Method and apparatus for cancellation of third order intermodulation distortion and other nonlinearities

• US 20030179041A1
• Filed: 03/19/2002
• Published: 09/25/2003
• Est. Priority Date: 03/19/2002
• Status: Active Grant

• Current Assignee: University of North Carolina At Charlotte (University of North Carolina System)
• Original Assignee: University of North Carolina At Charlotte (University of North Carolina System)
• Inventors: Weldon, Thomas Paul
• Granted Patent: US 6,794,938 B2
• Time in Patent Office: Days
• US Class Current: 330/149
• CPC Class Codes: H03F 1/3205 in field-effect transistor amplifiers
• CPC Class Codes: H03F 1/3211 in differential amplifiers
• CPC Class Codes: H03F 1/3229 using a loop for error extraction and another loop for error subtraction
• CPC Class Codes: H03F 1/3241 using predistortion circuits H03F1/3211, H03F1/3217 take precedence

Abstract

Methods and apparatus are provided for substantially reducing and/or canceling nonlinearities of any order in circuits, devices, and systems such as amplifiers and mixers. In particular, methods and apparatus are provided for substantially reducing and/or canceling third order nonlinearities in circuits, devices, and systems such as amplifiers and mixers. A first coupler is used to split an input signal into two equal-amplitude in-phase components, each component is processed by two nonlinear devices with different nonlinearities, and a final combiner, such as a 180-degree hybrid, recombines the processed signals 180 degrees out of phase and substantially reduces and/or cancels the undesired nonlinear distortion components arising due to nonlinearities in the nonlinear devices.

Claims

1. An apparatus for substantially reducing nonlinear distortion, the apparatus comprising:

a first coupler having an input and first and second outputs, the first coupler capable of splitting an input signal into first and second coupled signals having equal amplitude and in-phase with respect to each other;

a first nonlinear device having an input in communication with the first output of the first coupler and an output;

a second nonlinear device having an input in communication with the second output of the first coupler and an output; and

a second coupler having a first input in communication with the output of the first nonlinear device, a second input in communication with the output of the second nonlinear device and an output, the second coupler capable of 180 degree phase shifting an output signal of the second nonlinear device and coupling the phase shifted output signal of the second nonlinear device with an output signal of the first nonlinear device to generate a final output signal.

2. The apparatus of claim 1, wherein the first nonlinear device further comprises a first amplifier and the second nonlinear device further comprises a second amplifier.

3. The apparatus of claim 1, wherein the first nonlinear device further comprises a first mixer and the second nonlinear device further comprises a second mixer.

4. The apparatus of claim 1, wherein the second nonlinear device has a different gain and a different third order intercept point than the first nonlinear device.

5. The apparatus of claim 1, wherein predetermined nonlinearities are substantially reduced in the final output signal by predetermined selection of a gain of the first nonlinear device, a gain of the second nonlinear device, a nonlinearity of the first nonlinear device and a nonlinearity of the second nonlinear device.

6. The apparatus of claim 1, wherein the first nonlinear device defines a gain as G₁ dB, the second nonlinear device defines a gain as G₂ dB, the first nonlinear device defines a third order output intercept point as OIP3₁ dBm and the second nonlinear device defines a third order output intercept point as OIP3₂ dBm such that the first and second nonlinear devices are provided such that most nearly 2(OIP3₁−

OIP3₂)=3(G₁−

G₂), where G₁ is not equal to G₂ and such that the first and second nonlinear devices have substantially equal time delay and phase to substantially reduce third order nonlinear distortion.

7. The apparatus of claim 1, wherein the first nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the first nonlinear device, y₁, in terms of an input signal of the first nonlinear device, x₁, as y₁=a₀+a₁x₁+a₂x₂+a₃x₁³+a₄⁴ . . . , the second nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the second nonlinear device, y₂, in terms of an input signal of the second nonlinear device, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₄x₂⁴ . . . , such that nonlinearities of order n are substantially reduced by setting most nearly a_n=b_n, and a₁ does not equal b₁.

8. The apparatus of claim 7, wherein signals x₁, x₂, y₁, and y₂ are voltages.

9. The apparatus of claim 7, wherein signals x₁, x₂, y₁, and y₂ are currents.

10. An apparatus for substantially reducing nonlinear distortion, the apparatus comprising:

an input coupling means having an input and first and second outputs, the input coupling means capable of splitting an input signal into first and second coupled signals that are in-phase with respect to each other;

a first nonlinear device having an input in communication with the first output of the input coupling means and an output;

a second nonlinear device having an input in communication with the second output of the input coupling means and an output; and

a subtractor having a first input in communication with the output of the first nonlinear device, a second input in communication with the output of the second nonlinear device and an output, wherein the subtractor is capable of subtracting an output signal of the second nonlinear device from an output signal of the first nonlinear device to generate a final output signal.

11. The apparatus of claim 10, wherein the first nonlinear device further comprises a first amplifier and the second nonlinear device further comprises a second amplifier.

