Method and apparatus for an improved nonlinear oscillator

• US 6,822,522 B1
• Filed: 05/23/2003
• Issued: 11/23/2004
• Est. Priority Date: 05/23/2003
• Status: Active Grant

• Current Assignee: The Government Of The United States As Represented By The Secretary Of The Navy, the united states of america as represented by the secretary of the navy
• Original Assignee: the united states of america as represented by the secretary of the navy
• Inventors: Neff, Joseph D., Hasler, Paul, Brown, Edgar A., DeWeerth, Steve P., Meadows, Brian Keith
• Primary Examiner(s): Pascal, Robert
• Assistant Examiner(s): Chang, Joseph
• Application Number:
  US10/446,286
• Time in Patent Office: 550 Days
• Field of Search: 331/135, 330/69, 330/85, 330/253, 330/257, 330/295
• US Class Current: 331/135
• CPC Class Codes: H03B 5/24 active element in amplifier being semiconductor device H03B5/26 takes precedence

Abstract

A nonlinear oscillator method and apparatus. According to one embodiment, a nonlinear oscillator is closed. The nonlinear oscillator includes a first linear amplifier, a second linear amplifier and nonlinear amplifier having a substantially similar design that includes an adjustable linear transconductance region width. The input/output characteristics of the nonlinear oscillator can be represented by van der Pol equations. In another embodiment, a method for providing nonlinear oscillations is disclosed.

Claims

1. A nonlinear oscillator comprising:

a) a first linear amplifier, capable of receiving an input voltage (V_in) and outputting a first output current (I₁);

b) a second linear amplifier, operatively coupled to said first linear amplifier, wherein said second linear amplifier is capable of receiving said first output current and outputting a second output current (I₂); and

c) a nonlinear amplifier, operatively coupled to said first linear amplifier and said second linear amplifier, wherein said nonlinear amplifier is capable of receiving said second output current and outputting a third output current (I₃);

wherein said nonlinear oscillator outputs a first oscillator voltage (V₁) and a second oscillator voltage (V₂), and wherein said first linear amplifier, said second linear amplifier and said nonlinear amplifier have a substantially similar design that includes an adjustable linear transconductance region width, and wherein input/output characteristics of said nonlinear oscillator maintain the following relationship;

{umlaut over (x)}=2μ

(1−

η

x²){dot over (x)}−

ω

²x.

2. The nonlinear oscillator of claim 1, wherein said adjustable linear transconductance region of said nonlinear amplifier is adjusted to provide nonlinear properties.

3. The nonlinear oscillator of claim 1, wherein said adjustable linear transconductance region of said first linear amplifier and said second linear amplifier is adjusted to provide linear properties.

4. The nonlinear oscillator of claim 1, wherein said first linear amplifier, said second linear amplifier and said nonlinear amplifier have an identical design.

5. The nonlinear oscillator of claim 1, further comprising:

i) a first capacitive element, operatively coupled to an output of said first linear amplifier, an input of said second linear amplifier, an input of said first linear amplifier, an input of said nonlinear amplifier and an output of said nonlinear amplifier; and

ii) a second capacitive element, operatively coupled to an output of said second linear amplifier, an input of said second linear amplifier and an input of said nonlinear amplifier.

6. The nonlinear oscillator of claim 1, further comprising:

i) a first capacitor having a first terminal operatively coupled to said first linear amplifier, said second linear amplifier and said nonlinear amplifier and a second terminal operatively coupled to ground; and

ii) a second capacitor having a first terminal operatively coupled to said second linear amplifier and said nonlinear amplifier and a second terminal operatively coupled to ground.

7. The nonlinear oscillator of claim 1, wherein an output of said first linear amplifier is operatively coupled to an input of said first linear amplifier, an input of said second linear amplifier, an input of said nonlinear amplifier and an output of said nonlinear amplifier, and wherein an output of said second linear amplifier is operatively coupled to an input of said second linear amplifier and an input of said nonlinear amplifier, and wherein an output of said nonlinear amplifier is operatively coupled to an input of said nonlinear amplifier, an input of said first linear amplifier and an input of said second linear amplifier.

8. The nonlinear oscillator of claim 1, wherein said substantially similar design comprises:

i) an above-threshold differential pair, capable of outputting a current;

ii) a diode pair, operatively coupled to the below-threshold differential pair; and

iii) a below-threshold differential pair, operatively coupled to said below-threshold differential pair and said diode pair;

wherein said current is renormalized by said below-threshold differential pair and said diode pair.

