Hi,

When I use the y-parameters to modelize the integrator, I got a feedback factor equals to sCf (Cf for feedback Capacitance).
However the feedback is in reality given by:

f=Cf/(Cs+Cs+Cp)

I ask myself from where comes formula (1) and why feedback factor got by the y parameters method is inexact?

Thanks for your answers.

Best Regards

Hmmm, I think a figure will be helpful for us to understand your question well.

-Terry

Hi Joeb,

The formula you mentioned can be derived considering the clock phase is such that Cs is connected to the OTA´s input and assuming a linear small signal model for the OTA.

You can consider the feedback network is such that you are feeding back a voltage signal VI' = VI'+ - VI'-, which is the OTA´s differential input signal. If this is the case, then the feedback factor will be the transfer function given by VI'/VO (for VI=0). Considering this transfer function the feedback factor is readily deduced as the voltage divider between Cf and the parallel combination of Cs and Cp (or Cin in your figure):

VI'/VO (VI=0) = [1/s(Cs+Cp)] / [1/s(Cs+Cp)+1/sCf]  = Cf/(Cf+Cs+Cp)  (1)

Now, the feedback network can also be considered as connected in series with the input of your controlled source (OTAs linear model), or in other words, it feeds back a current.
Since the output signal for your feedback network is now a current, the y parameters apply and you get -1/Zf, where Zf=1/sCf. Here the feedback factor is given by II'/VO @ VI=0, where II' is the differential input current coming out of the feedback network.
However, the INPUT signal to your system now must be a current and not a voltage. Such input input current can be found as:

VI/ZI, where ZI= 1/s(Cs+Cp).
Thus
VI' = VI-I×ZI = VI+[(VO-VI')×sCf]×1/s(Cs+Cp).

If VI=0 you get VI'/VO=[1/s(Cs+Cp)] / [1/s(Cs+Cp)+1/sCf]  = Cf/(Cf+Cs+Cp) , which is the same as (1)

So it is not that the y-parameters are wrong, it is just that you were considering different feedback networks when comparing the formulas. Therefore, the feedback factor will depend on what you consider is your feedback network and your input variables, but both must give you the same overall results.

Tosei

Hi,

I would like to note that in the book of Kennet S Kundert " The designers guide to Spice and Spectre" they note that the feedback factor is given by f=y12 ( p.89) when we talk on Y model parameters shunt shunt feedback. ( This is the same definition given in Razavi's Book).

So in  my switch cap circuit case (shunt shunt feedback) I got  f= -sCf.
But in the reality we have f=Cf/(Cf+Ci+Cp).

How we have to considerate this f ? as a feedback factor impedance?

Hi Joeb,

I kept thinking about this and I think there also another way to look at it.
When using y-model for determining the feedback factor, you are using the two-port model for describing the feedback loop. If this model is used, your feedback factor will depend on the type of input/output variables (and therefore on the two-port model you have to use).
On the other hand, the feedback factor you mention as f=Cf/(Cf +Cp + Cs), can be derived from the Return ratio feedback model: breaking the loop at -say - the OTA inputs you will find the feedback factor is the one you were asking about.
There is a good paper about return ratio vs two-port model you can look at that might help: "A comparison of two approaches to feedback circuit analysis", Paul J. Hurst - IEEE Transactions on Educations - Aug 1992

Tosei