You confused ω0 and f0 in your simplified switched capacitor formula. C1 should be 3.1 pF ac cording to your formula. The simplified formula isn't valid for the low sampling frequency however.
fs=2 kHz is effectively useless for a 1 kHz low pass due to aliasing effects.
An exact cut-off frequency calculation has to be based on z-transform. With sufficient large fs/vs ratio, the approximate relation assumed in post becomes true. Aliasing is a different issue, to avoid it, signal frequencies above fs/2 must be filtered out before entering the switched section.
Sorry for the typo. Should be fs/fc.
Bilinear transform is a possible method, but the bilinear equivalent of a time continuous first order low pass is a more complex switched capacitor circuit. You probably want a first order corresponding SC circuit.
There's apparently no significant aliasing in the post #1 results. Not sure if it's due to inappropriate analysis parameters (I'm not familiar with PSS/PAC analysis), it may be also an effect of relative large MOSFET rdson.
Are you aware that the non-switched capacitor must be very large if compared with the switched C ?
This is because the switchen capacitor in your circuit works only sufficiently (simulating the R), when also the right node of R is connected to a voltage source or to ground.
(a large C can mimic a voltage source).
Surprisingly, this fact (both ends of the switched C for EULER approximations to be connected to a voltage source) is not always mentioned in relevant articles/books.
If the right node of the R to be replaced is NOT connected to ground, the bilinear approximation can be used.
if you mean that R in the non-switching cap will be large to get an fc of 1KHz and 1pF, then yes I am aware.
So you are saying if the right node of R in the passive network is not connected to ground then i can use the bi linear approximation to model the switched cap network to replace the R?
disregarding mathematical models for a while, how do I design translate the RC filter with an fc of 1K into a switch cap circuit? The only way I come close to the fc value is if I increase the sampling frequency and consequently decrease the capacitor C1.
If someone could point in the right direction as to why this is happening, I would be grateful.
Also any suggestions on books which talk about transistor level design of active RC, switch cap, gm-C filters etc. will be helpful.
No - not accurately. That`s not possible.If both ends are connected to voltage sources the switched cap circuit accurately models the resistor.
For practical reasons, the requirement to have a fixed potential at the right node of the resistor R is fulfilled using the virtual ground of the inverting opam input with feedback
For this reason, S/C intergrators play a major role in all S/C circuits.
For example, see here (Lectures 9 and 10):
https://inst.eecs.berkeley.edu/~ee247/fa07/lectures.html
In most cases. a voltage opamp is used, however, use of an OTA is also possible.
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?
We use cookies and similar technologies for the following purposes:
Do you accept cookies and these technologies?