12. The apparatus of claim 10, wherein the first nonlinear device further comprises a first mixer and the second nonlinear device further comprises a second mixer.

13. The apparatus of claim 10, wherein the first nonlinear device further comprises an amplifier and the second nonlinear device further comprises a diode.

14. The apparatus of claim 10, wherein predetermined nonlinearities are substantially reduced in the final output signal by predetermined selection of a gain of the first nonlinear device, a gain of the second nonlinear device, a nonlinearity of the first nonlinear device, a nonlinearity of the second nonlinear device and selection of the input coupling means.

15. The apparatus of claim 10, wherein the first nonlinear device defines a gain as G₁ dB, the second nonlinear device defines a gain as G₂ dB, the first nonlinear device defines a third order output intercept point as OIP3₁ dBm and the second nonlinear device defines a third order output intercept point as OIP3₂ dBm, and K=10 log₁₀(p₂/p₁), where p₁ is the input signal power level of the first nonlinear device and p₂ is the input signal power level of the second nonlinear device, such that the first and second nonlinear devices and the input coupling means are provided such that most nearly 2(OIP3₁−

OIP3₂)=3(G₁−

G₂−

K), where G₁ is not equal G₂+K and such that the first and second nonlinear devices have substantially equal time delay and phase to substantially reduce third order nonlinearity.

16. The apparatus of claim 10, wherein the first nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the first nonlinear device, y₁, in terms of an input signal of the first nonlinear device, x₁, as y₁=a₀+a₁x₁+a₂x₁²+a₃x₁+a₄x₁⁴, . . . , the second nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the second nonlinear device, y₂ in terms of an input signal of the second nonlinear device, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₄x₂⁴ . . . , the ratio, k, is provided such that k=x₂/x₁, where k is set by the input coupling means provided, such that nonlinearities of order n are substantially reduced and/or canceled by setting most nearly k=(a_n/b_n)^1/n.

17. The apparatus of claim 16, wherein signals x₁, x₂, y₁, and y₂ are voltages.

18. The apparatus of claim 16, wherein signals x₁, x₂, y₁, and y₂ are currents.

19. A method for substantially reducing third order distortion in an apparatus, the method comprising the steps of:

splitting an input signal into first and second in-phase coupled signals, the ratio of a second in-phase coupled signal power, p₂, to a first coupled signal power, p₁, is defined as K=10 log₁₀(p₂/p₁);

processing the first in-phase coupled signal at a first nonlinear device and the second in-phase coupled signal at a second nonlinear device, the first nonlinear device has a gain defined as, G₁ dB, and a third order output intercept point defined as, OIP3₁ dBm, the second nonlinear device has a gain defined as, G₂ dB, and a third order output intercept point defined as, OIP3₂ dBm, such that the relationship between the first and second nonlinear devices and the input coupling means is defined as, most nearly 2(OIP³₁−

OIP3₂)=3(G₁−

G₂−

K), where G₁ is not equal to G₂+K and the first and second nonlinear devices have substantially equal time delay and phase; and

subtracting an output signal of the second nonlinear device from an output signal of the first nonlinear device to yield a final output signal that substantially reduces third order nonlinearities.

20. A method for substantially reducing nonlinear distortion in an apparatus, the method comprising the steps of:

splitting an input signal into first and second in-phase coupled signals, wherein the ratio of the second in-phase coupled signal, x₂, to the first in-phase coupled signal, x₁, is defined as k=x₂/x₁;

processing the first in-phase coupled signal at a first nonlinear device and the second in-phase coupled signal at a second nonlinear device, the first nonlinear device has a Taylor series expansion describing an output signal, y₁, in terms of an input signal, x₁, as y₁, =a₀+a₁x₁+a₂x₁²+a₃x₁³+a₄x₁⁴ . . . , the second nonlinear device has a Taylor series expansion describing an output signal y₂, in terms of an input signal, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₄x₂⁴ . . . , such that the first and second nonlinear devices and the input coupling means are defined as most nearly k=(a_n/b_n)^1/n; and

subtracting an output signal of the second nonlinear device from an output signal of the first nonlinear device to yield a final output signal that substantially reduces nonlinear distortion of order n.

21. The method of claim 20, wherein signals x₁, x₂, y₁, and y₂ are voltages.

22. The method of claim 20, wherein signals x₁, x₂, y₁, and y₂ are currents.

23. An apparatus for substantially reducing nonlinear distortion, the apparatus comprising:

a nonlinear device having an input and an output, the nonlinear device having a Taylor series expansion describing an output current, i_o, in terms of an input voltage, v, as i_o=b₀+b₁v+b₂v²+b₃v³+b₄v⁴ . . . ; and

a nonlinear load having an input in communication with the output of the nonlinear device and in communication with a final output, the nonlinear load has a Taylor series expansion describing a current through the nonlinear load, i_L, in terms of a terminal voltage, v_L, as i_L=a₀+a₁v_L+a₂v_L+a₃v_L+a₄v_L, such that the nonlinear device and the nonlinear load are provided such that most nearly b₀=a₀, b₁=ca₁, b₂=c²a₂, b₃=c³a₃, b_n=cⁿa_n where, c, is a constant, wherein the output of the nonlinear device substantially reduces nonlinearities of the nonlinear device and the nonlinear load.

