Instrumentation & Measurement Magazine 24-3 - 19

Fig. 2. a) Direct and b) Differential voltage measurements of an ac signal VAC with a JVS using a digitizer represented by an analog-to-digital converter (ADC).
Differential voltage measurements tend to be more accurate and stable since ADC's errors have second order effects on measurements.

digitizer or ADC can be used. As shown in Fig. 2a, direct measurements imply that the digitizer samples alternately the
JVS and in sequence the DUT. Signals shall be in phase (i.e.,
phase-aligned), so that samples from the JVS and VAC can be
compared with each other. Direct voltage measurements do
calibrate the sampling ADC first with the JVS, allowing samples of the DUT to be corrected for the ADC's gain. The ADC's
gain must obviously remain constant over a short time interval (usually a few seconds, depending on the length of the set
of samples acquired).
Differential measurements (Fig. 2b) [5] are more accurate
and precise, demanding the signals to be phase aligned (i.e.,
phase difference approaching zero) within a certain phase
threshold (usually of some hundreds of micro-radians or less)
to keep the differential voltage between the JVS and VAC small
enough to allow neglecting ADC errors during the sampling
process. Differential measurements may discriminate signal differences up to the nano-volt range, provided DUT's
amplitude remains constant (within such limits) for the measurement time duration. Since both ADC input leads are at
nearly the same potential above ground, the ADC's guard
must be driven with a unity-gain amplifier to preclude capacitive loading of both the JVS and DUT as shown. Sampled data
from the two configuration measurements can be treated both
in the time- or frequency domain (e.g., using discrete Fourier
transform-DFT). The NRC has attained good agreement between the two measurement configurations of around 6 nV/V
for signals at 96 Hz.
The NRC sampling system for JVS uses digital feedback
to phase align signals within phase thresholds (tolerances)
of sub-micro or even nano-radian. This process is fully automated [6] and requires no operator's intervention. It uses
direct-digital-synthesis of phenomenal frequency resolution
to make feeble frequency changes in the time-base of digital sources (such as DUTs), allowing them to be phase-shifted
May 2021

with respect to the JVS' signal. This process is controlled by
a digital regulator that employs adaptive digital filtering algorithms in software [6]. When a PJVS is used, Kalman filters
may be engaged to improve estimation of voltage plateaus.
Recently, a further refined version of a synchronizer and multiplexer with superb frequency resolution (of parts in 10+15 [Hz/
Hz]) and broader measurement capabilities (also applicable
to JAWS) entered operation [7]. The system will be the work
horse for future JVS investigations [8] and routine calibrations.
Despite the apparent simplicity of the voltage measurement configurations in Fig. 2, a new approach is needed when
dealing with ac signals in the microvolt level or lower. There
are still many ongoing investigations to solve some challenges
as pointed out next.

Lead-Effects
Signals are brought from the chip containing the Josephson
junctions at cryogenic temperatures over nearly 1.5 m out to
the ambient temperature (Fig. 1). The chip probe containing
wires and microwave waveguide represents a complex arrangement with irregular geometry that includes a series of
distributed non-linear elements (stray inductances, capacitances, conductance and dielectric losses). Wiring resistances,
for example, are dependent on the liquid Helium (cooler) level,
making any mathematical modeling (in the sense of " finding
an equivalent transmission line model " ) a very difficult endeavor. Heuristic models are still approximations and need to
be refined even further by mathematical modeling, especially
for frequencies above 1 kHz.

Loading-Effects
Any sampler (ADC) and its cablings represent a load with its
own non-linear and frequency dependent input impedance
and stray capacitances. The NRC is presently using a commercial 28-bit integrating ADC (model Keysight 3458A) as

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