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DATA COMMUNICATION THEORY

LAB REPORT

Report on Digital Transmission of Analogue Signals

Pulse Amplitude Modulation

INTRODUCTION:

The experiment uses the L.J.Electronics Modicom-1 board to investigate the sampling of signals, and the filter effects on the reconstruction of the original signal from the sampled input. The sample/Hold operation is also investigated in this experiment.

The Modicum -1 board allows an analogue signal to be sampled at a number of different rate(2kHz,4kHZ,8kHZ,16kHz,32kHz).The pulse width is varied in the steps of 0% from 0 to 90 of the sampling interval. Second order and fourth order low pass filter are available with cut-off frequencies set at 3.4 kHz.

BACKGROUND:

L.J.Electronics MODICOM-1 board is used to investigate the sampling of signals, and the effects of filter on the reconstruction of the original signal from the sampled input. In addition to this Sample/Hold operation is also investigated. [pic] MODICOM-1 board

The MODICOM-1 board is considered as five different blocks namely

1.) Power Input

2.) Sampling Control Logic

3.) Sampling Circuit

4.) Second Order Low Pass Filter and

5.) Fourth Order Low Pass Filter

Sampling Control logic:

It is used to generate the timing and control signals that sample the input waveform, and also creates a sinusoidal 1 kHz signal in order to perform the experiments.

[pic]

Power Input:

These are the input electrical connections necessary to provide the input power for the module.

[pic]

Sampling Circuit:

Sampling circuit is to sample the input waveform depending upon the sampling control signal.

[pic]

Second Order Low Pass Filter:

It is a Kind of Low pass Filter with a break frequency of 3.4 KHz and a pass band gain of 1.56. The input of the filter is attenuated by resistor chain R34 & R35 and its value is chosen in such a way to give the overall SECOND ORDER LOW PASS FILTER block a gain of unity. The final filter output appears at the terminal point TP (44).

[pic]

Fourth Order Low Pass Filter:

It has a break frequency of 3.4 kHz and a pass band gain of 2.55.The input of the filter is attenuated by resistor chain R24 & R 25 and its value is chosen in such a way to give the overall FOURTH ORDER LOW PASS FILTER block a pass band gain of unity. The final filter output appears at the terminal point TP (49).

[pic]

Frequency selector Push Button: It is used to select the frequency of the internal sampling control signal. Each time the push button is pressed, a different LED is illuminated in the sampling control logic block. The LED’s are labeled as 320kHZ,160kHZ,80kHz ,40kHz and 20kHz and the frequency is divided by 10 so the resulting sampling frequencies are given by 32kHz,16kHz,8kHz,4kHz and 2KHz. Duty Cycle Selector Switch: It is a ten position switch which allows the duty cycle of the sampling control signal to be varied in discrete steps of 0% to 90%.0% duty cycle indicates that there is no sampling and 90% indicates that analog signal is sampled 90% of the time. Sampling Control Switch: The sampling control switch allows a sampling control signal to be provided by an external source through the SAMPLING CONTROL UNIT. The sampling control switch must be in an external position in order to use an external sampling control signal. If on-board sampling control signal is going to be used then the sampling control switch must be in internal position. Oscilloscope: (commonly abbreviated to scope or O-scope) is a type of electronic test equipment that allows signal voltages to be viewed, usually as a two-dimensional graph of one or more electrical potential differences (vertical axis) plotted as a function of time or of some other voltage (horizontal axis). The oscilloscope is one of the most versatile and widely used electronic instruments. Oscilloscopes are widely used when it is desired to observe the exact wave shape of an electrical signal. In addition to the amplitude of the signal, an oscilloscope can measure the frequency, show distortion, and show the relative timing of two related signals. Oscilloscopes are used in the sciences, medicine, engineering, telecommunications, and industry. General-purpose instruments are used for maintenance of electronic equipment and laboratory work. Special-purpose oscilloscopes may be used for such purposes as adjusting an automotive ignition system, or to display the waveform of the heartbeat.

EXPERIMENT OBJECTIVE:

To investigate the principals of sampling to give Pulse Amplitude Modulation (P.A.M) and its characteristics.

EQUIPMENTS:

Equipments used in this Experiment are as follows:

1. L.J.Electronics Modicom-1 board
2. Power supplies
3. Oscilloscope

EXPERIMENT:

This experiment deals with

Sampling of signals, the effects filters have on the reconstruction of the signal.

PULSE AMPLITUDE MODULATION:

Pulse Amplitude Modulation can be defined as the amplitudes of regularly spaced pulses are varied in proportion to the corresponding sample values of a continuous message signal. Pulse-amplitude modulation, acronym PAM, is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses.Demodulation is performed by detecting the amplitude level of the carrier at every symbol period. Pulse-amplitude modulation is widely used in baseband transmission of digital data.P.A.M. and T.D.M are employed with Pulse Code Modulation (P.C.M.) technique in electronic telephone exchange switching and in digital transmission of voice and also television over telecommunication networks.