24. The apparatus of claim 23, wherein the nonlinear device further comprises:

a first n-channel field effect transistor (FET) having a gate in communication with an input source, a source and well in communication with ground, and a drain in electrical communication with an output, and

wherein the nonlinear load further comprises;

a second n-channel FET having a source and well in electrical communication with the drain of the first n-channel FET, and a gate and drain in common electrical communication; and

a third n-channel FET having a source and well in electrical communication with the drain of the second n-channel FET, and a gate and drain in common electrical communication with a power supply.

25. The apparatus of claim 23, wherein the nonlinear device further comprises:

a first npn bipolar junction transistor (BJT) having a base in electrical communication with an input source, an emitter in electrical communication with ground and a collector in electrical communication with an output, and

wherein the nonlinear load further comprises;

a second npn BJT having an emitter in electrical communication with the collector of the first npn BJT, and a base and collector in common electrical communication; and

a third npn BJT having an emitter in electrical communication with a collector of the second npn BJT, and a base and collector in common electrical communication with a power supply.

26. A method for substantially reducing nonlinear distortion in an apparatus, the method comprising the steps of:

applying an input voltage to a nonlinear device, the nonlinear device having a Taylor series expansion describing an output current, i_o, in terms of an input voltage, v, as i_o=b₀+b₁v+b₂v²+b₃v³+b₄v⁴ . . . ;

coupling an output current of the nonlinear device to a nonlinear load, the nonlinear load having a Taylor series expansion describing current through the nonlinear load, i_L, in terms of a terminal voltage, v_L, as i_L=a₀+a₁v_L+a₂v_L²+a₃v_L³+a₄v_L⁴ . . . , and the nonlinear device and the nonlinear load are provided such that most nearly b₀=a₀, b₁=ca₁, b₂=c²a₂, b₃=c³a₃, . . . , b_n=cⁿa_n, where, c, is a constant; and

outputting the terminal voltage at the nonlinear load to substantially reduce nonlinear terms and nonlinear signal distortion.

27. An apparatus for substantially reducing nonlinear distortion, the apparatus comprising:

a first nonlinear device having an input and an output;

a coupling means having an input in communication with the output of the first nonlinear device and first and second in-phase outputs;

a second nonlinear device having an input in communication with the first in-phase output of the coupling means and an output; and

a subtractor having a first input in communication with the output of the second nonlinear device, a second input in communication with the second in-phase output of the coupling means and an output, wherein the subtractor subtracts the output signal of the second nonlinear device from the second in-phase output of the coupler to generate a final output.

28. The apparatus of claim 27, wherein the first nonlinear device further comprises a first amplifier and the second nonlinear device further comprises a second amplifier.

29. The apparatus of claim 27, wherein the first nonlinear device further comprises a first mixer and the second nonlinear device further comprises a second mixer.

30. The apparatus of claim 27, wherein the first nonlinear device further comprises an amplifier and the second nonlinear device further comprises a diode.

31. The apparatus of claim 27, wherein predetermined nonlinearities are substantially reduced in the final output signal by predetermined selection of a gain of the first nonlinear device, a gain of the second nonlinear device, a nonlinearity of the first nonlinear device, a nonlinearity of the second nonlinear device and selection of the coupling means.

32. The apparatus of claim 27, wherein the first nonlinear device is provided to define a Taylor series expansion describing an output signal, y₁, in terms of an input signal, x₁, as y₁=a₀+a₁x₁+a₂x₁+a₃x₁+a₄x₁⁴ . . . , the second nonlinear is provided to define a Taylor series expansion describing an output signal, y₂, in terms of an input signal, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₄x₂⁴ . . . , and the ratio the first in-phase coupled signal to the second in-phase coupled being k.

33. The apparatus of claim 32, wherein signals x₁, x₂, y₁, and y₂ are voltages.

34. The apparatus of claim 32, wherein signals x₁, x₂, y₁, and y₂ are currents.

35. The apparatus of claim 32, wherein third order nonlinearities are substantially reduced by setting, k in the apparatus such that most nearly a₃−

a₃b₁k−

2a₁a₂b₂k²−

a₁³b₃k³=0, and such that a₁−

a₁b₁k does not equal zero.

36. The apparatus of claim 32, wherein second order nonlinearities are substantially reduced by setting, k, in the apparatus such that most nearly a₂−

a₂b₁k−

a₁²b₂k²=0, and such that a₁−

a₁b₁k does not equal zero.

