Definition of Single Sideband Phase Noise

Signal generators,  voltage controlled oscillators and other signal sources often come with a phase noise specification such as shown in Figure 1.2

Figure 1.2  VCO Phase Noise

This happens to be the phase noise of one of our VCO designs at 450MHz.   The view on a spectrum analyzer is given below in Figure 1.3.

The SSB Phase Noise,  often given the symbol L_f(f_m),  is a power ratio.   It is the ratio of the power in a 1Hz bandwidth a frequency f_m away from the carrier,   to the power in the carrier itself.  As it is a power ratio,  to convert to dBc/Hz,  use 10log₁₀(L_f(f_m))

Example: Looking at Figure 1.2,  we see that the SSB phase noise at an offset frequency of 10kHz is about -120dBc/Hz,    ( L_f(10kHz) = 10^-12 ).   This means that if the VCO was producing 0dBm at 450MHz,  a 1Hz wide filter at 450.01MHz would receive -120dBm,  and a second filter at 449.99MHz would also receive -120dBm.

Note that the definition of phase noise implicitly assumes that the spectrum is symmetric,  as it is for a signal that has only phase noise and no amplitude noise.   Signals with asymmetric spectrum (i.e. spectrum at f_c + f_m is different to spectrum at f_c - f_m  ),  have a combination of amplitude and phase noise,  and it is necessary to remove the amplitude noise before measuring L_f(f_m) on a spectrum analyser.

 Although SSB Phase Noise is conventionally defined in a 1Hz bandwidth,   in use it is necessary to determine the noise power in other bandwidths.   If the SSB Phase Noise is approximately constant over the bandwidth of interest then

Noise Power in bandwidth B Hz centered a distance f_m from the carrier (i.e. centered at  f_c + f_m    or    f_c -  f_m ) is approximately given by 

Power in B Hz = B L_f(f_m) P_c

where P_c is the power in the carrier.   It is generally more convenient to work in dB's,  the corresponding equation is

Power in B Hz [dBm] = 10 log₁₀(B)  + L_f(f_m) [dBc/Hz] +  P_c [dBm]

.. (1.10)     

Example: Looking at Figure 1.2 again,  and noting that the SSB phase noise at an offset frequency of 10kHz is -120dBc/Hz.   If the VCO was producing 0dBm at 450MHz,  then a 3kHz wide filter at 450.01MHz would receive approximately -85dBm,  and a second filter (also 3kHz wide) at 449.99MHz would also receive around -85dBm.   This is indicated by the following (simulated) spectrum analyzer display for the VCO with phase noise given in Figure 1.2,  where the resolution bandwidth is 3kHz.    This spectrum analyzer display shows the power received by a 3kHz wide filter as the filter center frequency is varied over the display sweep range.  

Figure 1.3 Spectrum Analyser display of VCO

The accuracy of (1.10) degrades as the bandwidth B increases,  as the phase noise slope is not linear (it appears linear in Figure 1.2 but that has logarithmic scales,  it is typically varying as 1/f_m²).     To accurately determine the power in adjacent channels,  it is necessary  to integrate the phase noise curve.   If you have measurements of phase noise you can integrate them numerically,  if you are designing a synthesizer then using a simulation tool like SimPLL can do this automatically.