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Scientific Reports

Maximizing multiplexing in 1–100 MHz frequency domain readout of transition edge sensor arrays via crosstalk suppression

Xin Gao, Qian Wang, Jing-Yi Zhang, Zhiyong Long

Published Aug 3, 2026• 0 citations
Publisher

Abstract

Abstract The 1-100 MHz frequency band remains relatively unexplored for Frequency Division Multiplexing (FDM) readout of TransitionEdge Sensor (TES) arrays, despite its potential to increase channel counts beyond the traditionally used 1-5 MHz range. Thisgap, however, is becoming increasingly addressable with advancements in the fabrication of high-resonance-frequency LCresonators and wide-band Superconducting Quantum Interference Devices (SQUIDs). It still partly stems from understudiedcrosstalk challenges in this higher-frequency regime, where mutual inductance, SQUID input inductance, and carrier leakageeffects tend to be more pronounced, which may limit the feasibility of high-multiplexing systems.In this work, we aim to addressthis less explored area by modeling crosstalk between the 1-100 MHz range under a lumped-parameter framework, with afocus on static crosstalk (ECTstatic)—a metric that has received less attention in lower-frequency studies. To mitigate mutualinductance, we propose a chessboard pixel arrangement that maximizes frequency differences between adjacent channels.Leveraging the 1-100 MHz bandwidth with a 0.1 MHz channel spacing, this configuration can suppress crosstalk by up to 59.4dB.Our simulations show that with this layout and through dynamic carrier frequency design, reducing mutual inductance to 3nH enables 186 channels under a 1% ECTstatic constraint when the SQUID input inductance is 1 nH; this count increases to 299channels when the input inductance is reduced to 0.5 nH. Relaxing the threshold to 3.2% or 10% further expands the channelcounts—for instance, reaching 612 or 2067 channels with 1 nH input inductance, respectively.This study preliminarily exploresthe crosstalk characteristics of 1-100 MHz FDM for TES arrays, offering a framework for low-crosstalk, high-channel-countreadout systems and highlighting key trade-offs in this relatively unexplored frequency range.

