how this result appear?

[dgnani]

based on post #31, assuming we have a resonance (use the complex zeros condition), Q will be higher for small values of
2*zeta=w0 (LG+RC)
and in that case the resonance peak will be close to
w0=1/sqrt(LC)
(this is the expression for w0 that the thesis uses, but this is not the value of the peak in general)

if you want your initial peak to be at 4GHz just choose the values that generate LC to have w0 at 4GHz, then make sure zeta is small by changing other parameters w/o changing w0, e.g. you can rewrite 2*zeta by setting L=1/(w0*C)
2*zeta = w0*RC+G/C= w0 gds1 Cgs1 /(gm1 gm2) + gm1/Cgs1
where you can minimize for say Cgs1 (zero the derivative wrt Cgs1) to get
Cgs1=gm1 sqrt( gm2/(gds1 w0) )
while Cgs2 is defined by having fixed w0 as
Cgs2 = gm1 gm2 / (Cgs1 w0^2)

 

[perado]

now my problem is how to simulate the circuit and draw Q vs frequency, before I use image(Zin)/real(Zin) but now I find it is not true (even for pure parallel RLC circuit and just is true for a series RL circuit) but I dont know how I should simulate the Q-factor of the circuit, do you have any idea?

 

[rezaee]

Hello

I have same problem, how is it possible to draw Q vs frequency for the basic gyrator-C circuit with ADS simulator?

 

[dgnani]

Hi perado and rezaee

I did a bit of reading about different definitions of Q and I have to say I am quite confused, there are a lot of references to Q being defined as
Im(Z)/Re(Z)
at 'resonance' but...

...this definition usually provides a different result for Q than the other common definition that holds for second order systems with complex conjugate poles/zeros
1+1/Q (s/w0) + (s/w0)^2

I am under the impression that the two are related but do not coincide even in the case of high Q (the first definition seems to be a factor of 2 larger than the second)

Given that the system you guys are looking at has second order behavior at resonance (the admittance pole R/L is much smaller than w0), I would stick with the second definition, in that case you can easily calculate (see #41)
Q = 1/(2*zeta) ~ w0 (LG+RC) ~ w0/LG =sqrt(C/L)/G ~sqrt(gm2/gm1) sqrt(Cgs1/Cgs2)

a possible way to get Q in ADS (beware I have never even seen the tool) would be to find the value of Y at resonance as the minimum of Y(iw), the value should be in linear scale
ymin = sqrt(C/L)/Q

not a direct measure but still...
__________________

This link should cast some light on the different definitions: according to it, both definitions are used as figure of merit for resonant circuits and at high Q the two Q's are proportional but not the same

I guess in your case all that matters is consistency between what you calculate for the active inductor from small-signal parameters and what you simulate in ADS; in one case (second order Q parameter) the hand calculation result is simpler, in the other (ratio of imag/real at resonance) the simulation is easier to perform but hand calculation results are harder to get and the result more cumbersome

 

[LvW]

now my problem is how to simulate the circuit and draw Q vs frequency, before I use image(Zin)/real(Zin) but now I find it is not true (even for pure parallel RLC circuit and just is true for a series RL circuit) but I dont know how I should simulate the Q-factor of the circuit, do you have any idea?

perado, I have seen your circuit in posting #24.
Perhaps the following may help a little.
In principle, it looks like a tank circuit (with parallel resonance effect).
For such a circuit the tank quality factor (describing the relative bandwidth) is the ratio Qo=IMG(Yin)/R(Yin) measured at the resonant frequency ( Yin=input conductance).
It turns out that the quality factor of the inductive part of your circuit (if all losses are allocated to the inductance)
is the same QL=IMG(Yin)/R(Yin).
(For a series tank circuit input impedance must be used).

Remark: In this thread also the denominator D(s) of 2nd order transfer function was mentioned. This denominator is identical to the characteristic polynominal of the circuit, which determines the pole location in the complex s-plane. If this denominator D(s) is written in normal form there are explicitely the pole data to read: pole frequency wp and pole quality factor Qp. This parameter Qp describes the pole position and has - in principle - nothing to do with the quality factors described above. However, there is one exception: In case of a bandpass, we have Qp=Qo (pole Q=tank Q) .

Added later: Regarding simulation: If you place an ac voltage source Vac=1V across the active circuit, the resulting current that flows into the whole circuit is identical to the input conductance; then, you can split into magnitude and phase or in real and imaginary part.

 

[LvW]

perado, perhaps it's helpful to give some additional information - resulting from a recent "brainstorming".

1.) At first, it doesn`t matter if you rely on the transconductance Y or the impedance Z of the circuit. In both cases gives the ratio IMG/R the corresponding Q value.

2.) What is the physical meaning of Q?
Answer: Q is a measure for the deviation of the expected/desired behaviour of a real "part" from the behaviour of the ideal part. In our case: Deviation from the ideal phase shift beween voltage and current (90 deg).
Based on this Q is defined as Q=1/tanß. The angle ß is the difference between 90 deg and the actual angle (deviation from ideal).
For each circuit it is easy to display the phase relation between voltage and current - and also the difference to 90 deg.
I have convinced myself by simulation that this definition gives exactly the same curve Q=f(w) as the ratio IMG/R (based on Y or Z).

(Hint: To display the tan function (and its reciprocal) it might be necessary (like in PSpice) to change the angle from deg to rad before.)

From the above it clearly follows that in case of a resonant effect (due to a parralel C) the inductor quality factor goes to zero for w=wo because the phase deviation with respect to 90 deg is also 90deg. Thus, in between the inductor Q has a maximum.