37. A method for substantially reducing nonlinear distortion in an apparatus, the method comprising the steps of:

processing an input signal at a first nonlinear device, the first nonlinear device having a Taylor series expansion describing an output signal, y₁, in terms of an input signal, x₁, as y₁=a₀+a₁x₁+a₂x₁²+a₃x₁³+a₄x₁⁴ . . . ;

splitting, at a coupling means, an output signal of the first nonlinear device into first and second in-phase coupled signals;

processing the first in-phase coupled signal at a second nonlinear device, the second nonlinear device having a Taylor series expansion describing output signal, y₂, in terms of an input signal, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₄x₂⁴ . . . ; and

subtracting an output signal of the second nonlinear device from the second in-phase coupled signal to yield an output difference signal, wherein the output difference signal has substantially reduced nonlinear distortion.

38. The method of claim 37, wherein signals x₁, x₂, y₁, and y₂ are voltages.

39. The method of claim 37, wherein signals x₁, x₂, y₁, and y₂ are currents.

40. The method of claim 37, wherein predetermined nonlinearities are substantially reduced in the final output signal by predetermined selection of a gain of the first nonlinear device, a gain of the second nonlinear device, a nonlinearity of the first nonlinear device, a nonlinearity of the second nonlinear device and selection of the coupling means.

41. The method of claim 37, wherein the ratio of a first in-phase coupled signal to a second in-phase coupled signal, is defined as k and third-order nonlinearities are substantially reduced by setting, k, such that most nearly a₃−

a₃b₁k−

2a₁a₂b₂k²−

a₁³b₃k³=0, and such that a₁−

a₁b₁k does not equal zero.

42. The method of claim 37, wherein the ratio of a first in-phase coupled signal to a second in-phase coupled signal, is defined as k and second order nonlinearities are substantially reduced by setting, k, such that most nearly a₂−

a₂b₁k−

a₁²b₂k²=0, and such that a₁−

a₁b₁k does not equal zero.

43. An apparatus for substantially reducing nonlinear distortion, the apparatus comprising;

an input coupling means having an input and first and second outputs that is capable of splitting an input signal into first and second in-phase signals;

a first nonlinear device having an input in communication with the second output of the input coupling means and an output;

a subtraction means having a first input in communication with the first output of the input coupling means, a second input in communication with the output of the first nonlinear device and an output, the subtraction means phase-shifts 180-degrees an output signal of the first nonlinear device and combines such with the first in-phase signal to generate a difference signal; and

a second nonlinear device having an input in communication with the output of the subtraction means and an output, wherein the difference signal is processed at the second nonlinear device resulting in a final output signal having substantially reduced nonlinear distortion.

44. The apparatus of claim 43, wherein the first nonlinear device further comprises a first amplifier and the second nonlinear device further comprises a second amplifier.

45. The apparatus of claim 43, wherein the first nonlinear device further comprise a first mixer and the second nonlinear device further comprises a second mixer.

46. The apparatus of claim 43, wherein the first nonlinear device further comprises an amplifier and the second nonlinear device further comprises a diode.

47. The apparatus of claim 43, wherein the first nonlinear device is provided to define a Taylor series expansion describing an output signal, y₂, in terms of an input signal, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₄x₂⁴ . . . , the second nonlinear device is provided to define a Taylor series expansion describing an output signal, y₁, in terms of an input signal, x₁, as y₁=a₀+a₁x₁+a₂x₁²+a₃x₁³+a₄x₁⁴ . . . , and the ratio, k, of the input signal of the first nonlinear device to the first in-phase coupled signal is a constant value provided by the input coupling means.

48. The apparatus of claim 47, wherein signals x₁, x₂, y₁, and y₂ are voltages.

49. The apparatus of claim 47, wherein signals x₁, x₂, y₁, and y₂ are currents.

50. The apparatus of claim 43, wherein predetermined nonlinearities are substantially reduced in the final output signal by predetermined selection of a gain of the first nonlinear device, a gain of the second nonlinear device, a nonlinearity of the first nonlinear device, a nonlinearity of the second nonlinear device and selection of the coupling means.

51. The apparatus of claim 47, wherein third-order nonlinearities are substantially reduced by setting, k such that most nearly 2a₂b₁b₂k³−

2a₂b₂k²−

a₁b₃k³+a₃−

3a₃b₁k+3a₃b₁²k²−

a₃b₁³k³=0, and such that a₁−

a₁b₁k does not equal zero.

52. The apparatus of claim 47, wherein second-order nonlinearities are substantially reduced by setting, k, such that most nearly a₂b₁²k²−

a₁b₂k₂−

2a₂b₁k+a₂=0, and such that a₁−

a₁b₁k does not equal zero.

