{"id":"c5d0aa62-517d-4b4c-a6c4-0eb4dbe2b932","arxiv_id":"2509.01850","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"A Thevenin-equivalent circuit analysis shows electrothermal feedback suppresses Johnson noise from the bolometer but not Johnson noise from external series resistance, which sets a noise floor at high loop gain.","lead":"This paper derives formulas for how electrical noise is suppressed in superconducting bolometer detectors when they are read out with alternating current and have extra unwanted resistances in the wiring. The result matters for building next-generation cosmic microwave background detectors, because it shows wire resistance sets a noise floor that more feedback cannot remove.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (11) rests on an unjustified phase-independent treatment of Johnson noise in the AC power balance: Re(V_J I)=|I|V_J discards the phase on which ETF cancellation depends.","rationale":"The reader's weakest_assumption is the same phase-independent Johnson-noise treatment, so I agree. My stress-test focuses on that step because it is upstream of the algebra: Eq. (5) is the bridge between the circuit equations and the ETF loop-gain result; if its phase treatment is wrong, every downstream expression is affected. The reader's separate observation that Eqs. (9)-(10) look algebraically inconsistent with Eq. (7) is also real and independently supports REJECT: solving Eq. (7) for δRb yields a factor R_b |Z|^2 (R_b - R_Thév), not R_b^2 (R_b - R_Thév), unless a compensating definition of L is supplied, and no such definition is given. I would not soften the reader's REJECT: the main result is claimed as exact for arbitrary parasitic impedance, but both the phase assumption and the apparent algebra error leave Eq. (11) unsupported. The qualitative asymmetry at high loop gain is plausible and is the kind of result that could survive a corrected derivation, but the paper as written overclaims exactness.","tokens_in":8067,"tokens_out":13914,"duration_ms":148462,"concrete_test":"Model VJb and VJTh as complex Gaussian noise phasors with random phase and RMS amplitudes sqrt(8kT R Δf); solve the linearized KVL and thermal balance (Eqs. 2-4) exactly for δI as a function of the noise phasors; compute the output NEI PSD by ensemble-averaging |δI|^2 and compare the low-frequency result with Eq. (11). If the ensemble average reproduces Eq. (11), the phase-independent replacement is valid; if phase factors or cross terms differ, Eq. (5) and the central suppression claim fail.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central result Eq. (11) is built on Eq. (5), which is obtained after the statement (just before Eq. 5) that Johnson noise voltages are \"phase-independent white noise amplitudes with Re(V_J I)=|I|V_J.\" In the linearized AC circuit, the power fluctuation on the thermal island is the real part of a voltage-current cross product; for a noise phasor V_J near the bias frequency, the low-frequency beat with the bias current is Re(V_J I0* e^{iΔωt}), whose amplitude and sign depend on the relative phase of V_J and I0. Replacing this with a fixed scalar |I|V_J is not a standard small-signal noise operation. ETF responds to this phase-dependent beat; the amount of Johnson current that survives is determined by that phase. If the correct ensemble-averaged phasor treatment gives a different coefficient in Eq. (5), then Eqs. (7), (9)-(11) do not follow, and the claimed high-loop-gain asymmetry between on-island and off-island Johnson noise is not established. This is independent of, and more fundamental than, the R_b^2-vs-|Z|^2 inconsistency between Eqs. (7) and (9).","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript develops a Thevenin-equivalent circuit model for Johnson noise in AC-biased TES bolometers read out through a general series impedance z_Thev = R_Thev + iX_Thev. It derives an expression for the total noise-equivalent current (NEI), Eq. (11), and claims that electrothermal feedback suppresses bolometer Johnson noise by (1+L) while leaving parasitic Johnson noise from R_Thev unsuppressed. The framework is clear and the zero-parasitic limit reproduces the familiar V_J,b/[R_b(1+L)] suppression. I checked the derivation algebraically. The main result