Methodology for design of oscillator delay stage and corresponding applications

• US 7,039,885 B1
• Filed: 01/21/2003
• Issued: 05/02/2006
• Est. Priority Date: 01/21/2003
• Status: Expired due to Term

• Current Assignee: Synopsys Incorporated
• Original Assignee: Barcelona Design, Inc.
• Inventors: Mohan, Sunderarajan S.
• Primary Examiner(s): Siek, Vuthe
• Assistant Examiner(s): Kik, Phallaka
• Application Number:
  US10/348,723
• Time in Patent Office: 1,197 Days
• Field of Search: 716/4, 716/2, 703/16, 331/1.R, 331/52, 331/57, 331/107.R, 327/182, 327/191, 327/548
• US Class Current: 716/102
• CPC Class Codes: G06F 30/30 Circuit design
• CPC Class Codes: H03K 3/0322 with differential cells
• CPC Class Codes: H03K 5/133 using a chain of active delay devices
• CPC Class Codes: H03L 7/0995 the oscillator comprising a ring oscillator

Abstract

Methods are described that involve characterizing an oscillator'"'"'s jitter or phase noise over a plurality of the oscillator'"'"'s effective number of delay stages. The oscillator comprises a series of delay stages. Each one of the effective number of delay stages, if selected for the oscillator, describes a respective permissible range of inverter drive strengths that may be used within each delay stage of the oscillator to achieve a respective jitter or phase noise characteristic.

Claims

1. A method, comprising:

A) defining characteristics of an oscillator, said oscillator comprising a series of delay stages, each of said delay stages comprising;

a) at least one differential input;

b) a pair of single ended inverters for each differential input, each pair of single ended inverters further comprising, for their corresponding differential input;

i) a first single ended inverter whose input is coupled to a +input of said corresponding differential input;

ii) a second single ended inverter whose input is coupled to a −

input of said corresponding differential input; and

,

c) a differential output, said differential input further comprising;

i) a +output that is coupled to a respective each said second single ended inverter output;

ii) a −

output that is coupled to a respective each output of said first single ended inverter,

where said characteristics allow a permissible range of drive strengths for each a respective output of said inverters; and

,

B) defining said drive strengths as scaled versions of one another.

2. The method of claim 1 wherein said characteristics further comprise a number N of said delay stages within said oscillator.

3. The method of claim 1 wherein said characteristics further comprise a particular semiconductor manufacturing process that said oscillator is to be manufactured with.

4. The method of claim 1 wherein said characteristics further comprise a nominal output signal frequency of oscillation.

5. The method of claim 1 wherein said characteristics further comprises said oscillator'"'"'s external capacitance.

6. The method of claim 1 wherein said characteristics further comprises jitter and power consumption.

7. The method of claim 6 further comprising presenting a designer with a graphical depiction of a tradeoff between jitter and power consumption.

8. The method of claim 7 wherein said tradeoff is presented as a function of an effective number of delay stages (Neff) within said oscillator.

9. The method of claim 8 further comprising selecting a Neff value so as to define jitter and power consumption characteristics for said oscillator.

10. The method of claim 1 wherein said characteristics further comprises phase noise and power consumption.

11. The method of claim 10 further comprising presenting a designer with a graphical depiction of a tradeoff between phase noise and power consumption.

12. The method of claim 11 wherein said tradeoff is presented as a function of an effective number of delay stages (Neff) within said oscillator.

13. The method of claim 12 further comprising selecting a particular Neff value so as to define phase noise and power consumption characteristics for said oscillator.

14. The method of claim 1 wherein said defining said drive strengths as scaled versions of one another further comprises:

a) articulating permissible combinations of inverter drive strengths as scaled versions of one another; and

,

b) selecting a specific combination from said permissible combinations.

