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

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

System Overview: The Modified Wheatstone Bridge

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

System Overview: The Automatic High Value Resistance Calibration System

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

System Overview: The Voltage Sources and the Null Detector

System Overview: Real Time Display of Measurement Results

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

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

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

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

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

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

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

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

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

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

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

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

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

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

The results are agreed within: (1)Rx at 1 G  and below: 2  for; and (2)Rx > 1 G  : 10  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

System Performance: Estimated Measurement Uncertainties

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