does not follow from the paper's own equations: (i) the loop gain defined in Eq. (6) is dimensionful and differs from the standard loop gain in the ideal limit; (ii) solving the paper's own power-balance equation (7) gives factors |Z|^2 in deltaR_b that are absent from Eqs. (9)-(10), changing the numerical prediction substantially (e.g., 0.42 vs 0.54 V_J,b for R_b=1, R_Thev=0.2); (iii) Eq. (5) is inconsistent with Eqs. (3)-(4) for finite reactance; and (iv) the phase-independent treatment of Johnson noise is an unproven shortcut. The qualitative asymmetry claim may survive a corrected derivation for real impedances, but the quantitative content of the paper is not valid as written.","tokens_in":8358,"tokens_out":58002,"duration_ms":489209,"significance":"The intended contribution is practically relevant: frequency-multiplexed TES readouts contain parasitic series impedance, and a closed-form NEI would help analyze systems like SPT-3G and LiteBIRD. The explicit, parameter-free, algebraically checkable nature of the derivation is a genuine strength - it makes the verification above possible. The qualitative message (off-island Johnson noise is not suppressed by ETF at high L) is important and appears correct for purely resistive parasitics. However, the checkability cuts both ways: the printed formulas fail their own algebra check at several load-bearing points, so the quantitative results - the point of the paper - cannot be used.","major_comments":[{"comment":"The loop gain as printed is dimensionally inconsistent: alpha V^2/(G T_b R_b) is dimensionless, but (R_b^2 - |z_Thev|^2)/|Z|^4 has units of Ohm^-2, so L is dimensionful. In the zero-parasitic limit z_Thev=0 this reduces to L = alpha V^2/(G T_b R_b^3), not the standard loop gain alpha V^2/(G T_b R_b). Yet the reduction claimed after Eq. (9) (deltaI_b = V_J,b/(R_b(1+L))) and the suppression factor (1+L)^2 in Eq. (12) require the standard, dimensionless loop gain. Equation (6) therefore introduces a spurious factor R_b^2/|Z|^2 into every subsequent expression and must be corrected before Eqs. (9)-(12) can be interpreted.","section":"§3, Eq. (6)"},{"comment":"Solving the bolometer-noise case of Eq. (7) (V_J,Thev=0) gives deltaR_b = L/(1+L) * V_J,b/V * R_b^2(R_b - R_Thev)|Z|^2/(R_b^2 - |z_Thev|^2); the factor |Z|^2 is missing in the printed deltaR_b, and consequently Eq. (9) has 1/Z inside the bracket where the exact solution gives |Z|^2/Z. The parasitic case Eq. (10) has the same defect. A numerical check for R_b = 1 Ohm, R_Thev = 0.2 Ohm, X_Thev=0, L=1: printed Eq. (9) gives |deltaI_b| = 0.54 V_J,b, whereas the solution of Eq. (7) gives 0.42 V_J,b. Because Eqs. (9) and (10) are the building blocks of Eq. (11), the advertised main result is not the NEI of the stated model.","section":"§4, Eqs. (9)-(10) vs Eq. (7)"},{"comment":"For X_Thev != 0, Eq. (5) does not follow from Eqs. (3)-(4). Expanding deltaP_b = Re(deltaV_island I0* + V_island0 deltaI*) with Eq. (4) and using the paper's own substitution Re(V_J I) = |I| V_J yields a parasitic-noise coefficient 2 R_b V_J,Thev V/|Z|^2, whereas Eq. (5) has (R_b - R_Thev) V_J,Thev V/|Z|^2 + V_J,Thev V/|Z|; these agree only when X_Thev=0. The claim following Eq. (11) that no assumptions are made on the parasitic impedance is therefore unsupported; Eq. (11) is only consistent with Eq. (5) in the purely resistive case.","section":"§3, Eq. (5)"},{"comment":"The substitution 'Re(V_J I) = |I| V_J' is an ad hoc modelling step, not a standard noise operation. For a noise component at omega +/- Omega, the down-converted power beat with the AC bias is Re(V_J I0* e^{i Omega t}), whose amplitude and sign depend on the random relative phase of V_J and I0; the electrothermal feedback response, and hence the surviving current fluctuation, depend on that phase. Replacing the phasor product by a fixed scalar pre-averages the very quantity the feedback acts on. The result should be checked against a two-sideband linearized calculation (complex thermal-electrical responsivity) with the output PSD averaged over the noise phase; a simple series R-L-C parasitic circuit would suffice as a test. This concern is independent of the algebraic errors above: even with corrected coefficients, the factor conventions (amplitudes vs. two-sided PSDs, V_J^2 = 8kTR) are n","section":"§3, before Eq. (5)"}],"minor_comments":[{"comment":"The caption says 'representative system parameters' but no parameter values are given; the figure is not reproducible and the claimed trends cannot be verified.","section":"Fig. 2"},{"comment":"The text mixes amplitude notation (V_J, 'V_J,b != 0') with spectral densities (V_J,b^2 = 8kT_b R_b). Readers should be told whether all quantities are PSDs (per Hz) or rms amplitudes, and whether densities are one- or two-sided.","section":"Eq. (8) and surrounding text"},{"comment":"Formatting issues: 'Th´ evenin' appears with broken accents; Eq. (6) is rendered ambiguously (missing parentheses make the denominator hard to parse); the symbols NEP/NEI are never explicitly defined.","section":"Throughout"},{"comment":"The sentence 'No assumptions have been made regarding the magnitude of the parasitic impedance' is misleading given that Eq. (5) fails for X_Thev != 0 (major comment 3) and Eq. (12) explicitly restricts to X approximately 0.","section":"After Eq. (11)"}],"recommendation":"reject","confidential_remarks":"To the editor: the rejection is driven by algebra that can be verified by substitution into the paper's own equations (most clearly, Eqs. (7) vs. (9)). I also note that the same loop-gain definition is attributed to the author's SPIE paper [7] and is already implemented in the DfMux analysis code [9]; if [7]/[9] contain the same erroneous L, the error could affect deployed noise modeling. This is a fit concern for the journal, but the manuscript errors are sufficient grounds for rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: the qualitative point is worth taking seriously—series resistance in AC-biased TES readouts adds Johnson noise that electrothermal feedback won't suppress at high loop gain—but the paper's central result, Eq. (11), is not established. Solving the paper's own Eq. (7) gives a different expression than Eq. (9): the numerator should be |Z|^2, not R_b^2. That is not a minor typo; it changes the claimed exact result for arbitrary impedance. There is also a more fundamental problem with Eq. (5). The power fluctuation from a noise voltage in the AC linearized circuit depends on the phase of the noise phasor relative to the bias current. The paper just states Re(V_J I) = |I| V_J, treating it as a scalar. That is not a standard small-signal treatment; only the in-phase component of the Johnson noise couples to ETF. A correct derivation would split the noise into quadrature components. Without that, the asymmetry between on-island and off-island noise isn't properly derived.\n\nWhat's good: the Thevenin framing is clean, the distinction between island and parasitic noise is the right one to draw, and the Taylor expansion in Eq. (12) gives practical guidance for system design. The author knows the literature and the context; the references are appropriate. The qualitative conclusion about parasitic resistance setting a noise floor is likely right and useful for experiments like SPT-3G and LiteBIRD.\n\nBut between the algebra error and the phase assumption, the exact formulas in Eqs. (9)–(11) are not trustworthy. The paper also overstates that it made 'no assumptions' about the parasitic impedance. If the author fixes the algebra and redoes the power balance with a proper treatment of noise quadratures, the paper could be salvageable. As it stands, it is not ready for publication. It deserves a serious referee, because the question is important and the groundwork is decent, but I would not cite it in its current form.","headline":"Useful qualitative insight about parasitic Johnson noise in AC-biased TES readouts, but the central formula contains a clear algebra error and the power-balance derivation uses an unjustified phase-independent treatment of noise.","tokens_in":8814,"tokens_out":9205,"would_cite":false,"duration_ms":95179,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"In AC-biased TES bolometers, electrothermal feedback suppresses Johnson noise from the bolometer but not from external series resistance.","keywords":["transition-edge sensor","Johnson noise","electrothermal feedback","Thevenin equivalent circuit","noise-equivalent current","frequency-domain multiplexing","parasitic impedance","AC