3.3 Noise
3.3.2 Multiplicative Electronics
In this section we present several empirical facts regarding the multiplicative electronics noise that will be used to inform the removal algorithm. All of these results followed from the study of off-resonance carrier timestreams measured with the MUSIC readout electronics. The fact that the noise is multiplicative was easily confirmed by examining the power spectral density as a function of carrier power at the ADC. In the limit of zero carrier power the measured power spectral density is constant and coincides with the expected value of the electronics white noise floor. As the carrier power is increased we observe 1/f and drift type noise rise above this white noise floor, and find that the normalization of these components scale asA2.
The MUSIC readout board is equipped with two switches that place the board in different “loopback modes” wherein the output signal is sent directly to the input, bypassing certain segments of the receiver chain. These switches enable us to study the contribution of various subsystems to the total noise. The base- band (BB) loopback mode sends the output of the DAC directly to the ADC, bypassing the entire process of up-converting to microwave frequencies and then down-converting to base band. The intermediate-frequency (IF) loopback mode sends the output of the IF board to the third IF amplifier (labeled IF-Amp-2 in Table 2.2), bypassing the cryostat and the first two room-temperature amplifiers. Finally, an external (Ext) loopback mode can be implemented by connecting the output of the readout board to the input with an SMA cable, bypassing the cryostat but including all room temperature electronics.
Figure 3.9 presents the noise power spectral density measured in BB loopback mode, IF loopback mode, and standard operations (Cryo). The carrier power at the ADC was maintained at a fixed value for all mea- surements, approximately equal to that used during observing. The dashed lines denotes the white noise floor of each of the subsystems. We find that in all cases 1/f and drift type noise dominate over the additive white noise across the frequency range of interest. We also find that in all cases the noise in the amplitude direction is comparable in magnitude to the noise in the phase direction. In switching from BB to IF loopback we have added up-conversion, down-conversion, and two stages of amplification. Somewhat surprisingly this intro- duces very little noise at short timescales. It does, however, introduce significant drift type noise resulting in a noticeable degradation in the long timescale stability. In switching from IF to Cryo we see an approxi- mately 20 dB increase in the noise level at high frequencies and a 10-20 dB increase at low frequencies; the timestreams are entirely dominated by the noise from the cryogenic components.
It was not always the case that the noise from the room temperature components was subdominant to the noise from the cryogenic components. The two were comparable in magnitude throughout most of the development of the MUSIC readout. In the final version of the readout boards we did a better job heat sinking the ADC, DAC, and IF board, and also improved air flow by placing the boards in a ventilated crate.
This reduced the drift noise from the room temperature electronics by two orders of magnitude. As a result, the total noise from the room temperature electronics is below the white noise floor of the system at high frequencies (>1 Hz) and below the cryogenic 1/f and drift type noise at low frequencies. It is still large enough, however, that it must be removed in order to achieve a white spectrum at frequencies below 1 Hz.
The blue and green lines in Figure 3.9 were collected with setups that differ only in the method used to stabilize the bias power being supplied to the HEMT. For the green line we have set the power supply to provide a specific gate and drain voltage and done nothing else. For the blue line we have set the gate and drain voltage to the same values, but have also implemented a feedback loop that varies the gate voltage in order to keep the drain current constant. This results in a fairly significant decrease in the magnitude of the amplitude noise, presumably because the gain of the HEMT is more sensitive to fluctuations in the drain current than the gate voltage. The feedback loop also decreases the magnitude of the phase noise, although the improvement is not as noticeable as that seen in the amplitude direction.
Figure 3.10: Left: The median power spectral density in the amplitude and phase direction in units of dBc / Hz. The median was taken over approximately 200 off-resonance carriers across two readout boards. The different colors denote different HEMT amplifiers.Right:The median power spectral density in the amplitude and phase direction relative to HEMT 289D, which has the best noise performance.
We attribute the large increase in 1/f and drift type noise between the IF and Cryo measurement primarily to the HEMT. Figure 3.10 compares the median off-resonance noise power spectral density collected during an actual observation for six of the readout channels. There is significant variation across the readout channels in both the magnitude of the noise and its spectral shape (due to differences in the relative contribution of 1/f and drift). The noise from the room temperature electronics is approximately uniform for the different readout boards, and the variation seen is entirely due to differences in HEMT noise performance. This variability can only partially be explained by the susceptibility of the HEMTs to fluctuations in bias voltage. Table 3.1 gives the measured susceptibility∂G/∂Vdrain and∂G/∂Vgate of the gain of the HEMTs to fluctuations in the drain and gate voltage at their operating bias. We see that the HEMT that has the worst noise performance (266D) is also extremely susceptible to voltage fluctuations. In general, however, we do not observe the expected scaling in the magnitude of the HEMT noise with susceptibility. This suggests the presence of an additional source of noise internal to the amplifier. The large variation in HEMT noise performance means that the
multiplicative electronics noise will be prevalent in some detector arrays and entirely subdominant in others.
