Active All-Pass / Phase Equalizer for Group-Delay Shaping
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Active all-pass / phase equalizers reshape phase and group delay while keeping magnitude nearly unchanged, so transients, imaging, and multi-channel timing can be aligned within a measurable band. The goal is a repeatable, budgeted phase/τg correction that survives real hardware non-idealities, tolerances, and verification traps.
Core idea: An active all-pass / phase equalizer reshapes phase and group delay while keeping magnitude nearly unchanged, so timing/transient fidelity improves without “revoicing” the passband.
H2-1. What an Active All-Pass / Phase Equalizer Does (and When You Need It)
An active all-pass / phase equalizer is used when a signal chain needs timing/phase correction but should keep the passband magnitude essentially the same. It is the analog tool for group-delay shaping: smoothing in-band delay ripple, aligning channels, and improving transient accuracy.
- Transient smear: attacks/edges feel softened even when amplitude response looks “right”.
- Stereo image shift: L/R localization changes with frequency; phase mismatch is audible.
- Multi-channel misalignment: channels do not line up in time (e.g., array sensors, multi-path measurement chains).
- Pulse/step distortion: step response overshoots or “leans” due to frequency-dependent delay.
- Timing errors in measurement: time-of-arrival, cross-correlation, or gating thresholds drift with frequency content.
- In-band phase curvature that turns into group-delay ripple.
- Channel-to-channel phase/delay mismatch within a defined correction band.
- Delay “bumps” around crossovers or analog blocks that cause timing skew.
- Clipping/compression, headroom collapse, or slew-limited waveform distortion.
- Large magnitude ripple or stopband requirements (use magnitude filters/biquads for that).
- Noise floors dominated by source impedance or upstream stages (budget first, then correct).
- Amplitude looks OK but transients/time alignment are wrong → phase/group-delay correction is a good first suspect.
- Amplitude errors dominate (clear peaks/dips) → correct magnitude first, then revisit phase correction.
- THD/noise budget is tight → treat phase EQ as an added analog stage that must be justified by measurable timing gain.
Next step: translate the observed timing/phase error into an in-band group-delay target that can be measured and fitted.
H2-2. Group Delay in Practice: What You Actually Correct
In practice, the correction target is in-band group-delay error: frequency-dependent timing shift that smears transients or breaks channel alignment. Group delay is the slope of unwrapped phase, so the measurement must be stable and coherent before any fitting is attempted.
- Delay: a near-constant time shift (mostly harmless if consistent across channels).
- Group delay τg(f): frequency-dependent delay that reshapes the time-domain waveform.
- Phase φ(f): the underlying representation; τg(f) is derived from its unwrapped slope.
The most actionable target is τg ripple inside the correction band, plus channel-to-channel τg skew if alignment matters.
Use when the goal is transient fidelity or consistent timing across the band. Acceptance is usually defined by τg ripple staying below a system budget.
Use when a channel must match a known reference path (multi-channel, calibration fixtures, measurement comparators). The objective is a bounded residual to the reference τg(f).
- Correct only where the response is measurable, stable, and relevant to the application.
- Do not “chase” noisy out-of-band phase; it produces fragile fits and tolerance sensitivity.
- Define the correction band explicitly: fL…fH with a guardband for process/temperature.
With a measurable τg(f) target, all-pass sections can be synthesized and verified without drifting into magnitude-filter territory.
- Unwrap integrity: phase should not show random 2π jumps in-band.
- Coherence: low coherence makes τg look “spiky” and unfittable.
- Probe loading: probe capacitance and grounding can change phase more than the DUT.
Example criteria format: in-band τg ripple < X, channel τg skew < Y, and residual to target profile < Z. Choose X/Y/Z from the system timing/noise budget and verification repeatability.
H2-3. The All-Pass Building Blocks You’ll Actually Use (1st/2nd-Order Sections)
Practical phase equalization is built from a small set of repeatable all-pass sections. Each section keeps the passband magnitude close to unity, but reshapes phase φ(f) and therefore group delay τg(f). The design goal is to match a measured in-band τg(f) error profile using a limited number of sections that remains robust to tolerance and drift.
- All-pass target: reshape phase so τg(f) meets the in-band goal; keep |H(f)| nearly unchanged.
- Section knobs: a 1st-order section provides broad, gentle shaping; a 2nd-order section creates a localized delay bump.
