how this result appear?

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Y(s) that you drived at #8 ( Y(s)= gm1+ s Cgs1 + gm1 gm2 / (gds1+s Cgs2) ) is true and is like (5.7) equation of thesis but gm2 must place with gm1.
in this way the centeral frequency and Q can be drived as (5.12) and (5.13) that showed the relation of Q and central frequency with parameters,
I simulated this circuit at 0.18um tsmc technology with ADS and saw the Q factor has direct relation with Cgs2 at low frequency and inverse relation with Cgs2 at higher frequency,
I read at this thesis (end line of page 93): "at high frequencies this approach is usually unsuccessful due to the excess phase error contributed by the interinsic device capacitances" , whats your idea about this? and if you think the Y(S) that drived with 2assumption is valid for all frequency range, then how I must describe the circuit simulation results?
 

It is possible that some of the capacitances that were neglected already in the small signal model, should have not been neglected for their contribution at high frequency. What we derived is simply valid over the whole range of frequency where that small signal representation is valid. If that becomes inaccurate so is our result.

You can try simulating the small signal model, using vccs and such and see that it behaves as we calculated. I will have a look later... gotta go
 


I had another look and I think the problem is actually that the thesis uses the wrong formulas for Q and w0, he uses the formula for a pure LC circuit instead of those for this specific topology where we have damping.

I will work out the correct expressions out of curiosity, we can compare notes at some point
 
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    perado

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I think he uses Q=L*omega/R and omega0=1/sqrt(L*C) for this circuit:

now what is your idea? what formulate we can use to drive correct result?
 

Hi perado,

simulating side by side the small-signal equivalent and real mosfets from a .13 process, the sweeps of Cgs1 and Cgs2 were (almost) perfect matches on a range from 1 to 10GHz

Cgs' in the mosfet circuit were increased by adding external ideal components, the initial value of Cgs is not easy to get from BSIM model parameters as the AC transconductances are in the form of a non-symmetric matrix that can take negative values, so I just calibrated them to match the curve for low values of the external Cgs caps

This does not matter for large values of the caps

Now what did you simulate in ADS? was Cgs a parameter extracted from the model or the value of an external component?
 

I simulated the circuit and draw Q and then put an external capacitor in parallel with Cgs2 and change its value.
you told truth he calculate Q and central frequency for pure RLC circuit but how I can formulate this two parameters for the target circuit?
 

I think that in this case
w0 ~ G/C ~ gm1/Cgs1

but i have to double check for this estimate and for Q, please verify that the above result works (approximately) in simulation. I'll be back later...

_______
well not really, forget the result above... and see a few posts down
 
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thanks, OK I will check this, I want to calculate W0 and Q
I must calculate input impedance relation and then for W0 I must put imaginary part equal to zero? and for Q I must calculate Image(Zin)/Real(Zin)? Is it true??
 

I am not sure if that definition holds in general or only for large enough Q, I will have to dig a bit to find out if there is any approximation involved...

In any case calculating those expressions is trivial so you might simply try and see if they work... not much time of this now
 

Yes , maybe calculating those expressions be trivial but its important for me to show the relation of Q and W0 variation with circuit parameters and not just with simulation
when I had simulated the circuit in ADS I defined Q as Image(Zin)/Real(Zin) , maybe it was wrong?
how I see variation of central frequency vs Cgs1 in simulation?
 

here is how it goes
Y=G+sC+1/(R+sL)=[LCs^2+(LG+RC)s+1+RG]/(R+sL)
but
RG=gds1/gm2<<1
so we neglect it, while for
RC=Cgs1 gds1 / (gm1 gm2)
LG=Cgs2/gm2
initially RC<<LG but it will not be the case if you sweep Cgs1 to a large number

As long as the pole R/L ~ gds1/Cgs2, is much smaller than the zeros, all we need to focus on is the numerator of Y that creates the zeros that define the resonance
LCs^2 + (LG+RC)s + 1 [eq 1]
we can treat this with the usual formalism for second order systems (e.g. see here)
w0^2=1/LC
zeta=1/2 w0 (LG+RC)
which yields a resonant peak at
w1=w0 sqrt(1-2*zeta^2)
notice that this is not what you get by setting the imaginary part to zero...

This only works for complex (conjugate) zeros, if the discriminant of [eq 1]
(LG+RC)^2-4LC
is positive we end up with regular real zeros and the resonant peak goes away replaced by a wide flat region between the two zeros

I am not sure how to get Q though...
 
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I am not sure if that is the general definition of Q but you can definitely compare that to the calculation from the equivalent circuit
Q1 = Im Z / Re Z = - Im Y / Re Y = w [L-(R^2+w^2 L^2)C] / [R+(R^2+w^2 L^2)G]

e.g. this foresee that at very high w, Q will increase linearly with w
w->oo => Q1 ~ -w C/G
not sure about the - sign though...
 
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dgnani whats your idea about this: I think if I convert R-L series to parallel R-L and then use Q and W0 equation for parallel pure RLC is better. now my problem is I dont know how do this convert.

Is it possible to write Lnew and Rnew vs L and R2 ?
 

I search and convert series RL to parallel RL like the picture that I attached here, I think the author of thesis use this approximation and then used Q and w0 equation for a pure RLC circuit of course this approximation is valid for high frequency whereas he told this approach isnt for high frequency!!!
but now regardless to author of thesis , is it true that we tell at high frequency W0 and Q can calculate from the (5.12) and (5.13) (with approximation and equation that you see in attached picture) ?
 

Hi perado

that's an interesting option, 1/Rnew would be smaller than G over the whole frequency range and you can avoid making approximations for Lnew and keep it as is, that should provide a way to calculate a good approximation of Q and w0 over the whole frequency range using the RLC formulas
 

is your idea that with this approximation I can calculate an experssion for Q that be valid for whole range of frequency?
with this approximation (Lnew=L and Rnew is negligible vs R2) the (5.13) is not true?
I think for high frequency this approximation "Lnew=L & Rnew negligible vs R2" must be true and then (5.13) can be drived for Q ,that showed Q is proportional to Cgs2, now I dont know how its possible for me to describe inverse result at simulation for high frequency!
 

no the idea is that
- Rnew (parallel to G) could be ignored because always much smaller than G at any frequency
- Lnew is kept as is with its frequency dependence and used in the calculations for w0 and Q, which will become dependent on frequency through Lnew
- in summary your admittance would become
Y(s) ~ G + sC + 1/(s Lnew)

This approximation would hold across the frequency range, the only constraints might be that the parallel RLC circuit has to have a resonance, that is it has to be underdamped

The problem I have with this approach is that once you allow for Rp and Lp (intended as generic values of the parallel RL circuit) to be frequency dependent then there is an infinite number of equivalent parallel RL circuits that are equivalent to the original series RL circuit, so how did you choose Rnew an Lnew among all possible Rp, Lp combinations?
 

If your mean from this approach is relation of converting series RL to parallel RL , I saw it at this link: Wcalc Series/Parallel RL Networks

for pure RLC circuit Q=wL/R , now here for calculating Q , I use this equation : Q=wLnewG that w is 1/sqrt(LnewC) and C and G are like thesis but Lnew is differ from thesis ??
 
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According to the link the approximation is narrow-band only valid around the resonance frequency
 

then now what I do? :sad:

if the Q equation at thesis ( 5.13 ) is wrong then how he continue his thesis with that and design his novel schematic and doing simulation!??

another question: when I simulate the the circuit and draw Q factor the maximum point of Q is under 1 GHz but I want the maximum point be at around 4-5 GHz, what I should do?
 
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