DOI
10.1038/s41598-026-49891-4

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Abstract The 1-100 MHz frequency band remains relatively unexplored for Frequency Division Multiplexing (FDM) readout of TransitionEdge Sensor (TES) arrays, despite its potential to increase channel counts beyond the traditionally used 1-5 MHz range. Thisgap, however, is becoming increasingly addressable with advancements in the fabrication of high-resonance-frequency LCresonators and wide-band Superconducting Quantum Interference Devices (SQUIDs). It still partly stems from understudiedcrosstalk challenges in this higher-frequency regime, where mutual inductance, SQUID input inductance, and carrier leakageeffects tend to be more pronounced, which may limit the feasibility of high-multiplexing systems.In this work, we aim to addressthis less explored area by modeling crosstalk between the 1-100 MHz range under a lumped-parameter framework, with afocus on static crosstalk (ECTstatic)—a metric that has received less attention in lower-frequency studies. To mitigate mutualinductance, we propose a chessboard pixel arrangement that maximizes frequency differences between adjacent channels.Leveraging the 1-100 MHz bandwidth with a 0.1 MHz channel spacing, this configuration can suppress crosstalk by up to 59.4dB.Our simulations show that with this layout and through dynamic carrier frequency design, reducing mutual inductance to 3nH enables 186 channels under a 1% ECTstatic constraint when the SQUID input inductance is 1 nH; this count increases to 299channels when the input inductance is reduced to 0.5 nH. Relaxing the threshold to 3.2% or 10% further expands the channelcounts—for instance, reaching 612 or 2067 channels with 1 nH input inductance, respectively.This study preliminarily exploresthe crosstalk characteristics of 1-100 MHz FDM for TES arrays, offering a framework for low-crosstalk, high-channel-countreadout systems and highlighting key trade-offs in this relatively unexplored frequency range.
In order to read out current signals from large-scale arrays of transition edge sensors (TES), microwave SQUID multiplexers (MW-MUX) have been developed by several groups. Reduction of crosstalk induced in the multiplexer is important in order to maintain the energy resolution or the noise equivalent power of detector arrays. In the present study, crosstalk between channels in MW-MUX with five different designs is experimentally evaluated. The resonance frequency separation is ten times as large as the resonator bandwidth. Without flux-ramp modulation, crosstalk between two adjacent channels neighboring in position decreases to ≈1 × 10-3with increasing resonance frequency separation to ≈100 MHz. Crosstalk between SQUID channels neighboring in resonance frequency also decreases to 4 × 10-3with increasing the distance to 2.5 mm. We show that nonlinear error can occur due to the crosstalk with flux-ramp modulation. Flux readings from a well-designed multiplexer exhibit crosstalk of less than 1 mΦ0peak-to-peak and nonlinear errors of less than 2 mΦ0peak-to-peak, which is sufficient for the readout of the gamma-ray TES arrays being developed. These results can provide guidelines for suppressing both the crosstalk and the nonlinear error to less than the criterion of TES spectrometers with typical energy-resolving ability.
We describe the development of a frequency-domain multiplexer (MUX) to read out arrays of superconducting transition-edge sensors (TES). Fabrication of large-format arrays of these sensors is becoming practical; however, reading out each sensor in the array is a major instrumental challenge. Frequency-domain multiplexing can greatly simplify the instrumentation of large arrays by reducing the number of SQUID's (superconducting quantum interference devices) and wires to the low temperature stages. Each sensor is AC biased at a different frequency, ranging from 380 kHz to 1 MHz. Each sensor signal amplitude-modulates its respective AC bias frequency. An LC filter associated with each sensor suppresses Johnson noise from the other sensors. The signals are combined at a current summing node and measured by a single SQUID. The individual signals from each sensor are then lock-in detected by room temperature electronics. Test chips with fully lithographed LC filters for up to 32 channels have been designed and fabricated. The capacitance and inductance values have been measured and are close to the design goals. We discuss the basic principles of frequency-domain multiplexing, the design and testing of the test chips, and the implementation of a practical system.
The frequency domain multiplexing (FDM) readout of arrays of transition edges sensors for the X-IFU/Athena and SAFARI/SPICA instruments requires SQUID amplifiers with low input inductance, low flux noise, high-dynamic range and low power consumption. We report the performance of two-stage SQUID amplifiers developed at VTT coupled to multiple high-Q LC resonators of the SRON FDM readout operating in the frequency range from 2 to 5 MHz. The SQUIDs have been tested in the following configurations: 1) the two SQUIDs at base temperature with open input; 2) the amplifier SQUID at 1K temperature and the front-end SQUID at base temperature in the FDM readout of low-G TES bolometers; and 3) and in the FDM readout of X-ray microcalorimeter arrays with both SQUIDS at base temperature. We measured an input flux noise equal to 0.18 μΦ0/Hz1/2at 20 mK, equivalent to an energy resolution of 9 b. The measured current noise at the SQUID input is ~1 pA/Hz1/2at 20 mK, which corresponds to a coupled energy resolution of about 15 b.
We describe our frequency-domain readout multiplexer for transition-edge sensor (TES) bolometers and present measurements of an eight-channel multiplexer. Each sensor is biased with a sinusoidal bias at a distinct frequency. As the sensor absorbs power, it amplitude-modulates its sinusoidal bias. Sensor currents are summed and measured with a single superconducting quantum interference device (SQUID) array. The SQUID array consists of 100 dc-SQUID's in series and is operated with shunt feedback electronics which have a slew rate of 1.210/sup 7/ /spl Phi//sub 0//s. A tuned filter consisting of an inductor and capacitor are placed in series with each sensor to both limit the bandwidth of the Nyquist noise from each sensor and to allow us to bias all multiplexed sensors with a common wire. We place an upper limit on crosstalk between adjacent channels of 0.004, well below our design requirements. Demodulated noise spectra from multiplexed sensors show the expected white noise levels at frequencies above 200 mHz.
Abstract A microwave SQUID multiplexer ( μ MUX) with a high multiplexing factor is a promising readout approach for large-scale superconducting transition-edge sensor (TES) bolometer arrays. This paper reports on the characteristics of 16-channel μ MUX prototype chips and a 60-channel readout module developed to read out TES bolometers for the Ali cosmic microwave background polarization telescope (AliCPT). We designed two different coupling structures between the resonator and the radio-frequency superconducting interference device: design A with a mutual inductance ( M T ) of 2.3 pH and design B with an M T of 6.5 pH. For design A, the mean resonator bandwidth ( Δ f BW ) and peak-to-peak frequency shift ( Δ f pp ) are approximately 610 kHz and 290 kHz, respectively. The measured mean open-loop current noise is less than 40 pA / Hz . Preliminary results indicate that crosstalk between adjacent channels is below 1% in our design A μ MUX chip. A measured channel with design B shows a Δ f BW of 586 kHz and a current noise of 33 pA / Hz , similar to the design A channels. In comparison, the Δ f pp of 803 kHz is much larger than the design A channels due to a larger M T . The readout module, consisting of two design A chips and two design B chips, shows 60 resonances, corresponding to a yield of 94%. In the future, we will place 32 design A channels within the same chip dimension to increase the channel density and build a larger readout module suitable for AliCPT TES arrays.
We describe the development of a frequency-domain multiplexer (MUX) to read out arrays of superconducting transition-edge sensors (TES). Fabrication of large-format arrays of these sensors is becoming practical; however, reading out each sensor in the array is a major instrumental challenge that is possibly solved by frequency-domain multiplexing. Each sensor is AC biased at a different frequency, ranging from 380 kHz to 1 MHz. The sensor signal amplitude-modulates its respective AC bias frequency. An LC filter associated with each sensor suppresses Johnson noise from the other sensors. The signals are combined at a current summing node and measured by a single superconducting quantum interference device (SQUID). The individual signals from each sensor are then lock-in detected by room temperature electronics. Test chips with fully lithographed LC filters for up to 32 channels have been designed and fabricated. The capacitance and inductance values have been measured and are close to the design goals. We discuss the basic principles of frequency-domain multiplexing, the design and testing of the test chips, and the implementation of a practical system.