- Band discipline: section tuning is referenced to the correction band only (do not chase out-of-band phase noise).
A 1st-order section is the workhorse for slow, wideband delay shaping. It rotates phase smoothly and creates a wide, low-amplitude change in group delay across frequency.
Place the corner roughly where the measured τg(f) begins to deviate. Use 1st-order sections first to remove broad structure before adding localized bumps.
A 2nd-order section concentrates delay shaping around a center frequency ω0. It is used to correct a localized timing feature such as a “bump” or “dip” in the measured τg(f).
Move ω0 to align the bump with the frequency region where residual timing error is concentrated.
Higher Q → narrower and taller bump (more sensitive to tolerance and drift). Start with lower Q, then refine.
- Phase adds: cascading all-pass sections sums phase contributions.
- Group delay adds: τg(f) contributions add, enabling step-by-step matching to a target profile.
- Practical limit: more sections increase noise/THD risk and tolerance sensitivity—use the fewest that meets the pass criteria.
Next step: choose a PCB-friendly topology that realizes these sections with stable tuning and predictable non-idealities.
H2-4. Practical Architectures: How Active All-Pass Is Implemented on Real PCBs
The math sections in the previous chapter must be mapped onto a PCB-friendly circuit architecture. The choice is driven by tuning needs, tolerance stability, and chain constraints (single-ended vs differential). The goal remains the same: keep the passband magnitude near unity while achieving the required in-band τg(f).
- Best for: predictable tuning of ω0/Q using familiar resistor/cap ratios.
- Watch out: finite GBW/SR shifts phase and can create magnitude tilt; section interactions may require buffering.
- Tuning handle: adjust section ratios for ω0 and Q; keep component families matched.
- Verification tip: measure τg on each section first, then cascade and re-check in-band residual.
- Best for: convenient parameter control when the design naturally uses integrator-style blocks.
- Watch out: integrator offsets and drift can move the effective phase; noise shaping may differ by output combination.
- Tuning handle: ω0 set by integrator time constants; Q set by feedback ratios.
- Verification tip: confirm phase unwrap stability; check temperature drift of ω0/Q.
- Best for: classic audio phase correction with intuitive networks and modest complexity.
- Watch out: matching/tolerance directly translates into phase error; tuning is less “orthogonal” than in biquads.
- Tuning handle: use matched RC pairs; keep thermal coupling consistent for repeatability.
- Verification tip: compare a bypass path vs equalized path to isolate the equalizer’s contribution.
- Best for: differential signal chains that require common-mode control and symmetric timing across the pair.
- Watch out: VOCM stability, imbalance from layout asymmetry, and output drive limits at target swing.
- Tuning handle: keep differential RC networks symmetric; maintain consistent loading on both legs.
- Verification tip: measure differential transfer and verify channel-to-channel (and leg-to-leg) τg skew within the band.
H2-5. Design Workflow: From “Measured Phase Error” to “All-Pass Sections”
A phase equalizer design should follow a repeatable workflow: define the correction band and pass criteria, measure a stable baseline φ(f)/τg(f), compute the required compensating profile, then implement and iterate with a closed loop until the in-band residual meets budget. The scope here is strictly phase/group-delay correction; magnitude filtering targets are not part of this workflow.
- Band: choose fL…fH (add a guardband to cover tolerance and drift).
- Target type: “flatten τg ripple” or “match a reference τg profile”.
- Pass criteria (placeholders): in-band τg ripple < X, channel τg skew < Y, and equalizer-induced |H| ripple < A as a guardrail.
- Measure outputs: unwrapped φmeas(f) and derived/direct τg,meas(f).
- Sanity checks: no random 2π jumps in-band; coherence/averaging sufficient for a smooth τg curve.
- De-embed: remove fixture/cable phase if it is not part of the target path.
- Define target: τtarget(f) = constant (flatten) or τtarget(f) = τref(f) (match).
- Residual: τerr(f) = τmeas(f) − τtarget(f) computed only inside the correction band.
- Compensation goal: τcomp(f) ≈ −τerr(f) in-band (band edges should be treated with guardband).
- Start broad: use 1st-order sections to remove slow structure in τerr(f).
- Then localize: add 2nd-order bumps near the largest residual features (ω0 at peak/valley).
- Q strategy: begin with low Q and increase only if residual width demands it (high Q is tolerance sensitive).