53. A method for substantially reducing nonlinear distortion in an apparatus, the method comprising the steps of:

splitting, at an input coupling means, an input signal into first and second in-phase coupled signals,

processing the second in-phase coupled signal at a first nonlinear device, wherein the first nonlinear device has a Taylor series expansion describing an output signal y₂, in terms of an input signal, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₄x₂⁴ . . . ;

subtracting an output signal of the first nonlinear device from the first in-phase coupled signal to yield an output difference signal; and

processing the output difference signal at a second nonlinear device, wherein the second nonlinear device has a Taylor series expansion describing an output signal, y₁, in terms of an input signal, x₁, as y₁, =a₀+a₁x₁+a₂x₁²+a₃x₁+a₄x₁⁴ . . . , wherein processing the output signal at a second nonlinear device results in a final output signal having substantially reduced nonlinear distortion.

54. The method of claim 53, wherein signals x₁, x₂, y₁, and y₂ are voltages.

55. The method of claim 53, wherein signals x₁, x₂, y₁, and y₂ are currents.

56. The method of claim 53, wherein predetermined nonlinearities are substantially reduced in the final output signal by predetermined selection of a gain of the first nonlinear device, a gain of the second nonlinear device, a nonlinearity of the first nonlinear device, a nonlinearity of the second nonlinear device and selection of the coupling means.

57. The method of claim 53, wherein the ratio of the second in-phase coupled signal, to the first in-phase coupled signal, is defined as k and third-order nonlinearities are substantially reduced by setting, k, such that most nearly 2a₂b₁b₂k³−

2a₂b₂k²−

a₁b₃k³+a₃−

3a₃b₁k+3a₃b₁²k²−

a₃b₁³k³=0, and such that a₁−

a₁b₁k does not equal zero.

58. The method of claim 53 wherein the ratio of the second in-phase coupled signal, to the first in-phase coupled signal, is defined as k and second-order nonlinearities are substantially reduced by setting, k, such that most nearly a₂b₁²k²−

a₁b₂k²−

2a₂b₁k+a₂=0, and such that a₁−

a₁b₁k does not equal zero.

59. An apparatus for substantially reducing nonlinear distortion, the apparatus comprising:

a first differential subcircuit comprising;

a first n-channel field-effect transistor (FET) having a gate in electrical communication with a first bias voltage source, a source in electrical communication with ground and a drain; and

a first differential pair comprising second and third n-channel FETs, the second n-channel FET having a gate in electrical communication with a positive terminal of a differential input source, a source in electrical communication with the drain of the first n-channel FET and a drain in electrical communication with a negative terminal of a differential output, the third n-channel FET having a gate in electrical communication with a negative terminal of the differential input source, a source in electrical communication with the drain of the first n-channel FET and a drain in electrical communication with a positive terminal of the differential output;

a second differential subcircuit comprising

a fourth n-channel FET having a gate in electrical communication with a second bias voltage source, a source in electrical communication with ground and a drain; and

a second differential pair comprised of fifth and sixth n-channel FETs, the fifth n-channel FET having a gate in electrical communication with the positive terminal of the differential input source, a source in electrical communication with the drain of the fourth n-channel FET and a drain in electrical communication with the positive terminal of the differential output, the sixth n-channel FET having a gate in electrical communication with the negative terminal of the differential input source, a source in electrical communication with the drain of the fourth n-channel FET and a drain in electrical communication with the negative terminal of the differential output;

a first load resistor electrically connected between a power supply and the drains of the second and sixth n-channel FETs; and

a second load resistor electrically connected between the power supply and the drains of the third and fifth n-channel FETs,

wherein a differential input signal is connected in-phase to the first and second differential subcircuits such that an output of the first differential subcircuit is subtracted from the output of the second differential subcircuit to substantially reduce nonlinearities.

60. The apparatus of claim 59, wherein predetermined nonlinearities are substantially reduced in the differential output signal by predetermined selection of a gain of the first differential subcircuit, a gain of the second differential subcircuit, a nonlinearity of the first differential subcircuit, and a nonlinearity of the second differential subcircuit.

61. The apparatus of claim 59, wherein the first differential subcircuit defines a gain as G₁ dB, the second differential subcircuit defines a gain as G₂ dB, the first differential subcircuit defines a third order output intercept point as OIP3₁ dBm and the second differential subcircuit defines a third order output intercept point as OIP3₂ dBm, such that the first and second differential subcircuits are provided such that most nearly 2(OIP3₁−

OIP3₂)=3(G₁−

G₂) to substantially reduce third order nonlinear distortion, where G₁ is not equal to G₂.

62. A circuit comprising:

a primary circuit with an input and a first and second output;

a nonlinear device having an input in communication with the first output of the primary circuit and an output; and

a time delay means having an input in communication with the second output of the primary circuit and an output, wherein the time delay through the time delay means substantially equals a time delay through the nonlinear device.

63. The circuit of claim 62, wherein the nonlinear device comprises a first amplifier and the time delay means comprises a second amplifier.

64. The circuit of claim 62, wherein the nonlinear device comprises a first mixer and the time delay means comprises a second mixer.

