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# Figure of Merit (FOM), Oscillator

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#### hrkhari

##### Full Member level 4
Hi Guys:

I have a problem here, lets say an integrated LC-CMOS osc has a power comsumption, P=6mW, center frequency, fo=1.8GHz, phase noise L{Δf}=-116dBc/Hz, at offset frequency, Δf=600kHz, according to the formula in determining FOM, given as:

FOM=10log{(fo/Δf)²/L{Δf}.P}

I could get the FOM as 71.12, but it is stated in the journal as 177.8, can anyone assist me in calculting the FOM. Thanks in advance

Rgds

Hi,

There is a different formula for calculating FOM, see Equation 2 in paper page 1:

The reciprocal of your (fo/Δf)² is used in it.

There are other, maybe useful papers for you to digest, see formula 3 in

and some good data collection on FOM of different designs in the last pages of this paper:

http://www-smirc.stanford.edu/papers/islped98s-tam.pdf

I tried to use your data info for checking 71.12 or 177.8 but I must have made mistakes somewhere. Perhaps going through thorougly on the above papers and your original journal paper you can figure out the truth.

rgds
unkarc

Hi:

Thanx unkarc, it was some good reading materials, but I still could not compute the FOM factor to obtain the same values proposed by the journals, I don't really know where I'm going wrong, I hope someone could shed some light on it. Thanks in advance

Rgds

Anyone has experience in computing the FOM factor of the osc, pls do comment on this inquiry.......

Rgds

All references take advantage of good passive Q factors. So if Q is high the FOM is also good. But the intention is that the FOM should indicate good circuits. If you design a relative bad circuit but with a good tank Q you will have a goog FOM. That is what I think goes wrong.

I have a different view of the FOM. I think an oscillator is nothing more or less than a DC/AC converter. The phase noise is good if the ratio of tank power to noise power is good. So you need less DC power to drive a high Q tank to the same tank power. Also the phase noise is better.

The best FOM is simply the conversion effciency of DC power to AC power required to drive the tank.

rfsystem said:
All references take advantage of good passive Q factors. So if Q is high the FOM is also good. But the intention is that the FOM should indicate good circuits. If you design a relative bad circuit but with a good tank Q you will have a goog FOM. That is what I think goes wrong.

I have a different view of the FOM. I think an oscillator is nothing more or less than a DC/AC converter. The phase noise is good if the ratio of tank power to noise power is good. So you need less DC power to drive a high Q tank to the same tank power. Also the phase noise is better.

The best FOM is simply the conversion effciency of DC power to AC power required to drive the tank.

Do you mean if the Q of VCO tank is high, we should reduce the bias current
to reduce the thermal noise so as to get better phase noise performance?

Phase noise is related to ratio of stored energy or circulated energy between L and C to the tank looses at relative frequencies. So a high frequency oscillator have the same PN at higher frequency derivation.

What I suggest is that the FOM does not say much about the quality of the circuit regarding phase noise. I would differentiate the quality of the passive tank components from the active circuit.

A more simplified view is treating the active part of oscillator as DC/AC converter which should compensate the ohmic losses. The the circuit quality is simply the conversion efficiency.

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