Claims
- 1. A cascaded filter with low sensitivity to component values and gain, said filter comprising:
- a first resistor-capacitor section comprising a first resistor having a first terminal and a second terminal and a first capacitor having a first terminal and a second terminal, said first resistor having a value R.sub.1, said first capacitor having a value C.sub.1, wherein the first terminal of said first capacitor is electrically coupled to said second terminal of said first resistor;
- a second resistor-capacitor section electrically coupled to said first resistor capacitor section, said second resistor-capacitor section comprising a second resistor having a first terminal and a second terminal and a second capacitor having a first terminal and a second terminal, said second resistor having a value R.sub.2, said second capacitor having a value C.sub.2, wherein the first terminal of said second capacitor is electrically coupled to said second terminal of said second resistor;
- a third resistor-capacitor section electrically coupled to said second resistor-capacitor section, said third resistor-capacitor section comprising a third resistor having a first terminal and a second terminal and a third capacitor having a first terminal and a second terminal, said third resistor having a value R.sub.3, where R.sub.3 =(R.sub.2 .times.r.sub.1), where r.sub.1 is greater than 1, said third capacitor having a value C.sub.3 wherein the first terminal of said third capacitor is electrically coupled to the second terminal of said third resistor; and
- a fourth resistor-capacitor section electrically coupled to said third resistor-capacitor section, said fourth resistor-capacitor section comprising a fourth resistor having a first terminal and a second terminal and a fourth capacitor comprising a first terminal and a second terminal, said fourth resistor having a value R.sub.4, said fourth capacitor having a value C.sub.4, wherein the first terminal of said fourth capacitor is electrically coupled to said first terminal of said fourth resistor, wherein the value C.sub.2 =C.sub.1 .rho., wherein .rho. is greater than 1, and wherein C.sub.4 =C.sub.3 /.rho..sub.2, wherein .rho..sub.2 is greater than 1.
- 2. The filter of claim 1 wherein R.sub.2 =(R.sub.1 .times.r), wherein r is greater than 1 and wherein R.sub.4 =(R.sub.3 .times.r.sub.2) wherein r.sub.2 is greater than 1.
- 3. The filter of claim 1 wherein C.sub.3 =(C.sub.2 .div..rho..sub.1), wherein .rho..sub.1 is greater than 1.
- 4. A cascaded filter with low sensitivity to component values and gain, said filter comprising:
- a first resistor-capacitor section comprising a first resistor having a first terminal and a second terminal and a first capacitor having a first terminal and a second terminal, said first resistor having a value R.sub.1, said first capacitor having a value C.sub.1, wherein the first terminal of said first capacitor is electrically coupled to said second terminal of said first resistor;
- a second resistor-capacitor section electrically coupled to said first resistor capacitor section, said second resistor-capacitor section comprising a second resistor having a first terminal and a second terminal and a second capacitor having a first terminal and a second terminal, said second resistor having a value R.sub.2, said second capacitor having a value C.sub.2, wherein the first terminal of said second capacitor is electrically coupled to said second terminal of said second resistor;
- a third resistor-capacitor section electrically coupled to said second resistor-capacitor section, said third resistor-capacitor section comprising a third resistor having a first terminal and a second terminal and a third capacitor having a first terminal and a second terminal, said third resistor having a value R.sub.3, where R.sub.3 =R.sub.2 .times.r.sub.1 and where r.sub.1 is greater than 1, said third capacitor having a value C.sub.3, wherein the first terminal of said third capacitor is electrically coupled to the second terminal of said third resistor; and
- a fourth resistor-capacitor section electrically coupled to said third resistor-capacitor section, said fourth resistor-capacitor section comprising a fourth resistor having a first terminal and a second terminal and a fourth capacitor comprising a first terminal and a second terminal, said fourth resistor having a value R.sub.4, said fourth capacitor having a value C.sub.4, wherein the first terminal of said fourth capacitor is electrically coupled to said first terminal of said fourth resistor, wherein R.sub.2 =R.sub.1 .times.r, wherein r is greater than 1, and wherein R.sub.4 =R.sub.3 .times.r.sub.2 wherein r.sub.2 is greater than 1.
- 5. The filter of claim 4 wherein C.sub.2 =C.sub.1 .div..rho., wherein .rho.0 is greater thin 1.
- 6. The filter of claim 5 wherein C.sub.3 =C.sub.2 .div..rho..sub.1, wherein .rho..sub.1 is greater than 1.
- 7. The filter of claim 7 wherein C.sub.4 =C.sub.3 .div..rho..sub.2, wherein .rho..sub.2 is greater than 1.
- 8. A method of designing a cascaded filter with low sensitivity to component values comprising the steps of:
- designing a first filter circuit having a first filter section and a second filter section, said first filter section comprising a first resistor having a value R and a first capacitor having a value C, said second filter section comprising a second resistor having a value R.sub.2 and a second capacitor having a value C.sub.2 wherein said second filter section has a higher impedance than said first filter section;
- designing a second filter circuit having a first filter section and a second filter section, said first filter section of said second filter circuit comprising a third resistor having a value R.sub.3, where R.sub.3 =R.sub.2 .times.r.sub.1, and where r.sub.1 is greater than 1, and a third capacitor having a value C.sub.3, said second filter section of said second filter circuit comprising a fourth resistor having a value R.sub.4, and a fourth capacitor having a value C.sub.4, wherein said second filter section of said second filter circuit has a higher impedance than said first filter section of said second filter circuit; and
- cascading said first and second filter circuits.
- 9. The method of claim 8 wherein r.sub.1 is less than or equal to 10.
- 10. The method of claim 8 wherein R.sub.2 =R.times.r, wherein r is greater than 1.
- 11. The method of claim 10 wherein r is less than or equal to 10.
- 12. The method of claim 8 wherein R.sub.4 =R.sub.3 .times.r.sub.2, wherein r.sub.2 is greater than 1.
- 13. The method of claim 12 wherein r.sub.2 is less than or equal to 10.
- 14. The method of claim 8 wherein C.sub.2 =C.div..rho., wherein .rho. is greater than 1.
- 15. The method of claim 14 wherein .rho. is less than or equal to 10.
- 16. The method of claim 14 wherein C.sub.3 =C.sub.2 .div..rho..sub.1, wherein .rho..sub.1 is greater than 1.
- 17. The method of claim 16 wherein .rho..sub.1 is greater than or equal to 10.
- 18. The method of claim 16 wherein C.sub.4 =C.sub.3 .div..rho..sub.2, wherein .rho..sub.2 is greater than 1.
- 19. The method of claim 18 wherein .rho..sub.2 is greater than or equal to 10.
CROSS REFERENCE TO RELATED APPLICATION
This application claims priority to and the benefit of the filing data of copending provisional application entitled A CASCADED HIGHER ORDER FILTER WITH LOW SENSITIVITY TO COMPONENT VALUES AND A METHOD FOR DESIGNING THE SAME, assigned Ser. No. 60/032,809, filed Dec. 11, 1996 (Attorney Docket Number 60704-8030). The above-referenced provisional application is incorporated herein by reference.
Non-Patent Literature Citations (2)
Entry |
Moschytz, "A Universal LOW-Q Active-Filter Building Block Suitable for Hybrid-Integrated Circuit Implementation," IEEE Transactions on Circuit Theory, vol. CT-20, No. 1, pp. 37-47, Jan. 1973. |
Moschytz et al. , Active Filter Design Handbook, Wiley & Sons, pp. 169-170, 1981. |