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The figure below is a switched-capacitor voltage replicator. It is from Reconfigurable Switched-Capacitor Power Converters by Dongsheng Ma and Rajdeep Bondade. You can read it here.

As you can see the output voltage Vout is finally charged to Vin. So why it is useful to use this circuit while it has a voltage gain of unity? It also doesn't seem to be a voltage buffer either.

circuit schematic extracted from figure 3.2 of book

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    \$\begingroup\$ The circuit provides an isolation between Vin and Vout as S_1 and S_2 are never on at the same time. \$\endgroup\$ – Pau Coma Ramirez Nov 3 '16 at 8:23
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    \$\begingroup\$ This may be useful for example as a short circuit on Vout will not be seen by Vin as a short circuit, just as a discharged capacitor, limiting the current consumed from Vin by short circuit depending on the values of S_1 t_on, C_1, C_1 ESR and Vin series resistance. \$\endgroup\$ – Pau Coma Ramirez Nov 3 '16 at 8:33
  • \$\begingroup\$ Also looks like: electronics.stackexchange.com/questions/5458/… \$\endgroup\$ – Phil Nov 3 '16 at 20:42
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As FakeMoustache explained, the switches and C1 behave as a resistor. The usefulness of the circuit is that it it takes less real estate in an integrated circuit to make to make than an actual resistor. This creates the possibility of making integrators, RC filters, A2D converters and other functions needing large resistors on a chip. So for example you can build an imager with the A2D built in so the chip provides. Look at this one for example; Image Chip Datasheet This could not be done without switched capacitor resistors. It is not very useful in discrete circuits design.

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    \$\begingroup\$ The usefulness of the circuit is that it it takes less real estate in an integrated circuit to make to make than an actual resistor. That is only true if you'd want to make large value resistors. Capacitors also take considerable space on chip though. But in an SC filter all caps are relatively small. Also (metal) caps can be made quite accurately. On-chip resistors have unpredictable values. When an accurate external clock can be provided (this is often not a problem) then an accurate yet complex filter can be made reliably. \$\endgroup\$ – Bimpelrekkie Nov 3 '16 at 10:45
  • \$\begingroup\$ This site; swarthmore.edu/NatSci/echeeve1/Ref/FilterBkgrnd/… and many others say what I will put in my next comment because it won't fit in one. \$\endgroup\$ – owg60 Nov 3 '16 at 10:57
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    \$\begingroup\$ many active filters with resistors and capacitors have been replaced with a special kind of filter called a switched capacitor filter. The switched capacitor filter allows for very sophisticated, accurate, and tuneable analog circuits to be manufactured without using resistors.� This is useful for several reasons.� Chief among these is that resistors are hard to build on integrated circuits (they take up a lot of room), and the circuits can be made to depend on ratios of capacitor values (which can be set accurately), and not absolute values (which vary between manufacturing runs) \$\endgroup\$ – owg60 Nov 3 '16 at 11:00
  • \$\begingroup\$ An even more useful aspect of this circuit is that the ratio between "pseudo-resistors" and capacitors will--absent parasitic effects--vary linearly with frequency. \$\endgroup\$ – supercat Nov 3 '16 at 16:30
  • \$\begingroup\$ Supercat - I suppose you mean "clock rate", right? \$\endgroup\$ – LvW Nov 3 '16 at 19:06
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You already assume that this circuit has a direct application and that it is supposed to be an amplifier (you mention voltage gain) or buffer. Why would you assume that it has this function?

In the book this circuit is used to explain the basics of a switched capacitor circuit. There is no direct mention on how to use it.

In general such a circuit consisting of S1, C1 and S2 behaves as a resistor. Remove C1 and replace S1 and S2 by a single resistor. Now how would the charging curve for charging C2 look? Do you spot the similarity?

It behaves the same way as a simple first order RC lowpass filter. This is one application of this circuit: switched capacitor filters. This is used to filter / process signals which could carry information. In power electronics there is no signal (carrying information) but the circuit can still be used.

If you load the output and control the switching of S1 and S2 in a certain way that depends on the output voltage (in a feedback loop) you can use this as a voltage regulator. That is the point of the book, I believe, as it is about switched capacitor power converters.

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    \$\begingroup\$ Fake Moustache, good explanation. Perhaps one could add that the circuit represents a first order passive lowpass in S/C technique (sampled data system), see the step response Vout=f(t). \$\endgroup\$ – LvW Nov 3 '16 at 8:53
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    \$\begingroup\$ You're right that was a typo, indeed S1, C1 and S2 are the "resistor" \$\endgroup\$ – Bimpelrekkie Nov 3 '16 at 10:40
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    \$\begingroup\$ @anhnha, it is not a time-continuous system, but instead a "sampled data system". Hence, we cannot give a time-continuous output function, but only an expressions in the following form: Vout(n)=f[Vout(n-1)]. \$\endgroup\$ – LvW Nov 3 '16 at 11:28
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    \$\begingroup\$ @anhnha, see here (page 13):de.scribd.com/document/205403453/Chapter09-2UP-2-25-03 \$\endgroup\$ – LvW Nov 3 '16 at 11:57
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    \$\begingroup\$ @anhnha, here is a better working pdf-link:google.de/… \$\endgroup\$ – LvW Nov 3 '16 at 13:16
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So, I am unaware of the use of switched capacitors as a replacement for an RC circuit, though I suppose I can see the similarity. However, a use I am more familiar with is as an isolated buffer for transferring a voltage between potentials.

In this example, both terminals of the capacitor are switched, allowing the differential input to take any voltage that the switches can handle. This voltage is then presented to the input of the op amp, but now it is in reference to ground. This allows for very good common mode rejection of the differential input, and with attention to the switching building blocks can also be a decent way of allowing small signal measurement of very high voltage signals.

switched capacitor example

See this app note from linear for more information on this.

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