The Improvement of the Mathematical Model of a Calculable Voltage Standard with a Single Junction Thermal Voltage Converter

This paper presents the modification and experimental validation of a mathematical model for a single junction thermal voltage converter (SJTC) designed for high-precision alternating current (AC) voltage transfer. The original model is severely constrained by two main issues: (1) computational instability above 50 MHz due to the limitations of the housing impedance approximation, and (2) insufficient accuracy above 1 MHz due to the neglect of high-frequency skin effect and magnetic core effects in the Dumet wire leads. Significant refinements are subsequently implemented to extend the calculable frequency range of the standard from 1 to 100 MHz. This required re-evaluation of the Dumet wire leads’ frequency-dependent resistance and inductance using finite element method (FEM) simulations, which accounted for the skin effect and the magnetic permeability of the FeNi42 core. Additionally, the housing impedance calculation is stabilized using a formulation based on scaled modified Bessel functions, and the electrical conductivity of the input N-type connector pin is explicitly modeled. The improved model is validated against a reference calorimetric thermal voltage converter (CTVC) using 3 and 5 V nominal voltage standards. The results indicated excellent agreement between the calculated and measured AC-direct current (DC) transfer differences up to 10 MHz. In the extended frequency regime, the model correctly predicted the transition to negative transfer differences observed above 2 MHz for the 5 V standard. The largest discrepancies between the measured and calculated values occurred at 100 MHz. The measured transfer difference reached −15,090 (µV/V) with an expanded uncertainty (k = 2) of 190 (µV/V), whereas the calculated value is −12,500 (µV/V) with an expanded uncertainty of 3900 (µV/V). Although the deviation between the model and measurement increased above 30 MHz, the results remained consistent within the expanded measurement uncertainties across the entire 10 kHz to 100 MHz range, demonstrating the model’s suitability for providing traceability in high-frequency voltage metrology.