High stability gain structure and filter realization with less than 50 ppm/° c. temperature variation with ultra-low power consumption using switched-capacitor and sub-threshold biasing

A differential amplifier circuit, comprising:

• (a) a constant gm bias circuit operating in the subthreshold region for ultra-low power consumption generating a biasing current (I0), said constant gm bias circuit including a switched capacitor resistor having a first capacitor, wherein the biasing current (I0) is given by:
• I0=VT ln(M)/R1,
• where VT is the thermal voltage of the constant gm bias circuit, where the thermal voltage is kT/q, where k is the Boltzman's constant, T is the temperature in Kelvin, and q is the unit of charge,
• M is a multiplication factor relating two transistors in the constant gm bias circuit,
• R1=1/f1C1,
• C1 is a capacitance of the first capacitor, and
• f1 is a frequency of a reference clock of the constant gm bias circuit;
• and
• (b) a differential amplifier biased with the biasing current, the differential amplifier including a load switched capacitor resistor having a second capacitor, wherein the differential amplifier has constant gain (Av) given by:
• Av=ln(M)f1C1/ηf3C3
• where η is a process constant value for the differential amplifier;
• C3 is a capacitance of the second capacitor, and
• f3 is a frequency of the load switched capacitor resistor of the differential amplifier.

A second-order biquad filter, comprising:

• (a) a constant gm bias circuit operating in the subthreshold region for ultra-low power consumption generating a biasing current (I0), said constant gm bias circuit including a switched capacitor resistor having a first capacitor, wherein the biasing current (I0) is given by:
• I0=VT ln(M)/R1,
• where VT is the thermal voltage of the constant gm bias circuit, where the thermal voltage is kT/q, where k is the Boltzman's constant, T is the temperature in Kelvin, and q is the unit of charge,
• M is a multiplication factor relating two transistors in the constant gm bias circuit,
• R1=1/f1C1,
• C1 is a capacitance of the first capacitor, and
• f1 is a frequency of a reference clock of the constant gm bias circuit;
• and
• (b) a second order biquad filter biased with the biasing current to obtain a stable cut-off frequency.

A method comprising:

• generating a biasing current (I0) using a constant gm bias circuit operating in the subthreshold region for ultra-low power consumption, said circuit including a switched capacitor resistor having a first capacitor, wherein the biasing current (I0) is given by:
• I0=VT ln(M)/R1,
• where VT is the thermal voltage of the constant gm bias circuit, where the thermal voltage is kT/q, where k is the Boltzman's constant, T is the temperature in Kelvin, and q is the unit of charge,
• M is a multiplication factor relating two transistors in the constant gm bias circuit,
• R1=1/f1C1,
• C1 is a capacitance of the first capacitor, and
• f1 is a frequency of a reference clock of the constant gm bias circuit, and
• wherein generating a biasing current (I0) includes suppressing ripple originating from the switched capacitor resistor in the constant gm bias circuit using one or more decoupling capacitors.

A method comprising:

• generating a biasing current (I0) using a constant gm bias circuit operating in the subthreshold region for ultra-low power consumption, said circuit including a switched capacitor resistor having a first capacitor, wherein the biasing current (I0) is given by:
• I0=VT ln(M)/R1,
• where VT is the thermal voltage of the constant gm bias circuit, where the thermal voltage is kT/q, where k is the Boltzman's constant, T is the temperature in Kelvin, and q is the unit of charge,
• M is a multiplication factor relating two transistors in the constant gm bias circuit,
• R1=1/f1C1,
• C1 is a capacitance of the first capacitor, and
• f1 is a frequency of a reference clock of the constant gm bias circuit;
• and
• biasing a second order biquad filter with the biasing current to obtain a stable cut-off frequency.