\begin
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Lab Report
\begin
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\begin{document}
%************************************TITLE PAGE**************************************%
\begin{titlepage}
\begin{center}
\textbf{\LARGE University Tunku Abdul Rahman}\\[0.5cm]
\textbf{\large FACULTY OF ENGINEERING AND GREEN TECHNOLOGY}\\[0.2cm]
\vspace{20pt}
\includegraphics{Logo_Utar.png}\\[1cm]
\par
\vspace{20pt}
\textbf{\Large UGEA2523 COMMUNICATION SYSTEMS}\\
\vspace{15pt}
\myrule[1pt][7pt]
\textbf{\LARGE LABORATORY REPORT 1}\\
\vspace{15pt}
\textbf{\large Signal Transmission $\&$ Distortion}\\
\myrule[1pt][7pt]
\vspace{25pt}
\textbf{\large Student Name \hspace{20pt} Student ID}\\
1. Low Hui Tyen \hspace{45pt} 14AGB06230 \\ % No1
% 2. Low Hui Tyen \hspace{45pt} 14AGB06230 \\ % No2
\vspace{45pt}
\textbf {\large Lecturer in charge:}\\[0.2cm]
\Large {Ir. Chan Cheong Loong}\\[0.1cm]
\end{center}
\par
\vfill
\begin{center}
\textbf{Submission Date : 16/06/2017}\\
\end{center}
\end{titlepage}
%************************************TABLE OF CONTENTS**************************************%
% %Sumário
% \newpage
% \tableofcontents
% \thispagestyle{empty}
% %End Sumário
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%***********SECTION 1************%
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\newpage
\section{Introduction}
The process of sending, propagating and receiving an analogue or digital information signal over a physical point-to-point or point-to-multipoint transmission medium, either wired, optical fiber or wireless is called transmission. A distortion is defined as the alteration of the original shape of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted, and often many methods are employed to minimize it in practice.
\newline
In this experiment, we are dealing with frequency response of RC circuit. Frequency response is defined as the analysis of circuit with different frequency of a sinusoidal source. With the sinusoidal source, the transfer function, $H(s)$ will be the magnitude and phase of output voltage to the magnitude and phase of input voltage of a circuit :
\begin{gather*}
H(s) = \frac{V_o(s)}{V_i(s)}\\
\end{gather*}
The circuit in Figure~\ref{fig:Lowpass} is a first order low pass filter circuit. First order is defined as 1 pair of resistor and capacitor connected in series in a circuit. A low pass filter attenuates high frequency signal input and only allows low frequency which below the cut-off frequency to pass through. Cut-off frequency is the frequency filter start to attenuate the passage of the input signals: $f_c = 2\pi RC$. At low frequncy, the reactance of capacitor is high and the resistance is low. This result the voltage potential across the capacitor is higher than voltage drop across the resistor. Therefore, high frequency signals are attenuated in the experiment.
\newline
The circuit in Figure~\ref{fig:Highpass} is acting as second order high pass filter which is oppose to the meaning of low pass filter. High pass filter passes signals above the cut-off frequency and attenuates low frequency signals. By reversing the roles of resistors and capaciors, the reactance of capacitors are low at high frequency signals. Therefore, the capacitors in the circuit act as open circuit and attenuate low frequency input signals until cut-off frequency reached.
\newline
In last part of this experiment, we are studying the multipath propagation as show in Figure~\ref{fig:Multipath}. Multipath occurs when a signal takes more than one path from the transmitting antenna to the receiving antenna. Regarding to lecture notes, the signals are received in a terrestrial environment, i.e. where reflections are present and signals arrive at the receiver from the transmitter via a variety of paths. The overall signal at the radio receiver is a summation of the variety of signals being received. As they all have different path lengths, the signals will add and subtract from the total dependent upon their relative phases. Sometimes these will be in phase with the main signal and will add to it, increasing its strength. At other times they will interfere with each other. This will result in the overall signal strength being reduced.
%********************************%
%***********SECTION 2************%
%********************************%
\newpage
\section{Objectives and Learning Outcomes}
\begin{enumerate}
\item Distortion of signal during transmission occurs if the frequency response of the transmission channel is not of constant amplitude and linear phase. In this laboratory work, the student will:
\begin{enumerate}
\item Design and conduct an experiment to analyse the frequency, amplitude and
phase responses of a RC transmission line model.
\item Conduct an experiment to demonstrate the frequency sensitive fading phenomenon using a simple two-path model of multi-path propagation.
\end{enumerate}
\item To understand some factors that may cause signal transmission distortion, and be motivated to study further other factors such as non-linearity, load mismatching, time variant transmission medium properties and Gaussian noise.