bias"],"falsifier":"Measure the current-noise spectral density of a TES as a function of bias voltage while a known series resistor is inserted at the bias line. If the noise floor at high loop gain approaches 8kT_parasitic R_parasitic / |Z|^2 rather than decreasing as 1/(1+L), the asymmetry claim is confirmed; if the parasitic term is suppressed along with the bolometer term, the claim fails. A phase-resolved AC circuit simulation would settle the same question by checking Eq. (11) against a random-phase calculation.","tokens_in":7948,"feed_emoji":"📉","tokens_out":6052,"duration_ms":70936,"temperature":0.7,"pith_summary":"Transition-edge sensor bolometers rely on voltage bias and electrothermal feedback to stabilize operation and suppress noise. This paper asks what happens when the bias circuit is not ideal but includes arbitrary series impedance—resistance and reactance from cabling, multiplexers, and other parasitics. Using a Thevenin-equivalent circuit, the author derives a closed-form expression for the total Johnson-noise-equivalent current. The central result is an asymmetry: feedback suppresses Johnson noise generated inside the bolometer's thermal island, but leaves Johnson noise from the external series resistance essentially unsuppressed at high loop gain. For instrument design, this means parasitic resistance sets a noise floor that no amount of feedback can remove.","feed_headline":"Parasitic resistance sets a Johnson noise floor no loop gain can remove","feed_subtitle":"Electrothermal feedback quiets detector Johnson noise but leaves series-resistance Johnson noise untouched.","key_machinery":"The carrying object is the Thevenin-equivalent circuit: any linear readout circuit collapsed to an ideal AC voltage source in series with a complex impedance z_Thev = R_Thev + iX_Thev, plus the bolometer resistance R_b on the thermal island. The associated electrothermal loop gain L encodes how strongly resistance changes feed back through electrical power dissipation. The main result, Eq. (11), combines the two incoherent Johnson contributions into the total noise-equivalent current; its structure shows different prefactors for island versus external noise, which is what produces the suppression asymmetry.","core_discovery":"The paper's central claim is that in an AC-biased transition-edge sensor, electrothermal feedback suppresses Johnson noise from the bolometer's own resistance but leaves Johnson noise from external series resistance essentially unsuppressed. This asymmetry is derived through a Thevenin-equivalent circuit: the entire readout external to the thermal island is collapsed into an ideal AC source plus a complex series impedance, and only the bolometer resistance and its Johnson source sit on the thermal island governed by the power-balance equation. Solving the linearized equations gives Eq. (11), a closed-form total noise-equivalent-current expression valid for arbitrary parasitic impedance, with","pith_inferences":["The island-versus-external split likely generalizes to other off-island noise sources: voltage noise injected anywhere in the Thevenin impedance should escape the (1+L) suppression, which could be tested by injecting a calibrated noise signal at the bias node.","Crosstalk between multiplexed channels acts through mutual Thevenin impedances; the same derivation could be applied per channel to predict how much crosstalk-induced noise survives feedback.","A direct experimental test: add a known series resistor on the bias line and vary its physical temperature while holding loop gain fixed; if the residual noise scales with the resistor's temperature and resistance, the unsuppressed parasitic term is confirmed."],"forward_implications":["For practical TES readout systems with resistive parasitics, increasing electrothermal loop gain indefinitely does not reduce Johnson noise; the unsuppressed parasitic term sets the floor.","Equation (11) provides a complete noise-equivalent-current formula for arbitrary complex Thevenin impedance, so noise budgets can include parasitic resistance and reactance without idealized-bias assumptions.","When reactance is tuned out and parasitic resistance is small, the series impedance has three first-order effects: it changes detector responsivity, reduces the