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Op Amp Noise Modeling & Budgeting: en/in, BW Integration, 1/f vs Chopper

Op Amp Noise Modeling & Budgeting: en/in, BW Integration, 1/f vs Chopper

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This page turns op-amp noise specs into a repeatable system budget: model Zs(f), combine en/in and resistor noise at one reference (RTI/RTO), integrate with the correct ENBW, then validate with short → Rs → Rs+Cs tests. The result is a noise number you can trust—and a workflow that explains exactly which term dominates and how to fix it.

What this page solves: from datasheet noise to system error

This page turns op-amp noise specs into a repeatable, system-level budget that can be calculated and verified. The goal is not to list parameters, but to answer three practical questions: where noise comes from, how much falls inside the measurement bandwidth, and what the total becomes once everything is referred to a single reference point.

The 3 questions every noise budget must answer
  • From where: op-amp en and in, source impedance thermal noise, feedback-network resistor noise, and downstream stages (including measurement-chain noise).
  • Over what bandwidth: noise is defined inside an equivalent noise bandwidth (ENBW), not by a single “-3 dB” corner. Bandwidth must be stated for every reported RMS number.
  • Referred to where: all noise terms must be converted to one reference point before summing: RTI (input-referred) for fair part comparison, or RTO (output-referred) for meeting system limits at the output.
RTI vs RTO — enforce one reference

Use RTI to compare op amps and front-end concepts fairly. Use RTO to validate that the final output meets a system noise limit. A single budget must not mix RTI and RTO terms.

Budget currency — RMS first

Treat RMS noise as the primary budgeting unit because independent contributors can be summed by RSS. Peak-to-peak is a presentation metric that depends on observation time and probability.

Always state gain + ENBW

Any quoted noise number is incomplete without the closed-loop gain and the ENBW used for integration. Without those two, the number cannot be reproduced on the bench.

Mini example (concept only)
  • If the dominant input-referred density is en,eq (V/√Hz) and the effective bandwidth is ENBW (Hz), then the integrated input-referred RMS is approximately: erms,RTI ≈ en,eq · √ENBW
  • Convert to output-referred by multiplying by the closed-loop gain magnitude: erms,RTO ≈ |ACL| · erms,RTI
  • Combine independent contributors using RSS at one reference point: etotal = √( e12 + e22 + … )

SNR, dynamic range, or “effective bits” can be computed at the system boundary from the final RTO RMS and the full-scale reference, but the budget itself should remain RMS-based.

System noise path: source impedance to total RMS inside measurement bandwidth Block diagram showing source impedance, op amp en and in, gain and ENBW integration, and a stacked contribution bar leading to total RMS and RTI/RTO reference points. System-level noise budgeting path (single reference + ENBW) Source Zs R + sensor model Op Amp eₙ iₙ Feedback network R noise (4kTR) Rf Rg Gain + Filter noise integration ENBW (Hz) Total RMS RSS at one reference eₙ iₙ·|Zs| Zs R net Reference RTI RTO Rule: pick one reference and keep all terms consistent.

Noise vocabulary that actually matters (en, in, 1/f, 0.1–10 Hz, RTI/RTO)

Noise specs only become usable when every term is expressed at the same reference point and inside a defined bandwidth. This section sets the minimum vocabulary required to compute and interpret a noise budget without mixing incompatible units or measurement conditions.

en — voltage noise density

Expressed in V/√Hz. It is modeled as a voltage source at the input. In a budget, it becomes RMS by integrating over ENBW.

in — current noise density

Expressed in A/√Hz. It becomes an input-referred voltage term through the source impedance magnitude: ein→v = in · |Zs(f)|

1/f noise and the corner

The 1/f corner indicates where low-frequency noise rises above the white-noise floor. Below the corner, integrated noise becomes strongly dependent on the low-frequency cutoff and observation time.

0.1–10 Hz noise (low-frequency RMS)

This spec is best treated as a direct low-frequency RMS budget block for slow measurements. It is not a constant V/√Hz value and should not be converted by dividing by √BW.

