SBOA597 November   2024 OPA928

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Introduction
  5. 2Architecture of Small Current Measurement
    1. 2.1 Coulombmeter
    2. 2.2 Using the Coulombmeter to Determine IB
    3. 2.3 Leakage of Integration Capacitor
  6. 3Benchmarking
    1. 3.1 Point to Point Wiring
    2. 3.2 Shielding
    3. 3.3 PCB Cleaning
    4. 3.4 Temperature Stability
  7. 4Calibration Using a Coulombmeter for Application Circuits
    1. 4.1 Calibration of Common Application Circuits
    2. 4.2 Calibration of Inverting Input
    3. 4.3 Calibration of Non-Inverting Input
    4. 4.4 Determine Resistance of the Capacitor Using Zero-Cross Method
    5. 4.5 Dielectric Absorption and Relaxation
    6. 4.6 Calibration at 85°C
    7. 4.7 Calibration at 25C
  8. 5Summary
  9. 6References

4.7 Calibration at 25C

Figure 4-23 shows an example of the measurement at 25°C. Although most of the procedure is the same as for 85°C, the example shows the output voltage did not cross zero volts. In this case, one additional step is needed. To remove the effects of the leakage in the parasitic resistance of the capacitor, the parasitic resistance must be calculated.

  • Transform the circuit into calibration mode.
  • Monitor the output voltage over time.
  • Find a point where the output voltage is away from dielectric relaxation.
  • Calculate the parasitic resistance of the integration capacitor.
  • Calculate current using the derivative of the output over time multiplied by the capacitance.
  • Apply the leakage current using the resistance oc the capacitor.
  • Make sure the point to calculate derivative is away from dielectric relaxation.
  • Apply a temperature coefficient of the capacitor for calculation.

In the example, the output voltage (buffer with a gain of ten) moved from 0.05V to 1.3V. As the curve does not cross zero volts, we need to take a leakage current into account. Leakage across the capacitor is proportional to the voltage across the capacitor multiplied by the resistance of the capacitor.

Calibration at 25C (Buffer Out Over Time) Figure 4-23 Calibration at 25C (Buffer Out Over Time)

Plot current over the output voltage. The curve indicates dielectric relaxation settles at around output voltage 0.3V. The fitting curve shows -0.93aA/V. The resistance of the integration capacitor is calculated as 1 / (-0.93aA/V) / 10.1 (gain) = 106PΩ at 25°C. The intercept of the fitting curve indicates IB is 79aA. In this example, the resistance of the capacitor is used as the output voltage does not cross zero.

Calibration at 25C (Current Over Buffer Out) Figure 4-24 Calibration at 25C (Current Over Buffer Out)

Go back to the original curve of output voltage over time. Zoom in the area where dielectric relaxation was settled. For example, take a derivative between 0.263V to 0.273V, dV/dt, to obtain a slope that is 6.73µV/sec. Apply the parasitic resistance of the capacitor of 106PΩ, on 0.268V / 10.1(gain) to obtain leakage of 0.25aA. IB is calculated as 6.73µV/sec / 10.1 x 117.4pF x (1-0.0002 x (25-20)) + 0.25 = 78.4aA. The calculation includes the temperature coefficient of the capacitor of -200ppm/°C.

Calibration at 25C (Buffer Out Over Time) Zoom Figure 4-25 Calibration at 25C (Buffer Out Over Time) Zoom

Comparing the number between the intercept of the fitting curve (79aA) and (78.4aA) gives a delta of 0.6aA. With that, IB is most likely between 79aA to 78.4aA at 25°C.