Linear phase filter with self-equalized group delay

• US 4,395,688 A
• Filed: 08/11/1981
• Issued: 07/26/1983
• Est. Priority Date: 08/11/1981
• Status: Expired due to Term

• Current Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Original Assignee: Harris Corporation (L3Harris Technologies, Inc.)
• Inventors: Sellers, Robert W.
• Primary Examiner(s): Nussbaum, Marvin L.
• Application Number:
  US06/291,937
• Time in Patent Office: 714 Days
• Field of Search: 333/167-171, 333/175-179, 333/138-140, 333/23
• US Class Current: 333/169
• CPC Class Codes: H03H 7/09 Filters comprising mutual inductance
• CPC Class Codes: H03H 7/175 Series LC in series path H03H7/1783 takes precedence
• CPC Class Codes: H03H 7/1783 Combined LC in series path
• CPC Class Codes: H03H 7/1791 Combined LC in shunt or branch path
• CPC Class Codes: H04B 3/147 fixed equalisers

Abstract

In modern communication systems, it has become important to provide filters, and in particular bandpass filters, which can provide substantially uniform group delay across the bandwidth of the filter while still achieving good amplitude response. In this regard, it is particularly desirable to substantially reduce the large variations in the phase characteristics found in conventional bandpass filters at the nominal band edge of the filter. To accomplish this, a filter is provided having at least one pair of lattice arms coupled in parallel to one another between the input and output of the filter. Each of the lattice arms includes a plurality of resonant LC resonators, each of the resonators having a different resonant frequency than the center frequency of the filter. In particular, within the bandwidth of the filter, the exponential damping coefficients for the resonators in each arm are set to decay at the same rate. This desired decay can be accomplished by exponential sizing of the components.

Claims

1. A filter for filtering an electrical signal to pass said electrical signal within a predetermined bandwidth of frequencies centered around a predetermined center frequency comprising:

an input coupled to receive said electrical signal;

an output for providing a filtered output signal; and

a pair of lattice arms coupled in parallel between said input and output, wherein each arm includes a plurality of parallel resonant LC resonators connected in series along each arm, each of said resonators having a different resonant frequency within the bandwidth of said filter,

wherein the capacitors of the resonators in each arm have values which are substantially exponentially related in accordance with the frequency of resonance of the resonator they are in to the capacitance determined for resonance at the center frequency.

2. A filter according to claim 1, wherein the values of inductance and capacitance in each of the resonators are set so that when parallel resonance occurs in one of the parallel resonators in one of said arms, series resonance will occur between a pair of said parallel resonators in the other arm.

3. A filter according to claim 1, wherein the frequency of resonance for the respective resonators is spaced linearly, relative to one another, across the bandwidth of the filter with a spacing of 2 Δ

f=bandwidth of the filter/number of resonators within the bandwidth.

4. A filter according to claim 3, wherein each arm includes a corrector resonator tuned for parallel resonance outside of the bandwidth of the filter, and wherein the values of inductance and capacitance for said corrector resonators are set to provide series resonance with another resonator in the same arm as the corrector resonator at a frequency adjacent to a nominal band edge of the filter at which one of the resonators in the other arm attains parallel resonance.

5. A filter according to claim 4, wherein the value of capacitance in the corrector resonator is set to be substantially exponentially related to the capacitance which is determined for resonance at the center frequency.

6. A filter according to claim 4 or 5, wherein the corrector resonators are tuned for resonance at a frequency outside of the nominal band edge of the filter by a frequency equal to 20% of 2 Δ

f.

7. A filter according to claim 1 or 5, wherein the value of the capacitors in the resonators in one arm increase exponentially from the lowest value of resonant frequency to the highest value of resonant frequency while the values of capacitance in the resonators in the other arm decrease exponentially from the lowest value of resonant frequency to the highest value of resonant frequency, and wherein the respective exponential increase and decrease in the arms are centered around the same value of capacitance determined for resonance at the center frequency.

8. A bandpass filter for filtering an electrical signal to pass said electrical signal within a predetermined bandwidth of frequencies centered around a predetermined center frequency with a substantially constant group delay and with a phase characteristic which converges toward the amplitude characteristic near a nominal band edge of the filter comprising:

an input coupled to receive said electrical signal;

an output for providing a filtered output signal;

a pair of lattice arms coupled in parallel between the input and output of each lattice arm including a plurality of parallel LC resonators connected in series along each arm, each of said resonators having a different resonant frequency within said bandwidth of said filter, wherein the values for inductance and capacitance in each resonator are set so that when parallel resonance occurs in one of said arms, series resonance will occur between a pair of said parallel resonators connected in series in the other arm, and wherein the frequencies of parallel resonance are spaced linearly, relative to one another, across the bandwidth of the filter with the spacing of 2 Δ

f=bandwidth of the filter/number of resonators within the bandwidth;

a transformer coupled between the arms and the output of the filter, said transformer being coupled to cancel the electrical signal passing through each arm to the transformer if the value of the electrical signal is the same in each arm so that the output will be zero when the electrical signal is the same in each arm,

wherein the capacitance of the resonators in each arm have values which are substantially exponentially related in accordance with the frequency of resonance of the resonator they are in to the capacitance which is determined for resonance at the center frequency, and further wherein each arm includes a corrector resonator tuned for parallel resonance outside of the bandwidth, said corrector resonators each having values of conductance and capacitance set to provide series resonance with another resonator in the same arm as the corrector resonator at a frequency adjacent to the nominal band edge of the filter at which one of the resonators in the other arm attains parallel resonance.

