What is Phase and Amplitude Noise?

A perfect sinusoidal oscillator would produce an ideal sine wave

s(t) = A sin(wt)

.. (1.1)     

but in practice the signal always contains some noise.   This can be represented by fluctuations in the amplitude of the signal (variations in A) and by fluctuations in the signal phase (so phase becomes wt + phase noise).  

In general we can represent the noisy oscillator signal as

s(t) = (A + a(t)) sin(wt + f(t))

.. (1.2)     

where:  

a(t) represents the amplitude fluctuations in the signal - the  amplitude noise and
f(t) represents the phase fluctuations or the phase noise.

Notice that the amplitude noise does not affect the zero crossings and that the phase noise does not affect the amplitude of the signal peaks.

Well designed signal sources have small amplitude noise.   Amplitude noise can also be removed using automatic level control (ALC) systems,  or by passing the signal through a limiting amplifier.   (The output of an ideal limiting amplifier is determined only by the zero crossings of the signal,  and these are unaffected by the amplitude noise.)   Amplitude noise is also rejected to some degree by many of the mixers used in radio systems.

Phase noise is another matter.   Once present on a signal it is very difficult to remove,  and as will be explained later,  it can have a major impact on system performance.  Thus for the rest of this reference,  we will assume that the signal contains only phase noise and so is of the form

s(t) = A sin(wt + f(t))

.. (1.3)     

In the time domain,  if the signal s(t) from (3) was viewed on an ideal oscilloscope,  the effect of f(t) would be to cause timing jitter on the zero crossings of the waveform.  

Figure 1 - Signal with very bad phase noise

 This timing jitter can be significant in many applications,  for example if s(t) is used as a data clock in a digital transmission systems,  the timing jitter could cause erroneous data sampling.   This is not the major concern to radio engineers,  the phase noise usually has to be severe (as in Figure 1) to cause significant timing errors.   

Levels of phase noise that are far too small to detect on an oscilloscope can cause changes to the spectrum of a signal that can be very important in radio applications .    Such minute amounts of phase noise on a transmitter signal can result in the transmitter causing significant interference to other services,  whereas minute amounts of phase noise on a receiver local oscillator can severely reduce the receiver selectivity or cause other undesirable effects.    These effects are of major concern to radio engineers and are addressed in later sections.