- Simulate with op-amp models and loads to predict section interaction and drift sensitivity.
- Build/measure τg,hw(f), compute in-band residual, then update ω0/Q (or ratios) iteratively.
- Guardrails: track equalizer-induced |H| ripple and THD/noise penalty as “do-not-break” limits.
- Bypass path: enable A/B comparison and service isolation without rework.
- Trim points: reserve small-range R/C trims where ω0/Q sensitivity is highest (especially high-Q sections).
- Freeze: lock component families and accept only if the in-band τg residual meets budget with guardband across temperature.
H2-6. Non-Idealities & Error Budgets (Why “Flat Magnitude” Won’t Stay Flat)
An all-pass section is “magnitude-flat” only in the ideal math model. Real implementations add poles/zeros through finite loop gain, output impedance, large-signal limits, and component drift. These non-idealities can distort phase, introduce small |H| ripple, and grow the in-band τg residual that the equalizer was meant to reduce. Treat them as an error budget, not as surprises discovered after layout.
- Finite loop gain adds extra phase lag and can tilt magnitude in-band.
- Loading and interaction between cascaded sections changes the realized ω0/Q.
- Signal-dependent behavior (slew/headroom) makes phase differ between small-signal and large-signal conditions.
Impact: phase lag + small |H| droop; section interaction grows. Hook: limit ω0/Q per stage; include op-amp model in the fit loop.
Impact: amplitude-dependent phase shift and higher THD at large signal. Hook: define test level in pass criteria; keep margin from rails.
Impact: in-band noise penalty; τg curve becomes less repeatable. Hook: avoid excessive resistor values; reduce stage count where noise dominates.
Impact: ω0/Q shift → over/under-compensation; high-Q is most sensitive. Hook: NP0/C0G, matched networks, symmetric placement, optional trim.
Impact: drift grows residual over time; calibration may be needed. Hook: specify warm-up and drift limits; add guardband or re-trim triggers.
- Residual budget: allocate how much τg residual is allowed after equalization across tolerance and temperature.
- Guardrails: limit equalizer-induced |H| ripple and THD/noise delta to avoid “fixing timing by breaking quality”.
- Stop rule: do not add sections when improvement is below measurement repeatability or when guardrails are violated.
- If temperature drift pushes the in-band τg residual beyond guardband → reserve trim points or schedule re-calibration.
- If τg differs strongly between small-signal and large-signal tests → revisit headroom/SR limits before increasing Q.
- If τg measurement is not repeatable inside the band → improve test setup (coherence/averaging/de-embed) before fitting more sections.
H2-7. Synthesis Patterns That Work (Without Overfitting)
Robust analog all-pass synthesis should prioritize repeatability and manufacturability over a visually perfect fit. Overfitting usually appears as excessive section count, overly narrow delay bumps (high Q), or “corrections” outside the verified band. The patterns below keep phase equalization stable across tolerance, temperature, and measurement repeatability limits.
Only correct the band that can be verified with stable measurements. Out-of-band phase often becomes dominated by fixtures, probing, unwrap artifacts, or noise.
- How: fit/optimize with zero or near-zero weight outside fL…fH, and add a guardband at band edges.
- Pass: in-band τg residual meets target while out-of-band behavior is not used to drive tuning.
Add sections only when the residual error is repeatable and “shaped” (broad hump or localized bump). Random jaggedness is usually measurement repeatability, not a correctable feature.
- How: measure repeatability first; treat it as the lower bound of achievable residual.
- Stop rule: if one more section improves residual less than repeatability (or violates guardrails), stop.
Wide corrections are more tolerant to drift. Narrow, high-Q bumps should be reserved for the final residual and used only when the tolerance/temperature budget allows.
- How: use 1st-order for broad shaping; use 2nd-order with low Q to pin the main feature; increase Q only if required.
- Pass: highest Q appears only where the residual width demands it and remains stable across tolerance corners.
A “perfect” nominal fit often has zero margin. Real systems require guardband for R/C tolerances, op-amp parameter spread, temperature drift, and aging.
- How: evaluate corners/Monte Carlo inside the correction band; reduce Q or N if stability is not met.
- Pass: in-band τg residual stays below the limit across tolerance + temperature while |H|/THD/noise guardrails remain intact.