\end{enumerate}
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%***********SECTION 3************%
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\section{Equipments}
\begin{itemize}
\item Breadboard, two 100 Ohm resistors, two 51 Ohm resistors, and three 10 k Ohm resistors, four 1µF capacitors and three µ741 Op-Amp.
\item DC power supply, Function generator, Oscilloscope and Digital multi- meter.
\end{itemize}
%********************************%
%***********SECTION 4************%
%********************************%
\section{Methodology}
%***********************************************SUBSECTION 1************************************************%
\subsection{Frequency Response Measurement}
%*******************SUBSUBSECTION 1******************%
\subsubsection{Part 1}
\begin{enumerate}
\item An experiment was designed to study the amplitude and frequency response of the circuit shown in Figure ~\ref{fig:Lowpass}.
\item Data collected was recorded in an appropriate format. The results were analysed and interpreted.
\end{enumerate}
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=100mm,scale=0.5]{Lowpass.png}
\end{center}
\caption{\label{fig:Lowpass}RC circuit(Low pass filter)}
\end{figure}
%*******************SUBSUBSECTION 2******************%
\subsubsection{Part 2}
\begin{enumerate}
\item A 100 Hz square wave was applied to the input and the effect on the output waveform $V_2$ was observed.
\item Repeated with 1kHz follow by 10 kHz square wave.
\item The observations were analysed and interpreted.
\end{enumerate}
%*******************SUBSUBSECTION 3******************%
\subsubsection{Part 3}
\begin{enumerate}
\item The changes in the results obtained in Part 2 were discussed if the circuit shown in Figure~\ref{fig:Lowpass} is replaced with circuit shown in Figure~\ref{fig:Highpass} below:
\end{enumerate}
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=100mm,scale=0.5]{Highpass.png}
\end{center}
\caption{\label{fig:Highpass}CR circuit(High pass filter)}
\end{figure}
%***********************************************SUBSECTION 2************************************************%
\subsection{Fading due to Multipath Propagation}
\begin{enumerate}
\item $V_s$ was set to sine wave, frequency 500 Hz and Amplitude 10 volts, the waveform $V_2$ was sketched and its amplitude was recorded.
\item Repeated for frequencies 1, 1.5, 3 and 5 kHz and identify the frequency that results in fading.
\end{enumerate}
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=100mm,scale=0.5]{Multipath.png}
\end{center}
\caption{\label{fig:Multipath}Multipath circuit(Band pass filter)}
\end{figure}
%********************************%
%***********SECTION 5************%
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\null\newpage
\section{Result}
%***********************************************SUBSECTION 1************************************************%
\subsection{Frequency Response Measurement for RC circuit(Low pass filter)}
%*******************SUBSUBSECTION 1******************%
\subsubsection{Experimental Result}
%****************************************Table 1******************************************%
\begin{table}[!ht]
\caption{\label{tab:Table 1} Experimental result for Second order low pass filter}
\centering
\begin{tabular}{c c c c c}
\toprule
\textbf{$ V_{in} (mV)$}
& \textbf{$ f $}
& \textbf{$V_{2} (mV)$}
& \textbf{(I.L)dB}
& \textbf{Phase ($\phi $)} \\
\cmidrule[0.4pt](r{0.125em}){1-1}%
\cmidrule[0.4pt](lr{0.125em}){2-2}%
\cmidrule[0.4pt](lr{0.125em}){3-3}%
\cmidrule[0.4pt](lr{0.125em}){4-4}%
\cmidrule[0.4pt](lr{0.125em}){5-5}%
% \midrule
5760 & 100 Hz & 1190 & -13.70 & $-5^{\circ}$ \\
\myrowcolour%
5730 & 200 Hz & 1160& -13.87 & $-11^{\circ}$ \\
5630 & 500 Hz & 1070 & -14.42 & $-21^{\circ}$ \\
\myrowcolour%
5320 & 1 kHz & 849 & -15.94 & $-38^{\circ}$ \\
4930 & 2 kHz & 560 & -18.89 & $-65^{\circ}$ \\
\myrowcolour%
4830 & 5 kHz & 265.1 & -25.21 & $-74^{\circ}$ \\
4780 & 10 kHz & 123.86 & -31.73 & $-77^{\circ}$ \\
\myrowcolour%
4700 & 20 kHz & 32.55 & -43.19 & $-79^{\circ}$ \\
4700 & 50 kHz & 7.7 & -55.7 & $-83^{\circ}$ \\
\myrowcolour%
4700 & 100 kHz & 2.29 & -63.26 & $-85^{\circ}$ \\
\bottomrule\\
\end{tabular}
\end{table}
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=140mm,scale=0.5]{P1_fr.png}
