Circuit with commutated capacities

The circuits with commutated capacities or circuits SC (in English Switched-Capacitor) allow the emulation of a resistance thanks to a Capacité associated with transistors MOS used like switches. It is into 1972 that Fried proposed such a circuit making it possible to remove resistances and to replace them by circuits with capacities commutated. The first filter integrated using this innovation was employed in 1977.

The circuits with commutated capacities have many advantages among which:

they make it possible to obtain a variable resistor according to the frequency of clock. This makes it possible to produce filters whose cut-off frequency is function of the frequency of clock
they occupy a surface weaker than that which would occupy equivalent resistance integrated
in general (this depends on technology employed), the precision of the integrated capacities is larger than that of resistances. This point is important at the time of the realization of a filter.

Principle of the circuits with commutated capacities

  S1 S2
    //
O--/ ---/ --O
      |                            Req
in    |    out ___
     == <==> O----|    |----O
      | Cs                        -----
      |
O-----------O

The switches S1 and S2 are ordered by two clocks Phi1 and Phi2. These two switches are complementary, i.e. when the S1 switch is opened, the S2 switch is closed and when the S2 switch is closed, the S1 switch is open. One can consider that the tensions Vin (T) and Vout (T) are constant during a prériode of clock because these tensions vary little. The load of the capacity during the phase of activity of the Phi1 clock is $q1 = Cs*Vin$ and the load of the capacity during the phase of activity of the Phi2 clock is $q2 = Cs*Vout$ . For one period, the transfer of the load corresponds to $\ Delta Q = q1 - q2$ of the entry towards the exit. What is equivalent to an average current $I_ {moy} = \ Delta Q /T_ {E}$ . Equivalent resistance between the entry and the exit is thus: $R_ {eq} = \ frac {V_ {in} - V_ {out}} {I_ {moy}} = \ frac {T_ {E}} {C_ {S}} = \ frac {1} {f_ {E} C_ {S}}$

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