65. An apparatus for substantially reducing nonlinear distortion, the apparatus comprising:

an input coupling means having an input and first and second outputs, the input coupling means splits an input signal into a first and second in-phase coupled signals;

a first nonlinear device having an input in communication with the first output of the input coupling means and an output;

a second nonlinear device having an input in communication with the second output of the input coupling means and an output; and

a second coupling means having a first input in communication with the output of the first nonlinear device, a second input in communication with the output of the second nonlinear device and an output, wherein the second coupling means 180-degree phase shifts and multiplies by a constant factor, k₂, an output signal of the second nonlinear device and combines such with the output of the first nonlinear device, to generate a final output signal having substantially reduced nonlinear distortion.

66. The apparatus of claim 65, wherein the first nonlinear device further comprises a first amplifier and the second nonlinear device further comprises a second amplifier.

67. The apparatus of claim 65, wherein the first nonlinear device further comprises a first mixer and the second nonlinear device further comprises a second mixer.

68. The apparatus of claim 65, wherein the first nonlinear device further comprises an amplifier and the second nonlinear device further comprises a diode.

69. The apparatus of claim 65, wherein predetermined nonlinearities are substantially reduced in the final output signal by predetermined selection of a gain of the first nonlinear device, a gain of the second nonlinear device, a nonlinearity of the first nonlinear device, a nonlinearity of the second nonlinear device and selection of the first and second coupling means.

70. The apparatus of claim 65, wherein the first nonlinear device defines a gain as G₁ dB, the second nonlinear device defines a gain as G₂ dB, the first nonlinear device defines a third order output intercept point as OIP3₁ dBm and the second nonlinear device defines a third order output intercept point as OIP3₂ dBm, such that K1=10 log₁₀(p₂/p₁), where p₁ is the input signal power level of the first nonlinear device and p₂ is the input signal power level of the second nonlinear device, K2=20 log₁₀(k₂), where k₂ is the multiplicative factor established by the second coupling means, such that the input coupling means, the second coupling means, and the first and second nonlinear devices are provided such that most nearly 2(OIP3₁−

OIP3₂−

K2)=3(G₁−

G₂−

K1−

K2), and where G₁ is not equal G₂+K₁+K2, to substantially reduce third order nonlinear distortion.

71. The apparatus of claim 65, wherein the first nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the first nonlinear device, y₁, in terms of an input signal of the first nonlinear device, x₁, as y₁=a₀+a₁x₁+a₂x₁²+a₃x₁³+a₄x₁⁴ . . . , the second nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the second nonlinear device, y₂, in terms of an input signal of the second nonlinear device, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₄x₂⁴ . . . , where the ratio k₁=x₂/x₁, k₂ is determined by selection of the second coupling means and where nonlinearities of order n are substantially reduced by setting most nearly a_n−

k₂b_nk₁ⁿ=0, and such that a₁−

k₂b₁k does not equal zero.

72. The apparatus of claim 71, wherein signals x₁, x₂, y₁, and y₂ are voltages.

73. The apparatus of claim 71, wherein signals x₁, x₂, y₁, and y₂ are currents.

74. The apparatus of claim 65, further comprising an adaptive control and feedback means having an input in communication with the output of the second coupling means and an output in communication with the first and second coupling means and the first and second nonlinear devices, wherein the adaptive control and feedback means controls the nonlinearity, gain and phase of the first and second coupling means and the first and second nonlinear devices.

75. An apparatus for substantially reducing nonlinear distortion, the apparatus comprising:

a first nonlinear device having an input and an output;

a second nonlinear device having an input and an output, the inputs of the first and second nonlinear devices are in communication with an input signal;

an attenuator having an input in communication with output of the first nonlinear device and an output;

a first subtractor having a first input in communication with the output of the second nonlinear device, a second input in communication with the output of the attenuator and an output;

wherein the first subtractor subtracts an output of the second nonlinear device from an output of the attenuator;

a third nonlinear device having an input in communication with the output of the first nonlinear device and an output;

a fourth nonlinear device having an input in communication with output of the first subtractor and an output; and

a second subtractor having a first input in communication with the output of the third nonlinear device, a second input in communication with the output of the fourth nonlinear device and an output, wherein the second subtractor subtracts the output of the fourth nonlinear device from the output of the third nonlinear device to form a final output signal.

76. The apparatus of claim 75, wherein the first nonlinear device further comprises a first amplifier, the second nonlinear device further comprises a second amplifier, the third nonlinear device further comprises a third amplifier and the fourth nonlinear device further comprises a fourth amplifier.

77. The apparatus of claim 75, wherein the first nonlinear device further comprises a first mixer, the second nonlinear device further comprises a second mixer, the third nonlinear device further comprises a third mixer and the fourth nonlinear device further comprises a fourth mixer.

78. The apparatus of claim 75, wherein the first nonlinear device and the second nonlinear device are substantially equal in time delay and phase, the third and fourth nonlinear devices are substantially equal in time delay and phase, and predetermined order nonlinearities are substantially reduced in the final output signal by predetermined selection of attenuation in the attenuator and predetermined selection of the gain, nonlinearity, and intercept points of the first, second, third and fourth nonlinear device.

