Time-division multiplexed readout of TES detectors
J.P. Filippini for the
CMB-S4 readout working group
August 2, 2016
1
Introduction
In this report we provide a brief overview of time-division multiplexing (TDM) as
applied to the readout of large arrays of transition-edge sensors (TESs). We focus
primarily on the system architecture developed at NIST [1, 2] and readout electronics
developed at UBC [3]. This architecture is now very mature and has extensive field
heritage on a variety of CMB instruments, including ABS [4], ACT [5], ACTpol [6],
Bicep2 [7], Bicep3 [8], CLASS [9], Keck Array [10], and Spider [11]. This system
has also seen application in sub-millimeter observations with SCUBA-2 [12], and a
similar system is under development for X-ray applications [13].
In Section 2 we review the general features of the time-division mulitplexing
system for TES arrays. Section 3 outlines key design parameters and their effect
on performance. Section 4 discusses the key advantages and disadvantages of this
technique, and its prospects for use in CMB-S4.
2
2.1
System architecture
General overview
Multiplexing combines the signals from multiple detector channels so that they can
share a common amplifier chain, interconnects, or other expensive resource. In a
cryogenic instrument it is advantageous to limit the number of interconnects from
ambient temperature to the cold space, since each adds both thermal load and assembly labor. Cold and warm amplifiers can also be a limiting resource, since they are
often significant contributors to both the thermal and financial budgets. Shared readout is accomplished by multiplying each detector data stream by a member of some
1
set of orthogonal basis functions and summing to yield a combined data stream. The
combined data stream is amplified, carried out of the cryostat, and finally separated
into its components in the warm electronics using the same set of basis functions.
The net effect is to divide the total readout system bandwidth among N individual
detectors, each of which is thus confined to use at most 1/N of the readout system’s
bandwidth. For further discussion of general multiplexers see e.g. [14].
In a time-division multiplexer we perform this combination by addressing each
detector one a time in sequence. Detectors are arranged logically in a two-dimensional
array: each “column” drives a single readout chain (amplifiers and interconnects),
with a single “row” of detectors connected to those readouts at any given time.
The combined data stream is an interleaved sequence of samples, with each of the
N detectors visited at 1/N of the total sampling rate. The key component of a
time-division multiplexer is thus some system for switching rapidly between rows,
which includes gathering the outputs of the various rows (active and inactive) to a
single cold amplifier. The bandwidth of each detector must be limited below 1/N of
that of the readout chain to avoid aliasing detector noise. Equivalently, the readout
chain must be fast enough to allow rapid slewing at each row-switch, so that each
detector may be sampled frequently enough to avoid aliasing its noise. Aliasing of
the amplifier chain’s noise is unavoidable, however, and must be kept sub-dominant
by appropriate design choices.
2.2
Cold hardware
The most mature implementation of time-division multiplexing in the CMB community is that developed by NIST [2, 15]. In this system the current signal from
each TES is amplified by a dedicated first-stage SQUID. Most fielded instruments
have used a “flux-summing” SQUID readout technique, in which a flux transformer
gathers signals from all of the first-stage SQUIDs in a column (only one of which
is on at a time) for detection by a second-stage SQUID. This scheme has robust
heritage, but is not ideal for expansion to much larger arrays.
NIST has recently developed an alternate “voltage-summing” arrangement, first
deployed in the field by Bicep3 and now in use by other third-generation instruments:
Advanced ACTPol [16] and CLASS [9]. This arrangement is shown schematically
in Figure 1. Each first-stage SQUID is wired in parallel with a Josephson junction
switch, and their series sum across the column is amplified by a series SQUID array
(SSA) for transmission to the warm electronics. During multiplexing all but one
of the switches are closed to short out the inactive SQUIDs, so that only a single
first-stage SQUID feeds the SSA at any given time. This system employs many
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more Josephson junctions than the previous scheme, but has the advantages of lower
power dissipation and improved fabrication yield (since smaller 11-row chips may
be daisy-chained to produce a desired multiplexing factor). Cold-stage power dissipation is also substantially reduced. This system may be controlled by the same
warm electronics as the flux-summing system, with only software- and firmware-level
changes.
SSA BIAS
Warm Electronics
Voltage-summing
MUX chip
SSA IN
SSA FB
simplified schematic
11-channels/chip
xN
Series SQUID Array
(SSA)
1.0 Ω
SQ1 flux feedback
from warm electronics
SQ1 BIAS+-
SQ1 FB+-
Flux-activated
switch (FAS)
x33
Multiplexer chip
SQ1FB
x33
x33
Further chips
in series
...
Figure 1: Schematic illustration of the voltage-summing NIST SQUID multiplexer
system. Each TES is coupled inductively to a first-stage SQUID array (SQ1). All
SQ1s in a column are wired in series to the input of a series SQUID array (SSA),
but at any given time all but one row of SQ1s is bypassed by a flux-activated switch.
Figure adapted from one by Kent Irwin.
