Filter commutated capacities

The filters commutated capacities are electronic filters using circuits with commutated capacities in the place of resistances. Indeed, the replacement of resistances by commutated capacities allows a better integration of the filters, resistances occupying an enormous place in the integrated circuits.

Principle

The realization of the filters commutated capacities is based primarily on structures of the first and the second order. Indeed thanks to such structures, filters of a higher nature can be realized by using the principle of the Synthèse in cascade. This principle consists in putting in “cascade” of the filters of the first and the second order to produce a filter of a higher nature.

Advantages and disadvantages

A commutated capacity filter allows the realization of filters of a nature raised without comprising resistances and external capacities, moreover its cut-off frequency is adjustable, it is proportional to the clock of commutation. However, a commutated capacity filter carries out a sampling of the signal it can thus create a folding up of spectrum. He also adds to the signal a parasite at the frequency of the clock used for commutation.

first order commutated capacity filters

The first order commutated capacity filters are deduced easily from their resistive counterparts by replacing resistances of the filters by circuits to commutated capacities.

capacity filters commutated of the second order

The realization of the capacity filters commutated of the second order is more complex to implement than the method described previously. This one would result to complex structures in implementing and whose surfaces of occupations of the capacities would lead in a nonoptimal approach. This is why the method based on the operational graphs is preferable. For that, one leaves the following transfer transfer function of the biquad:

$H (p) = \ frac {V_ {O} (p)}{V_ {I} (p)} = - \ frac {k_ {2} p^2 + k_ {1} p + k_ {0}} {p^2 + \ frac {\ omega_ {0}} {Q} p + \ omega_ {0} ^2}$

This equation can be rewritten in the following form:

$V_ {O} (p) = - \ left (k_ {2} + \ frac {k_ {1}} {p} + \ frac {k_ {0}} {p^2} \ right) V_ {I} (p) - \ left (\ frac {\ omega_ {0}} {Qp} + \ frac {\ omega_ {0} ^2} {p^2} \ right) V_ {O} (p)$

While posing:

$V (p) = \ frac {1} {p} \ left (\ frac {k_ {0}} {\ omega_ {0}} V_ {I} (p) + \ omega_ {0} V_ {O} (p) \ right)$

The preceding relation becomes then:

$V_ {O} (p) = \ frac {1} {p} \ left (\ left (k_ {1} +k_ {2} p \ right) V_ {I} (p) + \ frac {\ omega_ {0}} {Q} V_ {O} (p) - \ omega_ {0} V (p) \ right)$

It can be translated by the operational graph into p of the figure above:

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The graph opératinonel out of p, makes it possible to deduce the electric diagram from the biquad:

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See too

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