15. The method of claim 14 wherein said inverter drive strengths are articulated as scaled versions of one another according to:

$\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i=1$

where;

a) for i=0;

k_i is the drive strength of each inverter of another pair of single ended inverters between said +output and said −

output, a first inverter of said another pair of single ended inverters having an input coupled to said +output and an output coupled to said −

output, a second inverter of said another pair of single ended inverters having an input coupled to said −

output and an output coupled to said +output;

b) for integers i from 1 to M where M is a number of differential inputs of said at least one differential input;

k_i is the drive strength of each inverter of said pair of inverters coupled to i^th differential input of said at least one differential input; and

c) for integers i from M+1 to N−

1 where N is a number of delay stages within said series of delay stages (if any such integers exist);

k_i=0.

16. The method of claim 14 wherein said permissible combinations are articulated as a function of an effective number of delay stages (Neff).

17. The method of claim 16 wherein said permissible combinations are articulated as a function of Neff according to:

$\frac{1}{N_{\mathrm{eff}}}=\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}$

where;

a) for i=0;

k_i is the drive strength of each inverter of another pair of single ended inverters between said +output and said −

output, a first inverter of said another pair of single ended inverters having an input coupled to said +output and an output coupled to said −

output, a second inverter of said another pair of single ended inverters having an input coupled to said −

output and an output coupled to said +output;

b) for integers i=1 to M where M is a number of differential inputs of said at least one differential input;

k_i is the drive strength of each inverter of said pair of inverters coupled to i^th differential input of said at least one differential input; and

,

c) for integers i=M+1 to N−

1 where N is a number of delay stages within said series;

k_i=0.

18. The method of claim 16 wherein said permissible combinations are articulated as a function of Neff according to:

$\frac{1}{N_{\mathrm{eff}}}=\left(\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}\right)<br><br>\left\{1+\frac{C_{N_{\mathrm{eff}}}}{e}\left[\frac{\tan <br><br>\left(\mathrm{\pi <br><br>}<br><br>\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}\right)}{\mathrm{\pi <br><br>}}-\left(\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}\right)\right]\right\}$

wherein N is a number of delay stages, i is integer value, Ki is a drive strength of each inverter, C_Neff is a manufacturing related constant and e is a constant.

19. The method of claim 14 wherein said selecting a specific combination from said permissible combinations further comprises selecting a combination that results in said oscillator having a lower minimum differential mode gain needed for differential mode oscillation than minimum common mode gain needed for common mode oscillation.

20. The method of claim 19 wherein said minimum common mode gain needed for common mode oscillation is infinite.

21. A method, comprising:

characterizing an oscillator'"'"'s jitter over a plurality of said oscillator'"'"'s effective number of delay stages, said oscillator comprising a series of delay stages, each one of said effective number of delay stages, when selected for said oscillator, to describe a respective permissible range of inverter drive strengths that may be usable within each delay stage of said oscillator to achieve a respective jitter characteristic.

22. The method of claim 21 further comprising choosing an actual number of delay stages N within said series prior to said characterizing.

23. The method of claim 21 further comprising choosing a semiconductor manufacturing process that said oscillator is to be manufactured with prior to said characterizing.

24. The method of claim 21 further comprising choosing a nominal output signal frequency of oscillation for said oscillator prior to said characterizing.

25. The method of claim 21 further comprising choosing said oscillator'"'"'s external capacitance prior to said characterizing.

26. The method of claim 21 further comprising choosing prior to said characterizing:

a) said oscillator'"'"'s actual number of stages N;

b) a manufacturing process said oscillator is to be manufactured with;

c) a nominal output signal frequency of oscillation for said oscillator, and,

d) said oscillator'"'"'s external capacitance.

27. The method of claim 21 further comprising characterizing said oscillator'"'"'s power consumption as a function of said effective number of delay stages to demonstrate a tradeoff between power consumption and said jitter.

28. The method of claim 21 further comprising selecting a particular effective number of delay stages to define a particular permissible range of inverter drive strengths and to define a particular jitter characteristic.

29. The method of claim 28 further comprising articulating said inverter drive strengths as scaled versions of one another to further refine said particular permissible range of inverter drive strengths.

30. The method of claim 29 further comprising analyzing a common mode gain and differential mode gain for various implementations of said oscillator, each implementation having a different combination of inverter drive strengths.

31. The method of claim 30 further comprising selecting a specific one of said combinations of inverter drive strengths to select a specific one of said oscillator implementations.