The first-stage SQUIDs and flux-activated switches are for 11 rows of a single
readout column are patterned on a single “multiplexer chip”. Each multiplexer chip
is mated to a corresponding “Nyquist chip”, which contains the bias resistors for
each TES and series inductors to define the TES bandwidth. Several such chip pairs
may be bonded together in series to achieve higher multiplexing factors: Advanced
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ACTPol has achieved N = 64 [16]. The lines connecting the multiplexer and Nyquist
chips to the TESs must have low parasitic resistance (typically superconducting), so
these chips are typically operated at the detector temperature (0.1-0.3 K) and either
bonded directly to the detectors (e.g. Bicep2) or connected to them via superconducting flexible circuits (e.g. Spider). The SSAs may be operated at a warmer
temperature, typically 1-4 Kelvin, in order to better manage their significant power
dissipation.
The complete open-loop response function of this system is a sinusoidal composition of the modulation curves of the three SQUID stages. The warm electronics
provide bias currents and flux offsets for all three stages, to control the shapes and
relative alignments of the various modulation curves. The warm electronics linearize
this complex response function through flux feedback to the first-stage SQUIDs, keeping each locked at an appropriate point along its modulation curve. This feedback
constitutes the recorded signal for each detector.
2.3
Warm electronics
The most mature warm electronics for time-division multiplexing in CMB work
and related fields is the Multi-Channel Electronics (MCE), developed by UBC for
SCUBA-2 [3]. Each MCE crate contains all of the low-noise DACs, ADCs, and digital processing necessary to operate a full TDM array of up to 32 columns and 41
rows. This includes providing TES and SQUID bias currents, SQUID flux biases, and
operating a digital-PID feedback computation for each TES simultaneously. Each
circuit board in the crate is controlled by an FPGA, allowing for feature additions
and bug fixes through firmware updates. The entire crate communicates with a control computer through a single fiber optic pair, ensuring electrical isolation. Multiple
MCEs can be synchronized with one another (and with external hardware) using a
shared “sync box”, which distributes trigger signals and time stamps from a crystal
oscillator.
The MCE is controlled and read out by a mature and versatile software code base,
developed by the UBC group and the larger user community. Robust automation
of biasing, data acquisition, and error recovery with minimal human intervention
has been demonstrated for kilopixel arrays, both for terrestrial receivers and for for
the balloon-borne Spider instrument. Both software and firmware development are
ongoing, regularly incorporating feature requests from the various instrument teams.
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2.4
Interconnects
Like all systems in which the multiplexing operation is carried out outside the detector wafer, the NIST TDM system makes heavy hybridization demands. In order to
limit parasitic resistance, the connection between the TESs and first-stage SQUIDs
must be superconducting. We must typically make at least six superconducting
wire bonds per TES: two from detector to circuit board, two from circuit board
to multiplexer chip, and two between multiplexer and Nyquist chips. Intermediate
flexible circuits such as those used by Spider and Advanced ACTPol add four additional bonds per TES. This hybridization job can be automated using automatic
bonding tools, or replaced with a multi-connection (though typically less reversible)
process such as indium bump-bonding. Connections between the multiplexer chips
and SSAs can be made with superconducting Nb wiring for low parasitic resistance
and acceptable thermal isolation.
In the TDM system the number of wires to ambient temperature scales roughly
as the perimeter of the 2D readout array, while the pixel count scales as the area.
The voltage-summing scheme requires one pair per row (row select) and four per
column (bias and feedback for the first-stage SQUIDs and SSA). These connections
are typically twisted pairs with few-MHz bandwidth. Multiplexer performance is
not especially sensitive to cable resistance (typical fielded values are in the 100200 Ω range round-trip), so there is some flexibility in cable construction to ensure
low thermal conductance where appropriate. Spider, for example, has successfully
operated with 3 m twisted-pair cables from 4 K to ambient temperature.
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3.1
Key performance characteristics
Achieved multiplexing factor
As with other multiplexing systems, the achievable multiplexing factor is constrained
by the ratio of readout bandwidth to TES bandwidth. TES bandwidth is generally
bounded below at several kHz by considerations of stability [17], so higher multiplexing factors require higher readout bandwidth. Readout bandwidth is typically
set by the SQUID amplifier and interconnects, notably by the L/R time constant
of the first-stage SQUIDs driving the SSA input coil, and the RC time constant of
the cables to ambient temperature. Readout chain bandwidths of ∼6 MHz has been
demonstrated for X-ray systems with voltage-summing TDM [13].
CMB and sub-millimeter instruments have been fielded with multiplexing factors
of 32 (ACT, Bicep2, Spider) and 40 (SCUBA-2) TES channels per readout column,
5
both based upon flux-summing TDM with a typical bandwidth of ∼2-3 MHz. Bicep3
has deployed voltage-summing TDM with a muxing factor of 22, but this was driven
by focal plane architecture rather than the multiplexer itself. Advanced ACTpol
is currently deploying an array with a multiplexing factor of 64 using the higherbandwidth voltage-summing TDM [16]. The QUBIC team has recently demonstrated
a 128-fold TDM system using custom electronics, notably by passing some of the rowswitching and amplification burdens to a cryogenic (60 K) integrated circuit [18].