Consistency rules (keep budgets reproducible)
  • Convert every contributor to one reference point (RTI or RTO) before summing.
  • Convert densities to RMS using ENBW, not an unspecified bandwidth.
  • Treat 0.1–10 Hz noise as its own low-frequency RMS term when the application cares about slow readout stability.
  • When Zs is frequency-dependent (capacitive sensors, RC sources), use |Zs(f)| for the in contribution instead of a single resistance value.
Noise spectrum vocabulary: white noise, 1/f, corner, and 0.1–10 Hz region A simplified log-frequency noise density plot showing a white-noise floor, 1/f rise at low frequency, the corner marker, and a shaded 0.1–10 Hz integration band. Noise density view (concept): white floor + 1/f rise + corner + 0.1–10 Hz band Frequency (log) Noise density 0.1–10 Hz white floor 1/f rise corner integrate over ENBW → RMS (use a defined bandwidth) Vocabulary eₙ: V/√Hz iₙ: A/√Hz RTI/RTO LF HF

The one formula set: how en/in meet source impedance

A usable noise budget starts by expressing every contributor as an input-referred equivalent. The key is that voltage noise en adds directly, while current noise in turns into a voltage term through the source impedance magnitude |Zs(f)|. Once all terms share the same reference point and units, they can be combined by RSS.

Core terms (input-referred)
Source thermal noise (resistive)
eRs = √(4kTR) (V/√Hz)

Treat this as the unavoidable noise floor of a real source resistance. (k: Boltzmann constant, T: Kelvin, R: Ω)

Current noise becomes voltage noise
ein→v(f) = in · |Zs(f)|

If the source is not purely resistive, use the magnitude of impedance in the frequency range that matters for the budget.

Minimum complete input-referred sum
en,eq2(f) = en2 + ( in·|Zs(f)| )2 + eRs2

Use this equivalent density as the starting point for bandwidth integration in the next step.

Dominance check and matching strategy (quick rules)
  • When current noise dominates: if in·|Zs| ≥ en in the frequency region that contributes most to RMS, the current-noise path is a primary term.
  • For purely resistive sources: the crossover resistance is approximately R* ≈ en/in (Ω). Below R*, focus on low en; above R*, focus on low in.
  • If |Zs(f)| is frequency-dependent: treat R* as a frequency-dependent boundary. A simple RC source can shift the dominance across frequency even if its DC resistance is high.
  • Selection guidance: low-Z sources typically benefit from low-voltage-noise inputs; high-Z sources typically benefit from low-current-noise inputs. Device-family details belong in the dedicated input-type pages.
Mini example (dominance by crossover)

If en = 5 nV/√Hz and in = 0.5 pA/√Hz, then R* ≈ (5e-9)/(0.5e-12) ≈ 10 kΩ. A 1 kΩ source is typically en-driven; a 100 kΩ source is typically in-driven (at frequencies where |Zs| ≈ R).

Dominance map: voltage noise versus current-noise-through-source-impedance Plot-style diagram with log source resistance axis showing a flat voltage noise line and a rising current noise contribution line, with a crossover point R* and shaded dominance regions. en vs (in · Rs): which term dominates (concept) Source resistance Rs (log) Input-referred contribution en dominates in·Rs dominates eₙ iₙ · Rs R* ≈ eₙ/iₙ low high Use |Zs(f)| for non-resistive sources; dominance can shift with frequency.

Bandwidth integration: from nV/√Hz to µV RMS

Noise density becomes a meaningful system number only after integration inside a defined bandwidth. The correct tool is the equivalent noise bandwidth (ENBW), which captures how the filter response weights noise power. Using a “-3 dB bandwidth” as ENBW underestimates RMS noise and breaks reproducibility.

The budgeting identity (white-noise region)
erms ≈ en,eq · √ENBW

ENBW is the bandwidth of an ideal rectangular filter that passes the same noise power as the real filter. This makes RMS calculations consistent across different filter shapes.

1st-order low-pass (common rule)

For a simple single-pole low-pass with -3 dB corner fc:

ENBW ≈ 1.57 · fc
Why “-3 dB = BW” is a trap

If ENBW is larger than fc, then RMS noise is larger by √(ENBW/fc). For a 1st-order pole, that factor is about √1.57 ≈ 1.25 (≈25%).

Noise gain (mention only)

If the circuit’s noise gain differs from its signal gain, use the appropriate input-referred density before integrating. Detailed noise-gain handling belongs in the dedicated section on gain distribution.

Mini example (ENBW prevents underestimation)

With en,eq = 10 nV/√Hz and a 1st-order low-pass at fc = 1 kHz: ENBW ≈ 1.57 kHz, so erms ≈ 10 nV/√Hz · √1570 ≈ 0.40 µV RMS. Using 1 kHz instead of ENBW would give ≈0.32 µV RMS and understate noise.

