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CMS ECAL Phase-2 upgrade: characterisation and stability analysis of a three-stage low-voltage power-conversion system

This paper characterizes the stability of a three-stage low-voltage power-conversion system for the CMS ECAL Phase-2 upgrade by validating Nyquist-based interface analysis and demonstrating that staggered converter enables effectively mitigate inrush currents to prevent overcurrent protection triggers.

Original author: Liv Anke Richter, Günther Dissertori, Werner Lustermann, Krzysztof Stachon

Published 2026-11-05

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CC BY 4.0

Original author: Liv Anke Richter, Günther Dissertori, Werner Lustermann, Krzysztof Stachon

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the author. For technical accuracy, refer to the original paper. Read full disclaimer

Deep inside the heart of the European particle physics community, a massive machine known as the Large Hadron Collider is preparing for its most intense era yet. To handle the sheer volume of data generated during these high-energy collisions, scientists are upgrading the detectors that record the results. One of the most critical components is the electromagnetic calorimeter, a device designed to measure the energy of particles with extreme precision. However, to function correctly in this new, high-luminosity environment, the electronics at the very front of the detector need a complete overhaul. These new electronics are incredibly sensitive and require very specific, low-voltage power to operate. The challenge lies in delivering this power. Simply running long cables from a distant power source would waste too much energy as heat, so engineers must bring the power conversion right to the point where the electronics sit. This creates a complex chain of power converters working together, and if they do not play nicely with one another, the entire system could become unstable, causing the detector to fail.

The researchers behind this study focused on a specific three-stage power system designed for the barrel section of the Compact Muon Solenoid detector. Imagine a relay race where the baton is electrical power. The first stage takes high-voltage electricity from the wall and converts it to a steady intermediate level. The second stage takes that intermediate level and steps it down further. The third and final stage delivers the precise, low voltages needed by the sensitive readout chips. While each of these stages works perfectly on its own, the danger arises when they are connected in a line. The output of one stage becomes the input for the next, and their electrical characteristics can interact in unexpected ways. If the timing and resistance of these interactions are not just right, small fluctuations can amplify into large oscillations, causing the power to wobble or shut down entirely. The team needed to prove that this specific chain of three converters would remain steady under all expected conditions.

To solve this, the team built a detailed digital model of the system and then verified it with real-world measurements. They did not just guess how the system would behave; they measured the electrical resistance and response of the actual hardware while it was running under load. They used a specialized instrument to inject tiny, harmless electrical signals into the connections between the stages to see how the system reacted. This allowed them to map out the behavior of the power flow across a wide range of frequencies. Their analysis confirmed that the system is stable. Even in the most demanding scenarios, where many converters are working together and long cables are involved, the system does not spiral into chaos. The mathematical distance between the system's behavior and the point of failure was found to be safe, with the closest approach to instability still leaving a comfortable margin. This means the power supply will not spontaneously oscillate or shut down due to internal interactions.

However, stability is not the only hurdle. The researchers also investigated what happens when the system is first turned on. When power is first applied, the capacitors inside the final stage act like empty buckets that need to be filled instantly. This sudden demand creates a surge of current, known as inrush current. In their initial tests, when two sections of the detector were powered up simultaneously, the combined surge was strong enough to trip the safety mechanisms of the second stage, causing the power to cut out before the system could even start. The team identified that the charging of capacitors in the final stage was the primary culprit. To fix this, they introduced a simple but effective timing strategy. Instead of turning on all the power converters at the exact same moment, they staggered the start times. By delaying the activation of certain converters by a fraction of a second, they spread out the demand for power.

The results of this adjustment were immediate and successful. With the staggered start sequence, the peak current drawn during startup dropped significantly, staying well below the safety limit that would trigger a shutdown. The system could now be powered up reliably without tripping its own protections. This work provides a clear path forward for the detector upgrade, ensuring that the complex power distribution network will remain steady during operation and start up smoothly when needed. The findings confirm that the design is robust, with the power flowing smoothly from the source to the sensitive electronics, ready to capture the next generation of particle physics discoveries.

