# Why cosine wave for phase deviation in phase modulation?

1. ### asitiaf

21
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?

### Staff: Mentor

Could you upload scans of these figures? That would make it easier for us to explain what is going on...

3. ### meBigGuy

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. ### Baluncore

3,235
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. ### the_emi_guy

634
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: Jan 2, 2014