9. A filter for filtering an electrical signal to pass said electrical signal within a predetermined bandwidth of frequencies centered around a predetermined center frequency comprising:

an input coupled to receive said electrical signal;

an output for providing a filtered output signal; and

a pair of lattice arms coupled in parallel between said input and output, wherein each arm includes a plurality of LC resonators along each arm, each of said resonators having a different resonant frequency within the bandwidth of said filter,

wherein the exponential damping coefficients for the resonators in each arm are set to decay at the same rate within the bandwidth of the filter.

10. A filter according to claim 9, wherein the resonators in each arm are parallel LC resonators connected in series with one another along each arm.

11. A filter according to claim 10, wherein the values of inductance and capacitance in each of the resonators are set so that when parallel resonance occurs in one of the parallel resonators in one of said arms, series resonance will occur between a pair of said parallel resonators in the other arm.

12. A filter according to claim 11, wherein the frequency of resonance for the repective resonators is spaced linearly, relative to one another, across the bandwidth of the filter with a spacing of 2 Δ

f=bandwidth of the filter/number of resonators within the bandwidth.

13. A filter according to claim 10, wherein the capacitors of the resonators in each arm have values which are substantially exponentially related in accordance with the frequency of resonance of the resonator they are in to the capacitance determined for resonance at the center frequency.

14. A filter according to claim 12, wherein each arm includes a corrector resonator tuned for parallel resonance outside of the bandwidth of the filter, and wherein the values of inductance and capacitance for said corrector resonators are set to provide series resonance with another resonator in the same arm as the corrector resonator at a frequency adjacent to a nominal band edge of the filter at which one of the resonators in the other arm attains parallel resonance.

15. A filter according to claim 14, wherein the value of capacitance in the corrector resonator is set to be substantially exponentially related to the capacitance which is determined for resonance at the center frequency.

16. A filter according to claim 14 or 15, wherein the corrector resonators are tuned for resonance at a frequency outside of the nominal band edge of the filter by a frequency equal to 20% of 2 Δ

f.

17. A filter according to claim 13 or 14, wherein the value of the capacitors in the resonators in one arm increase exponentially from the lowest value of resonant frequency to the highest value of resonant frequency while the values of capacitance in the resonators in the other arm decrease exponentially from the lowest value of resonant frequency to the highest value of resonant frequency, and wherein the respective exponential increase and decrease in the arms are centered around the same value of capacitance determined for resonance at the center frequency.

18. A filter according to claim 9, wherein the exponential damping coefficient α

_N for each resonator is set to equal

space="preserve" listing-type="equation">α

.sub.N =F.sub.N /F.sub.O α

.sub.O

where;

F_O is the predetermined center frequency,

F_N is the resonant frequency of the resonator, and

α

_O is the exponential damping coefficient determined for the center frequency.

19. A bandpass filter for filtering an electrical signal to pass said electrical signal within a predetermined bandwidth of frequencies centered around a predetermined center frequency with a substantially constant group delay and with a phase characteristic which converges toward the amplitude characteristic near a nominal band edge of the filter comprising:

an input coupled to receive said electrical signal;

an output for providing a filtered output signal;

a pair of lattice arms coupled in parallel between the input and output of each lattice arm including a plurality of parallel LC resonators connected in series along each arm, each of said resonators having a different resonant frequency within said bandwidth of said filter, wherein the values for inductance and capacitance in each resonator are set so that when parallel resonance occurs in one of said arms, series resonance will occur between a pair of said parallel resonators connected in series in the other arm, and wherein the frequencies of parallel resonance are spaced linearly, relative to one another, across the bandwidth of the filter with the spacing of 2 Δ

f=bandwidth of the filter/number of resonators within the bandwidth;

a transformer coupled between the arms and the output of the filter, said transformer being coupled to cancel the electrical signal passing through each arm to the transformer if the value of the electrical signal is the same in each arm so that the output will be zero when the electrical signal is the same in each arm,

wherein the exponential damping coefficients for the resonators in each arm are set to decay at the same rate within the bandwidth of the filter, and further wherein each arm includes a corrector resonator tuned for parallel resonance outside of the bandwidth, said corrector resonators each having values of conductance and capacitance set to provide series resonance with another resonator in the same arm as the corrector resonator at a frequency adjacent to the nominal band edge of the filter at which one of the resonators in the other arm attains parallel resonance.

20. A filter according to claim 19, wherein the exponential damping coefficient α

_N for each resonator within the bandwidth of the filter is set to equal

space="preserve" listing-type="equation">α

.sub.N =F.sub.N /F.sub.O α

.sub.O

where;

F_O is the predetermined center frequency,

F_N is the resonant frequency of the resonator, and

α

_O is the exponential damping coefficient determined for the center frequency.