79. The apparatus of claim 75, wherein predetermined order nonlinearities are substantially reduced in the final output signal by predetermined selection of the attenuation in the attenuator and predetermined selection of a Taylor series expansion of the first, second, third and fourth nonlinear devices.

80. The apparatus of claim 75, wherein the first nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the first nonlinear device, y₁, in terms of an input signal of the first nonlinear device, x₁, as y₁=a₀+a₁x₁+a₂x₁²+a₃x₁³+a₄x₁⁴ . . . , the second nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the second nonlinear device, y₂ in terms of an input signal of the second nonlinear device, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₄x₂⁴ . . . , the third nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the third nonlinear device, y₃ in terms of an input signal of the third nonlinear device, x₃, as y₃=c₀+c₁x₃+c₂x₃²+c₃x₃³+c₄x₃⁴ . . . , the fourth nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the fourth nonlinear device, y₄ in terms of an input signal of the fourth nonlinear device, x₄, as y₄=d₀+d₁x₄+d₂x₄²+d₃x₄³+d₄x₄⁴ . . . , the ratio, k, is provided such that k equals the ratio of the output signal of the attenuator to the input signal of the attenuator, such that third order nonlinear distortion is substantially reduced by setting most nearly b₁³d₃+b₃d₁+2a₁b₂d₂k−

2b₁b₂d₂−

2a₁a₂d₂k2+3a₁²b₁d₃k²−

3a₁b₁²d₃k−

a₁³d₃k³+2a₁a₂c₂+a₁³c₃+a₃c₁+2a₂b₁d₂k−

a₃d₁k=0, and such that b₁d₁+a₁c₁−

a₁d₁k≠

0.

81. The apparatus of claim 80, wherein signals x₁, x₂, x₃, x₄, y₁, y₂, y₃, and y₄ are voltages.

82. The apparatus of claim 80, wherein signals x₁, x₂, x₃, x₄, y₃, y₂, y₃, and y₄ are currents.

83. The apparatus of claim 75, wherein the first nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the first nonlinear device, y₁, in terms of an input signal of the first nonlinear device, x₁, as y₁=a₀+a₁x₁+a₂x₁²+a³x₁²+a₄x₁⁴ . . . the second nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the second nonlinear device, y₂ in terms of an input signal of the second nonlinear device, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₂⁴ . . . , the third nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the third nonlinear device, y₃ in terms of an input signal of the third nonlinear device, x₃, as y₃=c₀+c₁x₃+c₂x₃²+c₃x³³+c₄x₃⁴ . . . , the fourth nonlinear device is provided such that it has a Taylor series expansion describing the output signal of the fourth nonlinear device, y₄ in terms of an input signal of the fourth nonlinear device, x₄, as y₄=d₀+d₁x₄+d₂x₄²+d₃x₄³+d₄x₄⁴ . . . , the ratio, k, is provided such that k equals the ratio of the output signal of the attenuator to the input signal of the attenuator, where second order nonlinear distortion is substantially reduced by setting most nearly b₂d₁+a₁²c₂−

b₁²d₂+2a₁b₁d₂k+a₂C₁−

a₁²d₂k²−

a₂d₁k=0, and such that b₁d₁+a₁c₁−

a₁d₁k≠

0.

84. The apparatus of claim 83, wherein signals x₁, x₂, x₃, x₄, y₁, y₂, y₃, and y₄ are voltages.

85. The apparatus of claim 83, wherein signals x₁, x₂, x₃, x₄, y₁, y₂, y₃, and y₄ are currents.

86. The apparatus of claim 75, further comprising an adaptive control and feedback means having an input in communication with the output of the second subtractor, and an output in communication with the first, second, third and fourth nonlinear devices and the attenuator, wherein the adaptive control and feedback means controls the nonlinearity, gain and phase of the first, second, third and fourth nonlinear devices and the attenuation of the attenuator.

87. An apparatus for substantially reducing nonlinear distortion, the apparatus comprising:

an input coupling means having an input and first and second outputs that is capable of splitting an input signal into first and second in-phase signals;

a first nonlinear device having an input in communication with the first output of the input coupling means and an output;

a second nonlinear device having an input in communication with the second output of the input coupling means and an output;

an attenuator having an input in communication with output of the first nonlinear device and an output;

a second coupling means having a first input in communication with the output of the second nonlinear device, a second input in communication with the output of the attenuator and an output;

the second coupling means combines a 180 degree phase shifted and attenuated output of the second nonlinear device with an output of the attenuator;

a third nonlinear device having an input in communication with output of the first nonlinear device and an output;

a fourth nonlinear device having an input in communication with the output of the second coupling means and an output; and

a third coupling means having a first input in communication with the output of the third nonlinear device, a second input in communication with the output of the fourth nonlinear device and an output, wherein the third coupling means combines a 180 degree phase shifted and attenuated output of the fourth nonlinear device with the output of the third nonlinear device to form a final output signal.