\caption{\label{fig:P1_fr}Graph of insertion loss versus frequencies (Low pass filter)}
\end{center}
\end{figure}
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=140mm,scale=0.5]{P1_pr.png}
\caption{\label{fig:P1_pr}Graph of phase versus frequencies (Low pass filter)}
\end{center}
\end{figure}
\FloatBarrier
%**************************************** END ******************************************%
%*******************SUBSUBSECTION 2******************%
\subsubsection{Transmission distortion over a RC channel}
\begin{figure}[!ht]
\centering
\subfloat[frequency = 100Hz]{\includegraphics[width=0.4\columnwidth]{LPF100.png}}
\qquad
\subfloat[frequency = 1kHz]{\includegraphics[width=0.4\columnwidth]{LPF1k.png}}
\qquad
\subfloat[frequency = 10kHz]{\includegraphics[width=0.4\columnwidth]{LPF10k.png}}
\caption{Signal Transmission Distortion for LPF}
\label{fig:STDLPF}
\end{figure}
%***********************************************SUBSECTION 2************************************************%
\newpage
\subsection{Frequency Response Measurement for the CR circuit(High pass filter)}
%*******************SUBSUBSECTION 1******************%
\subsubsection{Experimental Result}
%************************************Table 1**************************************%
\begin{table}[!ht]
\caption{\label{tab:Table 2} Experimental result for Second order low pass filter}
\centering
\begin{tabular}{c c c c c}
\toprule
\textbf{$ V_{in} (mV)$}
& \textbf{$ f $}
& \textbf{$V_{2} (mV)$}
& \textbf{(I.L)dB}
& \textbf{Phase ($\phi $)} \\
\cmidrule[0.4pt](r{0.125em}){1-1}%
\cmidrule[0.4pt](lr{0.125em}){2-2}%
\cmidrule[0.4pt](lr{0.125em}){3-3}%
\cmidrule[0.4pt](lr{0.125em}){4-4}%
\cmidrule[0.4pt](lr{0.125em}){5-5}%
% \midrule
7310 & 100 Hz & 14.19 & -54.24 & $173^{\circ}$ \\
\myrowcolour%
7040 & 200 Hz & 40.0& -44.91 & $164^{\circ}$ \\
6720 & 500 Hz & 170.0 & -31.94 & $151^{\circ}$ \\
\myrowcolour%
6430 & 1 kHz & 492.85 & -22.31 & $131^{\circ}$ \\
5370 & 2 kHz & 1050 & -14.18 & $108^{\circ}$ \\
\myrowcolour%
3920 & 5 kHz & 1840 & -6.57 & $72^{\circ}$ \\
3180 & 10 kHz & 2040 & -3.86 & $45^{\circ}$ \\
\myrowcolour%
2840 & 20 kHz & 2170 & -2.34 & $25^{\circ}$ \\
2530 & 50 kHz & 2200 & -1.21 & $12^{\circ}$ \\
\myrowcolour%
2580 & 100 kHz & 2230 & -1.27 & $7^{\circ}$ \\
\bottomrule\\
\end{tabular}
\end{table}
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=140mm,scale=0.5]{P2_fr.png}
\caption{\label{fig:P2_fr}Graph of insertion loss versus frequencies (High pass filter)}
\end{center}
\end{figure}
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=140mm,scale=0.5]{P2_pr.png}
\caption{\label{fig:P2_pr}Graph of phase versus frequencies (High pass filter)}
\end{center}
\end{figure}
\FloatBarrier
%**************************************** END ******************************************%
%*******************SUBSUBSECTION 2******************%
\subsubsection{Transmission distortion over a CR channel}
\begin{figure}[!ht]
\centering
\subfloat[frequency = 100Hz]{\includegraphics[width=0.4\columnwidth]{HPF100.png}}
\qquad
\subfloat[frequency = 1kHz]{\includegraphics[width=0.4\columnwidth]{HPF1k.png}}
\qquad
\subfloat[frequency = 10kHz]{\includegraphics[width=0.4\columnwidth]{HPF10k.png}}
\caption{Signal Transmission Distortion for HPF}
\label{fig:STDHPF}
\end{figure}
%***********************************************SUBSECTION 3************************************************%
\subsection{Frequency Response Measurement for Fading due to Multipath Propagation (Band pass filter)}
%*******************SUBSUBSECTION 1******************%
\subsubsection{Experimental Result}
%************************************Table 1**************************************%
\begin{table}[!ht]
\caption{\label{tab:Table 3} Experimental result for Multipath Propagation (Band pass filter)}
\centering
\begin{tabular}{c c c}
\toprule
\textbf{$ f $}
& \textbf{$V_{2} (mV)$}
& \textbf{(I.L)dB} \\
\cmidrule[0.4pt](r{0.125em}){1-1}%
\cmidrule[0.4pt](lr{0.125em}){2-2}%
\cmidrule[0.4pt](lr{0.125em}){3-3}%
% \midrule
500 Hz & 1520 & -13.27\\
\myrowcolour%
1000 Hz & 1320& -14.49\\
1200 Hz & 1260 & -14.89\\
\myrowcolour%
1400 Hz & 1120& -15.92\\
1600 Hz & 1280 & -14.76\\
\myrowcolour%
1800 Hz & 1310 & -14.56\\
2000 Hz & 1450 & -13.67\\
\myrowcolour%
2500 Hz & 1490 & -13.44\\
3000 Hz & 1510 & -13.32\\
\myrowcolour%
5000 Hz & 1650 & -12.55\\
\bottomrule\\