21. A filter for filtering an electrical signal to pass said electrical signal within a predetermined bandwidth of frequencies centered around a predetermined center frequency comprising:

an input coupled to receive said electrical signal;

an output for providing a filtered output signal; and

a pair of lattice arms coupled in parallel between said input and output, wherein each arm includes a plurality of series resonant LC resonators connected in parallel to one another in each arm, each of said resonators having a different resonant frequency within the bandwidth of said filter,

wherein the inductors of the resonators in each arm have values which are substantially exponentially related in accordance with the frequency of resonance of the resonator they are in to the inductance determined for resonance at the center frequency.

22. A filter according to claim 21, wherein the values of inductance and capacitance in each of the resonators are set so that when series resonance occurs in one of the series resonators in one of said arms, parallel resonance will occur between a pair of said series resonators in the other arm.

23. A filter according to claim 21, wherein the frequency of resonance for the respective resonators is spaced linearly, relative to one another, across the bandwidth of the filter with a spacing of 2 Δ

f=bandwidth of the filter/number of resonators within the bandwidth.

24. A filter according to claim 21, wherein each arm includes a corrector resonator tuned for series resonance outside of the bandwidth of the filter, and wherein the values of inductance and capacitance for said corrector resonators are set to provide parallel resonance with another resonator in the same arm as the corrector resonator at a frequency adjacent to a nominal band edge of the filter at which one of the resonators in the other arm attains series resonance.

25. A filter according to claim 24, wherein the value of inductance in the corrector resonator is set to be substantially exponentially related to the inductance which is determined for resonance at the center frequency.

26. A filter for filtering an electrical signal to pass said electrical signal within a predetermined bandwidth of frequencies centered around a predetermined center frequency comprising:

an input coupled to receive said electrical signal;

an output for providing a filtered output signal; and

a pair of lattice arms coupled in parallel between said input and output, wherein each arm includes a plurality of series resonant LC resonators connected in parallel to one another in each arm, each of said resonators having a different resonant frequency within the bandwidth of said filter,

wherein the exponential damping coefficients for the resonators in each arm are set to decay at the same rate within the bandwidth of the filter.

27. A filter according to claim 26, wherein the exponential damping coefficient α

_N for each resonator is set to equal

space="preserve" listing-type="equation">α

.sub.N =F.sub.N /F.sub.O α

.sub.O

where;

F_O is the predetermined center frequency,

F_N is the resonant frequency of the resonator, and

α

_O is the exponential damping coefficient determined for the center frequency.

28. A method for filtering an electrical signal to pass said electrical signal within a predetermined bandwidth of frequencies centered around a predetermined center frequency comprising:

applying said electrical signal to a pair of lattice arms coupled in parallel between an input and an output terminal, wherein each arm includes a plurality of parallel resonant LC resonators connected in series along each arm, each of said resonators having a different resonant frequency within the bandwidth of said filter,

wherein the capacitors of the resonators in each arm have values which are substantially exponentially related in accordance with the frequency of resonance of the resonator they are in to the capacitance determined for resonance at the center frequency.

29. A method for filtering an electrical signal to pass said electrical signal within a predetermined bandwidth of frequencies centered around a predetermined center frequency comprising:

applying said electrical signal to a pair of lattice arms coupled in parallel between an input and an output terminal, wherein each arm includes a plurality of parallel resonant LC resonators connected in series along each arm, each of said resonators having a different resonant frequency within the bandwidth of said filter,

wherein the exponential damping coefficients for the resonators in each arm are set to decay at the same rate.

32. A method according to claim 29 or 31, wherein the exponential damping coefficient α

_N for each resonator within the bandwidth of the filter is set to equal

space="preserve" listing-type="equation">α

.sub.N =F.sub.N /F.sub.O α

.sub.O

where;

F_O is the predetermined center frequency,

F_N is the resonant frequency of the resonator, and

α

_O is the exponential damping coefficient determined for the center frequency.

30. A method for filtering an electrical signal to pass said electrical signal within a predetermined bandwidth of frequencies centered around a predetermined center frequency comprising:

applying said electrical signal to a pair of lattice arms coupled in parallel between an input and an output terminal, wherein each arm includes a plurality of series resonant LC resonators connected in parallel to one another in each arm, each of said resonators having a different resonant frequency within the bandwidth of said filter,

wherein the inductors of the resonators in each arm have values which are substantially exponentially related in accordance with the frequency of resonance of the resonator they are in to the inductance determined for resonance at the center frequency.

31. A method for filtering an electrical signal to pass said electrical signal within a predetermined bandwidth of frequencies centered around a predetermined center frequency comprising:

applying said electrical signal to a pair of lattice arms coupled in parallel between an input and an output terminal, wherein each arm includes a plurality of series resonant LC resonators connected in parallel to one another in each arm, each of said resonators having a different resonant frequency within the bandwidth of said filter,

wherein the exponential damping coefficients for the resonators in each arm are set to decay at the same rate within the bandwidth of the filter.