H2-8. Measurement & Verification: How to Measure Group Delay Without Lying to Yourself
Group delay is derived from phase, so the fastest way to “lie to yourself” is to accept phase data that is corrupted by probing, poor coherence, or unstable unwrap. Verification should use a method that matches the band and accuracy needs, then apply a short checklist that rejects measurements that are not repeatable inside the correction band.
- FRA/VNA: calibrated frequency response → unwrap φ(f) → τg(f). Best for precision and repeatability.
- Dual-channel FFT transfer function: estimate H(f)=Sxy/Sxx with coherence monitoring; good for audio/DAQ benches.
- Chirp + cross-correlation: time alignment from correlation; then infer delay vs band segments (field-friendly, needs window discipline).
- Step/deconvolution: sanity check only; bandwidth limits and ringing can mislead τg if used as a primary method.
Quick check: phase changes when probe type/ground lead changes. Fix: use low-C or differential probing; short ground spring; minimize loop area.
Quick check: isolated 2π jumps create τg spikes. Fix: improve SNR/averaging; constrain unwrap to the correction band; avoid fitting edge artifacts.
Quick check: low coherence regions show jagged τg. Fix: increase averaging, adjust windowing, raise stimulus while staying in linear range.
Quick check: changing cable/fixture length shifts phase materially. Fix: measure and subtract a reference path; keep the setup fixed for verification runs.
- In-band ripple: passband τg ripple_pp < X (or < X% of target delay).
- Skew: channel-to-channel τg skew < Y µs inside fL…fH.
- Guardrail: equalizer-induced |H| ripple < A dB in-band.
- Guardrail: THD/noise delta < B under the specified stimulus level and load.
Each criterion should be bound to stimulus amplitude, load, averaging/coherence settings, and temperature conditions to ensure reproducibility.
H2-9. Implementation Details: Stability, Headroom, and Layout Rules
A phase equalizer only works when its phase behavior is repeatable on real hardware. Instability, early clipping inside a section, and layout-caused drift can all destroy group-delay correction even when the magnitude response looks “flat”. The rules below focus strictly on phase stability, headroom, and layout practices that keep τg predictable.
Cascaded all-pass sections can load each other and shift the realized ω0/Q. High-Q sections are the most sensitive to source impedance and next-stage input networks.
- Action: place broad/low-Q shaping first; place narrow/high-Q bumps later to reduce upstream stress.
- Action: add a buffer only when section-to-section loading changes in-band τg beyond the repeatability floor.
- Quick check: compare τg with the next stage disconnected or replaced by a high-Z probe load.
- Pass: adding downstream stages does not shift the in-band τg profile beyond the residual budget.
Magnitude can look flat while internal nodes clip or enter slew-limited behavior. This often shows up as amplitude-dependent phase and a sudden τg error increase at higher level.
- Action: bind verification to a specified stimulus level and load; do not tune at one level and validate at another.
- Action: reserve extra headroom around high-Q bumps and near their ω0 region.
- Quick check: sweep level and verify τg/φ does not “move” once within the linear region.
- Pass: τg criteria hold at the maximum intended signal level without violating THD/noise guardrails.
Supply impedance and unpredictable return paths can add phase modulation and reduce repeatability. This is especially visible when τg is derived from small phase changes.
- Action: place local decoupling tight to each amplifier supply pin to keep the HF loop short.
- Action: keep the signal return path continuous; avoid crossings over splits in the reference plane.
- Quick check: a different probe ground method should not materially shift in-band phase.
- Pass: repeated measurements produce consistent τg curves within the repeatability floor.
High-impedance nodes are vulnerable to leakage, flux residue, and humidity. Leakage changes effective R/C and shifts ω0/Q, turning a stable correction into over/under compensation.
- Action: use guard rings around sensitive nodes; keep them short and away from “dirty” routing regions.
- Quick check: repeat τg measurements after warm-up or humidity/temperature change and watch for band shifts.
- Pass: τg residual remains within guardband across the specified temperature range.
If a differential chain is used, asymmetry and local heating create channel mismatch and delay skew. Thermal gradients can also shift matched R/C ratios unequally.
- Action: route differential pairs symmetrically; mirror critical R/C placement and keep environments matched.
- Action: keep heat sources away from the most sensitive section(s), especially high-Q bump stages.
- Pass: channel-to-channel τg skew meets the target across temperature with stable repeatability.