Workflow: noise density through filter to ENBW and RMS Four-step flow diagram showing PSD in V per root Hz, filter magnitude response, ENBW as equivalent rectangle, and final RMS output, with a note that -3 dB is not ENBW. PSD → Filter |H(f)| → ENBW → RMS (repeatable integration) PSD V/√Hz Filter |H(f)| ENBW Hz RMS V Key rule -3 dB corner ≠ ENBW Use ENBW for noise-power equivalence across filters Result: RMS noise becomes reproducible between calculation and bench measurement.

Input vs output: where the gain and noise gain bite

The same op amp can produce very different output noise after a feedback change because the signal gain, the noise gain, and the resistor-network noise do not always scale the same way. A reproducible budget separates these roles: combine noise in one reference (RTI), then translate to the output using the correct gain path.

Rules that prevent “same op amp, different noise” confusion
  • Signal gain maps signal to the output. Noise gain maps input error sources (including op-amp en) to the output.
  • For a non-inverting stage: Asig = 1 + Rf/Rg and typically Anoise ≈ 1 + Rf/Rg.
  • For an inverting stage: Asig = −Rf/Rin but Anoise = 1 + Rf/Rin. Noise gain can exceed the magnitude of signal gain.
  • The resistor network adds its own thermal noise (4kTR), and those terms follow their own transfer to the output—often becoming dominant in high-value networks.
  • “Front-load the noise” only when it changes ownership: increasing signal amplitude at the boundary can make downstream noise irrelevant, but only if the front stage’s RTI budget stays below target.
Mini example (gain change without changing the op amp)
  • If the dominant input-referred white noise density is en,eq, then output-referred RMS scales roughly with the relevant gain path.
  • A non-inverting stage from 1× to 11× increases the output noise by about 11× (white-noise region).
  • An inverting stage with Asig=−10 still has Anoise=11, which can explain why a measured output noise looks larger than expected when only |Asig| is considered.
Non-inverting versus inverting: signal gain and noise gain Two stacked block diagrams comparing non-inverting and inverting feedback, with labeled signal gain and noise gain and resistor noise sources. Signal gain vs noise gain (same op amp, different feedback) Non-inverting Input Vsig Op Amp eₙ Rf / Rg 4kTR Output Vout A_sig = 1 + Rf/Rg | A_noise ≈ 1 + Rf/Rg Inverting Input Vsig Rin 4kTR Op Amp eₙ Rf 4kTR Output Vout A_sig = −Rf/Rin | A_noise = 1 + Rf/Rin Resistor noise enters the budget as 4kTR terms and follows its own transfer to the output.

1/f vs 0.1–10 Hz: when low-frequency noise dominates accuracy

In slow or DC-focused measurements, accuracy is often limited by low-frequency noise rather than by the white-noise floor. The 1/f region grows in importance as observation time increases, and the datasheet 0.1–10 Hz noise should be treated as a direct low-frequency RMS budget item.

Practical rules for low-frequency noise budgeting
  • White noise integrates mainly with ENBW. 1/f noise depends strongly on the effective low-frequency cutoff set by the measurement window.
  • Treat 0.1–10 Hz noise as a direct RMS budget block for slow readout stability. Do not convert it into V/√Hz by dividing by √BW.
  • Keep budgets reproducible by separating two lines: wideband RMS (density + ENBW) and low-frequency RMS (0.1–10 Hz).
  • Use time-window checks to distinguish noise from drift: longer windows pull in lower frequencies and can increase observed RMS if 1/f or drift is present.
Engineering criteria to separate 1/f, 0.1–10 Hz noise, and drift
Window-length test

Compute RMS with 1 s, 10 s, and 100 s windows at constant conditions. If RMS grows strongly with window length, low-frequency content is significant.

Correlation to temperature

If output changes correlate with board or package temperature in a repeatable way, drift-like behavior is present and must be budgeted separately from random noise.

Detrend check

Remove a linear trend over the window. If RMS drops sharply, a deterministic drift component dominates; if not, low-frequency noise dominates.

Mini example (why averaging may not help as expected)

If a 1 s window shows small RMS but a 100 s window shows noticeably larger RMS under constant input, the limiting term is not purely white noise. Low-frequency noise or drift is contributing, and the 0.1–10 Hz RMS spec becomes a primary budget item.

