1. An Automatic Calibration System for 10 M  to 1 T  DC Standard Resistors D.W.K. Lee and Y.C. Chau The Government of the Hong Kong Special Administrative Region Standards and Calibration Laboratory (SCL) 2002 NCSLI Workshop and Symposium

2. Areas of Presentation Introduction -System Overview -The Equivalent Circuit -The Mathematical Model Salient Features of the SCL System -Dealing with Errors due to the System’s Voltage Sources -Dealing with Errors due to Leakage - Algorithm for Checking the System’s Stable Condition -Algorithm for Checking the System’s Balance Condition System Performance -Measurement Results -Estimation of Measurement Uncertainties

3. System Overview: The Modified Wheatstone Bridge

4. System Overview: Ranges of Operations Test Ratios and Voltages: 10 MOhm to 1 TOhm Test Resistance:

5. System Overview: The Automatic High Value Resistance Calibration System

6. The Standard Resistor and the Resistor Under Test System Overview: Connections for the Reference and UUT Resistors

7. System Overview: The Voltage Sources and the Null Detector

8. System Overview: Real Time Display of Measurement Results

9. System Overview: The Equivalent Circuit Notations:- V X, V S : Settings of the voltage sources (i.e. the DCV calibrators) G X, G S : Gains of the voltage sources V OX, V OS : Zero offsets of the voltage sources I D : Reading of the null detector I O : Zero offset of the Bridge I X, I S : Currents flowing through the unknown and standard resistors R X, R S : Resistance of the unknown and standard resistors

10. System Overview: Zero Offsets and Gain Errors of the Voltage Sources

11. System Overview: The Mathematical Model R X = -(V X /V S ).R S.Correction Factor

12. Mathematical Expression of the RCF for Nominal Voltage Ratio of 1:1 System’s Salient Feature: Dealing with Gain Errors of the DCV Calibrators

13. System’s Salient Feature: Dealing with Gain Errors of the DCV Calibrators Determining the RCF for Nominal Voltage Ratio of 1:1

14. System’s Salient Feature: Dealing with Gain Errors of the DCV Calibrators Circuit Arrangement for Determining the RCFs for Nominal Voltage Ratios of 10:1 and 100:1

15. System’s Salient Feature: Dealing with Gain Errors of the DCV Calibrators Determining the RCFs for Nominal Voltage Ratios of 10:1 and 100:1

16. To Evaluate the Effect on the RCFs due to Calibrator Polarities System’s Salient Feature: Dealing with Gain Errors of the DCV Calibrators

17. A High Valued Resistance Artefact (R L is the leakage path) System’s Salient Feature: Dealing with Errors due to Leakage

18. System’s Salient Feature: Dealing with Errors due to Leakage

19. Circuit Schematic of the modified Wheatstone Bridge (using the “3-terminal” configuration to deal with leakage errors.) Notations:- V X, V S : voltage sources (i.e. DCV calibrators) R LX1, R LX2, R LS1, R LS2 : leakage resistance R X, R S : unknown and reference resistance D: null detector r: lead resistance System’s Salient Feature: Dealing with Errors due to Leakage

20. To allow for the bridge to settle into a stable condition before readings are taken, the Bridge’s electrometer takes 10 readings for ID in a period of 10 seconds. The standard deviation (s.d.) for ID is calculated. The Bridge is considered as stabled if: s.d. of ID / IX < s where s is an operator selected parameter; and s is selectable between 10 ppm and 1000 ppm System’s Salient Feature: Algorithm for Checking the System’s Stable Condition

21. System’s Salient Feature: Algorithm for Checking the System’s Balance Condition

22. Checking the Errors for Nominal Voltage Ratio of 1:1 : With two resistors, R 1 and R 2, of nominally equal values, the bridge’s ratio error, , is determined as: System Performance: Measurement Results

23. The results are agreed within: (1)Rx at 1 G  and below: 2  10 -6 for; and (2)Rx > 1 G  : 10  10 -6. System Performance: Measurement Results The system’s performance at Nominal Voltage Ratios of 10:1 and 100:1 is evaluated as follows: The same set of unknown resistors were calibrated against the same set of reference resistors by the system. The results were compared with those obtained by the following systems: (1) Rx at 100 M  : ESI 242D Kelvin-Varley Bridge (2) Rx > 100 M  : Manual Modified Wheatstone Bridge

24. System Performance: Estimated Measurement Uncertainties

26. Conclusions An Automatic Calibration System for 10 M  to 1 T  DC Standard Resistors has been developed. The system has the following salient features: - Correcting the Errors due to Calibrators by Ratio Correction Factors - Minimizing the Errors due to Leakage by “3-terminal” Connections - Checking the System’s Stable Condition by Software Algorithm - Checking the System’s Balance Condition by Software Algorithm