FOM Calculation for VCO

[tfwee]

vco fom

I have an issue on the calculation of FOM for VCO, I have been reading paper on comparsion of FOM but I always find that my calculation is different. Can anyone help me to identify what is the problem with my calculation.

FOM = 10 log [(fo/Δf)²*1/P] - L{Δf}

where fo is the center frequency, Δf is the frequency offset, L{Δf} is the phase noise at Δf and P is the power.

Case 1:

P=230uW
fo=0.4GHz
L{Δf} @ 1MHz = -118dBc/Hz

The FOM is 177dB in the paper but my calculation is 207dB. I wonder where did I go wrong in my calculation. Where does my 30dB extrac come from? :?: Can anyone enlighten me. Thank.

 

[rfsystem]

fom vco

My understanding of the always used FOM is in contradiction with the use. You can have a very good FOM if the passive tank circuit has a very Q. Because PN is ~1/Q^2 you can have 30dB difference.

Because FOM is used to demonstrate circuit cleverness it should be separated from the passive technology. So if you get a good inductor, or tank, you can make a lousy oscillator.

My understanding of the FOM is that it should be normalized to the power needed to restore the tank looses. So if you have a high Q tank you need less power to restore the tank but the stored energy is the same. The quality measure of the circuit is the efficiency of converting DC power into AC power to restore the tank and how much noise power is added by this active circuit. So an oscillator is more seen as an effective DC to AC converter. And please restore the energy losses at times where it does impact the phase. That is the common understanding of noise shaping.

Coming back to your question. Is the tank of relative high Q?

 

[tfwee]

fom calculation

Yes, I agree that High Q would provide good phase noise for the design of the VCO but the issue that I have here is the calculation of the FOM. As I has mentioned, the FOM figure that I get is always 30dB higher then what is stated in the paper attached. There must be some error in my calculation but I just could not find out what is the problem. I just substitute the figure provided for Case 1 example and the FOM figure I get is around 207dB.

 

[rfsystem]

vco power calculation

The reference [17] in the IEEE-Solid-State was not clear. Kinget from [17] does not use SI units! P have to use in the formula as mW.

 

[tfwee]

dco fom

So that is the case, that is why my calculation has additional 30dB due to the fact of the power should be in mW. Since FOM is a calculation to compare result between each design. It does not really matter as it would give the same comparsion for all case.:idea: