Quantum-based impedance bridges

Traditional impedance bridges make use of inductive dividers and achieve, in their frequency range from 500 Hz to 10 kHz, excellent relative measurement uncertainties of only a few parts in 10–9. The bridges must, however, be adjusted for each frequency of operation and this involves a complex manual procedure.

PTB's newly developed Josephson impedance bridge can be adjusted very easily. The AC voltage amplitudes from two Josephson arrays are adjusted over their microwave frequency, and the phase angle between the synthesised voltages is adjusted via delay electronics with a resolution of 10 ps. Both processes are fully automatic. The utilisation of quantum standards to generate a voltage on both sides of the bridge renders new adjustments at all other frequencies unnecessary. It is therefore possible to perform precise measurements at 20 different frequencies within just 30 minutes.

The efficiency of the new procedure has been demonstrated by measuring the 1:1 ratio between two 10 kΩ resistors and two 100 pF capacitors. The resistance ratio over the frequency range from 25 Hz to 10 kHz was determined with a measurement uncertainty of approx. 2 • 10^–8. For capacitance ratios, the uncertainty lies in the kHz range below 1 • 10^–8. With decreasing frequency, the uncertainty increases as a function of the impedance 1/ωC. With 2 • 10^–7 at 25 Hz, the uncertainty is, however, still 20 times smaller than when measuring with traditional bridges.

In further development steps, the new Josephson bridge is to be used also for ratio measurements where a resistor is compared to a capacitor. By integrating the frequency-independent quantum Hall resistor, the frequency response of capacitors could then be calibrated up to the range of technical frequencies (in Germany: 50 Hz) with high precision.