the gain and phase angle.
C = 0.1 ?F
|Vi| = 1 V
R = 1.5 k?
AC
Vo
Fig. 5. First order RC high pass filter system with 1 V amplitude sinusoid input voltage. The
output voltage is measured across the resistor.
Frequency, f
(Hz)
Table 2 Case 2 circuit data and calculations
Gain Ratio
Gain
|Vo|/|Vi|
20Log10(|Vo|/|Vi|)
Lag ?t, (s)
(dB)
10.0
31.6
100
316
1,000
3,160
10,000
31,600
100,000
*To convert to degrees multiply by 180/?.
5
Phase Angle
???2?f?t
IV. Report
Write a short technical report, with an abstract, that includes your plots and analysis. Your
abstract should only be one paragraph and less than 200 words in length. The details of any
derivations and tables should be put in appendices and the question answers included as part of
the discussion. Remember to adhere to IEEE standards when using equations, figures, and
subplots. Write in third person, not first or second person. For example, avoid we, I, and you.
When using an abbreviation, always define the term first and put the abbreviation in brackets the
first time it is used. Avoid starting a sentence with an abbreviation. When listing equipment, use
a generic term, such as oscilloscope or breadboard, and next to this generic term put the company
name and model number in brackets. Equations should be part of a sentence and successively
labeled with numbers. Define all variables. Make sure you label your subplots (a) and (b).
Your plots should also include a caption and descriptive sentences. Avoid passive tense where
possible. Use complete paragraphs and consistent tenses. In addition, your conclusion section
should simply state whether your theoretical systems analysis successfully predicted your
measurements. Do not extrapolate your conclusions beyond what your current study has actually
demonstrated.
A. Plots
1. Using two subplots, graph the gain, in dB, and phase angle versus the log10 frequency for
the low pass filter. Watch the sign of your phase!
2. Using two subplots, graph the gain, in dB, and phase angle versus the log10 frequency for
the high pass filter.
B. Analysis
1. Using Kirchhoffs current and voltage laws, prove the voltage divider law.
2. Calculate the transfer functions, H(s), for the low pass and high pass filters.
3. Based on the transfer functions, determine the frequency responses, H(j?), for the low
and high pass filters.
4. Treating your frequency responses, H(j ?), as a complex number, calculate the magnitude
and phase of the frequency responses for the low and high pass filters.
5. Plot the theoretical gain and phase predictions on your corresponding data plots.
C. Questions
1. How well does the theory agree with the measured experimental results?
2. Why is case 1 referred to as a low pass filter and case 2 a high pass filter?
6
Common Technical Writing Mistakes
Abstract
Always include an abstract, even for a technical memo. The abstract should be less than 200
words. Include the studys purpose, or objective, and summarize the methods, results, and
conclusions. By reading the abstract, the reader should be able to understand the study without
reading the body of the text.
Abstract mistakes
1.
2.
3.
4.
5.
6.
7.
8.
9.
Not including an abstract.
Using more than one paragraph.
Not stating the purpose or objective of the study.
Not summarizing the methods.
Not summarizing the results.
Not summarizing the conclusion(s).
Not defining all abbreviations used in the abstract the first time they are used.
Starting a sentence with an abbreviation or number.
Making reference to figures or tables in your abstract.
Introduction
The introduction should provide enough material to orient the reader to the subject of your
research. The last part of your introduction should outline the study.
Introduction mistakes
1.
2.
3.
4.
Not including an introduction.
Referencing web sites and web pages. Reference books, journal articles etc.
One sentence paragraphs.
Methods and Materials
The purpose of the methods and materials section is to give the reader enough information so
that they can repeat the experiment. The methods and materials should describe what was done
and what equipment and materials were used.
Methods and materials mistakes
1. Not including a methods and materials section.
2. Copying the lab procedure into the methods section.
3. Listing equipment. For example
? Oscilloscope
? Voltmeter
? Etc.
4. Incorrect equipment referencing. When describing equipment in the methods and
materials section use the generic name followed by the manufacturer and model number.
For example: An oscilloscope (Tektronix MPR304) measured the time dependent
voltages. A low pass filter was designed using filter circuit simulation software (Texas
Instruments FilterPro 3.1).
5. Not using a consistent tense.
Results
The results section should present the data to the reader using paragraphs, figures, and tables.