32. The method of claim 31 wherein said selecting a specific one of said combinations further comprises selecting a combination that results in said oscillator having a lower minimum differential mode gain needed for differential mode oscillation than minimum common mode gain needed for common mode oscillation.

33. The method of claim 32 wherein said minimum common mode gain needed for common mode oscillation is infinite.

34. The method of claim 21 wherein each of said delay stages within said series further comprises:

a) at least one differential input;

b) a pair of single ended inverters for each differential input, each pair of single ended inverters further comprising, for their corresponding differential input;

i) a first single ended inverter whose input is coupled to a +input of said corresponding differential input;

ii) a second single ended inverter whose input is coupled to a −

input of said corresponding differential input; and

,

c) a differential output, said differential input further comprising;

i) a +output that is coupled to a respective each output of said second single ended inverter;

ii) a −

output that is coupled to a respective each output of said first single ended inverter.

35. The method of claim 34 further comprising choosing an actual number of delay stages N within said series prior to said characterizing.

36. The method of claim 34 further comprising choosing a semiconductor manufacturing process that said oscillator is to be manufactured with prior to said characterizing.

37. The method of claim 34 further comprising choosing a nominal output signal frequency of oscillation for said oscillator prior to said characterizing.

38. The method of claim 34 further comprising choosing said oscillator'"'"'s external capacitance prior to said characterizing.

39. The method of claim 34 further comprising choosing prior to said characterizing:

a) said oscillator'"'"'s actual number of stages N;

b) a manufacturing process said oscillator is to be manufactured with;

c) a nominal output signal frequency of oscillation for said oscillator; and

,

d) said oscillator'"'"'s external capacitance.

40. The method of claim 34 further comprising characterizing said oscillator'"'"'s power consumption as a function of said effective number of delay stages to demonstrate a tradeoff between power consumption and said jitter.

41. The method of claim 34 further comprising selecting a particular effective number of delay stages to define a particular permissible range of inverter drive strengths and to define a particular jitter characteristic.

42. The method of claim 41 further comprising articulating said inverter drive strengths as scaled versions of one another to further refine said particular permissible range of inverter drive strengths.

43. The method of claim 42 wherein said inverter drive strengths are articulated as scaled versions of one another according to:

$\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i=1$

where;

a) for i=0;

k_i is the drive strength of each inverter of another pair of single ended inverters between said +output and said −

output, a first inverter of said another pair of single ended inverters having an input coupled to said +output and an output coupled to said −

output, a second inverter of said another pair of single ended inverters having an input coupled to said −

output and an output coupled to said +output;

b) for integers i from 1 to M where M is a number of differential inputs of said at least one differential input;

k_i is the drive strength of each inverter of said pair of inverters coupled to i^th differential input of said at least one differential input; and

c) for integers i from M+1 to N−

1 where N is the number of delay stages within said series of delay stages (if any such integers exist);

k_i=0.

44. The method of claim 43 wherein said selected particular effective number of delay stages said defines said particular permissible range of inverter drive strengths according to:

$\frac{1}{N_{\mathrm{eff}}}=\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}$

where;

a) for i=0;

k_i is the drive strength of each inverter of another pair of single ended inverters between said +output and said −

output, a first inverter of said another pair of single ended inverters having an input coupled to said +output and an output coupled to said −

output, a second inverter of said another pair of single ended inverters having an input coupled to said −

output and an output coupled to said +output;

b) for integers i=1 to M where M is the number of differential inputs of said at least one differential input;

k_i is the drive strength of each inverter of said pair of inverters coupled to the i^th differential input of said at least one differential input; and

,

c) for integers i=M+1 to N−

1 where N is the number of delay stages within said series;

k_i=0.

45. The method of claim 43 wherein said selected particular effective number of delay stages said defines said particular permissible range of inverter drive strengths according to:

$\frac{1}{N_{\mathrm{eff}}}=\left(\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}\right)<br><br>\left\{1+\frac{C_{N_{\mathrm{eff}}}}{e}\left[\frac{\tan <br><br>\left(\mathrm{\pi <br><br>}<br><br>\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}\right)}{\mathrm{\pi <br><br>}}-\left(\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}\right)\right]\right\}$

wherein C_Neff is a manufacturing related constant and e is a constant.