88. The apparatus of claim 87, wherein the first nonlinear device further comprises a first amplifier, the second nonlinear device further comprises a second amplifier, the third nonlinear device further comprises a third amplifier and the fourth nonlinear device further comprises a fourth amplifier.

89. The apparatus of claim 87, wherein the first nonlinear device further comprises a first mixer, the second nonlinear device further comprises a second mixer, the third nonlinear device further comprises a third mixer and the fourth nonlinear device further comprises a fourth mixer.

90. The apparatus of claim 87, wherein predetermined order nonlinearities are substantially reduced in the final output signal by predetermined selection of the attenuation in the attenuator, coupling coefficients of the first, second, and third couplers, and Taylor series expansion of the first, second, third and fourth nonlinear devices.

91. The apparatus of claim 87, further comprising an adaptive control and feedback means having an input in communication with the output of the third coupling means, and an output in communication with the first, second and third coupling means, the first, second, third and fourth nonlinear devices and the attenuator wherein the adaptive control and feedback means controls the nonlinearity, gain and phase of the first, second and third coupling means, the first, second, third and fourth nonlinear devices and the attenuation of the attenuator.

92. A method substantially reducing nonlinear distortion, in accordance with an embodiment of the present invention comprising the steps of:

transmitting an input signal to an input coupling means that splits the input signal into first and second in-phase coupled signals;

transmitting the first coupled signal to a first nonlinear device, having a Taylor series expansion describing a first nonlinear device output signal, y₁, in terms of a first nonlinear device input signal x₁, as y₁=a₀+a₁x₁+a₂x₁+a₃x₁³+a₄x₁⁴ . . . ;

transmitting the second coupled signal to a second nonlinear device, having a Taylor series expansion describing a second nonlinear device output signal, y₂ in terms of a second nonlinear device input signal, x₂, as y₂=b₀+b₁x₂+b₂x₂²+b₃x₂³+b₄x²⁴ . . . , and with substantially equal time delay and phase in the first and second nonlinear devices;

transmitting the first nonlinear device output signal to an attenuator such that an attenuator output signal is, k, times an attenuator input signal;

subtracting the second nonlinear device output signal from the attenuator output signal to form a difference signal;

transmitting the first nonlinear device output to a third nonlinear device, with Taylor series expansion describing a third nonlinear device output y₃, in terms of a third nonlinear device input signal x₃, as y₃=c₀+c₁x₃+c₂x₃²+c₃x₃³+c₄x₃⁴ . . . ;

transmitting the difference signal to a fourth nonlinear device, with Taylor series expansion describing a fourth nonlinear device output signal, y₄, in terms of a fourth nonlinear device input signal, x₄, as y₄=d₀+d₁x₄+d₂x₄²+d₃x₄³+d₄x₄⁴ . . . , and with substantially equal time delay and phase in the third and fourth nonlinear devices; and

subtracting the fourth nonlinear device output signal from the third nonlinear device output signal to form a final output signal.

93. The method of claim 92, wherein the relationship between the attenuator, first, second, third, and fourth nonlinear devices being defined such that third order nonlinear distortion is substantially reduced by setting most nearly b₁³d₃+b₃d₁+2a₁b₂d₂k−

2b₁b₂d₂−

2a₁a₂d₂k²+3a₁²b₁d₃k²−

3a₁b₁²d₃k−

a₁³d₃k³+2a₁a₂c₂+a₁³c₃+a₃c₁+2a₂b₁d₂k−

a₃d₁k=0, and such that b₁d₁+a₁c₁−

a₁d₁k≠

0.

94. The method of claim 92, wherein second order nonlinear distortion is substantially reduced by setting most nearly b₂d₁+a₁²c₂−

b₁²d₂+2a₁b₁d₂k+a₂c₁−

a₁²d₂k²−

a₂d₁k=0, and such that b₁d₁+a₁c₁−

a₁d₁k≠

0 so that the desired linear output is not canceled.

95. The method of claim 92, wherein the first nonlinear device further comprises a first amplifier, the second nonlinear device further comprises a second amplifier, the third nonlinear device further comprises a third amplifier and the fourth nonlinear device further comprises a fourth amplifier.

96. The method of claim 92, wherein the first nonlinear device further comprises a first mixer, the second nonlinear device further comprises a second mixer, the third nonlinear device further comprises a third mixer and the fourth nonlinear device further comprises a fourth mixer.

97. The method of claim 92, wherein predetermined order nonlinearities are substantially reduced in the final output signal by predetermined selection of the attenuation in the attenuator, coupling coefficients of the first, second, and third couplers, and Taylor series expansion of the first, second, third and fourth nonlinear devices.

98. The method of claim 92, further comprising the step of adjusting, adaptively the gain, phase and nonlinearity of the first, second, third and fourth nonlinear devices and adjusting, adaptively, the attenuation of the attenuator based on feedback from the final output signal.