Smooth traces can still fail verification
The antenna looks better through a cable, and every calibration standard remeasures perfectly. What has actually improved?
The fictional 2.450 GHz condition-monitoring node needs two different port measurements: an antenna-feed impedance and a PCB filter’s two-port response. In one investigation the engineer adds a lossy cable and sees return loss improve from 6.021 to 8.021 dB. In another, a calibration with the wrong load definition still draws beautifully smooth curves. Neither observation alone establishes the DUT response.
Think about itWould an unused verification load necessarily agree if the three calibration standards agree?
No. The wrong-load example below fits the standards exactly but misses an independent load by 0.019123505976 in absolute complex reflection. That exceeds this lesson’s local 0.01 criterion.
This lesson follows measurement uncertainty and stable lab connections. We replace the portfolio’s generic QPSK stimulus with the explicitly named SYN-VNA-CW-v1 stepped continuous-wave variant. All numerical data are Illustrative / Derived, noiseless calculations at a frozen evaluation date of 2026-09-09 UTC. They are not hardware captures, a wireless-standard waveform or a calibration certificate.
| Observation | Tempting conclusion | Discriminating evidence |
|---|---|---|
| Cable-input return loss 8.020599913280 dB | Antenna match improved | At R2-FEED, Γ = 0.5 and return loss remains 6.020599913280 dB. |
| Wrong SOL standard fit ≈ 0 residual | Calibration is accurate | Unused Γv = −0.2 recovers as −0.219123505976. |
Calibration estimates corrections under defined models and conditions. Its validity can be lost, and its residual uncertainty remains. Independent verification asks whether different evidence supports using those corrections now.
Open M08-04-FILTER-PLAN-A and M08-04-FEED-PLAN-A. Record DUT change, wrong standard definition and changed fixture as competing hypotheses. Keep the earlier raw IDs unchanged; reserve “inspect,” “blocked” and “invalid” outcomes.
Measure complex wave ratios at named planes
What does a VNA receiver ratio know about the plane you want?
A source excites one port. A reference receiver samples the incident wave; test receivers sample reflected and transmitted waves. Ratios retain amplitude and relative phase while reducing common source variation. Couplers, switches and receivers are imperfect, so a raw normalized ratio is not yet the DUT’s scattering parameter. The naming of receiver channels varies by instrument. [VNA-ERROR]
M-CAL is the instrument calibration plane. With a fixture present it coincides with F-IN; F-OUT coincides with the product’s R2-FEED. For the two-port filter, its ports are R1-DUT port 1 and port 2, bounded by separately named left and right fixtures. R3 remains the receiver decision boundary; S0 remains the spatial/OTA boundary. Neither is another name for a VNA connector.
Think about itCan a raw open observation of 1.02 prove that the open delivers gain?
No. Directivity and tracking errors can make raw m exceed one. Passivity concerns corrected network waves at the declared reference plane, not an uncorrected receiver ratio.
Go deeperKeep the network conventions with the data
Revisit two-port networks and S-parameters for wave normalization and chain conversion. This lesson retains the real 50 Ω convention throughout; a file normalized to another impedance requires an explicit compatible transformation before comparison.
Name every port and plane in the raw-data header, including direction, reference impedance, terminations, fixture order and whether instrument correction was already applied.
Separate systematic, random, and drift errors
Which errors can a fitted correction remove, and which change after you fit it?
Systematic errors are reproducible within the model and state. Random receiver noise and connection variation need statistical evidence. Drift changes the system with time or environment. A calibration can estimate systematic terms; it does not freeze a moving cable or eliminate all uncertainty. [VNA-ERROR]
| Contribution | Forward excitation at port 1 | Reverse excitation at port 2 |
|---|---|---|
| Directivity | Leakage in reflection at port 1 | Leakage in reflection at port 2 |
| Source match | Incident-wave interaction at port 1 | Incident-wave interaction at port 2 |
| Load match | Imperfect receiving termination at port 2 | Imperfect receiving termination at port 1 |
| Reflection tracking | Reflection amplitude/phase path at port 1 | Reflection amplitude/phase path at port 2 |
| Transmission tracking | Forward ratio path, 1 → 2 | Reverse ratio path, 2 → 1 |
| Isolation | Forward leakage bypassing DUT path | Reverse leakage bypassing DUT path |
The numerical one-port witness uses only three terms: directivity leakage d, reflection tracking t and source match s. They are complex functions of frequency in real equipment; this bounded fixture holds their supplied values constant across its grid.
