Method for measuring capacitance and equivalent parallel resistance

• US 20070100566A1
• Filed: 10/28/2005
• Published: 05/03/2007
• Est. Priority Date: 10/28/2005
• Status: Active Grant

• Current Assignee: Agilent Technologies, Inc.
• Original Assignee: Agilent Technologies, Inc.
• Inventors: Coley, William
• Granted Patent: US 7,225,090 B2
• Time in Patent Office: Days
• US Class Current: 702/64
• CPC Class Codes: G01R 27/2605 Measuring capacitance capacitive sensors G01D5/24

Abstract

C_X is measured in the presence of R_P by charging C_X with a constant current I_C for a period time and taking four (time, voltage) pairs: (t_A,V_A), (t_B,V_B), (t_C,V_C) and (t_D,V_D). The first pair are sufficiently close together that the short straight line segment connecting (t_A, V_A) and(t_B, V_B) is not significantly different from the corresponding segment of a true graph of the capacitor'"'"'s actual charging. A similar requirement is imposed on the time interval between t_C and t_D. The time interval t_At_B need not be the same as t_Ct_D. The interval t_Bt_C should be long enough that if there is significant R_P present then there is at least a discernable difference between the true graph and a straight line between the first pair and the second. C_X and R_P are computed as a function of the four pairs and I_C, and C_X may then be diminished by a previously measured value for a stray capacitance present in the absence of C_X.

Claims

1. A method of measuring the capacitance C_X of a work capacitor in the presence of a parallel resistance R_P, the method comprising the steps of:

(a) charging the work capacitor for a selected interval of time with a constant current I_C having a selected value;

(b) approximating a first slope (dv/dt)₁ of the voltage waveform across the work capacitor at a first time near but after the start of the selected time interval;

(c) finding the voltage V₁ across the work capacitor at the first time;

(d) approximating a second slope (dv/dt)₂ of the voltage waveform across the work capacitor at a second time near but before the end of the selected time interval;

(e) finding the voltage V₂ across the work capacitor at the second time;

(f) computing a value of C_X as a function of I_C, (dv/dt)₁, (dv/dt)₂, V₁ and V₂.

2. A method as in claim 1 further comprising, subsequent to steps (a)-(f), the step of diminishing C_X by a previously measured value of a stray capacitance present in the absence of the work capacitor.

3. A method of measuring the capacitance C_X of a work capacitor in the presence of a parallel resistance R_P, the method comprising the steps of:

(a) charging the work capacitor for a selected interval of time with a constant current I_C having a selected value;

(b) measuring the voltage V_A across the work capacitor at a first time near but after the start of the selected time interval;

(c) measuring the voltage V_B across the work capacitor at a time At after the first time;

(d) measuring the voltage V_C across the work capacitor at a second time near but before the end of the selected time interval;

(e) measuring the voltage V_D across the work capacitor at a time Δ

t after the second time and before the end of the selected time interval;

(f) computing a value of C_X as a function of I_C, Δ

t, V_A, V_B, V_C, and V_D.

5. A method of measuring the capacitance C_X of a work capacitor in the presence of a parallel resistance R_P, the method comprising the steps of:

(a) charging the work capacitor for a first selected interval of time with a constant current I_C having a selected value;

(b) approximating a first slope (dv/dt)₁ of the voltage waveform across the work capacitor at a first time near but after the start of the first selected time interval;

(c) finding the voltage V₁ across the work capacitor at the first time;

(d) approximating a second slope (dv/dt)₂ of the voltage waveform across the work capacitor at a second time near but before the end of the first selected time interval;

(e) finding the voltage V₂ across the work capacitor at the second time;

(f) finding a first difference V₂−

V₁;

(g) finding a second difference (dv/dt)₁V₂−

(dv/dt)₂V₁;

(h) finding a first quotient by dividing the first difference by the second difference; and

(i) finding a first value of C_X as the product of I_C and the first quotient.