Time-domain variation versus frequency-domain 1/f noise Stacked diagram: top shows a slow drift with noise in time domain and two window lengths; bottom shows PSD with white floor and 1/f rise plus a shaded 0.1–10 Hz band, connected by dashed guides. Time-domain readout stability ↔ 1/f region in PSD (concept) Time short window long window PSD Frequency (log) 0.1–10 Hz white floor 1/f Longer observation windows pull in lower frequencies where 1/f grows.

Chopper / zero-drift tradeoffs: ripple, aliasing, and filtering strategy

Chopper and zero-drift techniques can flatten offset and 1/f behavior, improving low-frequency stability. The tradeoff is that modulation introduces ripple and discrete spurs plus switching residue that must be controlled by filtering and by sampling-aware bandwidth choices. A robust budget treats chopper artifacts as spurs + residual RMS, not as a single “noise number”.

What improves (low-frequency)
  • Lower effective offset contribution in slow readouts.
  • Reduced 1/f dominance; better long-window stability.
  • Cleaner low-frequency budget when 0.1–10 Hz is the main limiter.
What gets added (modulation artifacts)
  • Ripple / spurs near the chopping-related frequencies.
  • Switching residue that becomes in-band RMS after imperfect filtering.
  • Aliasing risk if a sampled stage can fold artifacts into the measurement band.
When chopper is a poor fit (practical criteria)
  • Wideband or fast-transient chains: required bandwidth and step response leave little room for post-filtering of modulation residue.
  • Spur-sensitive signal paths: discrete tones inside the band (or after folding) violate SFDR / spur limits even if RMS looks acceptable.
  • Sampling interaction: a sampled downstream stage can fold chopping-related tones into the passband unless analog filtering keeps them well below limits.
Budget expression: treat artifacts as spurs + residual RMS
Spur line (discrete)
  • Frequency: fripple (and harmonics if relevant).
  • Amplitude after filter attenuation (RTI or RTO).
  • Margin to spur limit (in-band or after folding).
Residual RMS line (continuous)
  • In-band RMS after the chosen low-pass response.
  • Compute using ENBW (or measure) and include margin.
  • Combine with other RMS terms by RSS.
Chopper modulation: blocks plus ripple spur and residual after filtering Top shows a block chain: low-frequency input, chop, amplify, demod, low-pass filter, output. Bottom shows a simplified spectrum with a ripple spur near chop frequency and residual in-band after filtering, with a marked measurement bandwidth. Chopper artifacts: ripple spur + residual RMS after filtering Signal path Input LF CHOP Amplify DEMOD LPF strategy Output ripple / spurs Spectrum (simplified) Frequency measurement BW residual RMS ripple spur filter lowers residue aliasing risk Budget: keep spurs below limits, and integrate residual with ENBW.

Practical noise budget workflow (7-step): allocate, compute, verify

A repeatable noise budget is a workflow, not a single formula. The steps below standardize reference points (RTI/RTO), model the source impedance, compute contributors with ENBW, reserve margin, and define verification tests that reveal modeling mistakes.

The 7-step workflow (short, reusable)
  1. Define metric: choose RTI or RTO and the acceptance number (RMS / pp / SNR).
  2. Model Zs(f): represent the source as R, C, or RC over the relevant frequency region.
  3. Choose ENBW: pick the filter structure and compute ENBW (avoid “-3 dB = BW”).
  4. Compute terms: en, in·|Zs|, 4kTR of resistors, and any reference/supply contributors.
  5. Refer one point: translate each term to RTI or RTO using the correct gain/noise-gain path.
  6. RSS + margin: combine by RSS and keep 20–30% margin for tolerances and modeling gaps.
  7. Verify tests: short input, swap Zs, and change BW to confirm ownership and scaling.
Verification hooks (designed to expose wrong assumptions)
Short input

Validates the amplifier + resistor-network baseline without source impedance uncertainty.

Swap Zs

Replace the source with different R / RC to confirm whether in·|Zs| scaling matches the model.

Change BW

Change the filter corner and verify RMS tracks √ENBW. This confirms integration assumptions and reveals hidden tones.