impedance to noise current, and adds its own Johnson noise.","At high loop gain, the bolometer Johnson noise remains suppressed by roughly (1+L), while the parasitic Johnson noise persists at its full amplitude, so minimizing non-superconducting cables, inductor ESR, and coupling to normal metals is essential.","The finite-frequency extension replaces L by L/(1+iωτ), so the same framework describes noise suppression away from the low-frequency limit."],"supporting_citations":[{"why":"Establishes the voltage-biased strong-ETF operating mode that this paper generalizes to arbitrary parasitic impedances.","marker":"[2]"},{"why":"Introduces electrothermal feedback in TES detectors, the mechanism whose noise suppression is analyzed here.","marker":"[3]"},{"why":"Provides the standard statement that ETF suppresses bolometer Johnson noise, the baseline result extended by this work.","marker":"[5]"},{"why":"Documents realistic parasitic impedances in frequency-multiplexed SQUID readouts, motivating the Thevenin treatment.","marker":"[6]"},{"why":"Supplies the loop-gain definition and prior TES nonlinearity model that Eq. (6) builds on.","marker":"[7]"},{"why":"Supports setting beta = 0, the approximation used to simplify the power-balance equations.","marker":"[8]"}],"fun_headline_variants":["Feedback silences detector noise but not parasitic resistance noise","AC-biased TES: loop gain can't silence external resistor noise","Johnson noise from series resistance defeats electrothermal feedback","One noise source escapes TES feedback: the parasitic resistor","Why TES noise floor is set by untamable series resistance"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The calculation treats each Johnson noise voltage as a phase-independent white noise amplitude when computing dissipated power, using the scalar rule Re(V_J I) = |I| V_J; if the random phase relative to the bias current actually matters, every suppression factor would need to be recomputed.","fun_headline_variants_meta":{"raw":{"variants":["Feedback silences detector noise but not parasitic resistance noise","AC-biased TES: loop gain can't silence external resistor noise","Johnson noise from series resistance defeats electrothermal feedback","One noise source escapes TES feedback: the parasitic resistor","Why TES noise floor is set by untamable series resistance"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00092,"raw_usage":{"total_tokens":3746,"prompt_tokens":667,"completion_tokens":3079,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":411,"completion_tokens_details":{"reasoning_tokens":2999}},"tokens_in":411,"tokens_out":3079,"duration_ms":23697,"temperature":1.0,"reasoning_tokens":2999,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T12:09:28.142947+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the current-noise spectral density of a TES as a function of bias voltage while a known series resistor is inserted at the bias line. If the noise floor at high loop gain approaches 8kT_parasitic R_parasitic / |Z|^2 rather than decreasing as 1/(1+L), the asymmetry claim is confirmed; if the parasitic term is suppressed along with the bolometer term, the claim fails. A phase-resolved AC circuit simulation would settle the same question by checking Eq. (11) against a random-phase calculation.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the voltage-biased strong-ETF operating mode that this paper generalizes to arbitrary parasitic impedances."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces electrothermal feedback in TES detectors, the mechanism whose noise suppression is analyzed here."},{"cited_title":"Irwin and G","cited_arxiv_id":null,"evidence_quote":"Provides the standard statement that ETF suppresses bolometer Johnson noise, the baseline result extended by this work."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents realistic parasitic impedances in frequency-multiplexed SQUID readouts, motivating the Thevenin treatment."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the loop-gain definition and prior TES nonlinearity model that Eq. (6) builds on."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supports setting beta = 0, the approximation used to simplify the power-balance equations."}],"review_version":1}