Think about itIf you average the same biased ratio 64 times, does the bias shrink by eight?
No. An average of identical biased values is the same value. A square-root averaging law requires a specified random process and independence assumptions. This explorer has no stochastic noise model.
| Quantity | True Γ or term | Raw observation m |
|---|---|---|
| Directivity / tracking / source match | d = 0.02; t = 0.9; s = 0.1 | All real; dimensionless |
| Open | +1 + j0 | 1.020000000000 + j0 |
| Short | −1 + j0 | −0.798181818182 + j0 |
| Load | 0 + j0 | 0.020000000000 + j0 |
| Separate DUT | 0.5 + j0 | 0.493684210526 + j0 |
| Unused verification | −0.2 + j0 | −0.156470588235 + j0 |
Separate error mechanism, fitted correction and residual uncertainty in the record. Receiver noise, standard uncertainty, connector repeatability and drift are different contributors, even if all affect the same S11 trace.
Choose what the calibration can solve
Do your standards provide the independent information your correction needs?
One open gives one complex response constraint. Three distinct, characterized reflection standards can identify the three-term one-port model. A two-port measurement needs additional information about transmission, both excitation directions and the receiving-port match. Choose the method from accessible interfaces and credible standard models before acquiring the DUT.
| Method | Information and applicability | Coverage / numerical implementation here |
|---|---|---|
| Response | A known through or reflection response supplies tracking normalization for that measurement. | Here only m/m_open. Does not independently solve directivity/source match; matched-load residual .019607843137. |
| One-port SOL | Three distinct complex reflection standards at one plane, with their frequency-dependent models. | Solves d,t,s for that reflection port. Implemented here; not a two-port solution. |
| Full two-port SOLT | Characterized SOL at both interfaces, a suitable characterized/solvable thru, both source directions and load-match information. Isolation handling follows the selected procedure. | Complete applicable error correction requires all selected observations and model assumptions. Taught; numeric solver not implemented. |
| TRL / multiline TRL | Compatible thru and lines; common high reflection with enough phase information to resolve ambiguity. Line impedance establishes the reference; lengths must distinguish the standards. | Both directions with method-specific error-box assumptions. Multiple line lengths extend useful coverage. Taught; numeric solver not implemented. |
| LRM / LRL variants | Line/thru, reflect and match (or second line); the chosen method determines known quantities and symmetry assumptions. Match quality/model matters. | Useful when realizable standards differ from ideal coaxial SOL. Taught; numeric solver not implemented. |
| Known fixture inverse | Independently known, stable left/right networks and compatible already calibrated exterior S-data. | Removes those networks. Implemented here; supplies no missing unknown analyzer calibration observations. |
The distinctions above are informative method planning, grounded in the accessible TRL and LRM descriptions. Exact standard classes and algorithm assumptions belong to the selected instrument/method. [VNA-TRL] [VNA-LRM]
Give a TRL line enough distinction
For a separate ideal line-separation example, Δτ = 100 ps and Δφ = 360° fΔτ. Its one-way separation is 88.2° at 2.450 GHz, 0° at DC and 180° at 5 GHz. Near integer multiples of 180°, the ideal distinction degenerates. A 20°–160° interior guideline suggests 0.556–4.444 GHz for this first branch, but that alone cannot establish a valid band: loss, dispersion, impedance, phase branch, model assumptions and uncertainty still matter. [VNA-TRL]
The line establishes the reference under the method’s assumptions. Its characteristic impedance needs characterization or justified renormalization if a 50 Ω result is required. A convenient line length does not determine that impedance.
Record the method, standard IDs, model versions, frequency coverage, branch choice and both-direction requirements. Mark an unavailable commercial solve as unimplemented; do not relabel a known-box inverse.
Standards are models with physical interfaces
What if the calibration load is repeatable but its model is wrong?
An open has fringing capacitance, a short has inductance, and each standard can have offset delay, loss and a defined connector reference plane. A kit definition binds those quantities to frequency limits and standard classes. Its coefficients have specific units: an open polynomial C(f) = C0 + C1f + C2f² + C3f³ uses coefficients in F/Hzⁿ when f is in Hz; an inductance polynomial uses H/Hzⁿ. Do not paste values from another unit convention. [VNA-KIT]
Think about itIf actual load Γ = .02 but the fit assumes zero, will remeasuring that load expose the error?
