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A Problem in AC Quantized Hall Resistance Measurements and a Proposed Solution
Summary
Measurements of the ac quantized Hall resistance (R_H) are affected by probe capacitance, causing frequency dependence. Quadruple-series connections may enable precise measurements of R_H - R, overcoming this challenge for impedance standards.
Area of Science:
- Metrology
- Condensed Matter Physics
- Electrical Engineering
Background:
- The ac quantized Hall effect (QHE) has shown frequency-dependent resistance values, deviating from DC measurements.
- This variability hinders its application as an absolute impedance standard.
Purpose of the Study:
- To investigate the impact of probe-to-shield capacitances on ac quantized Hall resistance (R_H) measurements.
- To identify the source of frequency dependence in ac QHE measurements.
Main Methods:
- Development of equivalent electrical circuit models incorporating capacitances, leakage resistances, and longitudinal resistances.
- Algebraic analysis of these circuits to determine R_H values and quantized Hall voltages (V_H).
Main Results:
- Analysis revealed significant out-of-phase contributions to V_H due to probe capacitances.
- These contributions can explain the observed linear frequency dependence in previous R_H measurements.
- Quadruple-series connections are predicted to minimize these out-of-phase contributions.
Conclusions:
- Probe-to-shield capacitances are a likely cause of frequency dependence in ac QHE measurements.
- Quadruple-series connections offer a potential solution for accurate R_H measurements, enabling precise determination of R_H - R.
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