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(Color online) A four-row implementation of code-division multiplexing by flux summation (Φ-CDM). The TESs are dc-biased and thus on at all times. The current signal from TES j inductively couples to all four first-stage SQUID amplifiers (SQ1) with coupling polarity defined by column j in the modulation matrix W 4 (Eq. (1)). Oppositely oriented inductors (red/bold) produce a negative coupling polarity. Each row of inductors (shaded boxes) is transformer-coupled to one SQ1. Rows of SQ1s are operated with a standard TDM protocol (see Ref. 13): the rows are activated sequentially via I ad k , so the signal from one SQ1 at a time passes to a second-stage SQUID (SQ2). The output of SQ2 is routed to a 100-SQUID, series-array amplifier and then to room-temperature electronics. To keep the three-stage SQUID amplifier in its linear range, the multiplexer is run as a flux-locked loop (Ref. 13). The series array output (SA-out) is digitally sampled; a flux-feedback signal FB1 is then applied inductively to each SQ1 to maintain SA-out at a constant value.
(Color online) Example raw and demodulated data from four detectors in a single 20 ms period. (a) The raw, encoded outputs, Rk, from the SQ1 in four-detector Φ-CDM (with vertical offsets for clarity). The SQ1 outputs correspond to rows 1–4 in Eq. (1). Manganese fluorescence x-rays struck TESs 3, 1, 2, and 4 at 0, 5, 7, and 11 ms. (b) The same data demodulated by application of to show the per-detector signal currents. The signal-to-noise is too high for the noise to be seen in this example.
(Color online) The scaling of SQUID-amplifier noise in TDM and Φ-CDM. Noise was measured at 85 mK, with TESs superconducting to emphasize the amplifier noise (rather than TES noise) at high frequencies. The Johnson-noise contribution from the TES shunt resistor dominates below 1 kHz. The τ = L/R time constant of the shunt resistance and inductance in the TES bias loop causes the Johnson noise to roll off above 100 Hz. At high frequencies, the SQUID-amplifier noise is dominant. All measurements used t row = 640 ns and a 2.5 MHz, one-pole RC filter before the digitizer. (a) Noise from a single SQUID channel, referred to the first-stage SQUID, when read out with one, two, four, or eight TDM rows. Dotted lines show the single-row, high-f noise level (0.37 μΦ0/√Hz) multiplied by successive powers of . Due to aliasing, TDM amplifier noise grows with the number of rows as (see Ref. 7). (b) Noise in four- and eight-channel CDM readout. The signals, which have not been demultiplexed via the Walsh matrix, are referred to the first-stage SQUID. Lines are seen at the 60 Hz power line frequency and its harmonics. The dotted lines show the CDM-4, high- f noise level (0.65 μΦ0/√Hz) multiplied by 1 and . As in TDM, the aliased SQUID noise scales as . (c) Demodulated noise, referred to the TES current, in four- and eight-channel CDM. Both approach 19 pA/√Hz at high frequencies. We omit the unswitched channel from the average, making the 60 Hz line no longer visible.
(Color online) Mn Kα x-ray fluorescence spectra measured separately by eight TES x-ray calorimeters read out with Φ-CDM. Spectra are offset vertically for clarity. These data have been analyzed with corrected Walsh codes and a linear arrival-time correction, and a Gaussian energy resolution has been fit, techniques described previously in Ref. 11. All detectors have multiplexed energy resolution better than 3 eV except for TES 1*—the only detector subject to low-frequency noise pickup in the SQUID amplifier chain. The Φ-CDM resolution matches or exceeds that found with equivalent TESs read out by TDM.
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