H2-10. Calibration Hooks & Serviceability (Make It Field-Tunable)
Even a well-designed phase equalizer will drift under component tolerance, temperature, and aging. Practical systems need controlled trim points, safe bypass, and repeatable verification hooks so delay correction can be maintained in production and in the field. This section focuses on hooks that are specific to all-pass equalization (ω0/Q and section interaction), not general-purpose calibration theory.
- Rule: trim only parameters that move ω0/Q in a controlled and monotonic way inside the correction band.
- Rule: avoid placing tunable elements on noise-sensitive or distortion-sensitive nodes unless the range is small and verified.
- Pass: code steps shift τg in the expected direction without breaking |H| ripple and THD/noise guardrails.
Best for production consistency. Small step banks can tune ω0/Q with predictable sensitivity and low drift.
Use only where distortion/noise risk is acceptable and the tuning range is limited. Validate monotonicity and repeatability before committing to field tuning.
Useful for coarse adjustment or temperature compensation when an OTA-tunable stage is used. Keep the loop verifiable and guard against bias noise coupling.
- Bypass: a safe “equalizer off” path enables A/B verification and faster debugging when performance degrades.
- Loopback: a repeatable measurement path reduces setup variance and prevents false tuning caused by fixture changes.
- Pass: equalize mode improves in-band τg residual while bypass mode remains clean and stable for reference.
- Trigger: in-band τg residual exceeds guardband after warm-up or temperature shift.
- Workflow: warm-up → measure τg → choose trim code → re-measure → lock.
- Storage: store trim code + version + temperature point (concept only) for service traceability.
- Enter loopback / fixed measurement conditions.
- Read current trim code and revision.
- Toggle bypass to confirm whether the equalizer is the dominant cause.
- Adjust trim in small, monotonic steps (coarse → fine) while tracking τg residual.
- Store the final trim code and re-verify guardrails (|H| ripple, THD/noise delta).
H2-11. Applications (Audio & Measurement) — What “Good” Looks Like
An all-pass / phase equalizer is justified only when phase or group-delay error is the dominant problem. This section translates “phase correction” into repeatable acceptance checks for audio and measurement chains—without expanding into amplitude-equalization topics.
Audio A) Crossover phase alignment (keep magnitude intact, align time)
- Correct only the band that affects the crossover handoff (a bounded window around fxover).
- Target: reduce group-delay ripple and/or control phase difference between ways in that window.
- Measure transfer functions for both ways with the same reference point and fixture.
- Compute phase & group delay in the correction band (unwrap sanity + coherence checks).
- Use an A/B bypass path to confirm improvements are caused by the equalizer, not measurement drift.
- In-band group-delay ripple: τg,pp ≤ (5–10)% of target delay (starting point; set by system tolerance).
- In-band phase mismatch: |Δφ| ≤ X° (set X by localization and crossover slope requirements).
- Magnitude integrity: A/B change in |H| ripple ≤ 0.2–0.5 dB in the same band (starting point).
- Different mic/fixture placement between runs creates false “phase improvements.”
- Correcting beyond the verified band increases sensitivity to tolerance and drift.
Audio B) Transient fidelity & stereo imaging (reduce delay bumps that smear attacks)
- Identify structured τg “bumps” in the audible band and flatten only those features.
- Prioritize broad corrections first; add narrow/high-Q bumps only if residual error is repeatable and measurable.
- Channel-to-channel delay skew in the correction band: < Y µs (set Y by localization/measurement tolerance).
- Level sensitivity: τg shift vs amplitude sweep stays inside guardband (no large-signal phase drift).
Measurement) Pulse/step chains & multi-channel time alignment
- Step/impulse timing features drift with frequency content.
- Channels are “clock-aligned” but response-aligned still fails (transfer functions differ).
- Primary: transfer function → phase unwrap → group delay (repeatability + coherence).
- Secondary: time-domain sanity check only (avoid “single-shot” conclusions).
- Always include A/B bypass and a fixed fixture/loopback mode for reproducibility.
- In-band τg,pp stays below budget and remains stable across repeated runs.
- Channel-to-channel skew < Y µs in the specified band after warm-up.
H2-12. IC Selection & Engineering Checklist (Procurement + Bring-Up)
Selection for all-pass / phase equalizers is not about “highest specs.” It is about preserving the intended phase response under real loading, tolerance, temperature drift, and large-signal conditions—while keeping magnitude ripple small. The lists below are procurement-ready and verification-driven.
