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How to convert phase noise unit "dBc/Hz" to "rad/√Hz" ?

I want to get the phase noise with unit of "rad/√Hz", but from most notes, I only find  phase noise with unit of "dBc/Hz". How to convert phase noise unit "dBc/Hz" to "rad/√Hz" ?

  • Hello,
    I can help with going from dBc/Hz to rad or seconds.

    Say you have -150dB/Hz of phase noise. The 1st thing to do is to convert this to total integrated noise. I will assume the noise is flat across frequency and the clock frequency is 50 MHz. Also, assume an integration noise BW of 2*50 MHz = 100 MHz. In that case the total integrated noise is PN_dBc = -150 dBc + (10*Log(100 MHz)) = -150dBc + 80 = -70 dBc.

    To then get the rms phase noise in radians = SQRT[2*{10^(PN_dBc/10)}] = 4.47*10^(-4)

    At this point if you wanted rad/Hz, you would simply divide the number above by the clock frequency, so 4.47*10^(-4)/50 MHz =8.94*10^(-12)

    Now if you want the jitter in seconds which is fairly common, divide the number above by 2*pi, to get a jitter of 1.423 ps.

    Hope this helps.