Why cosine wave for phase deviation in phase modulation?

In summary, phase modulation is a system that maintains constant amplitude while varying the phase and rate of phase change of the modulated carrier through a modulating signal. The phase deviation is proportional to the instantaneous amplitude of the modulating voltage and the rate of phase variation is equal to the modulating frequency. However, in the case of a sine wave modulating signal, the curve for phase deviation is a cosine wave. This is because when analyzing modulation as a vector rotation, the real component is the cosine and the imaginary component is the sine of the modulation angle. This may also be due to the use of a VCO in the book, which introduces a 90 degree phase shift between the tuning voltage and the phase.
  • #1
asitiaf
21
0
Phase modulation is a system in which the amplitude of the modulated carrier is kept constant, while its phase and rate of phase change are varied by the modulating signal.
By the definition of phase modulation, the amount by which the carrier phase is varied from its unmodulated value, called the phase deviation, is made proportional to the instantaneous amplitude of the modulating voltage.
The rate at which this phase variation changes is equal oy the modulating frequency.
But in the book, i see that modulating signal is a sine wave, but the curve for phase deviation is cosine wave. Why?
 
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  • #2
asitiaf said:
Phase modulation is a system in which the amplitude of the modulated carrier is kept constant, while its phase and rate of phase change are varied by the modulating signal.
By the definition of phase modulation, the amount by which the carrier phase is varied from its unmodulated value, called the phase deviation, is made proportional to the instantaneous amplitude of the modulating voltage.
The rate at which this phase variation changes is equal oy the modulating frequency.
But in the book, i see that modulating signal is a sine wave, but the curve for phase deviation is cosine wave. Why?

Could you upload scans of these figures? That would make it easier for us to explain what is going on...
 
  • #3
I don't see how a 90 degree phase shift would be introduced. If the modulating voltage is zero, and it is really phase modulation, then the phase deviation would be zero unless there is some shift introduced that you are not mentioning. Maybe it is frequency modulation?
 
  • #4
When modulation is analysed as a vector rotation, the real component is the cosine while the imaginary component is the sine of the modulation angle. This may be why it is more natural to employ the cosine than the sine in the analysis of the modulation.
 
  • #5
If book is showing phase modulation using VCO, the tuning voltage (which is in phase with freq) will be 90 degree shifted from phase (integral of frequency).

This is speculation though since OP has not posted the figures.
 
Last edited:

1. Why is a cosine wave used for phase deviation in phase modulation?

The use of a cosine wave in phase modulation is due to its symmetrical and periodic nature. This makes it easier to interpret the changes in phase and allows for more efficient modulation.

2. What is the relationship between the cosine wave and phase deviation in phase modulation?

The cosine wave represents the change in phase of the carrier signal, with the amplitude of the wave corresponding to the amount of phase deviation. This allows for precise control of the phase and thus the modulation of the signal.

3. Can other types of waves be used for phase deviation in phase modulation?

Yes, other types of waves such as sine waves or square waves can also be used for phase deviation in phase modulation. However, the cosine wave is the most commonly used due to its smooth and symmetrical nature.

4. How does phase deviation affect the frequency of the carrier signal in phase modulation?

Phase deviation does not directly affect the frequency of the carrier signal. However, it does change the position of the signal in time, which can result in a perceived change in frequency.

5. What are the advantages of using a cosine wave for phase deviation in phase modulation?

Using a cosine wave for phase deviation allows for more precise and efficient modulation of the signal. It also helps to reduce distortion and interference in the transmitted signal, resulting in better overall signal quality.

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