[pic]

PAM Waveform

In the above figures, fig (a) represents the original signal, fig (b) represents the Pulse Amplitude Modulated signal and fig(c) represents the Sampling signal.

SAMPLING:
The process of converting a continuous time signal in to a discrete time signal is known as sampling. In this sampling is performed by the sampling circuit with the sampling frequency (fs). The sampling process is usually described in the time domain; it is basic to digital signal processing and digital communication. In order to have a practical utility, it is necessary to choose the sampling rate properly o that the sequence of samples uniquely defines the original analog signal. This is the essence of the sampling theorem.

[pic] The above diagram represents the sampled wave form using the sampling Frequency 32 KHz

PAM OUTPUT:
1 kHz sine wave (TP7) and the Sample Output (TP33)
The 1 kHz sine wave is sampled at 32 kHz sampling frequency and hence there will be 32 samples per cycle. The wave that we obtained after sampling is known as PAM wave form.

[pic]

1 kHz sine wave (TP7) and Sample output (TP33) In the above figures, figure1 represents the 1 kHz sine wave (TP7) and the figure 2 represents the SAMPLE OUTPUT (TP33) on the oscilloscope.
Here the 1 kHz sine wave is sampled at 32 kHz sampling frequency hence there is 32 samples per cycle and the resulting wave form is known as PAM signal.

Reconstruction of original sine wave:
The original sine wave is reconstructed using the Low Pass Filter, here the PAM signal is connected to the input of the Fourth Order Low Pass Filter and the output of the fourth order Low Pass Filter is displayed on the oscilloscope.

[pic][pic] Reconstructed Waveform
In the above figures, figure 1 represents the PAM signal (TP33) and the figure 2 represents the reconstructed sine wave from its samples using Fourth Order Low pass Filter.

Sample output (TP33) and fourth order Low Pass Filter Output (TP49):

[pic] For 2 kHz sampling Rate
[pic]
For 4 kHz sampling Rate
[pic]
For 8 kHz Sampling Rate
[pic]
For 16 kHz sampling Rate
[pic]
For 32 kHz sampling Rate
From the above figures it is clear that Lower sampling rate introduces distortion in to the filter’s output due to Aliasing because the sampling rate 2 kHz and 4 kHz is less than the Nyquist Rate.
Observation:
Aliasing
Aliasing refers to an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled. It also refers to the distortion or artifact those results when the signal reconstructed from samples is different than the original continuous signal. [pic] , [pic], Where [pic] is the Nyquist Rate and [pic] is the sampling frequency
In order to avoid Aliasing the sampling rate must be greater than the Nyquist rate.
Nyquist Rate Nyquist rate is defined as the minimum sampling rate required to avoid aliasing, it is equal to twice the highest frequency contained within the signal. [pic], [pic] is the Nyquist Rate
Since the sampling rates 2 kHz and 4 kHz are less than the Nyquist rate, the output of the Fourth order Low pass filter is obtained with distortion. In order to overcome the distortion, the sampling rate should be chosen in such a way that it should be greater than the Nyquist Rate.

Amplitude Changes of the Filter waveform:
Sampling Duty Cycle
The position of the duty cycle selector switch in position (5) indicates that the duration of each pulse is 50% of the sampling period and it is known as sampling duty cycle which varied in the proportion from 0% to (09% in the steps of 10%.

Sampling period
It is defined as the time between the beginnings of the adjacent samples. For 60 % duty (TP33) and(TP49 )Out put
[pic]
For 30% Duty Cycle TP (33) and TP (49) output
[pic]
In the above figures, figure 1 represents the sample output TP(33) and figure 2 represents the Filter output TP (49).
Observation:
Tabulation:
|Duty Cycle Values |Peak to Peak Voltage at TP(49) |
|(%) |(volts) |
| | |
|10% |0.4v |
|20% |1v |
|30% |1.52v |
|40% |1.96v |
|50% |2.44v |
|60% |3.04v |
|70% |3.44v |
|80% |3.84v |
|90% |4.32v |

The above table represents the amplitude values of filter output for various duty cycle values. When the value of the duty cycle is less, the amplitude value of the filter waveform is also less because decrease in the duty cycle value will decrease the pulse width of the sample output which in turn affects the amplitude value of the filter waveform. Hence when the duty cycle value is increased linearly, the amplitude value of the filter waveform is also increased.

Second Order and Fourth order Low pass Filter Outputs:

The second order and fourth order low pass filter output waveform is compared with each other under the input waveform given from the sample input.