The solver maps it back to its assumed zero. Use a separate reference. In this example the fitted directivity shifts to .038036072144 and the DUT becomes .484848484848 instead of .5.
| Quantity | Correct SOL | Actual load .02, assumed 0 |
|---|---|---|
| Raw load observation | 0.02 + j0 | 0.038036072144 + j0 |
| Estimated d | 0.02 + j0 | 0.038036072144 + j0 |
| Estimated t | 0.9 + j0 | 0.903249384541 + j0 |
| Estimated s | 0.1 + j0 | 0.080160320641 + j0 |
| Recovered DUT Γ | 0.5 + j0 | 0.484848484848 + j0 |
| Recovered unused Γv | -0.2 + j0 | -0.219123505976 + j0 |
| Unused reference residual | ≈ 0 | 0.019123505976 > 0.01 |
| Calibration-standard residual | ≈ 0 | ≈ 0 · fit to incorrect definitions |
Connector gender, pin depth, cleanliness, mating torque and adapters are part of the physical model boundary. Use the actual compatible hardware’s inspection and handling procedure. An adapter inserted after calibration adds a network; treating it as zero length or redefining a kit class does not characterize it. Offset loss in the cited kit help uses its own convention; it is not the explorer’s total matched dB loss parameter. [VNA-KIT]
Go deeperSeparate a standard definition from its uncertainty
Knowing nominal coefficients is not knowing them exactly. Record characterization evidence, covariance where available, connector repeatability and applicable frequency range. Correlated standard errors can move several corrected S-parameters together. The supplied ideal SOL values are synthetic choices, not a borrowed commercial kit.
Preserve actual standard identities and assumed model files separately. A corrected model creates a new derived calibration version linked to immutable raw standard observations; it never rewrites those observations.
Move the reference plane deliberately
Does your operation remove phase, loss, mismatch, or an already removed cable?
For e^(+jωt), forward propagation is exp(−γl), with γ = α + jβ. One-way physical length l and velocity v give τ = l/v. A matched line’s one-way power insertion loss LdB corresponds to voltage-wave factor 10^(−LdB/20). A reflection travels out and back.
| Stage / operation | Complex Γ | Magnitude / return loss |
|---|---|---|
| Actual R2-FEED load | .500000000000 + j0 | .5 / 6.020599913280 dB |
| M-CAL before 1 dB one-way cable | −.396380404700 − j.024938141268 | .397164117362 / 8.020599913280 dB; phase −176.4° |
| Phase-only extension to feed delay | .397164117362 + j0 | Same magnitude; loss remains |
| Matched loss-and-phase removal | .500000000000 + j0 | .5 restored when the line model is valid |
Port extension can include a loss model on some instruments; this lesson names its phase-only operation explicitly. A cable-end calibration already includes that cable in the calibration error network. Do not remove it again. A mismatched launch generally requires a full network model, beyond a scalar electrical delay. [VNA-EXT]
Remove the actual two-port network in the actual order
The filter proxy is a series impedance Zs = 10 Ω + j(ω·10 nH − 1/(ωC)), with C = 1/((2π·2.45 GHz)²·10 nH) = 0.421995766940 pF. At resonance its S11 = S22 = 1/11, S21 = S12 = 10/11 and transmission is −0.827853703165 dB. The antenna-load proxy uses 150 Ω plus the same reactance, giving Γ = (Z−50)/(Z+50). Both are passive lumped models; neither is a measured commercial device.
| Operation | Recovered S21 | Largest independent verification residual / status |
|---|---|---|
| Exact full fixture inverse | 0.909090909091 − j0 | 0 / supported |
| Wrong matched 50 Ω inverse | 0.921475475313 + j0.000506242881 | 0.067586382995 / blocked |
| Phase-only approximation | 0.731953987647 + j0.000402123014 | 0.166983085403 / blocked |
Reflections between networks require a compatible network interconnection calculation. Use the stated chain convention or a wave/nodal connection. The independent oracle here solves the connected nodal network without using the production S↔ABCD conversion.
