help with switched caps, what is the feedback type

[Fractional-N]

edaboard

in the above circuit (one phase of a switched capacitor circuit). what is the feedback type? and what is the feedback factor?

i think the feedback type is voltage-current or shunt-shunt, and the feedback element is just the capacitor C2. but in johns&martin book it says otherwise :!:

 

[LvW]

Re: help with switched caps

in the above circuit (one phase of a switched capacitor circuit). what is the feedback type? and what is the feedback factor?
i think the feedback type is voltage-current or shunt-shunt, and the feedback element is just the capacitor C2. but in johns&martin book it says otherwise :!:

Question: You ask for the feedback factor, but in your answer you mention a "feedback element". What are you interested in - and WHY ?

Is it really important for you ? For my opinion, it makes no sense to speak about a feedback factor since this parameter has a real technical meaning only in time continuous circuits. There, it appears as a factor in the denumerator of the transfer function and, thus, is a part of the loop gain.
In case of the s/c integrator the function is easy to explain: during the phase as shown, the load current through the input path is transferred to the feedback path. Thats all. The corresponding voltage is multiplied with the cap ratio.

 

[Fractional-N]

Re: help with switched caps

thank you for your reply.

actually, i am reading an example in "johns & martin" analog design book. there, to calculate the linear settling time and to determine the unity gain frequency of the opamp, the circuit is considered as a feedback network.

details of calculations is as follows:

settling time = 7? ? is the time constant of the opamp
?=1/?-3db ?-3db is the corner frequency of the opamp
and

?-3db=ß \[\times\] ?ta ?ta is unity-gain frequency of open-loop opamp and ß is feedback factor.

-------------------
thats why i need to know the feedback factor.
i think the feedback factor (ß) is C2. ie the only feedback element in the circuit is capacitor C2. but in the book the feedback factor is said to be C2/(C1+C2).

BTW it is welcome if you have an alternative approach to solve the problem:
the problem is: what is the open-loop unity gain frequency of opamp if a settling time of 0.1µs is required.

 

[LvW]

Re: help with switched caps

thank you for your reply.

actually, i am reading an example in "johns & martin" analog design book. there, to calculate the linear settling time and to determine the unity gain frequency of the opamp, the circuit is considered as a feedback network.
........................
-------------------
thats why i need to know the feedback factor.
i think the feedback factor (β) is C2. ie the only feedback element in the circuit is capacitor C2. but in the book the feedback factor is said to be C2/(C1+C2).

BTW it is welcome if you have an alternative approach to solve the problem:
the problem is: what is the open-loop unity gain frequency of opamp if a settling time of 0.1µs is required.

Hi FRACTIONAL-N !

Now I see what you are interested in.
However, I have some doubts if the opamp and its limited bandwidth mainly contributes to the settling time. For ideal conditions the settling time is zero.
If for real conditions a certain settling time is required I think that you have to take into account primarily
- the on resistance of the switches,
- parasitic capacitances
- the slew rate of the opamp,
- and (to a minor extent) the limited opamp bandwidth.

Question: Are you really sure that in the book mentioned by you the expression C2/(C1+C2) is called "feedback factor" ? According to my knowledge - and if one really wants to use this wording - the feedback factor is C2/C1 (certaily NOT C2 alone !).
Instead, the expression C2/(C1+C2) appears by Martin+Sedra
in a paper dealing with the non-ideal opamp effects as a factor determining the error due to the opamp (but NOT as something like "feedback factor").

 

[Fractional-N]

Re: help with switched caps

According to my knowledge - and if one really wants to use this wording - the feedback factor is C2/C1 (certaily NOT C2 alone !).

yes you are right. my bad

Are you really sure that in the book mentioned by you the expression C2/(C1+C2) is called "feedback factor" ?

yes i am sure. and that is what i can't understand.

in a paper dealing with the non-ideal opamp effects as a factor determining the error due to the opamp (but NOT as something like "feedback factor").

so you think this is a misprint or something like that?
and could you please give the exact tittle of the paper. or post it here

 

[safwatonline]

help with switched caps

C2/(C1+C2) is correct, the key point here is the feedforward path
which introduce another term C1/(C1+C2), so effectively u will get the C1/C2 gain of the stage

 

[Fractional-N]

Re: help with switched caps

C2/(C1+C2) is correct, the key point here is the feedforward path
which introduce another term C1/(C1+C2), so effectively u will get the C1/C2 gain of the stage

hi,
can you explain a little more. feedforward path :?: where is it?
thank you

 

[LvW]

Re: help with switched caps

C2/(C1+C2) is correct, the key point here is the feedforward path
which introduce another term C1/(C1+C2), so effectively u will get the C1/C2 gain of the stage

I seriously doubt that one can transfer expressions which are derived from continuous time circuits to sampled data systems. What you call "gain=C1/C2" is valid only for sinus waves !!

Therefore, I also do not believe that eq. (5.42) of the cited document can be used here. Remember: The impedance 1/ωC applies only to sinusoidal voltages or currents. But, here, we are facing small current pulses !

And that´s the reason I believe that the expression "feedback factor" is not applicable in this case and - more important for the settling time - that the limited bandwidth of the opamp plays not the dominant role, if compared with slew effects and parasitic resistances of the switches !

 

[safwatonline]

help with switched caps

Hello,
LVW:
Ok, let me tell you what is my point of view.
first the shown circuit is the general shape of any (or at least most) of the SC stages (considering ideal switches) in its evaluation phase.
so in this evaluation phase u can analyze the circuit by laplace transform and calculate the step response of the amplifier/integrator, the step response includes all the opamp non-idealities (slew rate, finite Gain, finite BW) plus the effect of the feedforward path.
so this method of analysis although continuous time it is valid as it takes all the transient effects into consideration (which actually can't be calculated except by continuous time analysis)

frac-N:
the feedforward path is the path due to the capacitor C2 as any steps on the input will pass through the C1 to the virtual ground then through C2 to the output.
for proper modeling: the input is connected to the output through two paths:
first path: input > forward gain > feedback loop > output
second path: input > feedforward path > output

forward gain is C1/(C1+C2)
feedback loop: i-A is the amplifier gain ii- feedback factor C2/(C1+C2)

feedforward path: [C1/(C1+C2)]

doing the math a complete solution is determined

note: i neglected the effect of Cin and Cload

 

[LvW]

Re: help with switched caps

Hi safwatonline,

OK, you have convinced me - under ideal conditions one can say that the circuit under discussion has a voltage gain of C1/C2 - because the step can be seen as a sum of sinusoidal voltages and the ratio of both impedances simplifies to the ratio of both caps.
However, as far as the settling time is concerned I stick to my restrictions.
Thank you and regards.