# What is the percentage modulation of phase modulation PM?

What is the percentage modulation of a phase modulation (PM)? Can you further explain and give detail? I am currently stuck in finding the information about this

• How long is a piece of string? Apr 18 '21 at 9:55
• @Andyaka "As long as it is." Apr 18 '21 at 10:01
• Percentage is just another way of expressing a ratio, ie a pure number. The top of the ratio is obviously the modulation, in radians. There are only a couple of options for the bottom of the ratio. a) One radian, so it means the same as modulation Index or b) the maximum rated or permitted modulation for that particular scheme, so 100% means rated modulation index. All that's needed now is a little more context in the question. Apr 18 '21 at 10:38
• Start with the definition of phase modulation. Look what happens when you raise the modulation; at one point something interesting happens, and that would be the 100% point Apr 19 '21 at 5:53

Phase Modulation is a broad category and generally refers to carrier modulation. However on baseband modulation this also spans a broad spectrum of modulation types like PWM, Bi-phase, Manchester, MFM, RLL etc.

There are tradeoffs for carrier spectral BW for small and large signal modulation for the % deviation ratio of maximum.

QPSK has 4 phases such that 2 (Sin+cos) patterns may each be binary modulated to produce 4 phase or Baud symbol patterns mapping 2 bits in about the same bandwidth, BW. This can be extended to 128 phases. But better modulation methods combining Amplitude Modulation with PM may compress even more logic states into one time symbol or Baud.

But as Shannon-Hartley’s theorem dictates this requires more signal to noise ratio SNR to achieve the same bit error rate (BER) to achieve this BW compression of bits/Baud but it does increases the channel capacity.

This is necessary in wide BW channels such as Modems so that the entire BW is sub-divided into smaller AM+PM or whatever sub-channels handled in parallel by a Digital Signal Processor (DSP).

Well, at any one moment in time you could advance the phase angle of the carrier by 180° and, at another moment in time you could retard the carrier phase angle by 180°. That covers the full spread of all possible angles. The question then remains how you want to approach this in terms of attributing a percentage value. You could say that the limits were +100% for an advance of 180° and -100% for a phase retard of 180°.

Or you could call it +/- 50% but, whatever you call it, you should define what is meant by the percentage value in case there was someone who didn't understand your definition.