If we exclude the outlier 266D, then at 1.0 Hz we see roughly 14 dB variation in the amplitude direction and 9 dB variation in the phase direction. We note that in the phase direction (and to a lesser extent the amplitude direction) at frequencies less than 0.1 Hz, the drift noise from room temperature electronics starts to become appreciable, which results in the noise power spectral density for the different detector arrays converging at low frequencies in Figure 3.10.
We claimed in Section 2.3.1.2 that the amplitude and phase fluctuations measured by carriers at different microwave frequencies are correlated. Our ability to remove the multiplicative electronics noise will depend on the degree to which this is true. Letxandydenote the time ordered data for two different carriers in a particular direction in the complex plane. We calculate the Pearson correlation coefficient betweenxandy in the Fourier domain as
ρx,y= x˜·y˜
p(˜x·x) (˜ y˜·y)˜ , (3.18)
wherex˜andy˜denote the Fast Fourier Transform (FFT) ofxandy. The dot product is given by
˜
x·y˜=
∑
k
˜
xk∗y˜k, (3.19)
where the summation runs over the frequency bins of interest. The Pearson correlation coefficient is a measure of the linear correlation betweenxandy. By definitionρx,y∈[−1,1], with 1 indicating perfect correlation, 0 indicating no correlation, and -1 indicating perfect anti-correlation. If|ρx,y|=1, then the relationship between xandyis perfectly described by a linear model.
Figure 3.11 shows the Pearson correlation coefficient between every pair of off-resonance carriers across four readout boards (and two readout channels) during a twenty-minute-long observation. We find that the time ordered data in both the amplitude direction and the phase direction is highly correlated between off- resonance carriers on the same readout board. This high degree of correlation persists between off-resonance carriers on different readout boards but the same readout channel (i.e., same detector array and same HEMT amplifier). This is not surprising since our previous considerations suggested that noise from the HEMT amplifier dominates in both the amplitude and phase direction. Finally, data collected with off-resonance carriers on different readout channels is completely uncorrelated. This is not surprising either since different readout channels do not share any electronic components, besides a common frequency reference.
There is additional structure in the correlation matrices beyond this simple picture. This is evident in the bottom row of Figure 3.11, which show the same data as the top row, but with a compressed color scale that highlights these secondary variations. In general, the high degree of correlation across each readout channel is more uniform in the amplitude direction than the phase direction. In the phase direction, the correlation degrades as one moves away from the diagonal of the matrix, which corresponds to moving toward pairs of
Amplitude Correlation Phase Correlation Amplitude-Phase Cross Correlation
Figure 3.11: Pearson correlation coefficients between the 388 off-resonance carriers probing L120210.2R and L120210.2L. The correlation coefficients were calculated using Equation (3.18). The left, middle, and right column show the amplitude correlations, phase correlations, and amplitude-phase cross correlations, respectively. Dashed black lines separate the different readout boards. Solid black lines separate the differ- ent detector arrays: L120210.2R (connected to HEMT 289D) corresponds to carriers numbered 0-193, and L120210.2L (connected to HEMT 258D) corresponds to carriers numbered 194-387. For a given detector array, the carriers are numbered in order of increasing carrier frequency. The correlation coefficients were calculated in the Fourier domain using only temporal frequencies between 0.2 Hz and 20.0 Hz. The bottom row is identical to the top row, but with a compressed color scale, so that variations in the correlation co- efficient between carriers on the same readout board are visible. Note that the white color corresponds to a correlation coefficientρx,y≈1.
carriers with larger frequency separations. This suggests that the phase fluctuations are somewhat local in microwave frequency.
The lower left corner of each matrix corresponds to the off-resonance carriers that probe detector array L120210.2R and HEMT 289D. The upper right corner corresponds to the off-resonance carriers that probe detector array L120210.2L and HEMT 258D. 289D has the best noise performance, while 258D has the second worst noise performance (see Figure 3.10). We note several differences in the correlation matrices between these two readout channels. The third column in Figure 3.11 shows the cross-correlation between the amplitude and phase direction. In the case of 258D, amplitude and phase noise are completely correlated.
This suggest a similar underlying cause, some source of low frequency noise internal to the HEMT amplifier that results in fluctuations in both its gain and phase delay. In the case of 289D, the HEMT noise is not as dominant. Indeed, in the phase direction it appears that the room temperature electronic noise is comparable, as evidenced by the reduced correlation between off-resonance carriers on separate readout boards. Inter- estingly, the amplitude and phase noise from 289D appear to be highly anti-correlated. We currently do not have a compelling physical explanation for the HEMT phase noise. It is either highly correlated or highly anti-correlated with the amplitude noise, depending on the amplifier.