# figure-of-merit (FoM) calculation & GSM local oscillator

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#### deepsetan Hi guys, 1. I know that this formula is only valid when L(fm) is in dBc/Hz. In SPICE simulation such as LTSPICE, the phase noise generated is always in in nV/Hz unit. Let say if the noise generated is 2.3505nV/Hz, how to convert this phase value to dBc/Hz? . I only managed to convert nV/Hz to dBm/Hz but I'm not satisfy with my calculation.

2. If my local oscillator is a 2.4-GHz oscillator, does it suitable to be use with GSM800 and GSM900? Do I need a new GSM with higher frequency to make it compatible with the 2.4-GHz oscillator?

#### erikl

##### Super Moderator
Staff member ... Let say if the noise generated is 2.3505nV/Hz, how to convert this phase value to dBc/Hz? . I only managed to convert nV/Hz to dBm/Hz but I'm not satisfy with my calculation.

dBc is related to the carrier signal power, s. here.

#### deepsetan dBc is related to the carrier signal power, s. here.

Hi,

I knew that dBc and dBm is two different things. Thats why I guess there is something wrong with my calculation. Do you have any reference on how to do the conversion of nV/Hz to dBc?

#### erikl

##### Super Moderator
Staff member Do you have any reference on how to do the conversion of nV/Hz to dBc?

AFAIK, noise voltage is measured in units of [V/√Hz], noise power in units of [W/Hz].

You need as reference the peak spectral voltage of your carrier signal Vc. If your noise voltage is Vn , then dBc = 20*log (Vn/Vc).

Example: Vc=1mV/√Hz ; Vn=1nV/√Hz ; L(fm)=-120dBc

#### deepsetan AFAIK, noise voltage is measured in units of [V/√Hz], noise power in units of [W/Hz].

You need as reference the peak spectral voltage of your carrier signal Vc. If your noise voltage is Vn , then dBc = 20*log (Vn/Vc).

Example: Vc=1mV/√Hz ; Vn=1nV/√Hz ; L(fm)=-120dBc

Hi,

Thanks, ok now I'm more understand. But what do you meant by 'peak spectral voltage of carrier signal'?. If I measure at frequency of 2.4-GHz, so I will get the value of Vn. But how I determine the value of Vc?

#### erikl

##### Super Moderator
Staff member ... what do you mean by 'peak spectral voltage of carrier signal'?.
If I measure at frequency of 2.4 GHz, so I will get the value of Vn. But how I determine the value of Vc?

I'd think fo is your oscillator frequency (2.4GHz), fm the measurement frequency (e.g. 2.0 GHz) where you measure the spectral noise voltage Vn = L (in units of V/√Hz).

So I think Vc is the 'peak spectral voltage of your carrier signal' (@ 2.4 GHz), whereas Vn is the spectral noise voltage at a certain measurement frequency of interest fm, where you want to diagnose the frequency-dependent FoM.

But I don't know your above equation, so perhaps I'm wrong.

• deepsetan

### deepsetan

Points: 2

#### deepsetan I'd think fo is your oscillator frequency (2.4GHz), fm the measurement frequency (e.g. 2.0 GHz) where you measure the spectral noise voltage Vn = L (in units of V/√Hz).

So I think Vc is the 'peak spectral voltage of your carrier signal' (@ 2.4 GHz), whereas Vn is the spectral noise voltage at a certain measurement frequency of interest fm, where you want to diagnose the frequency-dependent FoM.

But I don't know your above equation, so perhaps I'm wrong.

Yes erikl. I think you are might correct about the equation! My oscillator is 2.4-GHz.

2.400-GHz = Vc
2.401-GHz = Vn @ 1-MHz

#### deepsetan Hi,

This is what I got from my simulation.

Vc = 85.3808pV/Hz @ 2.4-GHz
Vn = 85.3804pV/Hz @ 2.401-GHz

Vn/Vc = 0.99

20*log (0.99) = -50.86u

I think there is something wrong with this value or the calculation. Any idea?

#### erikl

##### Super Moderator
Staff member Your Vc value is very low, so perhaps it's not Vc , but Vnoise(@fosc), i.e. the carrier signal voltage is already subtracted.

Or you have a very broad spectrum from your osc. Could you show its spectrum, say fosc±10MHz ?

#### deepsetan Your Vc value is very low, so perhaps it's not Vc , but Vnoise(@fosc), i.e. the carrier signal voltage is already subtracted.

Or you have a very broad spectrum from your osc. Could you show its spectrum, say fosc±10MHz ?

Hi,

Yes you are correct. 85.3808pv/Hz is the value that I obtain for Vnoise at 2.4-GHz. Is that correct? If not,so how do we calculate or get the Vc? At 10-MHz offset frequency, the value is 85.6531pV/Hz.

#### erikl

##### Super Moderator
Staff member As I told you above:
You need as reference the peak spectral voltage of your carrier signal Vc.

• deepsetan

### deepsetan

Points: 2

#### deepsetan As I told you above:

Hi,

Thanks erikl for reminding me about the spectral voltage. My peak spectral voltage for 2.4-GHz is 180mV/Hz. Therefore the phase noise is around -185 @ 1-MHz. I really appreciate your help. Thank you.

#### erikl

##### Super Moderator
Staff member My peak spectral voltage for 2.4-GHz is 180mV/Hz. Therefore the phase noise is around -185 @ 1-MHz.

-185 dBc , that's really a good SNR-1 for 1MHz carrier distance, congratulation!

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