Results mistakes
1. Only including graphs, plots, and tables in the results section. You must have organized
2. Using titles on figure plots or graphs.
3. Not using sentence capitalization to write figure captions.
4. Not including descriptive sentence(s) following your figure caption.
5. Not defining all figure variables.
6. Starting a figure caption with an abbreviation.
7. Plot and figure labels that are difficult to read.
10. Missing plot axis labels or units. Units must be in brackets. For example Voltage (mV).
11. Too many plots making the flow of the results difficult to follow. Consider placing extra
data in appendices.
12. Not including key figures or data in the results section.
Conclusions
Conclusions mistakes
1. Using more than one paragraph for your conclusions.
2. Extrapolating your conclusions beyond the study. The conclusions should simply state
whether the theoretical systems analysis or hypothesis successfully predicted the measurements.
Do not extrapolate the conclusions beyond what the current study has actually demonstrated.
References
References mistakes
1. Incorrect formatting. Use IEEE format for books, journal articles etc.
2. References to web links. Web links change. Use books, journal articles etc that will not
change over time.
Miscellaneous mistakes
1. Using first and second person. That is, avoid I, we, our, you, they etc
2. Undefined abbreviations. If you use an abbreviation in the abstract it must be defined
there. If you use an abbreviation in the body of the paper define it the first time it is used
even if it is defined in the abstract.
3. Not including equations as part of a sentence.
4. Not numbering equations.
5. Not defining all equation variables.
6. Confusing tenses.
7. Very long sentences. If a sentence is over thirty words consider breaking it into two
smaller sentences.
8. Excess use of passive tense.
9. Mixing up introduction, methods and materials, results, and discussion sections.
BME 306 Biomedical Engineering Lab II
Spring 2017
Instructions for Technical Report
1. Cover page
This section should be formatted according to the usual technical report format:
WESTERN NEW ENGLAND UNIVERSITY
SPRINGFIELD, MA
COLLEGE OF ENGINEERING
BME 306 BME Laboratory II
Spring 2017
Experiment Name
The report should begin on the page following the cover page.
2. Introduction
Brief discussion of the goals of the experiment, including why it is important or relevant to the
course you are studying. Introduce, if applicable, any similar work or studies that have been done
previously in this area. Discuss any relevant physiology that applies to this topic.
3. Materials & Methods
Explain the steps you took in completing the experiment, including your setup and analysis.
Identify any materials or equipment you used to solve the problem. Include technical figures, and
label all figures with appropriate dimensions and units.
4. Results & Discussion
State the factual findings of your experiment. Identify, if appropriate, the mean value of the data,
the standard deviation, the range, the maximum, the minimum, percent of increase, or decrease,
etc. Present results in text, tables, or graphs, depending on what format is the most appropriate.
Keep in mind that if you display data, it should be discussed. Explain why your results might
have turned out as they did. What differences or similarities exist between the findings and the
expected values? Explain why errors, unusual trends, or outlier points occurred among the results.
5. Conclusions
Summarize the highlights of the work and state how the findings may be helpful in future
engineering studies. Remember, these are brief concluding remarks. Data cannot be displayed
here for the first time, only repeated from the results section.
6. Acknowledgements
Use this section to thank those who have assisted with your work, including industrial sponsors,
equipment donator/supplier, professors (other than the course instructor) or others who gave you
guidance or assistance.
7. Appendix
Use appendices for information that is not central to the report, but important for a complete
understanding. Only include information that you are discussing in the main body of the text.
Each appendix should be labeled with a letter and should be cited within the body of the report.
Example appendix material:
? Long derivations
? Programming code that is relevant
? Alternative design schematics
? MSDS (material safety data sheets)
? IRB approval forms
Formatting Tables & Figures in Technical Reports
?
Captions for figures should be placed below the figure, whereas table heading are placed above
the table.
Be sure to mention the table or figure in the text before you display it. For example, if your
experiment was to conduct a survey, you would first describe the survey and then show the table
with the results:
To evaluate the food options in the hospital cafeteria, a survey was given to male and
female subjects aged 18-35. The results from the survey are shown in Table 1.
Table 1. Results of food choice survey for males and females aged 18-35.
Respondent
Score (0-10)
1
1
2
1
3
4
4
3
5
1
6
2
The results from the survey strongly suggest that new food options should be explored. A
subsequent analysis of the cafeteria food offerings was conducted and the results
displayed in Figure 1 as a function of frequency.
7
Frequency of Offering (per week)
?
6
5
4
3
2
1
0
Pizza
Pasta
Sandwiches
Fruit
Soup
Food Offering
Figure 1. Analysis of food offerings as function of frequency (offerings per week).
The results confirm a low variety in food choice offerings. A follow up survey 

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