Systems and methods for filter tuning using binary search algorithm

1. A filter tuning system comprising:

a time constant detector configured to detect a time constant of a filter based on an integral value of a reference input signal using a integrator when the time constant of the filter changes according to a variation of a manufacturing process or a temperature, the integrator including a capacitor changing according to a variation of the time constant of the filter, the capacitor included in the integrator being located in the same environment as the filter;

a comparator configured to compare the detected time constant with a reference value; and

a calibration unit configured to compensate the time constant of the filter using a binary search algorithm based on the comparison result until an error between the time constant and the reference value is reduced within an acceptable range,

wherein the calibration unit decreases the time constant by a unit of a calibration interval when the comparison result corresponds to a first logic value, the calibration unit increases the time constant by a unit of the calibration interval when the comparison result corresponds to a second logic value, and the calibration unit decreases a calibration interval for the next repetition by half of the calibration interval for a current repetition when repeating the increasing or decreasing of the time constant.

2. The filter tuning system of claim 1 , wherein the time constant detector includes an operational amplifier having a first input terminal coupled to a ground voltage, a second input terminal coupled to a resistor, and the capacitor is coupled between the second input terminal of the operational amplifier and the output terminal of the operational amplifier.

3. The filter tuning system of claim 1 , wherein the capacitor comprises:

a plurality of capacitors, the capacitance of each of the capacitors being double the capacitance of an adjacent capacitor; and

a plurality of switches coupled, each of the switches being coupled to a corresponding one of the plurality of the capacitors, each of the switches being controlled in response to each bit of a calibration signal.

4. The filter tuning system of claim 1 , wherein the comparator generates the first logic value when the detected time constant is higher than the reference value, and the comparator generates the second logic value when the detected time constant is lower than the reference value.

5. A method of tuning a filter, comprising:

detecting a time constant of the filter when the time constant of the filter changes according to a variation of a manufacturing process or a temperature;

comparing the detected time constant with a reference value; and

compensating the time constant of the filter using a binary search algorithm based on the comparison result until an error between the time constant and the reference value is reduced within an acceptable range,

wherein compensating the time constant comprises:

decreasing the time constant when the comparison result corresponds to a first logic value;

increasing the time constant when the comparison result corresponds to a second logic value; and

decreasing a calibration interval for the next repetition by half of a calibration interval for a current repetition when repeating the increasing or decreasing of the time constant.

6. The method of claim 5 , wherein detecting the time constant of the filter comprises:

detecting the time constant based on an integral value using a resistor and a capacitor changing according to a variation of the time constant of the filter, the capacitor being located in the same environment as the filter.

7. The method of claim 5 , wherein comparing the detected time constant with the reference value comprises:

generating the first logic value when the detected time constant is higher than the reference value; and

generating the second logic value when the detected time constant is lower than the reference value.

8. The method of claim 5 , wherein compensating the time constant comprises:

repeating the increasing or decreasing of the time constant of the filter based on the comparison result until the error between the time constant and the reference value is reduced within the acceptable range.

9. A signal processor comprising:

a filter, a cutoff frequency of the filter being determined by a time constant;

a filter tuning system configured to compensate the time constant when the time constant changes according to a variation of a manufacturing process or a temperature; and

a register block configured to maintain the compensated time constant,

wherein the filter tuning system comprises:

a time constant detector configured to detect the time constant of the filter when the time constant of the filter changes according to the variation of the manufacturing process or the temperature;

a comparator configured to compare the detected time constant with a reference value; and

a calibration unit configured to compensate the time constant of the filter using a binary search algorithm based on the comparison result until an error between the time constant and the reference value is reduced within an acceptable range.