Seven-step noise budget workflow with feedback loop Vertical flow diagram with seven rounded cards connected by arrows: define metric, model impedance, choose ENBW, compute terms, refer RTI/RTO, RSS plus margin, verify tests, with a loop back to earlier steps. 7-step workflow: allocate → compute → verify (repeatable) 1 Define metric 2 Model Zs(f) 3 Choose ENBW 4 Compute terms 5 Refer RTI/RTO 6 RSS + margin 7 Verify tests iterate budget sheet fields filled

Measurement & validation: how to measure op-amp noise without fooling yourself

Noise measurement is a process of ownership control. A reliable result requires three separations: instrument floor vs DUT, spurs vs noise, and shorted input vs real source impedance. Validation should reproduce the expected scaling with Zs(f) and with ENBW.

Short vs real Zs
  • Shorted input tests the DUT baseline with Zs≈0.
  • Real Zs adds in·|Zs| and source/noise terms.
  • Different results are expected when ownership changes.
Bandwidth & floor
  • Report the measurement BW/ENBW explicitly.
  • Instrument floor should be >6–10 dB below DUT.
  • Gain must avoid clipping and avoid quantization dominance.
Spurs vs noise
  • FFT contains spurs and noise together.
  • List top spurs (50/60 Hz) separately from noise RMS.
  • Use windowing to reduce leakage into the noise floor.
Minimal reproducible experiment (3 configs)
Config A — Short
  • Expect: baseline floor (DUT + network).
  • Check: above instrument baseline by 6–10 dB.
  • Red flag: strong 50/60 Hz dominates FFT.
Config B — Rs
  • Expect: floor increases vs short.
  • Check: increases with larger Rs.
  • Diagnose: in·|Zs| or 4kTR ownership.
Config C — Rs + Cs
  • Expect: high-frequency floor reduces.
  • Check: Zs(f) shaping matches the model.
  • Red flag: no change when Cs is added.
Recommended reporting: Noise RMS (spur excluded) + Top spurs amplitude + BW/ENBW + RTI/RTO.
Noise measurement setup: DUT, gain, anti-alias filtering, and FFT reporting Block diagram showing DUT followed by low-noise gain stage, anti-alias low-pass filter, and ADC/FFT analyzer. Includes labels for bandwidth/ENBW, baseline floor, and spur listing for 50/60 Hz. Measurement chain: separate baseline, BW, and spurs Setup DUT op amp stage Gain low-noise AA filter LPF ADC / FFT analyzer BW / ENBW Baseline floor Spurs listed Report Noise RMS spur excluded Top spurs 50/60 Hz BW / ENBW RTI / RTO Validation uses: short → Rs → Rs+Cs to confirm expected scaling with Zs(f) and ENBW.

Common pitfalls: the 10 mistakes that break noise budgets

Most noise-budget failures come from a small set of repeatable mistakes. Each item below ties a mistake to a concrete consequence and a quick check that can be run in minutes.

1) Using -3 dB BW as ENBW
Breaks: underestimates white-noise RMS.
Quick check: change filter corner/type and verify RMS tracks √ENBW.
2) Ignoring resistor-network noise
Breaks: misses dominant terms in high-value networks.
Quick check: scale R values up/down and confirm noise changes accordingly.
3) Ignoring in·|Zs|
Breaks: high-impedance sources look “mysteriously noisy”.
Quick check: increase Rs and verify noise increases (ownership shift).
4) Treating 0.1–10 Hz noise as a density
Breaks: low-frequency stability gets mis-budgeted.
Quick check: use long time windows and compare LF RMS directly to the LF spec.
5) Ignoring chopper ripple / folding risk
Breaks: RMS looks fine while spur limits fail.
Quick check: inspect FFT for discrete tones; change BW/filter and confirm expected attenuation.
6) Mixing RTI and RTO
Breaks: terms are added in incompatible units/locations.
Quick check: enforce a “Reference” field (RTI/RTO) for every budget line.
7) Not separating spurs from noise in FFT
Breaks: RMS is inflated or spur risk is hidden.
Quick check: report “Noise RMS (spur excluded)” plus “Top spurs amplitude”.
8) Instrument floor above the DUT
Breaks: measurement shows the instrument, not the DUT.
Quick check: measure instrument baseline first; require ≥6–10 dB margin to DUT.
9) Mains pickup misread as low-frequency noise
Breaks: wrong ownership; decisions chase environment, not the DUT.
Quick check: change window/averaging and confirm the 50/60 Hz line behaves like a spur.
10) No margin in the budget
Breaks: small modeling/tolerance errors become field failures.
Quick check: keep 20–30% margin and label where the margin is consumed.
Mistake to consequence map for noise budgets Left column lists common mistakes, right column lists consolidated consequences, with arrows connecting mistakes to outcomes such as underestimated RMS, spur violation, wrong ownership, unreproducible results, and field failures. Errors → consequences (budget failure map) Mistakes Consequences -3 dB as ENBW Ignore resistor noise Ignore iₙ·Zs 0.1–10 Hz as density Chopper spur ignored RTI/RTO mixed Spur vs noise not split Instrument floor too high Mains pickup misread No margin Underestimate RMS Overestimate RMS Wrong ownership Spur violation Unreproducible Field failures Each mistake should map to a check: change BW, change Zs, separate spurs, and confirm reference points.

