The Parasitic Sensitive Integrator
Often switched capacitor circuits are used to provide accurate voltage gain and integration by switching a sampled capacitor onto an op-amp with a capacitor in feedback. One of the earliest of these circuits is the parasitic-Sensitive integrator developed by the Czech engineer Bedrich Hosticka. Let us analyze what happens in this case. Denote by the switching period. Recall that in capacitors charge = capacitance x voltage. Then, at the instant when S1 opens and S2 closes, we have the following:
1) Because has just charged:
2) Because the feedback cap, is suddenly charged with that much charge (by the opamp, which seeks a virtual short circuit between its inputs):
Now dividing 2) by :
And inserting 1):
This last equation represents what is going on in - it increases (or decreases) its voltage each cycle according to the charge that is being "pumped" from (due to the op-amp).
However, there is a more elegant way to formulate this fact if is very short. Let us introduce and and rewrite the last equation divided by dt:
Therefore, the op-amp output voltage takes the form:
Note that this is an integrator with an "equivalent resistance" . This allows its on-line or runtime adjustment (if we manage to make the switches oscillate according to some signal given by e.g. a microcontroller).
Read more about this topic: Switched Capacitor
Famous quotes containing the words parasitic and/or sensitive:
“Art is parasitic on life, just as criticism is parasitic on art.”
—Kenneth Tynan (1927–1980)
“Every poem of value must have a residue [of language].... It cannot be exhausted because our lives are not long enough to do so. Indeed, in the greatest poetry, the residue may seem to increase as our experience increases—that is, as we become more sensitive to the particular ignitions in its language. We return to a poem not because of its symbolic [or sociological] value, but because of the waste, or subversion, or difficulty, or consolation of its provision.”
—William Logan, U.S. educator. “Condition of the Individual Talent,” The Sewanee Review, p. 93, Winter 1994.