SQUID-based Readout Schemes forMicrocalorimeter Arrays

• Mikko Kiviranta• Heikki Seppä• Jari S. Penttilä• Juha Hassel

• Jan van der Kuur• Piet de Korte• Martin Frericks• Wouter van Kampen• Piet de Groene

The Technical ResearchCenter of Finland

The Space Research Organization of the Netherlands

Motivated by the XEUSmission by the ESA

Single-pixel signal path

Absorber Transition edge SQUIDamplifier

Room-temperatureamplifier

Non-fedback bare parameters:

Power gain

−T

Tbath121 α ( ) 128 −

jSQCLπω Can be very large

BandwidthT

T

CG Input coil

resonanceCan be up to GHz’s or more

Dynamicrange

B

T

kG

TT

4∆

TkCL BjSQ4/14/3

0

8.9Φ ~ 109 with standard

analog circuits

Use negative feedback to trade gain for bandwidth & dyn rangeUse positive feedback to trade BW & dyn range for gain

The designer’s job

Dynamicrange

Phonon noise floor

X-ray maximumenergy / CT

(Absorber melts :)

Transitionnon-linearity

Johnson noiseSQUID noise

SQUIDnon-linearity

Gain

GainGain

RT amplifiersaturates

RT amplifier noise

Pow

er le

vel

• Take care of the bandwidths, too.• FB modifies input & output impedances (noise matching)

+_ +_

Standard arrangement for the feedback paths ...

“Electro-ThermalFeedback (ETF)”

“Flux Locked Loop”

+_

… but there’s a number of other possibilities, eg. :

“Temperature-locked loop”

+_ +_Local FBfor the SQUID

What if we have a large number of pixels?Direct readout:• Feasible (compare: MEG devices)• Heat leak through the wires• Complex and fragile

Correlation-based schemes:• Noises are summed - bad• Acceptable only when SNR can tolerate summation

2D-array: 3 x 3 pixels 3D-array: 2 x 2 x 2 pixels

Wiring to 20 mK stage(2.8 µWh cooling capacity [XEUS])

Multiplexing:• Fingerprint signals by multiplying by an orthogonal set of functions f1(t), f2(t) … ( sines & cosines; Hadamard functions; wavelets … )• Sum to a single wire• Detect the signals by multiplying with the same set f1(t), f2(t) … and integrate over all times• Multiplier: (i) TES, (ii) SQUID, (iii) some extra device

(a) (b) (c) (d) (e)

Hadamard codes(Karasik & McGrath)

Sines & cosines“frequency MUX”

Timeslot functions“time domain MUX”

Modified timeslotfunctions for enhancedduty cycle (4ch versionsare symmetrically bipolar)

TESes as modulators• I(t) = G(t) × Ub(t)• Conductance G carries the signal• Bias voltage carries the modulating function• No direct thermal response: average RMSheating• Magnetic nonlinearity?• Only N wires from TES chip to SQUID chip for N×M pixels• Only N SQUIDs

Current through TES oscillates ...

... creating oscillatory R-response (only one half shown)

SQUID as modulator

• Signal is multiplied by SQUID responsefunction I = MITES× ∂ I/ ∂ Φ.• ∂ I/ ∂ Φ is a non-linear function of Ub• Works best with two-level mod-functions• m × n wires from TES chip to SQUIDchip, if cannot be integrated monolithically

Noise folding

Without noise blockers

With noise blockers

Noise gets foldedto other pixels

No noise folding

• Wideband noise is added after the modulator• The noise from a given pixel aliases into frequency bands / timeslots / codes of other pixels• (i) Provide gain so that noise summing can be tolerated.• (ii) Use frequency-preferring / timeslot-preferring / code- preferring noise blocker.• In case of freq. MUX, the blocker is just an LC resonator• With other MUX schemes, active elements and external clock signal feeds are needed

Filter implementation

X-ray absorbersand TESes

Noise-blockingLC filters

• L is set by stability requirement• 80 nH fits in ~ 0.2 × 0.2 mm• C implementability sets lower limit to f ~ 25 MHz• Magnetic cross-coupling demands ~ 1 mm filter-to-filter separation: (i) crosstalk between different columns (ii) limits total BW available to a column• Band separation

- Only to avoid noise folding- Channel confusion: taken care bypost-detection filters

ω1

ω2

ωn

Common inductance in a column

• Parasitic inductance Lp in wiring: reactive parttuned out with Cc , Lp limits the bandwidth.

• Magnetic cross-coupling (example)appears as common series inductance, like Lp

• Transformers ramp up the impedance level, tohelp with parasitic L

23M 24M 25M 26M 27M-50

-40

-30

-20

-10APLAC 6.24 User: VTT Automation Jul 25 2001

40pH in series, not tuned out

log

[R]

Freq [Hz]|Z(w)|

23M 24M 25M 26M 27M-50

-40

-30

-20

-10APLAC 6.24 User: VTT Automation Jul 25 2001

40pH in series, tuned out

log

[R]

Freq [Hz]|Z(w)|

23M 24M 25M 26M 27M-50

-40

-30

-20

-10APLAC 6.24 User: VTT Automation Jul 25 2001

2nH in series, tuned out

log

[R]

Freq [Hz]|Z(w)|

10 mΩΩΩΩ

100 mΩΩΩΩ

• SQUID input inductance Lin can bescreened away with negative feedback

fRIIL n

nin ∆==

πε

421 2

2XEUS: R = 10 mΩ24 hbar for 32 chansseparated by 200 kHz

Wiring parasiticsTuneout cap

SQUID input

Quantum-limited bandwidth:

• Feedback by flux injection or current injection

Ifb

Dynamic range

TES current: iFWHMn

pp

EE

II

τ∆××= max36.222

~ 5 × 106 for XEUS

SQUID:Limited by self-noise

TkCL BjSQn4/14/3

00

8.92/ Φ=

ΦΦ ~ 2.4 × 107 for T = 1 K,

Cj = 0.5 pF, LSQ = 4 pH (ε ~ 2.2 hbar)

SQUID:Limited by cablenoise & RT amplifier nBjSQn TkCL 4/14/3

00

3.52/ Φ=

ΦΦ ~ 8 × 106 , when

Tn = 10 K + 20 K (for 30MHz RT amp + cables)

Need some more dynamic range for linearity ?• Harmonic production by an event ? (No, falls above the signal band)• Mixing between an event & imperfect idle current balancing ? (Probably not)• Mixing between two coincident events ? (Not likely if pixels are scattered)• Gain stability ? (Probably yes)

Dynamic range - how to improve ?

• Alleviate DR requirement?Increase integration time (= filtersettling time), still retaining thermalstability condition.

• Array SQUID for sqrt(n) -fold DR improvement?

• Long negative feedback at carrier freq. through RT not feasible, but...… (i) FB through low-dissipation MOS amplifier at 20 K?

… (ii) FB through RT at baseband rather than carrier frequency?

Filters againstnoise folding ...

… replaced byduplex filters

Total system: a scenario

Adaptive idle currentcancellation: grayed out