Go deeperConditioning is part of whether an inverse is usable
Normalize a chain to [[A,B/50],[50C,D]] before comparing conditioning. The implementation uses κF = ‖A‖F‖A⁻¹‖F, an independently tested conservative bound: κ2 ≤ κF ≤ nκ2 for an n×n matrix. Local rules warn above 10⁸ and reject at or above 10¹² or singularity. This can reject earlier than κ2. A one-port inverse also rejects a denominator no larger than 10⁻¹² times the sum of its constituent magnitudes. Exact zero is handled explicitly. Undefined chain conversion at vanishing transmission leaves available S-data visible and the cascade unavailable; it is not an invitation to divide by a tiny number.
Record calibration plane, each fixture ID, propagation convention, left/right order, reference impedance and every operation once. Retain the original exterior S-data and link the derived DUT-plane dataset to its model.
Acquire in a valid DUT and receiver state
Can cleaner averaging compensate for the wrong power state or insufficient frequency coverage?
Choose source power to preserve the DUT’s intended small-signal state and receiver linearity, with adequate observable signal. Lower IF bandwidth or more averaging can reduce applicable random contributions but cost acquisition time. They cannot correct deterministic standard bias, and longer sweeps can expose more drift. Actual safe levels, settling and coupling depend on the selected hardware and settings. [VNA-ERROR]
The explorer’s source power is context from −40 to +10 dBm; −10 dBm is the default. Its fictional small-signal ceiling is 0 dBm, inclusive. Exceeding it marks the inference invalid. IFBW choices are 10, 100, 1000 and 10000 Hz; averaging choices are 1, 4, 16 and 64. These controls do not modify the noiseless curves. A real power sweep and receiver checks must establish the appropriate region; the synthetic ceiling is not a safe equipment rating.
A time trace inherits the frequency experiment
The fixed grid has 101 points from 2.0 to 3.0 GHz at Δf = 10 MHz. Its span B = 1 GHz gives an inverse-span scale 1/B = 1 ns; periodic delay extent is 1/Δf = 100 ns. Neither is a promise to distinguish any two responses. For reflection at v = 2×10⁸ m/s, 100 ns round-trip corresponds to 10 m one-way before periodic ambiguity, subject to loss and observability.
Think about itIf a narrow gate hides the launch reflection, have you recovered a launch-free antenna measurement?
Not necessarily. Finite-band responses overlap; removing part of one may remove part of another. A prior mismatch also changes energy delivered downstream. Keep ungated data and verify the gated result independently.
A transform record needs actual frequency samples, bandpass or lowpass interpretation, start/stop values, DC extrapolation, interpolation, window and normalization. This grid contains no DC: a lowpass response would require additional assumptions. Tapering lowers sidelobes while broadening responses. Multiplication by a time gate convolves frequency data and can alter broadband magnitude and phase. It does not repair the discontinuity or establish absolute accuracy. [VNA-TIME]
Save the grid, power, IFBW, averaging, settling sequence, DUT bias/temperature and all transform settings. Give gated data a derived ID; preserve the full complex ungated sweep. Unknown ratings and residual uncertainty stay unknown.
Track what changes after calibration
What still belongs to the calibration after a connector is remated or the cable moves?
A successful calibration describes a particular bench state. Rerouting a cable, changing torque, adding an adapter, altering bias, warming the fixture or switching an instrument path can change that state. Define the expected validity conditions and review triggers in advance; repeatability of an unchanged setup cannot estimate the variability of remating it. [VNA-ERROR]
Think about itOur drift example still clears the numerical 0.01 verification tolerance. Does that make the unchanged-state condition true?
No. The supplied state changed after calibration, so the dataset is blocked until reviewed and reverified or recalibrated under a justified procedure. A tolerance and a state-validity condition answer different questions.
| Quantity | Pinned result at 2.450 GHz |
|---|---|
| New raw DUT m | 0.498684210526 + j0 |
| New raw verification mv | −0.151470588235 + j0 |
| Recovered DUT | 0.505011244066 + j0 |
| Recovered unused verification | -0.194223273478 + j0 |
| Absolute verification residual | 0.005776726522 |
| Averages 1 / 4 / 16 / 64 | Identical deterministic bias; unchanged-state gate remains blocked |
Plan a repeat acquisition before and after the intended change, an independent check device, and a return-to-baseline measurement when feasible. Keep cable route and thermal state with timestamps. If evidence cannot distinguish DUT drift from fixture drift, the honest next step is a discriminating measurement, not an automatic correction.