Engineering checklist (copy/paste)

This checklist standardizes noise budgets into a reusable template. Every line item should include Reference (RTI/RTO) and BW/ENBW/window. Validation should reproduce expected scaling with Zs(f) and with ENBW before trusting any numbers.

Stop-check #1
Instrument baseline is at least 6–10 dB below the DUT baseline.
Stop-check #2
Changing filter corner/type changes RMS by √ENBW trend (not “-3 dB BW”).
Stop-check #3
Short → Rs → Rs+Cs reproduces expected ownership shifts with Zs(f).
Copy/paste checklist table (fill every row)
Category Item What to record Method Pass/Target Example PNs (optional)
Input model Rs (Ω) Value, tolerance, TCR, temperature points BOM + temperature assumption Zs(f) defined for the full band Vishay VHP (Z-Foil), Susumu RG
Input model Cs (F) Dielectric, voltage rating, tolerance BOM + datasheet Zs(f) shaping matches intent Murata GRM (C0G), TDK CGA (C0G)
Input model Sensor equivalent R/RC or current-source model, temperature range Sensor datasheet + simplified equivalent Zs(f) defined (no gaps) —
Noise terms Op-amp en Density, band, 1/f corner (if given), RTI/RTO Datasheet + refer rules Included in RSS at the chosen reference AD797, OPA211, OPA1612
Noise terms Op-amp in·|Zs| in density, Zs(f), RTI/RTO Datasheet + Zs model Ownership checked by Rs sweep OPA140 (FET), ADA4625-1, LTC6240
Noise terms Resistor network 4kTR Which resistors contribute at RTI, values, temperature Compute + refer to RTI/RTO No “missing dominant” items Vishay VHP/VSM, Vishay ACAS (arrays)
Noise terms Reference / bias / supplies (if applicable) Noise metric + how it refers to RTI/RTO Datasheet + refer rule Included (or explicitly excluded) with reason —
Noise terms Chopper artifacts (if used) Spur amplitude + residual RMS, report separately FFT spur list + ENBW integration Spurs below limits; residual in RSS OPA388, OPA189, ADA4522-2
Bandwidth fc, filter order Corner, order, filter type Design intent + measurement config Matches the application window —
Bandwidth ENBW / window ENBW number, FFT window, averaging Compute + record measurement settings RMS scales with √ENBW —
Budget output Reference (RTI/RTO) Every row states RTI or RTO Budget template rule No mixed references —
Budget output Metric (RMS / pp) RMS in-band; pp rule (if used) stated ENBW integration + reporting Meets target with margin —
Budget output Margin Default 20–30% reserved Budget policy Meets target after margin —
Validation Short / Rs / Rs+Cs Record noise RMS + spur list for each config H2-9 minimal experiment Ownership trends match the model Relays: Omron G6K; Switches: ADG1201, TMUX1101
Validation BW sweep Change fc/order; record RMS vs ENBW Repeat measurement with same reporting RMS follows √ENBW —
Validation Repeatability Re-run after reconnect/power-cycle; compare distributions Same setup, same BW, same report format No unexplained drift across runs —
Checklist flow: input model, noise terms, bandwidth, budget output, validation Icon-style checklist with five modules connected by arrows: Input model, Noise terms, BW/ENBW, Output, Validate, and a large checkmark indicating readiness. Checklist modules (fill → verify → ready) Input model Rs / Cs Noise terms en / in / R BW / ENBW fc / window Output RTI/RTO Validate short / Rs Ready when: Baseline < DUT, RMS scales with √ENBW, Zs tests match ownership

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FAQs: noise modeling & budgeting

These answers keep noise discussions inside a clean budget workflow: same reference (RTI/RTO), correct ENBW, and repeatable validation. Each card includes a short answer and a data-ready structure for documentation.