\end{tabular}
\end{table}
\begin{figure}[!ht]
\begin{center}
\includegraphics[width=140mm,scale=0.5]{P3_fr.png}
\caption{\label{fig:P3_fr}Graph of insertion loss versus frequencies (Band pass filter)}
\end{center}
\end{figure}
\FloatBarrier
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%***********SECTION 6************%
%********************************%
\newpage
\section{Discussion}
A signal transmission system is the electrical channel between an information source and destination. Signal transmission distortion can be divided into amplitude distortion and frequency distortion. Linear distortion includes any amplitude or delay distortion associated with a linear transmission system. Amplitude distortion is easily described in the frequency domain; it means simply that the output frequency components are not in correct proportion. Since this is caused by $H(f)$ not being constant with frequency, amplitude distortion is sometimes called frequency distortion. The most common forms of amplitude distortion are excess attenuation or enhancement of extreme high or low frequencies in the signal spectrum. While the frequency-domain description is easy, the effects in the tie domain are far less obvious, except for very simple signals. The loss of the high-frequency term reduces the “sharpness” of the waveform. The “flat” frequency response means that the frequency range over which $|H(f)|$ must be constant to within a certain tolerance so that the amplitude distortion is sufficiently small.
\subsection{Part1}
For the part 1 of the experiment, we are dealing with the frequency response for a RC circuit which is also a first order low pass filter. The low pass filter only allows low frequency signals from 0Hz to its cut-off frequency, $f_{c}$ point to pass while blocking those any higher. The circuit shown in Figure~\ref{fig:Lowpass} uses two passive first-order low pass filters connected or “cascaded” together to form a second-order or two-pole filter network. Hence, we can see that a first-order low pass filter can be converted into a second-order type by simply adding an additional RC network to it and the more RC stages we add the higher becomes the order of the filter. As the order of the filter is increased, the roll-off slope becomes steeper and the actual stop band response of the filter approaches its ideal stop band characteristics \cite{LPF}.
\newline
Based on the Table~\ref{tab:Table 1}, we obtained that the range of insertion loss from -13.70dB to -63.26dB which is decreasing as the frequency increasing. The frequency response and phase response of the low pass circuit were show in Figure~\ref{fig:P1_fr} and Figure~\ref{fig:P1_pr} respectively. The result from the Frequency Response graph shows that the insertion loss decreases gradually as the frequency is increasing. Regarding to the Phase Response graph plotted, the degree of phase decreases as the frequency increases. The Frequency Response of the filter to be nearly flat for low frequencies until it reaches its Cut-off Frequency point $(f_{c})$. This is because the reactance of the capacitor is high at low frequencies and blocks any current flow through the capacitor. We obtained the cutoff frequency at -16.7dB (-13.7dB-3dB) which are 1100Hz experimental result. The phase shift for experimental result is $-43^{\circ}$.
\newline
Following, we have observed the transmission distortion for the RC circuit for different values of frequencies. The integrator is basically a low pass filter circuit operating in the time domain that converts a square wave “step” response input signal into a triangular shaped waveform output as the capacitor charges and discharges. A triangular waveform consists of alternate but equal, positive and negative ramps. From observation on the output waveform as show as Figure~\ref{fig:STDLPF}, the output become more triangle in shape as the frequency of the input signal increase. This is because of the exponential charging and discharging processes of the capacitor cause the triangular waveform at output. As our input waveform is square wave, it consists of summation of odd harmonic of sinusoid. Since LPF attenuates high frequency components, the summation of low frequency of odd harmonic sinusoid give rise to the triangle shape of output waveform.
