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