When does current noise dominate over voltage noise?

Current noise dominates when the in·|Zs(f)| term exceeds the op-amp’s voltage noise density en over the band that matters. This is common with high source impedance or when Zs(f) rises with frequency (e.g., capacitive sources).

Data-ready structure
Rule-of-thumb: in·|Zs(f)| > en ⇒ current-noise dominated (in that band)
Inputs: en [nV/√Hz], in [pA/√Hz], Zs(f) model, BW/ENBW, RTI/RTO reference
Quick test: measure noise with short → Rs → Rs+Cs; check whether noise increases with Rs
Common trap: using “shorted-input noise” as the system budget when Zs is not ~0
Connects to: H2-3 (en/in vs Zs)
Why does the noise get worse after increasing gain? (noise gain vs signal gain)

The output noise is set by noise gain (how the op-amp’s input-referred noise is amplified), not only by the signal gain. Feedback networks can raise noise gain and also add resistor thermal noise, so increasing “gain” can legitimately increase measured noise even if the op-amp is unchanged.

Data-ready structure
Rule-of-thumb: output noise ≈ (RTI noise) × (noise gain) integrated over ENBW
Inputs: topology (inv/non-inv), Rf/Rg, noise gain, en/in, resistor values, ENBW, RTI/RTO
Quick test: keep signal gain constant but change resistor ratios that increase noise gain; compare output RMS
Common trap: assuming “gain change” only scales signal and not noise gain or resistor noise
Connects to: H2-5 (input vs output and noise gain)
Is 0.1–10 Hz noise comparable to nV/√Hz specs?

They are not directly comparable. nV/√Hz is a spectral density (per √Hz), while 0.1–10 Hz noise is an integrated RMS result over a low-frequency band (dominated by 1/f and drift-like processes). Use 0.1–10 Hz as a direct low-frequency budget item, and use nV/√Hz with ENBW for broadband budgets.

Data-ready structure
Rule-of-thumb: 0.1–10 Hz spec = low-frequency integrated RMS; nV/√Hz = density for ENBW integration
Inputs: 0.1–10 Hz noise [µV RMS], 1/f corner (if known), broadband en, target time window / ENBW
Quick test: extend acquisition time (lower effective fmin) and check whether low-frequency RMS grows
Common trap: treating 0.1–10 Hz noise as a flat density value
Connects to: H2-2 (vocabulary), H2-6 (1/f vs 0.1–10 Hz)
How to convert nV/√Hz into µV RMS for my bandwidth?

Convert density to RMS by integrating over the correct bandwidth. For flat broadband noise, eRMS ≈ en·√ENBW at the chosen reference point. Then apply the correct gain/noise gain to move between RTI and RTO.

Data-ready structure
Rule-of-thumb: eRMS(RTI) ≈ en·√ENBW; eRMS(RTO) ≈ eRMS(RTI)·(noise gain)
Inputs: en [nV/√Hz], ENBW [Hz], noise gain, RTI/RTO, band (fmin..fmax)
Quick test: change filter corner/type; confirm RMS follows √ENBW scaling
Common trap: using -3 dB bandwidth instead of ENBW
Connects to: H2-4 (bandwidth integration)
What ENBW should be used for a 1st-order RC filter?

ENBW is larger than the -3 dB corner. For a 1st-order low-pass, a common engineering approximation is ENBW ≈ 1.57·fc. Use ENBW for RMS noise integration; use fc only to define the filter corner.

Data-ready structure
Rule-of-thumb: 1st-order LPF ENBW ≈ 1.57·fc
Inputs: fc [Hz], filter placement, ENBW, target band, reporting window/FFT RBW (if used)
Quick test: change fc by 4×; RMS should change by about √(1.57·4) vs √(1.57·1)
Common trap: integrating with BW = fc and underestimating RMS
Connects to: H2-4 (ENBW usage)
Why does shorting the input show much lower noise than in real use?

A shorted input forces Zs≈0, which removes the in·|Zs| contribution and reduces the source’s own thermal noise. Real sources add both, so higher in-use noise is expected. Use “short” only as a baseline, not as the system budget.

