Analog implementation of variable-gain differentiators based on voltage-controlled amplifiers

An nth order variable gain differentiator, comprising:

• a voltage generator configured to generate an alternating current input signal, u;
• a first voltage divider connected to the voltage generator;
• a non-inverting operational amplifier having a non-inverting operational amplifier input connected to the first voltage divider, and having a non-inverting operational amplifier output;
• a first comparator block including n comparators connected in series, wherein n is selected from the range of 1 to 20, wherein a first non-inverting comparator input is connected in series with the non-inverting operational amplifier output, and a first comparator block output is an output of the nth comparator;
• a DC voltage controlled variable gain amplifier (Vc) connected to a power input each of the n comparators of the first comparator block, the DC voltage controlled variable gain amplifier generating a gain, γ;
• a non-inverting difference amplifier block including n−1 non-inverting difference amplifiers, the non-inverting difference amplifier block having a non-inverting difference amplifier block input connected in series with the first comparator block output, the non-inverting difference amplifier block having a non-inverting difference amplifier block output at the (n−1)th non-inverting difference amplifier;
• an integrator block connected in series with the non-inverting difference amplifier block output, the integrator block having n integrator block outputs;
• a first intermediate difference amplifier connected in series with one of the n integrator block outputs, the first intermediate difference amplifier having a first intermediate difference amplifier output;
• a second comparator block connected in series with the first intermediate difference amplifier output, the second comparator block having a second comparator block output connected to the inverting input of the difference amplifier block, a second power supply input of the second comparator block connected to the DC voltage controlled variable gain amplifier;
• an nth integrator block output of the plurality of integrator block outputs connected to an inverting input of the non-inverting operational amplifier, wherein the nth integrator block output is the output, y, of the nth order variable gain differentiator;
• and
• wherein the DC voltage controlled variable gain amplifier is configured to vary a gain of the first comparator block and the second comparator block, wherein varying the gain of the first comparator block and the second comparator block varies an output gain of the nth order variable gain differentiator.

A method for nth order variable gain differentiation, comprising:

• generating an alternating current input signal, u;
• transmitting the alternating current signal to a non-inverting operational amplifier in series with n comparators, and generating a comparator output at the nth comparator;
• transmitting the comparator output to an input to n series connected integrators;
• generating an integrator output signal by each of the n series connected integrators;
• generating, by DC voltage controlled variable gain amplifier, a DC voltage signal having variable gain, γ;
• providing the DC voltage signal to an kth power supply input of each of n integrators, where n is selected from the range of 1-20;
• wherein an nth integrator output signal is an nth derivative of the alternating current input signal, u;
• wherein a gain of the comparator output at the nth comparator is equal to an nth power of the variable gain, γ.