Polar leapfrog filter

A polar leapfrog filter comprising:

• at least one polar network which comprises a differentiator constituted by an operational amplifier having input and output terminals, and a first integrator for providing negative feedback to said operational amplifier, said first integrator comprising a first capacitor and a first variable transconductance amplifier, and a second integrator for providing negative feedback to said first integrator, said second integrator comprising a second capacitor and a second variable transconductance amplifier;
• a third and a fourth integrator provided at input and output portions of said filter respectively;
• and
• a fifth integrator provided at a stage following said polar network;
• wherein the sum of all the circuits is selected to be even to the order of said filter;
• adjacent ones of said circuits are connected in such a manner that leapfrog type negative feedback is applied therebetween;
• and only said third integrator is constructed in the form of self negative feedback type;
• wherein said third integrator comprises a third variable transconductance amplifier and a third capacitor through which an output terminal of said third variable transconductance amplifier is grounded;
• said fourth integrator comprises a fourth variable transconductance amplifier and a fourth capacitor through which an output terminal of said fourth variable transconductance amplifier is grounded;
• and said fifth integrator comprises a fifth variable transconductance amplifier and a fifth capacitor through which an output terminal of said third variable transconductance amplifier is grounded;
• wherein in said polar network, said operational amplifier has its output terminal connected to a non-inverting input terminal of said first variable transconductance amplifier and also to an inverting input terminal of said third variable transconductance amplifier of said third integrator;
• said first variable transconductance amplifier has its output terminal connected to an inverting input terminal of said operational amplifier and also to a non-inverting input terminal of said second variable transconductance amplifier and grounded through said first capacitor;
• and said second variable transconductance amplifier has its output terminal connected to an inverting input terminal of said first variable transconductance amplifier and grounded through said second capacitor;
• wherein in said third integrator, said third variable transconductance amplifier has the output terminal thereof connected to a non-inverting input terminal of said operational amplifier of said polar network, the output terminal of said third variable transconductance amplifier being connected to another inverting input terminal thereof;
• wherein in said fourth integrator, said fourth variable transconductance amplifier has the output terminal thereof connected to a non-inverting input terminal of said fifth variable transconductance amplifier of said fifth integrator and also to another inverting input terminal of said operational amplifier and grounded through said fourth capacitor;
• wherein in said fifth integrator, said fifth variable transconductance amplifier has the output terminal thereof connected to a non-inverting input terminal of said fourth variable transconductance amplifier;
• and
• wherein an input terminal and output terminal are led out of a non-inverting terminal of said third variable transconductance amplifier and the output terminal of said fourth variable transconductance amplifier.