[pic]

For 4 kHz Sampling Rate, TP (44) and TP (49) outputs

[pic]

For 8 KHz Sampling Rate, TP (44) and TP (49) outputs

[pic]

For 16 KHz Sampling Rate, TP (44) and TP (49) outputs

[pic]

For 32 KHz Sampling Rate, TP (44) and TP (49) outputs

Observation:

In the above figures, figure 1 represents the Second order Low pass Filter output TP(44) and Figure 2 Represents the Fourth Order Low Pass Filter Output (TP49).By comparing the outputs of the second order and fourth order low pass filter outputs we can identify that fourth order low pass filter gives the best output because the fourth order filter’s pass band gain is more when compared to the second order low pass filter and the value of pass band gain of the fourth order low pass filter is given by 2.55

Fourth Order Low Pass Filter output is the Best

Sample output (TP33) and Sample/Hold output (TP35):

[pic]

For 32 kHz sampling Rate and 50% sampling Duty Cycle

Sample/Hold output (TP35) and Sample output (TP33)

[pic]

For 8 kHz sampling Frequency and 50% Duty Cycle

[pic]

For 8 KHz Sampling Frequency and 30% Duty Cycle

Observation:

The Sampling Frequency is varied from 32 kHz to 16 kHz, 8 KHz and 4 KHz. On the above mentioned sampling rate, the number of samples per cycle in the sample output decreases with the decrease in the value of sampling frequency.

Moreover when the duty cycle is varied, the pulse width of the sample output changes in turn. Hence when the value of the duty cycle is increased upon the time held, the pulse width of the sample output is also increased. The increase in value of duty cycle will result in the smoothening of the Sample/Hold waveform.

Sample/Hold Output (Tp35) and Filter Output (TP49):

[pic]

For 32 KHz Sampling Rate and 50% Duty cycle

[pic]

For 8 kHz Sampling Rate

[pic]

For 4 KHz Sampling Rate

[pic]

For 2 kHz sampling rate

Observation:

In the above figures, figure 1 represents the Sample/Hold output and Figure 2 represents the Filter output. When the sampling rate is decreased by the successive press of frequency selector switch, the output forms of the Sample hold output and the filter output is also changes. The out waveform if more distorted when the sampling rate is less.

Comparison of filter outputs (TP49) under Sample input (TP33) And Sample/Hold output (TP35):

Initially the sample output is given as the input to the filter and its corresponding amplitude value of the filter wave form ids noted down under different duty cycle values. Later the Sample/Hold output is given as the input to the filter and the corresponding amplitude values of the filter is noted down for different duty cycle values and the values are tabulated and compared with each other.

Filter output (TP49) with the sample input (TP33)

|Duty Cycle Values |Peak to Peak Voltage at TP(49) |
|(%) |(volts) |
| | |
|10% |0.4v |
| | |
|20% |1v |
|30% |1.52v |
|40% |1.96v |
|50% |2.44v |
|60% |3.04v |
|70% |3.44v |
| | |

Filter output (TP49) with the Sample/Hold input (T35)

|Duty Cycle Values |Peak to Peak Voltage at TP(49) |
|(%) |(volts) |
| | |
|10% |4.4v |
| | |
|20% |4.4v |
|30% |4.4v |
|40% |4.4v |
|50% |4.4v |
|60% |4.4v |
|70% |4.4v |
| | |

Observation:

The amplitude value of the filter waveform changes linearly with the change in duty cycle values when the sample output is given as the input of the filter. Whereas when Sample/Hold output is given as the input of the filter, the amplitude value of the filter waveform remains the same even when the duty cycle value changes.

Comparison of second order (TP44) and Fourth order Low pass Filter (TP49) Outputs under Sample/Hold input (TP35):

[pic]

For 4 KHz sampling Rate and 50% Duty cycle

Figure 1 (TP44) and Figure 2 (TP49)

[pic]

For 8 KHz Sampling Rate and 50% Duty Cycle

[pic]

For 16 KHz Sampling Rate and 50% Duty Cycle

Observation:

The outputs of the second order low pass filter and the fourth order low pass filter is displayed on the oscilloscope by adding the Sample/Hold output to the input of the second order low pass filter. The output wave form obtained in this case is less distorted when compared to the output of the filters with the sample input.

CONCLUSION:

The sampling of the signal is investigated using Modicom-1 board. Here the analogue signal is sampled at different rate (2 KHz, 4 KHz, 8 kHz, 16 KHz and 32 KHz).The Pulse Amplitude Modulated wave form is obtained by the sampling process and the original information signal is reconstructed from its samples using Filters. The Fourth order Low pass Filter produces better output when compared to the second order low pass filter, more over the output of the filter is less distorted when the input is a Sample/Hold waveform but it will be more distorted when the input is a sample input.

REFEReNCES :

WEBSITES:

http://en.wikipedia.org/wiki/Transformer

http://www.camiresearch.com/Data_Com_Basics/data_com_tutorial.html

http://wiki.answers.com/Q/

http://www.webopedia.com/TERM/P/

WWW.answers.yahoo.com/question/index

BOOKS:

1.communication systems by Simon Haykins-4th Edition.

2.Digital Communications by Bernard Sklar-2nd Edition.

3.Communication Systems by Proakis-4th and -5th Edition.

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