A) Op-amp / FDA requirements that actually protect phase correction
- Phase margin in the real section: stable with the intended R/C network and output load (no “mystery peaking”).
- GBW / bandwidth headroom: keeps the intended all-pass phase shape from collapsing (especially high-Q bumps).
- Slew rate & output swing: avoids large-signal phase drift and THD spikes that invalidate A/B verification.
- Noise: prevents correction from increasing in-band noise floor and reducing τg measurement coherence.
- Output drive: remains linear into the expected load and any isolation resistor / anti-alias interface.
- THD vs frequency at the expected output swing (not only small-signal plots).
- Stability guidance for capacitive loads and multi-stage chains.
- Input common-mode range and output swing vs load for the chosen supply rails.
- Noise density and 1/f corner (if low-frequency phase work matters).
B) Passive components (what keeps ω0/Q and delay bumps from drifting)
- Capacitors: prefer C0G/NP0 for the time-constant-setting caps to minimize temperature and voltage coefficient effects.
- Resistors: thin-film parts for low drift and predictable matching; matched networks reduce section-to-section variation.
- Guardbanding: design the residual error budget to survive tolerance + temperature drift (avoid razor-thin fits).
- C0G MLCC (0603, 50V):
GRM1885C1H102JA01D(1 nF),GRM1885C1H103JA01D(10 nF) - Thin-film resistor (0603, 0.1%):
TNPW060310K0BEEA(10 kΩ)
C) Field-tunable / production-friendly building blocks (trim + bypass)
- Switchable R/C banks for coarse section tuning without touching the analog core.
- Digital pots in controlled spots (small-signal nodes) for fine trim; validate noise/linearity impact.
- A/B bypass path for fast verification and fault isolation (bring-up and service).
- SPI digital potentiometer:
AD5270BRMZ-20(20 kΩ, 1024 taps, MSOP) - Low-voltage analog mux (4:1):
ADG704BRMZ-REEL7 - Precision mux (8:1):
TMUX1108
D) Reference amplifier part numbers (audio / differential / measurement)
OPA1656IDR— low-noise/low-distortion audio op-amp (SOIC-8)OPA1612AIDR— ultra-low-noise bipolar audio op-amp (SOIC-8)
THS4551IRGTT— wideband fully differential amplifier (VQFN/VSSOP family; orderable addendum applies)ADA4940-1ARZ-R7— low-noise/low-distortion differential ADC driverOPA1632DGNR— fully differential audio amplifier (note: some legacy order codes are obsolete; use active alternatives)
- Use them as datasheet anchors; choose the exact package/grade based on supply, temperature, and assembly constraints.
- Verify stability with the intended all-pass section values and downstream load before freezing procurement.
Engineering checklist (design → layout → test → production)
- Define correction band (fL…fH) and measurable pass criteria (τg,pp, skew, |H| ripple).
- Start with low section count; add sections only for repeatable residual structure.
- Headroom plan per node: identify the first clipping point (even if magnitude is “flat”).
- Include an A/B bypass path and test points for phase/τg verification.
- Keep return paths continuous; avoid cutting ground under sensitive analog nodes.
- Place decoupling at each amplifier supply pin pair; minimize loop area.
- Guard high-Z nodes (leakage + contamination sensitivity); keep them short and clean.
- For differential: enforce symmetry (length/impedance/component placement) to avoid skew.
- Unwrap sanity: avoid τg spikes from bad unwrap settings or low coherence regions.
- Use averaging/windowing consistently; confirm repeatability before “optimizing” section values.
- A/B bypass compare is mandatory: confirm phase/τg improvement without magnitude damage.
- Amplitude sweep: check τg does not drift with level (large-signal nonlinearity trap).
- Trim plan: coarse bank → fine trim (if used); validate monotonicity and sensitivity.
- Warm-up/soak rule: define “stable” by metrics, not time alone.
- Acceptance limits: τg,pp, channel skew, |H| ripple delta, and noise/THD delta vs bypass.
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H2-13. FAQs
These FAQs are strictly about phase / group-delay correction using active all-pass sections. Each answer uses the same 4-line, measurable structure: Likely cause / Quick check / Fix / Pass criteria.
Scoring rule: evaluate τg/phase only inside the verified correction band, and always report A/B vs bypass for repeatability. If distortion or magnitude errors dominate, fix headroom/linearity first.
