29-EFT.WP.TBN.Measurement v1.0 | Chapter 3 | Acquisition Front-End & Timebase (ADC / Trigger / Time Tags)

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Chapter 3 | Acquisition Front-End & Timebase (ADC / Trigger / Time Tags)

• One-line objective: Define coherence and error conventions for the acquisition front-end (ADC/AFE) and trigger/timebase/reference; provide computable postulates and workflows for phase/frequency and dual-form arrival-time measurements so that raw observations are traceable, comparable, and persistable.
  (All path integrals are taken along gamma(ell) with measure d ell.)
• I. Scope & Objects
• Inputs
• Front-end & channels: AFE={gain, BW, ENOB}, ADC={Fs, N, jitter_rms}, anti_alias={f_c, ENBW}, multi-channel MIMO/differential acquisition configs.
• Trigger & time tags: trig={type∈{ext,int,pps,twoway}, jitter_rms}, unified computed time tau_mono and publication instant ts, reference clock refclk with priors on offset/skew/J.
• Signals under test: x(t) (I/Q or pulse/timestamps), nominal frequency f_ref, measurement window W=[ts-Δt, ts], window function w(t).
• Outputs
• Normalized raw measurement: raw = {samples, meta} with unit/dimension/convention/window/bandwidth declared.
• Front-end & timebase coherence report, plus pre-check parameters prior to estimating S_phi/S_y/sigma_y.
• Dual-form arrival-time prep: sampling/timebase coherence for T_arr^{form1/form2} and the front-end error component feeding delta_form.
• Boundary
• Focus on the acquisition chain (AFE/ADC/trigger/timebase/reference). Algorithms & statistics are in Chs. 4–5; path/environment corrections are in Chs. 6–7.
• II. Terms & Variables
• Sampling & quantization: Fs (sample rate), Ts=1/Fs, N (bits), ENOB, q=V_FS/2^N (quantization step).
• Jitter & triggering: sampling jitter t_j, trigger jitter t_trig, reference-clock deviation offset, slope skew, and noise J(t).
• Noise & bandwidth: front-end equivalent input noise V_n, anti-alias cutoff f_c, RBW/ENBW (window & spectral-estimation bandwidths).
• Arrival time & path: T_arr, c_ref, n_eff(f,x), gamma(ell), delta_form.
• Dimension exemplars: unit(Fs)=[1/T], unit(t_j)=[T], unit(S_phi)="rad^2/Hz", unit(T_arr)=[T].
• III. Postulates P503-*
• P503-1 (Timebase anchoring): All sample timestamps must map to the unified computed time tau_mono and be published at ts; offset/skew/J must be persisted.
• P503-2 (Explicit measures): Acquisition and evaluation must declare W, w(t), and RBW/ENBW; all integrals use ( ∫_{t∈W} · dt ), ( ∫_{f∈B} · df ).
• P503-3 (Dimensional compliance): Fields entering equations—Fs/ENOB/jitter/offset/skew/J—must pass check_dim( y - f(x) ); conversions dB↔linear and rad↔cycle are written to scale.note.
• P503-4 (Channel coherence): Multi-channel/differential acquisition must report cross-channel bias/phase/delay and include them in uncertainty and contracts.
• P503-5 (Dual-form readiness): Provide a coherent timebase and sampling tolerance to support T_arr^{form1/form2} integrals; downstream assertion delta_form ≤ tol_Tarr.
• IV. Minimal Equations S503-*
• Sampling jitter as equivalent phase/frequency noise
• S503-1 (small-jitter approximation): sampling instants t_n = nTs + t_j(n), phase error at carrier f_c
  φ_j(n) ≈ 2π f_c t_j(n); if t_j is white, S_phi,j(f) ≈ (2π f_c)^2 S_tj(f).
• S503-2 (frequency-deviation spectrum): S_y,j(f) = ( f / 2π f_ref )^2 S_phi,j(f) (see Ch. 2).
• Quantization and front-end equivalent noise
• S503-3 (uniform quantization, in-band): N_q ≈ q^2/12, equivalent SNR_q ≈ 6.02N + 1.76 (dB);
  ENOB = (SNR_meas - 1.76)/6.02.
• S503-4 (front-end noise to phase): S_phi,AFE(f) ≈ S_v(f) / (k_v A)^2 (where k_v is the phase-detector/demod phase constant, A the carrier amplitude).
• Trigger and reference coherence
• S503-5 (time-alignment mapping): t_rx = (1+skew) t_tx + offset + J(t);
  trigger contribution to arrival time: ΔT_trig ≈ t_trig,rms (in RMS sense).
• S503-6 (PPS/Two-Way bias): round-trip τ_loop = τ_fwd + τ_rev, bias offset ≈ (τ_fwd - τ_rev)/2 (symmetric-path approximation).
• Anti-aliasing and bandwidth consistency
• S503-7 (RBW/ENBW): periodogram resolution Δf ≈ 1/Δt, Ŝ(f) = P(f)/ENBW; ENBW is set by w(t) and must be published.