Technical Summary: CMS ECAL Phase-2 Upgrade Power-Conversion System Characterisation

Problem Statement
The Compact Muon Solenoid (CMS) electromagnetic calorimeter (ECAL) barrel is undergoing a Phase-2 upgrade to support the High-Luminosity Large Hadron Collider (HL-LHC). This upgrade necessitates new front-end electronics requiring 1.2 V and 2.5 V supply rails. Distributing these low voltages from remote sources over long cables is inefficient due to prohibitive resistive losses ( $P_{loss} = I^2R$ ). Consequently, a point-of-load conversion strategy is adopted, resulting in a three-stage cascaded power-distribution system: an AC–DC rectifier (Stage 1), a 380 V to 12 V DC–DC converter (Stage 2), and low-voltage regulator (LVR) cards implementing 12 V to 1.2 V/2.5 V conversion (Stage 3).

While individual converter stages are stable, the interaction between cascaded stages can lead to instability. A regulated downstream converter acting as a constant-power load exhibits negative incremental input impedance, which can interact with the upstream converter's output impedance to amplify disturbances and cause oscillations. Additionally, the simultaneous turn-on of multiple converters in Stage 3 generates inrush currents that risk triggering the overcurrent protection of the Stage 2 supply.

Methodology
The authors employ a dual approach to assess system stability and transient behavior:

Small-Signal Stability Analysis:
- Modeling: Averaged small-signal models were constructed in LTspice. Stage 1 used a behavioral terminal model fitted to measured data. Stages 2 and 3 utilized canonical averaged switch models for synchronous buck converters, capturing control-loop dynamics and constant-power-load behavior while filtering out switching frequency effects.
- Measurement: In-situ impedance measurements were performed using a shunt-injection setup with a Bode 100 frequency-response analyser and a B-WIT 100 injection transformer. This allowed for the direct measurement of source output impedance ( $Z_{out}$ ) and load input impedance ( $Z_{in}$ ) under load conditions.
- Stability Criterion: Stability was assessed using the Nyquist criterion applied to the minor-loop gain, $T_m(s) = Z_{out}(s) / Z_{in}(s)$ . The analysis focused on the vector margin, defined as the minimum distance $|1 + T_m|$ from the critical point $(-1, 0)$ in the complex plane, rather than relying solely on the conservative Middlebrook magnitude condition ( $|Z_{out}| \ll |Z_{in}|$ ).
Turn-on Inrush Investigation:
- Oscilloscope measurements monitored the 12 V bus current during system startup.
- The study evaluated the impact of staggered converter enables on LVR cards (LVR5A and LVR5B variants), which utilize different RC delays on enable pins to sequence the startup of converter groups (A/B vs. C/D).

Key Results

Model Validation: Simulated terminal impedances showed good agreement with in-situ measurements up to approximately 1 MHz. Deviations observed above this frequency were attributed to unmodelled parasitic effects and signal-to-noise limitations.
Stability Assessment:
- Interface 1 (Stage 1–Stage 2): Despite local violations of the Middlebrook magnitude condition with ten parallel modules and short cables, the Nyquist plots showed no encirclement of the critical point. The minimum vector margin was calculated as 0.76 (occurring with a 100 m cable near 9 Hz).
- Interface 2 (Stage 2–Stage 3): For configurations involving one to two readout towers and cable lengths up to 40 m, no encirclement of $-1$ was observed. The minimum vector margin was 0.79 (at 0 m cable length with maximum capacitance). Cable damping was found to increase the stability margin.
Inrush Current Mitigation:
- Without staggering, the combined inrush current of two towers exceeded the 8.0 A overcurrent threshold of the Stage 2 MaraPOD supply, causing it to latch off.
- Implementing staggered enable configurations (LVR5A/5B variants) reduced the measured two-tower peak current to below 5 A, keeping operation safely within the protection threshold.

Significance and Claims
The paper demonstrates that the three-stage power-conversion system for the CMS ECAL Phase-2 upgrade is stable across evaluated configurations, provided that the specific staggered enable strategies are employed to manage inrush currents. The work validates the use of averaged converter models combined with in-situ impedance measurements to predict stability margins where traditional magnitude-based criteria are insufficient. The findings confirm that the system can operate reliably without oscillations and without tripping overcurrent protections, ensuring the power integrity required for the upgraded front-end electronics. The conclusions are explicitly limited to small-signal operation and rely on the accuracy of the fitted converter models.

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