\subsection{Part2}
In part 2 of the experiment, we are dealing with the frequency response for a CR circuit which is also a second order high pass filter. The high pass filter only allows high frequency signals from its cut-off frequency, $f_{c}$ point and higher to infinity to pass through while blocking those any lower. The circuit shown in Figure~\ref{fig:Highpass} uses two first-order high pass filters connected or cascaded together to form a second-order or two-pole high pass network.
\newline
Based on the Table~\ref{tab:Table 2}, we obtained that the range of insertion loss from -54.24dB to -1.27dB which is increasing as the frequency increasing. The frequency response and phase response of the high pass circuit were show in Figure~\ref{fig:P2_fr} and Figure~\ref{fig:P2_pr} respectively. The result Frequency Response graph shows a positive relationship between the insertion loss and the frequency. The insertion loss increases as the frequency increases. Whereas for the Phase Response graph, the degree of phase decreases as the frequency increases.
Frequency Response for high pass filter is the exact opposite to that of a low pass filter. It has a response curve that extends down from infinity to the cut-off frequency. We obtained the cutoff frequency at -4.27dB (-1.27dB-3dB) which are 10000Hz experimental result. Also we can see that the phase angle $(\phi)$ of the output signal LEADS that of the input and is equal to $+46^{\circ}$ for experimental result at frequency $f_{c}$.
\newline
Thereafter, we have observed the transmission distortion for the CR circuit for different values of frequencies. If we change the input signal to that of a “square wave” shaped signal that has an almost vertical step input, the response of the circuit changes dramatically and produces a circuit known commonly as a Differentiator. However, if we feed the High Pass Filter with a Square Wave signal operating in the time domain giving an impulse or step response input, the output waveform will consist of short duration pulse or spikes as shown in Figure~\ref{fig:STDHPF}. Each cycle of the square wave input waveform produces two spikes at the output, one positive and one negative and whose amplitude is equal to that of the input. The rate of decay of the spikes depends upon the time constant, (RC) value of both components, (t = R x C) and the value of the input frequency. The output pulses resemble more and more the shape of the input signal as the frequency increases.
\subsection{Part3}
In part 3 of the experiment, we have dealing with the fading due to the multipath propagation. The circuit is actually a combination of first order low pass filter and second order high pass filter to form a simple two-path model of multipath propagation. As the input signal transmitted through the low pass filter and high pass filter, each of the signal will be attenuated and cause the phase shift by different amount. Hence, when the signals reach the load resistance, the summation of each signal will cause interference and phase shift of output signal which is known as multipath fading. ‘Fading’ means rapid fluctuations of the amplitudes, phases or multipath delays of a radio signal over a short period or short travel distance. This might be so severe that large scale radio propagation loss effects might be ignored. The frequency response is shown in Figure~\ref{fig:P3_fr}. From the Table~\ref{tab:Table 3}, the fading frequency is 1.4kHz because it has the lowest amplitude among the 10 frequencies. The results proved that the frequency 1.4kHz has the narrowest bandwidth and allow minimum signal to pass through.
\newline
Last but not least, there are some precautions that we should realize throughout the experiment. The lesser number of wire are encouraged to avoid any confusion when having circuit checking if any error occurs. Moreover, the electrical devices and breadboard should be checked if its well-functioning before using it to avoid any delay. Lastly, the polarity of the capacitor must place correctly to avoid any accident happen.
%********************************%
%***********SECTION 7************%
%********************************%
\newpage
\section{Conclusion}
There are many factors may cause distortion in signal transmission. After completion of the experiment, we understand some factors from experiment, which are channel with insufficient bandwidth, multipath propagation channel and fading channel.
In the last part of this experiment, the frequency that caused fading due to multipath propagation is 1.4kHz.
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\patchcmd{\thebibliography}{\section*}{\section}{}{}
% Now we need a bibliography:
\begin{thebibliography}{99}
%Each item starts with a \bibitem{reference} command and the details thereafter.
\bibitem{LPF} % Web document
Electronics Tutorials Low Pass Filter
\url{http://www.electronics-tutorials.ws/filter/filter_2.html}.
\bibitem{HPF} % Web document
Electronics Tutorials High Pass Filter
\url{http://www.electronics-tutorials.ws/filter/filter_3.html}.
\bibitem{MVP} % Web document
Multipath Wave Propagation
and Fading
\url{http://www.iitg.ernet.in/scifac/qip/public_html/cd_cell/chapters/a_mitra_mobile_communication/chapter5.pdf}.
\bibitem{5}
Frequency response of RC and LR circuits
\url{http://www.ece.sunysb.edu/~oe/Leon/ESE211/Lab05}
\end{thebibliography}
\noindent
\end{document}