46. The method of claim 42 wherein said range further comprises selecting a combination that results in said oscillator having a lower minimum differential mode gain needed for differential mode oscillation than minimum common mode gain needed for common mode oscillation.

47. The method of claim 46 wherein said minimum common mode gain needed for common mode oscillation is infinite.

48. A method, comprising:

characterizing an oscillator'"'"'s phase noise over a plurality of said oscillator'"'"'s effective number of delay stages, said oscillator comprising a series of delay stages, each one of said effective number of delay stages, when selected for said oscillator, to describe a respective permissible range of inverter drive strengths that are useable within each delay stage of said oscillator to achieve a respective phase noise characteristic.

49. The method of claim 48 further comprising choosing an actual number of delay stages N within said series prior to said characterizing.

50. The method of claim 48 further comprising choosing a semiconductor manufacturing process that said oscillator is to be manufactured with prior to said characterizing.

51. The method of claim 48 further comprising choosing a nominal output signal frequency of oscillation for said oscillator prior to said characterizing.

52. The method of claim 48 further comprising choosing said oscillator'"'"'s external capacitance prior to said characterizing.

53. The method of claim 48 further comprising choosing prior to said characterizing:

a) said oscillator'"'"'s actual number of stages N;

b) a manufacturing process said oscillator is to be manufactured with;

c) a nominal output signal frequency of oscillation for said oscillator; and

,

d) said oscillator'"'"'s external capacitance.

54. The method of claim 48 further comprising characterizing said oscillator'"'"'s power consumption as a function of said effective number of delay stages to demonstrate a tradeoff between power consumption and said phase noise.

55. The method of claim 48 further comprising selecting a particular effective number of delay stages to define a particular permissible range of inverter drive strengths and to define a particular phase noise characteristic.

56. The method of claim 55 further comprising articulating said inverter drive strengths as scaled versions of one another to further refine said particular permissible range of inverter drive strengths.

57. The method of claim 56 further comprising analyzing a common mode gain and differential mode gain for various implementations of said oscillator, each implementation having a different combination of inverter drive strengths.

58. The method of claim 57 further comprising selecting a specific one of said combinations of inverter drive strengths to select a specific one of said oscillator implementations.

59. The method of claim 58 wherein said selecting a specific one of said combinations further comprises selecting a combination that results in said oscillator having a lower minimum differential mode gain needed for differential mode oscillation than minimum common mode gain needed for common mode oscillation.

60. The method of claim 59 wherein said minimum common mode gain needed for common mode oscillation is infinite.

61. The method of claim 48 wherein each of said delay stages within said series further comprises:

a) at least one differential input;

b) a pair of single ended inverters for each differential input, each pair of single ended inverters further comprising, for their corresponding differential input;

i) a first single ended inverter whose input is coupled to a +input of said corresponding differential input;

ii) a second single ended inverter whose input is coupled to a −

input of said corresponding differential input; and

,

c) a differential output, said differential input further comprising;

i) a +output that is coupled to each said second single ended inverter output;

ii) a −

output that is coupled to each said first single ended inverter output.

62. The method of claim 61 further comprising choosing an actual number of delay stages N within said series prior to said characterizing.

63. The method of claim 61 further comprising choosing a semiconductor manufacturing process that said oscillator is to be manufactured with prior to said characterizing.

64. The method of claim 61 further comprising choosing a nominal output signal frequency of oscillation for said oscillator prior to said characterizing.

65. The method of claim 61 further comprising choosing said oscillator'"'"'s external capacitance prior to said characterizing.

66. The method of claim 61 further comprising choosing prior to said characterizing:

a) said oscillator'"'"'s actual number of stages N;

b) a manufacturing process said oscillator is to be manufactured with;

c) a nominal output signal frequency of oscillation for said oscillator; and

,

d) said oscillator'"'"'s external capacitance.

67. The method of claim 61 further comprising characterizing said oscillator'"'"'s power consumption as a function of said effective number of delay stages to demonstrate a tradeoff between power consumption and said phase noise.

