We must then add extra parallel capacitance to the QVNS circuit, even though the individual QVNS cables must reach the bottom of a liquid helium Dewar and are therefore longer than the individual Johnson noise cables, because the JJ array on the QVNS acts as a low-inductance short.
In practice, the real part of the ratio [Real part][[C.sub.R]/[C.sub.Q]] is largely dependent on common changes to the tuning capacitors (for example, increasing both trim capacitors), which can be thought of as matching the QVNS arms to the Johnson noise arms.
However, this approach assumes that any undesired correlated noise [C.sub.n,R] that is not associated with Johnson noise is small; as shown in Sec.
The recent paper from NIM [36] used a slightly different approach, where the dc resistances of the QVNS channels were chosen to be twice the Johnson noise resistor channels.
However, the peaks in the frequency comb of the QVNS at frequencies above [f.sub.nyq] do not overlap with the peaks below [f.sub.nyq]; therefore, unlike with the Johnson noise, we separately measure the contributions from the first Nyquist zone and second Nyquist zone.
First, the Johnson noise data are averaged into maximally nonoverlapping bins centered on the frequencies of the QVNS comb.
The Johnson noise data [C.sub.R] are averaged over the full N x P, but the QVNS data [C.sub.Q] are only averaged over the (N - 1) x P set centered in time on the Johnson noise data.
In our case, [[GAMMA].sub.a] [approximately equal to] 27 000 [ohms] K; that is, the amplifier noise is about half the R = 200 [ohms] sense resistor Johnson noise at the TPW.
To determine the magnitude of reduction, we calculate the variance in the product of the FFTs of the measured Johnson noise voltages in two cases: the autocorrelation measurement for a single channel, A or B; and the cross-correlation measurement between channels A and B.
(25) can be used to quantify how much of our statistical uncertainty is associated with amplifier noise, as opposed to the inherent randomness of the Johnson noise signal.
In the EMI measurement, there are two separate sense resistors with uncorrelated Johnson noise as well as uncorrelated amplifier noise.
Two differences between the QVNS voltage and the Johnson noise voltage, in combination with measurement nonlinearities, can create errors in the results of the k measurement: differences in the dc voltage and differences in the ac magnitude of the signals [60].