9. A nonlinear oscillator comprising:

a) a first linear amplifier, capable of receiving an input voltage (V_in) and outputting a first output current (I₁), wherein a first input of said first linear amplifier is operatively coupled to an input node, and wherein an output of said first linear amplifier is operatively coupled to a second input of said first linear amplifier;

b) a second linear amplifier, capable of receiving said first output current and outputting a second output current (I₂), wherein a first input of said second linear amplifier is operatively coupled to said output of said first linear amplifier, and wherein an output of said second linear amplifier is operatively coupled to a second input of said second linear amplifier; and

c) a nonlinear amplifier, capable of receiving said second output current and outputting a third output current (I₃), wherein a first input of said nonlinear amplifier is operatively coupled to said second input of said second linear amplifier and said output of said second linear amplifier, and wherein an output of said nonlinear amplifier is operatively coupled to a second input of said nonlinear amplifier, said first input of said second linear amplifier, said output of said first linear amplifier, said second input of said first linear amplifier and an output node;

wherein said nonlinear oscillator outputs a first oscillator voltage (V₁) and a second oscillator voltage (V₂), and wherein said first linear amplifier, said second linear amplifier and said nonlinear amplifier have a substantially similar design that includes an adjustable linear transconductance region width, and wherein input/output characteristics of said nonlinear oscillator maintain the following relationship;

{umlaut over (x)}=2μ

(1−

η

x²){dot over (x)}−

ω

²x.

10. The nonlinear oscillator of claim 9, wherein said adjustable linear transconductance region of said nonlinear amplifier is adjusted to provide nonlinear properties.

11. The nonlinear oscillator of claim 9, wherein said first linear amplifier, said second linear amplifier and said nonlinear amplifier have an identical design.

12. The nonlinear oscillator of claim 9, further comprising:

i) a first capacitive element, operatively coupled to said output of said first linear amplifier, said first input of said second linear amplifier, said second input of said first linear amplifier, said second input of said nonlinear amplifier and said output of said nonlinear amplifier; and

ii) a second capacitive element, operatively coupled to said output of said second linear amplifier, said first input of said nonlinear amplifier and said second input of said second linear amplifier.

13. The nonlinear oscillator of claim 9, further comprising:

i) a first capacitor having a first terminal operatively coupled to said first linear amplifier, said second linear amplifier and said nonlinear amplifier and a second terminal operatively coupled to ground; and

ii) a second capacitor having a first terminal operatively coupled to said second linear amplifier and said nonlinear amplifier and a second terminal operatively coupled to ground.

14. A method for providing nonlinear oscillations in a nonlinear oscillator, the method comprising the steps of:

a) receiving an input voltage (V_in) and a first oscillator voltage (V₁) in a first linear amplifier;

b) converting a first difference voltage to a first linearly proportional current (I₁) via said first linear amplifier,

c) charging a first capacitor via output currents from said first linear amplifier and a nonlinear amplifier;

d) receiving a second oscillator voltage (V₂) and said first oscillator voltage in a second linear amplifier;

e) converting a second difference voltage to a second linearly proportional current (I₂) via said second linear amplifier;

f) charging a second capacitor via said second linearly proportional current;

g) receiving said second oscillator voltage and said first oscillator voltage in said nonlinear amplifier;

h) converting a third difference voltage to a nonlinearly proportional current (I₃) via said nonlinear amplifier;

i) returning to STEP (a);

wherein said first linear amplifier, said second linear amplifier and said nonlinear amplifier have a substantially similar design that includes an adjustable linear transconductance region width, and wherein input/output characteristics of said nonlinear oscillator maintain the following relationship;

{umlaut over (x)}=2μ

(1−

η

x²){dot over (x)}−

ω

²x.

15. The method of claim 14, wherein said STEP (c) comprises the following sub-steps:

i) charging a first capacitor via output currents from said first linear amplifier and a nonlinear amplifier;

ii) outputting said first oscillator voltage.

16. The method of claim 14, wherein said STEP (f) comprises the following sub-steps:

i) charging a second capacitor via said second linearly proportional current;

ii) outputting said second oscillator voltage.

17. The method of claim 14, wherein said method is capable of adjusting a set of parameters comprising linearity, amplitude and frequency to provide desired circuit behavior.

18. The method of claim 17, wherein said method adjusts one of said set of parameters to provide desired circuit behavior.

19. The method of claim 17, wherein said method adjusts at least two of said set of parameters to provide desired circuit behavior.

20. The method of claim 17, wherein said method maintains the relationship 0<

μ

<

1 to operate in a weak nonlinear mode.