Elapsed time is only one influence. A single changed connection can matter immediately; a stable bench can behave differently. Use evidence and the selected procedure’s validity conditions, not a made-up universal interval.
Create a new configuration/state ID after each consequential change. Preserve the old calibration and raw sweeps, document the trigger, and identify the verification needed before reusing a DUT inference.
Verify with evidence independent of the fit
What evidence could disagree with your correction without sharing its assumptions?
An unused, independently characterized device challenges the fitted correction. It needs a compatible reference value and uncertainty at the same planes and state. Reusing standards can detect changes but can also reproduce shared model error. A verification residual is valuable evidence; it is not itself the complete uncertainty of the DUT result. [VNA-VERIFY]
| Gate | When it prevents use |
|---|---|
| Schema and compatibility | Invalid draft is not committed. Wrong plane, port order, Zref, grid or calibration identity blocks inference. |
| Identification and numerics | Singular standards, unstable inverse or unsupported transformation is invalid. |
| Measurement state | Power outside the supplied small-signal limit is invalid. Changed connections/drift block reuse. |
| Independent evidence | Unknown standard/verification evidence means inspect. Failed residual means blocked. |
| Network plausibility | Check sampled passivity and reciprocity separately; neither proves calibration accuracy. |
| Residual uncertainty | Standard models, connections, fixture characterization, drift and receiver correlations still need evidence. No physical DUT acceptance is supplied. |
For a real-reference two-port, passivity requires the largest singular value σmax(S) ≤ 1 + 10⁻¹⁰ in this numerical check. Four separate |Sij| ≤ 1 tests are insufficient because coherent incident waves can combine. Reciprocity is a separate |S12−S21| ≤ 10⁻¹⁰ check; a passive nonreciprocal device is possible. Do not clip reflection to one or normalize a failing network to make it look passive.
At exact match, Γ = 0 has undefined phase and infinite return loss; the explorer labels those analytic limits. Checks cover sampled frequencies and the declared small-signal state. Real uncertainty requires a model of residual errors and their correlations; first-order propagation has conditions, developed in 08.1. [MET-NIST]
Retain the unused reference’s provenance, raw observations, comparison residuals and uncertainty. A supported synthetic criterion permits only the stated synthetic inference. It supplies no accreditation, radiation conclusion or conformity decision.
Defend two calibration and fixture plans
Can another engineer reproduce the calibration and explain why the resulting plane is defensible?
Start with correct SOL and reveal the unused load. Save a baseline, choose the wrong load model, and compare the perfect standard fit with the failed independent residual. Next choose the lossy line: predict the result of phase-only extension, then apply matched loss-and-phase removal. Finally choose the mismatched filter fixtures and compare the exact model with an assumed matched 50 Ω model. Keep the resulting warning with the data.
VNA Error & Plane Explorer
Fit SOL, test an unused load, then move a lossy fixture plane. Compare the standard fit with independent evidence before using the result.
Correct one-port SOL · committed result
The supplied synthetic reference criterion clears on all 101 points under unchanged, compatible conditions. Real residual uncertainty remains unknown.
Output plane: M-CAL = R2-FEED. Three-term SOL receiver correction precedes any fixture transformation; residual standard-model and state errors can remain. Acquisition context: -10 dBm CW, 1000 Hz IFBW, 1 averages. IFBW and averaging have no numerical effect in this noiseless model.
| Stage | Real + j imaginary | Magnitude | Phase (wrapped) | Reading |
|---|---|---|---|---|
| Synthetic truth at DUT | 0.5 + j0 | 0.5 | 0° | 6.020599913 dB |
| Raw at exterior plane | 0.493684210526 + j0 | 0.493684210526 | 0° | 6.131015251 dB |
| SOL-calibrated at M-CAL | 0.5 + j0 | 0.5 | 0° | 6.020599913 dB |
| After selected plane operation | 0.5 + j0 | 0.5 | 0° | 6.020599913 dB |
| Check | Result and meaning |
|---|---|
| DUT truth residual at cursor | 0 |
| Largest verification residual, all 101 points | 0; criterion ≤ 0.01 (inclusive) |
| Standard-system conditioning | κF = 4.720696; κ2 ≤ κF ≤ 3κ2 |
| Normalized fixture conditioning | κF = 2; [[A,B/50],[50C,D]] |
| Passivity at cursor | |Γ| = 0.5; within 1 + 10⁻¹⁰ |
| Reciprocity at cursor | Not a one-port property |
| Uncertainty | Actual standard, connection, drift, fixture and receiver covariance unknown; tolerance is not an accuracy specification. |
Independent verification and complete SOL witness
Independent load Γv = −0.2 real at R2-FEED; never fitted as a SOL standard. Values are conditional synthetic references; unknown evidence withholds a verification conclusion.
