System, apparatus, and method for measuring an oxygen concentration of a gas

1. A method of measuring an oxygen concentration of a gas, the method comprising:

receiving an output signal from an oxygen sensor cell positioned within a measuring chamber;

varying a flow of oxygen ions within the measuring chamber by varying a pump current through a pump cell controlling the flow of oxygen ions between a first constant pump current and a second constant pump current in response to the output signal; and

determining the oxygen concentration of the gas based on the pump current.

2. A method in accordance with claim 1 , wherein the determining comprises:

determining the oxygen concentration of the gas by comparing a pulse width ratio of a resulting square wave of the pump current to a pulse width ratio function.

3. A method in accordance with claim 2 , wherein varying the flow comprises:

directing the pump current in a positive direction at a constant magnitude until the output signal reaches an upper threshold; and

directing the pump current in a negative direction at the constant magnitude until the output signal reaches a lower threshold.

4. A method in accordance with claim 3 , wherein directing the pump current in a positive direction and directing the current in a negative direction forms an oscillating output signal having a varying pulse width ratio and a varying frequency.

5. A method in accordance with claim 4 , further comprising:

compensating for an offset of the oxygen concentration based on environmental conditions.

6. A method in accordance with claim 5 , wherein the compensating comprises adjusting a value for the oxygen concentration of the gas based on the frequency of the oscillating output signal.

7. A method in accordance with claim 5 wherein the compensating comprises changing a temperature of the pump cell based on the frequency.

8. A method in accordance with claim 6 , wherein adjusting the value for the oxygen concentration of the gas comprises:

determining an operating pump cell impedance of the pump cell; and

applying a corresponding Lambda associated with the operating pump cell impedance.

9. A method in accordance with claim 8 , wherein the compensating comprises changing a temperature of the pump cell based on the frequency.

10. A method in accordance with claim 8 , wherein determining the operating pump cell impedance comprises:

determining a gain of an inverting amplifier circuit directing the current, the inverting amplifier comprising an operational amplifier having an output connected to the pump cell, and an input resistor connected to the input of the operational amplifier.

11. A method in accordance with claim 2 , further comprising:

performing a calibration procedure by determining at least some factors of the pulse width ratio function.

12. A method in accordance with claim 11 , wherein performing the calibration procedure comprises:

exposing the oxygen sensor cell to a known gas with a known oxygen concentration; and

determining a corresponding oxygen ion flow for the pump current.

13. A method in accordance with claim 12 , wherein determining the corresponding oxygen ion flow for the pump current comprises:

determining a relationship between a Lambda coefficient of the oxygen sensor cell and the pulse width ratio.

14. A method in accordance with claim 13 , wherein determining a relationship between the Lambda coefficient of the oxygen sensor cell and the pulse width ratio comprises:

determining at least two points on a line representing the relationship between Lambda and the pulse width ratio.

15. A method in accordance with claim 14 , wherein determining at least two points on the line representing the relationship between Lambda and the pulse width ratio comprises:

directing the pump current in the positive direction until the upper threshold is reached;

directing no pump current until a lower threshold is reached; and

observing a calibration pulse width ratio.

16. A method in accordance with claim 11 , wherein performing the calibration procedure comprises:

exposing the oxygen sensor cell to a first known gas with a known oxygen concentration;

determining a positive corresponding oxygen ion flow for a positive constant pump current; and

determining a negative corresponding oxygen ion flow for a negative constant pump current.

17. A method in accordance with claim 1 , wherein varying a flow of oxygen ions within the measuring chamber comprises:

applying an input voltage at a resistor connected to a negative input of an inverting amplifier to vary the pump current through the pump cell in response to the output signal.

18. A method in accordance with claim 17 , further comprising:

determining the oxygen concentration based on the input voltage.

19. A method in accordance with claim 18 , wherein determining the oxygen concentration comprises:

applying a pulse width ratio of a square wave representing the pump current to a pulse width ratio function.

20. A method in accordance with claim 19 , wherein determining the oxygen concentration further comprises:

measuring a first time period of a positive pulse of the square wave corresponding to the first constant pump current;

measuring a second time period of a negative pulse of the square wave corresponding to the second constant pump current; and

calculating the pulse width ratio by dividing the difference between the first time period and the second time period by the sum of the first time period and the second time period.

21. A method in accordance with claim 20 , wherein applying the pulse width ratio comprises calculating the oxygen concentration in accordance with the equation: λ PRE =P/(PWM AIR −PWM RATIO ), where P=(1+PWM′ AIR )(1−PWM AIR )/(1−PWM′ AIR ), λ PRE is the oxygen concentration, PWM RATIO is the pulse width ratio, PWM AIR is a pulse width ratio for free air when the second current is negative, and PWM′ AIR is a pulse width ratio for free air when the second current is zero.

22. A method in accordance with claim 21 , wherein applying the pulse width ratio further comprises calculating the oxygen concentration in accordance with the equation λ=M*λ PRE +(1−M), where λ is the oxygen concentration when λ PRE is less than one, and M is a constant representing a correction factor for the measuring cell.