Name: Yoong Jia Wee ID: 011698Titile: Waveform and Frequency
SpectraObjectives1. To observe the waveforms and frequency spectra
of various commonly encountered communications signals.2. Explain
the principles of analogue modulation.3. Compare the experimental
results with theoretical predictions using spectrum analysis.
IntroductionIntelecommunications, modulation is the process of
conveying a message signal, for example a digital bit stream or
ananalogaudio signal, inside another signal that can be physically
transmitted. Modulation of a sine waveform transforms
abasebandmessage signal into apassbandsignal.Amplitude modulation
(AM)Amplitude Modulation, the message signal is being imposed on to
a single frequency carrier wave. The carrier waves amplitude will
increase and diminish along with the amplitude of the message
signal. The modulation depth is the ratio of the peak of the
modulating signal to the un-modulated signal. The frequency
spectrum [C(t)] can be written as the following:
According to the equation above the received signal consists of
two spectral lines at fc-fm and at fc+fm.fm carrying the message
whereas the spectral line fc representing the carrier containing no
information.
Frequency Modulation (FM)
Frequency Modulation, conveys information over a carrier wave by
varying its instantaneous frequency. The modulated carrier signal
is given by the equation below:
By expanding the above equation as a Fourier series. Set of
equations is obtained. This is an infinite series with each term
representing a harmonic in the spectrum.
Experiment A- Frequency ModulationDiscussions
1. The carrier frequency was set to be 2.3 MHz and message
signal was set to be 100kHz. After generating message signal and
carrier signal from the function generator, the amplitude was set
to 0 and the attenuation was set to 0dB. A single peak was obtained
from the spectrum analyser which is the peak of the carrier
signal.
2. The amplitude of the message signal was increased by using
the function generator. The amplitude of the sidebands increases as
the amplitude of the message signal increases. However, the
amplitude of the carrier decreased and then became zero zero at
modulating index of 2.4. The peak-to-peak value, Vx, of the
modulating "message" signal obtained was 650mV.
3. From Figure 1,the amplitude of the carrier signal at 2MHz is
zero. There are 6 pairs of side bands with decreasing amplitude.
According to Bessel Table, at the modulation index of 2.4, the
number of sidebands should be 5 pairs. As the amplitude of the
carrier signal is set to zero, all the power can be seen to reside
on the sidebands. When the carrier signal amplitude is zero, this
means that there is no power in the center frequency. All the power
is in the sidebands.
Figure 1
4. The frequency of the sidebands corresponds to the following
equation: Jn (, where n ranges from 0 to n+1. When n=0, the central
frequency is at 2.3MHz. The sideband frequency decreases at 100kHz
at the left hand side ( )and the sideband frequency increases at
100kHz at the right hand side of the central frequency().
Therefore, the number of sidebands are equal on both sides. As n
increases, the amplitude of the sidebands decreases.
5. The calculation of Vx for of=1.0 , 4.0 are shown below:
When When Vm = Vm = = 0.2708V = 1.0833V
Figure 3: = 4.0
Figure 2: = 1.0
6. From the Bessel table, when the modulating index is 1, there
will be 3 sidebands. There is a steady decrease in amplitude in
both theoretical and practical values.
7. From the Bessel table, the number of sidebands should be 7
when =4.0. The amplitude of the sidebands should have a gradual
decrease from the first band to the seventh band. However we
obtained more than 7 sidebands in this experiment.
Experiment B- Amplitude ModulationDiscussions
1. When the signal generator was set to AM, and a square wave
was set at a frequency of 2MHz, the resulting amplitude spectrum is
shown in figure 4.
Figure 4it is similar to the sinc function,
It is having discrete values, thus there are more than 1 spike
having discrete values with each separation of 2MHz. Therefore, the
result matches the theory. 2. Figure 6: 100% modulation depthFigure
5: 10% modulation depth
3. Modulation of a signal occurs when the modulating signal
voltage is less than the carrier signal voltage. Output power is
the highest at the transmitter when the signal is 100%
modulated.
4. The changes can be seen when message signal changes from 50
KHz to 500kHz.
Figure 7: message signal at 500kHz.From figure 7, we can see
that there are 1 pair of sidebands each at the right and left hand
side of the centre frequency.
Decreasing the modulation depth does not cause any change in the
power of the carrier signal, but it has an effect on the sidebands.
It decreases the power of the sidebands as the theoretical formula
states Ps=M2Pc/2. Therefore, as the modulation depth, M, decreases,
the power of the sidebands decreases, Ps. 5. Decreasing the
modulation depth decreases the power of the sidebands. This is
because Ps=M2Pc/2. As the modulation depth, M, decreases, the power
of the sidebands decreases, Ps.
6. When the modulating frequency increases, the distance between
the sideband and the distance between the carrier signal increases
and vice versa. On a smaller scale of the frequency analyser, the
carrier signal and the sidebands will shift to the left when the
modulating frequency decrease, and it shifts to the right when the
modulating frequency increase.ConclusionIn conclusion, the
objectives were met. The theoretical predictions and the results
obtained using the spectral analysis was compared. Better
understanding of AM and FM was achieved.
References1. http://en.wikipedia.org/wiki/Modulation