Hi,

I am trying to set-up a simple simulation to understand trade-offs between different integrated inductors and varactor combinations in a LC tank.
I wrote a netlist containing one ideal L , one ideal C and one ideal R in parallel. In addition I put a negative resistance element with current limiting, to make an oscillator, and I run a spice transient analysis.

The netlist is the following,

**** circuit

.param Fosc=1G
.param Per_osc='1/Fosc'                                                                  
.param twopi='4.0*asin(1.0)'                                                        
.param Wosc=twopi*Fosc                                                          
.param indvalue=10nH                                                            
.param capvalue='1/(indvalue*Wosc**2)'                                          
.param vosc_max=2V                                                              
.param Imax=0.1mA                                                                  
.param resvalue=10K                                                        
Gnres op on VALUE='-Imax*tanh(100*V(op,on))'                                
Losc1 op 0 'indvalue/2' IC=Imax                                                  
Losc2 0 on 'indvalue/2' IC=Imax                                                  
Cosc  op on capvalue IC=0                                                        
Rpar op on resvalue                                                              
                                                                                                                               
.param simtime='500*1/Fosc'                                                    
.param simstep='1/Fosc/10'                                                      
                       
**** simulation

.tran simstep simtime uic


**** outputs

.probe tran I(Gnres) I(Losc1) I(Losc2) I(Cosc) I(Rpar)
.probe tran v(op,on)

.measure tran  average(v(op,on)**2/resvalue) * average power dissipated on R
.measure tran  max(v(op,on))**2/2/resvalue    * avg power dissipated on R, assuming sine wave
.measure tran  average(v(op,on)*I(rpar))         * avg power dissipated on R, yet another way
.measure tran  average(v(op,on)*I(Gnres))      * avg power delivered by negative R element, NOT EQUAL TO THE ONES ABOVE!?

.end

This simulates fine, I see the tank voltage building up and stabilizing. Now, I am trying to figure out the Q of this tank circuit from the simulation results, and I'm totally confused!

If I compute the ratio max(I(Losc1))/max(I(rpar)) I obtain 156 ,  and it "should" be the Q of the tank...

If I calculate it as Q = resvalue/sqrt(indvalue/capvalue) I obtain 159.15, which is close, so theory and "practice" are hand in hand for now.

On the other hand , if I calculate Q = twopi*Fosc*Etank/Power where Etank= (capvalue/2*(max(v(op,on))**2)) and Power is the power dissipated obtained using one of the measure statements above I get values between 176 and 190 for Q, depending if I use the nominal
oscillating frequency of 1GHz or the actual one of 995.2819936583MEG , and also depending on which power dissipation measurement I take, absorbed by rpar or delivered by Gnres  (6.8457E-05   or  -7.2551E-05) .

Which one is the *true* Q of the tank, for phase noise optimization purposes ?

Is there a fool-proof way to extract the Q of a LC tank  , preferably looking only at V(op,on) and at the negative resistance current ?

Can anyone teach me the basics of Q-extraction from large-signal transient simulations ?

P.s. I don't have spectrerf, but I don't see how PSS would help me very much here... I'd like to hear your advice about it anyhow, please.