• S503-8 (out-of-band leakage correction): sidelobe leakage L_sidelobe enters u(Ŝ) and the window/bandwidth gates of C50-2x.
• Preparatory quantities for dual-form arrival time
• S503-9: maintain a consensus timebase for T_arr and hand off to Ch. 6:
  T_arr^{form1} = ( 1 / c_ref ) ( ∫_{gamma} n_eff d ell ),
  T_arr^{form2} = ( ∫_{gamma} ( n_eff / c_ref ) d ell ),
  and record the front-end contribution to u(delta_form | front-end).
• V. Metrology Flow M50-3 (Ready → Acquire → Check → Persist)
• Ready
• Bind refclk and tau_mono/ts; record ADC/AFE specs; set W, w(t), RBW/ENBW; freeze RefCond (source/version/hash/validity/coverage).
• Acquire
• Synchronize trigger and sampling; record t_j/t_trig and cross-channel biases; obtain raw.samples and meta.
• Check
• Estimate S_phi,j/S_y,j and quantization/front-end noise; apply ENBW correction; validate t_rx=(1+skew)t_tx+offset+J(t);
• Derive front-end-achievable precision for S_phi/S_y/sigma_y and compare to CRLB;
• Provide a consistent time axis for the T_arr dual forms and a front-end error budget u(delta_form|front-end).
• Persist
• manifest.tbn.frontend = {ADC:{Fs,N,ENOB,jitter}, AFE:{gain,BW,ENBW}, trig:{type,jitter}, refclk:{offset,skew,J_model}, window:{Δt, w, RBW, ENBW}, spectra_guard:{S_phi,j,S_y,j}, sync_model, cross_channel:{delay,phase}, Tarr_support:{timebase, u(delta_form|front-end)}, RefCond, contracts.*, signature}.
• VI. Contracts & Assertions C50-3x (Suggested thresholds)
• C50-301 (Timebase anchoring): |offset| ≤ offset_max, |skew| ≤ skew_max, |J|_p95 ≤ J_max.
• C50-302 (Sampling/trigger jitter): t_j,rms ≤ t_j,max, t_trig,rms ≤ t_trig,max; violations → downgrade or reject.
• C50-303 (ENOB/SNR): ENOB ≥ ENOB_min or SNR_meas ≥ SNR_min.
• C50-304 (RBW/ENBW consistency): persisted RBW/ENBW matches window w(t); sidelobe leakage and resolution gates are met.
• C50-305 (Channel coherence): cross-channel delay/phase biases ≤ τ_ch,max / φ_ch,max.
• C50-306 (Dual-form readiness): the front-end contribution to delta_form_p95 meets budget for tol_Tarr; otherwise widen guardband or reacquire.
• VII. Implementation Bindings I50-3* (Interface prototypes, I/O, invariants)
• I50-31 acquire_timing(frontends, refs, cfg) -> {raw:{samples,meta}, status}
• I50-32 characterize_jitter(raw, Fs, f_c) -> {t_j_rms, S_tj(f), meta}
• I50-33 correct_enbw(spectrum, window_fn) -> {Ŝ(f), ENBW, meta}
• I50-34 check_trigger_sync(trig, timestamps) -> {offset, skew, J_model, pass}
• I50-35 cross_channel_align(streams) -> {delay, phase, u, pass}
• I50-36 frontend_to_twoform_budget(meta) -> {u(delta_form|front-end), report}
• I50-37 emit_frontend_manifest(results, policy) -> {uri, status}
• Invariants: two_forms_present=true; check_dim(*) passes; RefCond/hash is traceable; window/bandwidth and window function are persisted.
• VIII. Cross-References
• Ch. 2 (mathematical baseline for S_phi/S_y/sigma_y and dual-form T_arr); Chs. 4–5 (estimators & Allan family);
• Chs. 6–7 (link delays & environmental corrections); TimeBase/Sync (synchronization model and offset/skew/J); Instrument (loopback/peer calibration);
• PathCorrection/Packets/PathRedshift (path & propagation dual forms, dispersion/FSO/worldline).
• IX. Quality & Risk Control
• SLIs/SLOs: offset/skew/J_p95, t_j,rms, ENOB/SNR_min, RBW/ENBW compliance rate, cross_channel_bias, front-end share of delta_form_p95.
• Fallback strategies: unstable trigger/reference → replace source or re-align; insufficient ENOB/SNR → reduce bandwidth/apply windowing/increase averaging; t_j over limit → clock cleaning or external sampling; dual-form budget over limit → widen guardband and rebuild path/environment parameters.
• Audit: acquisition & sync configs, source hashes, verification reports and evidence URIs, manifest signature chain and replay scripts.
• Summary
• This chapter fixes the engineering conventions for the acquisition front-end and timebase: timebase anchoring, jitter & quantization, RBW/ENBW, cross-channel coherence, and dual-form readiness.
• Anchored by M50-3 / C50-3x / I50-3* and manifest.tbn.frontend, it ensures consistent, traceable, and auditable inputs for downstream phase/frequency estimation, dual-form T_arr integration, and operational publication.