Low-pass filter with adjustable cut-off frequency
A low-pass filter includes an integrator having an adjustable unity frequency. The integrator includes a first input, first output and feedback loop between the first input and output of the integrator. The first input is connected to a branch that includes a first impedance, to which is applied a first input voltage of the low-pass filter. The feedback loop includes a second impedance and the first output of the integrator is the first output of the low-pass filter.
1. A low-pass filter, comprising:
a first input terminal configured to receive a first input voltage;
a first impedance coupled to the first input terminal;
an output terminal; and
an integrator having an adjustable unity frequency, said integrator including:
a first input coupled to the first impedance such that the first impedance is positioned between the first input terminal and the first input of the integrator;
a first output coupled to the output terminal of the low-pass filter;
an input stage coupled to the first input and including a transconductor;
an output stage coupled to the output terminal;
a variable gain control stage electrically coupled between an output of the transconductor and an input of the output stage and configured to adjust the unity frequency of the integrator; and
a feedback loop between said first input and first output of said integrator, said feedback loop including a second impedance.
2. A low-pass filter according to claim 1 , wherein the variable gain control stage is configured to allow the unity frequency of said integrator to be adjusted.
3. A low-pass filter according to claim 2 , wherein the variable gain control stage has a gain that is variable from a value α min to a value α max , with 1≦α max /α min ≦25.
4. A low-pass filter according to claim 1 , wherein the integrator comprises a second input and a second output, said second input and second output being coupled to ground.
5. A low-pass filter according to claim 1 , further comprising:
a second input terminal configured to receive a second input voltage;
a second output terminal; and
a third impedance coupled to the second input terminal, wherein the integrator comprises:
a second input coupled to the third impedance such that the third impedance is positioned between the second input terminal and the second input of the integrator;
a second output, coupled to the second output terminal of the low-pass filter; and
a second feedback loop between said second input and output of said integrator, said second feedback loop including a fourth impedance.
6. A low-pass filter according to claim 1 , wherein the first and second impedances are chosen such that 0.5≦Z 2 /Z 1 ≦5, with Z 1 and Z 2 being values of the first and second impedances, respectively.
7. A low-pass filter according to claim 1 , wherein the low-pass filter is of an order greater than or equal to 2.
8. A low-pass filter according to claim 1 , wherein the low-pass filter has a leapfrog cascade structure of plural low-pass filter circuits, wherein one of the low-pass filter circuits includes a first impedance and the integrator.
9. A system for processing an electrical signal comprising:
a first low-pass filter stage that includes:
a first input terminal configured to receive a first input voltage;
a first impedance coupled to the first input terminal;
a first output terminal configured to provide a first output signal; and
a first integrator having an adjustable unity frequency, said integrator including:
a first input coupled to the first impedance such that the first impedance is positioned between the first input terminal and the first input of the integrator;
a first output coupled to the first output terminal of the first low-pass filter stage;
an input stage coupled to the first input and including a transconductor;
an output stage coupled to the output terminal;
a variable gain control stage electrically coupled between an output of the transconductor and an input of the output stage and configured to adjust the unity frequency of the integrator; and
a first feedback loop between said first input and first output of said integrator, said first feedback loop including a second impedance.
10. A system according to claim 9 , comprising:
a second low-pass filter stage coupled to the first low-pass filter stage in a leapfrog configuration.
11. A system according to claim 10 , wherein the first low-pass filter stage includes a second input terminal and the second low-pass filter stage includes:
a third input terminal configured to receive the first output signal;
a third impedance coupled to the third input terminal;
a second output terminal configured to provide a second output signal; and
a second integrator having an adjustable unity frequency, said second integrator including:
a first input coupled to the third impedance such that the third impedance is positioned between the third input terminal and the first input of the second integrator;
a first output coupled to the second output terminal of the second low-pass filter stage; and
a second feedback loop between said first input and first output of said integrator, said second feedback loop including a fourth impedance.
12. A system according to claim 9 , wherein the variable gain control stage is configured to adjust the unity frequency of said first integrator.
13. A system according to claim 12 , wherein the variable gain control stage has a gain that is variable from a value α min to a value α max , with 1≦α max /α min ≦25.
14. A system according to claim 9 , wherein the first integrator comprises a second input and a second output, said second input and second output being coupled to ground.
15. A system according to claim 9 , further comprising:
a second input terminal configured to receive a second input voltage;
a second output terminal; and
a third impedance coupled to the second input terminal, wherein the integrator comprises:
a second input coupled to the third impedance such that the third impedance is positioned between the second input terminal and the second input of the integrator;
a second output, coupled to the second output terminal of the low-pass filter; and
a second feedback loop between said second input and output of said integrator, said second feedback loop including a fourth impedance.
16. A system according to claim 9 , wherein the first and second impedances are chosen such that 0.5≦Z 2 /Z 1 ≦5, with Z 1 and Z 2 being values of the first and second impedances, respectively.
17. A system according to claim 9 , wherein the low-pass filter is of an order greater than or equal to 2.