68. The method of claim 61 further comprising selecting a particular effective number of delay stages to define a particular permissible range of inverter drive strengths and to define a particular phase noise characteristic.

69. The method of claim 68 further comprising articulating said inverter drive strengths as scaled versions of one another to further refine said particular permissible range of inverter drive strengths.

70. The method of claim 69 wherein said inverter drive strengths are articulated as scaled versions of one another according to:

$\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i=1$

where;

a) for i=0;

k_i is the drive strength of each inverter of another pair of single ended inverters between said +output and said −

output, a first inverter of said another pair of single ended inverters having an input coupled to said +output and an output coupled to said −

output, a second inverter of said another pair of single ended inverters having an input coupled to said −

output and an output coupled to said +output;

b) for integers i from 1 to M where M is a number of differential inputs of said at least one differential input;

k_i is the drive strength of each inverter of said pair of inverters coupled to i^th differential input of said at least one differential input; and

c) for integers i from M+1 to N−

1 where N is the number of delay stages within said series of delay stages (if any such integers exist);

k_i=0.

71. The method of claim 70 wherein said selected particular effective number of delay stages defines said particular permissible range of inverter drive strengths according to:

$\frac{1}{N_{\mathrm{eff}}}=\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}$

where;

a)for i=0;

k_i is the drive strength of each inverter of another pair of single ended inverters between said +output and said −

output, a first inverter of said another pair of single ended inverters having an input coupled to said +output and an output coupled to said −

output, a second inverter of said another pair of single ended inverters having an input coupled to said −

output and an output coupled to said +output;

b) for integers i=1 to M where M is the number of differential inputs of said at least one differential input;

k_i is the drive strength of each inverter of said pair of inverters coupled to the i^th differential input of said at least one differential input; and

,

c) for integers i=M+1 to N−

1 where N is the number of delay stages within said series;

k_i=0.

72. The method of claim 70 wherein said selected particular effective number of delay stages said defines said particular permissible range of inverter drive strengths according to:

$\frac{1}{N_{\mathrm{eff}}}=\left(\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}\right)<br><br>\left\{1+\frac{C_{N_{\mathrm{eff}}}}{e}\left[\frac{\tan <br><br>\left(\mathrm{\pi <br><br>}<br><br>\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}\right)}{\mathrm{\pi <br><br>}}-\left(\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}\right)\right]\right\}$

wherein C_Neff is a manufacturing related constant and e is a constant.

73. The method of claim 69 wherein said range further comprises selecting a combination that results in said oscillator having a lower minimum differential mode gain needed for differential mode oscillation than minimum common mode gain needed for common mode oscillation.

74. The method of claim 73 wherein said minimum common mode gain needed for common mode oscillation is infinite.

75. A machine readable medium having stored thereon a sequence of instructions which when executed by a computing system cause said computing system to perform a method, said method comprising:

A) defining characteristics of an oscillator, said oscillator comprising a series of delay stages, each of said delay stages comprising;

a) at least one differential input;

b) a pair of single ended inverters for each differential input, each pair of single ended inverters further comprising, for their corresponding differential input;

i) a first single ended inverter whose input is coupled to a +input of said corresponding differential input;

ii) a second single ended inverter whose input is coupled to a −

input of said corresponding differential input; and

,

c) a differential output, said differential input further comprising;

i) a +output that is coupled to a respective output of each said second single ended inverter;

ii) a −

output that is coupled to a respective output of each output of said first single ended inverter,

where said characteristics allow a permissible range of drive strengths for each of said inverters; and

,

B) defining said drive strengths as scaled versions of one another.

76. The machine readable medium of claim 75 wherein said characteristics further comprise a number N of said delay stages within said oscillator.

77. The machine readable medium of claim 75 wherein said characteristics further comprise a particular semiconductor manufacturing process that said oscillator is to be manufactured with.

78. The machine readable medium of claim 75 wherein said characteristics further comprise a nominal output signal frequency of oscillation.

79. The machine readable medium of claim 75 wherein said characteristics further comprises said oscillator'"'"'s external capacitance.