3.2
Noise
Since the readout chain’s bandwidth must be much higher than the sampling rate
of any given TES, noise from the SQUIDs and warm amplifiers is heavily aliased.
As an example, Bicep2 with a 25 kHz TDM revisit frequency experienced ∼14%
aliased noise penalty to its total (photon-noise-dominated) NET [19]. This aliasing
contribution was dominated by excess detector noise, which will not be present in all
TES designs (and affects other multiplexing schemes as well); the impact of aliased
SQUID/amplifier noise alone was negligible. The aliasing penalty for r.m.s. noise is
proportional to the square root of the multiplexing factor, but there is some freedom
to limit the aliasing impact by reducing detector resistance or adding turns to the
SQUID input coil.
3.3
Thermal budget
Current instruments dissipate ∼10 nW per readout column at the detector temperature (100-300 mK). This should not scale strongly with multiplexing factor, since it
is dominated by the single first-stage SQUID that is operational at any given time.
Need numbers from Kent for 11-way mux, said to be lower. The EPIC-IM
study group [20] assumed that this might be reduced by a factor of two, but this has
not been a high priority for current ground-based instruments.
The series SQUID arrays dissipate substantially more power: ∼1 µW per readout
column. This power may be dissipated at a somewhat higher temperature (typically
1–4 K), and so is typically not a limiting factor.
The cryogenic cabling transports power to the cold stages, which must be accounted for in cooler specifications. As an example, a 1.5 m run of 38 AWG Manganin wire, intercepted at 50 K halfway down, is expected to dump ∼40 µW per
32-channel readout column on the 4 K stage.
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3.4
Crosstalk
TDM has several known crosstalk mechanisms, generally of modest amplitude [2, 7].
In recent designs each first-stage SQUID detects current from neighboring input coils
(adjacent rows in the same readout column) inductively at the ∼0.3 % level, and at
a yet smaller level to more distant rows. If the multiplexer bandwidth is inadequate
(i.e. the multiplexing factor is too high), each pixel may propagate signal to the
succeeding row in the same column due to inadequate settling; this is small in a
well-designed system (e.g. ∼-34 dB in Bicep2). There can also be small (<-20 dB)
crosstalk of large signals within a readout row due to shifting of the MCE’s common
ADC/DAC grounds. More complex nonlinear crosstalk may occur in the presence of
very large signals or DAC swings (e.g. massive cosmic rays or SQUID “flux jumps”),
but these are rare in terrestrial operation.
3.5
Warm electronics power and space requirements
A typical full-sized (72-HP) MCE crate serving a ∼1000 pixel (32 column by 32 row)
array consumes 85 watts, supplied by custom linear or switched DC supplies. The
crate dimensions are approximately 40 × 43 × 34 cm (depth / width / height) and
weighs approximately 13 kg, not including separate DC supplies. There has been
some effort to modestly reduce power consumption for specific experiments, e.g. the
Spider balloon-borne instrument.
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Discussion
4.1
Technology pros and cons
Key advantages of the time-division multiplexer include:
• Heritage the TDM system has almost a decade of field experience on science
instruments, leading to dozens of publications involving a total of more than
10,000 detectors. The software and hardware are well-characterized and wellsupported.
• Demonstrated multiplexing factor Fielded instruments have used multiplexing factors of 32 and 40, with 64 on the immediate horizon for Advanced
ACTPol. Deployed MHz frequency-domain multiplexing factors have been 8 –
16× thus far, with 40× and 64× deploying shortly with POLARBEAR-2 [21]
and SPT-3G [22], respectively.
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• Cable properties Deployed instruments have used relatively simple twistedpair cryogenic cables, as much as 3 m long.
Key challenges for this technology include:
• Cryocable count Since row-switching in TDM is carried out at ambient temperature, wires to room temperature are required for each row as well as each
column. That leads to a relatively high wire count per pixel: roughly 3 pairs
to sub-Kelvin per readout column for a 32×32 array.
• Power dissipation The first-stage SQUIDs dissipate power at the focal plane
temperature: ∼10 nW per readout column, substantially exceeding the typical
dissipation from the TESs and bias resistors.
• Hybridization Like other technologies where multiplexing is separated from
the detector wafer, the hybridization requirements are substantial: at least six
bonds per TES, plus three per readout column.
4.2
Path toward high multiplexing factors
Suppose that we start from the Advanced ACTpol 64-way multiplexer. It is plausible that careful tuning of TES and SQUID properties (and expansion of the readout
system) could double readout bandwidth while halving TES bandwidth, for a total factor of order ∼200. Larger factors seem difficult to reconcile with current
interconnect bandwidth and TES stability concerns. Such a multiplexing system
would currently, for each 32-column (6400 TES) readout array, incorporate more
than 70,000 Josephson junctions at base temperature, require ∼264 wire pairs to
base temperature, dissipate ∼320 nW at base temperature per array.
Larger multiplexing factors would likely require significant technology changes.
One promising avenue is the use of a code-division multiplexer scheme
√ [23] should
allow for more efficient use of bandwidth, in principle by a factor of Nmux . Hybrid
schemes between MHz time-division and GHz frequency-division multiplexing might
allow for yet higher factors, at least in principle [24].
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