Data-ready structure
Rule-of-thumb: short = instrument + amplifier baseline; source terms are removed or minimized
Inputs: short RMS, Rs RMS, Rs+Cs RMS, ENBW/window, RTI/RTO
Quick test: compare short vs Rs; if noise rises with Rs, source terms are real
Common trap: publishing “shorted noise” as the in-system noise spec
Connects to: H2-9 (measurement), H2-3 (ownership)
How to include resistor thermal noise correctly?

Resistors contribute 4kTR noise, but only the resistors that appear at the amplifier’s input (through the feedback network and source model) matter at RTI. The key is to refer every resistor’s noise to the same point (RTI or RTO) before RSS combining.

Data-ready structure
Rule-of-thumb: list “noise-contributing resistors” → refer to RTI/RTO → integrate with ENBW → RSS
Inputs: resistor list (R values), temperature, topology, noise gain, RTI/RTO, ENBW
Quick test: scale a dominant resistor by 10× (keeping ratios if needed) and check noise change trend
Common trap: ignoring large-value resistors in the feedback network or bias paths
Connects to: H2-5 (resistor network), H2-3 (source thermal noise)
Why do chopper amps show ripple even with low 0.1–10 Hz noise?

Chopper amplifiers reduce 1/f and offset by modulation, but modulation can create ripple/spikes that appear as discrete spurs. A low 0.1–10 Hz RMS spec does not guarantee spur-free outputs. Budget ripple as (1) spur lines plus (2) residual broadband RMS after filtering.

Data-ready structure
Rule-of-thumb: report ripple as spur list (f, amplitude) + residual RMS in-band
Inputs: spur list, ENBW, filter corner/order, RTI/RTO, measurement FFT settings
Quick test: add/adjust low-pass filtering; check spur attenuation while residual RMS follows √ENBW
Common trap: rolling spurs into a single “RMS noise” number without disclosure
Connects to: H2-7 (chopper tradeoffs), H2-9 (FFT measurement)
How to separate spurs from broadband noise in FFT measurements?

Treat spurs and broadband noise as different phenomena. First create a spur list (frequency + amplitude), then compute broadband RMS from the remaining bins using the correct ENBW/RBW conversion for the FFT setup. Changing window/averaging should not move true spurs the way it moves noise floor statistics.

Data-ready structure
Rule-of-thumb: output report = spur list + broadband RMS (spurs excluded from integration)
Inputs: FFT window, averaging count, RBW/bin width, spur bins to exclude, ENBW/window of analog filter
Quick test: change window/averaging; spurs remain at fixed f while noise floor stats shift modestly
Common trap: calling “spur + noise” a single RMS number and comparing to a pure-noise budget
Connects to: H2-9 (measurement), H2-10 (pitfalls)
What margin is reasonable for a noise budget?

A practical default is 20–30% margin on the final RMS budget to cover tolerance spreads, temperature shifts, and measurement uncertainty. If the budget includes chopper ripple or strong environmental coupling risks, reserve extra margin or separate the risk as an explicit spur allowance.

Data-ready structure
Rule-of-thumb: reserve 20–30% RMS margin; separate spurs as a dedicated allowance when present
Inputs: budgeted RMS, dominant owners, tolerance stack, temperature points, instrument baseline, repeatability
Quick test: repeatability runs (reconnect/power-cycle) stay within the reserved margin band
Common trap: using 0% margin and then “fixing” misses by changing reporting bandwidth
Connects to: H2-8 (workflow), H2-11 (checklist)
Why does my measured noise change with cable movement or touching?

This is usually a measurement artifact: moving cables changes parasitic coupling and reference conditions, injecting mains-related components or microphonic effects that look like “noise.” The giveaway is that the spectrum shows changed spurs (often near 50/60 Hz and harmonics) or a lifted low-frequency floor only when cables move.

Data-ready structure
Rule-of-thumb: if “touch/move” changes the spectrum, treat it as coupling artifact until proven otherwise
Inputs: spur list (50/60 Hz region), broadband RMS, cable length/routing, shielding reference, ENBW/window
Quick test: fix cable position, shorten leads, repeat FFT; compare spur amplitude changes vs RMS changes
Common trap: labeling mains-coupled spurs as “1/f noise” or “op-amp noise”
Connects to: H2-9 (measurement), H2-10 (pitfalls)
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