80. The machine readable medium of claim 75 wherein said characteristics further comprises jitter and power consumption.

81. The machine readable medium of claim 80 wherein said method further comprises presenting a designer with a graphical depiction of a tradeoff between jitter and power consumption.

82. The machine readable medium of claim 81 wherein said tradeoff is presented as a function of an effective number of delay stages (Neff) within said inverter.

83. The machine readable medium of claim 82, wherein said method further comprises selecting a Neff value so as to define jitter and power consumption characteristics for said oscillator.

84. The machine readable medium of claim 75 wherein said characteristics further comprise phase noise and power consumption.

85. The machine readable medium of claim 84, wherein said method further comprises presenting a designer with a graphical depiction of a tradeoff between phase noise and power consumption.

86. The machine readable medium of claim 85 wherein said tradeoff is presented as a function of an effective number of delay stages (Neff) within said inverter.

87. The machine readable medium of claim 86, wherein said method further comprises selecting a particular Neff value so as to define phase noise and power consumption characteristics for said oscillator.

88. The machine readable medium of claim 75 wherein said defining said drive strengths as scaled versions of one another further comprises:

a) articulating permissible combinations of inverter drive strengths as scaled versions of one another; and

,

b) selecting a specific combination from said permissible combinations.

89. The machine readable medium of claim 88 wherein said inverter drive strengths are articulated as scaled versions of one another according to:

$\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i=1$

where;

a) for i=0;

k_i is the drive strength of each inverter of another pair of single ended inverters between said +output and said −

output, a first inverter of said another pair of single ended inverters having an input coupled to said +output and an output coupled to said −

output, a second inverter of said another pair of single ended inverters having an input coupled to said −

output and an output coupled to said +output;

b) for integers i from 1 to M where M is a number of differential inputs of said at least one differential input;

k_i is the drive strength of each inverter of said pair of inverters coupled to i^th differential input of said at least one differential input; and

c) for integers i from M+1 to N−

1 where N is the number of delay stages within said series of delay stages (if any such integers exist);

k_i=0.

90. The machine readable medium of claim 88 wherein said permissible combinations are articulated as a function of an effective number of delay stages (Neff).

91. The machine readable medium of claim 90 wherein said permissible combinations are articulated as a function of Neff according to:

$\frac{1}{N_{\mathrm{eff}}}=\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>\text{\hspace{1em}<br><br>}<br><br>k_i<br><br>\frac{i}{N}$

where;

a) for i=0;

k_i is the drive strength of each inverter of another pair of single ended inverters between said +output and said −

output, a first inverter of said another pair of single ended inverters having an input coupled to said +output and an output coupled to said −

output, a second inverter of said another pair of single ended inverters having an input coupled to said −

output and an output coupled to said +output;

b) for integers i=1 to M where M is a number of differential inputs of said at least one differential input;

k_i is the drive strength of each inverter of said pair of inverters coupled to i^th differential input of said at least one differential input; and

,

c) for integers i=M+1 to N−

1 where N is the number of delay stages within said series,

k_i=0.

92. The machine readable medium of claim 90 wherein said permissible combinations are articulated as a function of Neff according to:

$\frac{1}{N_{\mathrm{eff}}}=\left(\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>k_i<br><br>\frac{i}{N}\right)<br><br>\left\{1+\frac{c_{N_{\mathrm{eff}}}}{e}\left[\frac{\tan <br><br>\left(\mathrm{\pi <br><br>}<br><br>\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>k_i<br><br>\frac{i}{N}\right)}{\mathrm{\pi <br><br>}}-\left(\underset{i=0}{\overset{i=\left(N-1\right)}{\sum <br><br>}}<br><br>k_i<br><br>\frac{i}{N}\right)\right]\right\}$

wherein N is a number of delay stages, i is integer value, Ki is a drive strength of each inverter, C_Neff is a manufacturing related constant and e is a constant.

93. The machine readable medium of claim 88 wherein said selecting a specific combination from said permissible combinations further comprises selecting a combination that results in said oscillator having a lower minimum differential mode gain needed for differential mode oscillation than minimum common mode gain needed for common mode oscillation.

94. The method of claim 93 wherein said minimum common mode gain needed for common mode oscillation is infinite.