6. A method as in claim 5 further comprising the subsequent steps of:

(j) charging the work capacitor for a selected interval of time with a constant current −

I_C having a selected value;

(k) approximating a third slope (dv/dt)₃ of the voltage waveform across the work capacitor at a third time near but after the start of the second selected time interval;

(l) finding the voltage V₃ across the work capacitor at the third time;

(m) approximating a fourth slope (dv/dt)₄ of the voltage waveform across the work capacitor at a fourth time near but before the end of the second selected time interval;

(n) finding the voltage V₄ across the work capacitor at the fourth time;

(o) finding a third difference V₄−

V₃;

(p) finding a fourth difference (dv/dt)₃V₄−

(dv/dt)₄V₃;

(q) finding a second quotient by dividing the third difference by the fourth difference;

(r) finding a second value of C_X as the product of −

I_C and the second quotient; and

(s) finding the average of the first and second values of C_X.

7. A method as in claim 5 further comprising the step of determining the value for I_C and the length of the first selected time interval based upon a previously performed trial measurement of C_X.

8. A method as in claim 5 further comprising the step of determining the value for I_C and the length of the first selected time interval based upon a previously performed trial measurement of C_X and a selected maximum voltage that the work capacitor is to experience.

9. A method as in claim 5 further comprising the step (j) of, subsequent to steps (a)-(i), of discharging the work capacitor through a resistance.

10. A method as in claim 9 further comprising, subsequent to step (j), the step of repeating steps (a)-(i).

11. A method as in claim 5 wherein the work capacitance for steps (a)-(i) is a stray capacitance, and further comprising the subsequent step (j) of connecting an actual work capacitance, and then repeating steps (a)-(i) with the actual work capacitance in parallel with the stray capacitance, and finally diminishing the value of C_X found for the actual work capacitance by the value of C_X found for the stray capacitance.

12. A method of measuring the capacitance C_X of a work capacitor in the presence of a parallel resistance R_P, the method comprising the steps of:

(a) charging the work capacitor for a selected interval of time with a constant current I_C having a selected value;

(b) measuring the voltage V_A across the work capacitor at a first time near but after the start of the selected time interval;

(c) measuring the voltage V_B across the work capacitor at a time Δ

t after the first time;

(d) measuring the voltage V_C across the work capacitor at a second time near but before the end of the selected time interval;

(e) measuring the voltage V_D across the work capacitor at a time Δ

t after the second time and before the end of the selected time interval;

(f) finding a first quantity V_D+V_C−

V_B−

V_A;

(g) finding a second quantity (V_BV_C)−

(V_AV_D);

(h) finding a first quotient by dividing the first quantity by the second quantity; and

(i) finding a first value of C_X as the product of Δ

tI_C/2 and the first quotient.

4. A method as in claim 13 further comprising, subsequent to steps (a)-(f), the step of diminishing C_X by a previously measured value of a stray capacitance present in the absence of the work capacitor.

13. A method as in claim 12 wherein the work capacitance for steps (a)-(i) is a stray capacitance, and further comprising the subsequent step (j) of connecting an actual work capacitance, and then repeating steps (a)-(i) with the actual work capacitance in parallel with the stray capacitance, and finally diminishing the value of C_X found for the actual work capacitance by the value of C_X found for the stray capacitance.

14. A method as in claim 12 further comprising the step of determining the value for I_C and the length of the selected time interval based upon a previously performed trial measurement of C_X.

15. A method as in claim 12 further comprising the step of determining the value for I_C and the length of the selected time interval based upon a previously performed trial measurement of C_X and a selected maximum voltage that the work capacitor is to experience.

16. A method as in claim 12 further comprising the step (j) of, subsequent to steps (a)-(i), of discharging the work capacitor through a resistance.

17. A method as in claim 16 further comprising, subsequent to step (j), the step of repeating steps (a)-(i).