| Quantity | Value |
|---|---|
| Reference Γv | −0.2 + j0 |
| Raw verification receiver mv | -0.156470588235 + j0 |
| SOL-calibrated at M-CAL · verification | -0.2 + j0 |
| Recovered Γv | -0.2 + j0 |
| Absolute DUT-plane residual | 0 |
| Calibration-plane residual before fixture removal | 0 |
| Standard | Actual Γ | Assumed Γ | Observed m | SOL re-fit Γ |
|---|---|---|---|---|
| Open | 1 + j0 | 1 + j0 | 1.02 + j0 | 1 + j0 |
| Short | -1 + j0 | -1 + j0 | -0.798181818182 + j0 | -1 + j0 |
| Load | 0 + j0 | 0 + j0 | 0.02 + j0 | 0 + j0 |
| Term | Actual at calibration | Estimated from standards |
|---|---|---|
| d | 0.02 + j0 | 0.02 + j0 |
| t | 0.9 + j0 | 0.9 + j0 |
| s | 0.1 + j0 | 0.1 + j0 |
Fit residual: 0. Three fitted standards can match their assumed definitions exactly even when those definitions are wrong. Post-fit drift changes actual d by +0.005 only, without re-fitting.
Committed configuration and evidence snapshot (included in print)
| Input | Committed value |
|---|---|
| Directivity magnitude |d| | 0.02 dimensionless |
| Directivity phase | 0 degrees |
| Tracking magnitude |t| | 0.9 dimensionless |
| Tracking phase | 0 degrees |
| Source match magnitude |s| | 0.1 dimensionless |
| Source match phase | 0 degrees |
| Actual load Γ (real) | 0 dimensionless |
| Assumed load Γ (real) | 0 dimensionless |
| Fixture one-way length | 0.02 m |
| Fixture phase velocity | 200000000 m/s |
| Fixture one-way matched loss | 1 dB |
| Actual fixture characteristic impedance | 50 Ω, real |
| Source available CW power at M-CAL | -10 dBm |
| Analytic DUT | antenna |
| One-port numerical calibration | sol |
| Fixture in signal path | absent |
| Plane operation | none |
| Removal model | actual |
| Post-calibration directivity change | off |
| Standard evidence | known |
| Independent verification evidence | known |
| Connections after calibration | unchanged |
| Dataset compatibility | compatible |
| IF bandwidth (Hz; context only) | 1000 |
| Sweep averaging (count; context only) | 1 |
vna-error-plane-explorer/2.0 · p08-m04-one-port-v1 · p08-m04-fixture-cascade-v1 · p08-m04-verification-rules-v1. SYN-VNA-CW-v1; fixed evaluation 2026-09-09 UTC; M-CAL-50-v1; no physical acquisition. Parent raw fixture remains immutable. Connection: unchanged; standard evidence: known; verification: known; compatibility: compatible. Apply each correction once. Numeric tolerances describe computation, not measured uncertainty.
Method planning · separate from numeric recovery
SOLT · numeric solver not implemented. Require characterized SOL at both ports, the applicable thru, both source directions and source/load-match information. Known-box inversion cannot supply these missing analyzer calibration observations.
Plan A · PCB filter in a two-port fixture
Planes and method. Define R1-DUT ports 1/2 and both exterior M-CAL planes. Plan full two-port SOLT at accessible connectors with characterized kit models and thru, both source directions and match information. For a suitable planar coupon, investigate TRL/multiline TRL directly at the DUT planes with line impedance, branch and band evidence. Select one documented procedure; the explorer implements neither commercial solve.
Fixtures and acquisition. Characterize left and right launches independently, retaining raw exterior 50 Ω complex S-data and actual port order. The local RLC fixture uses 2–3 GHz, 101 points, −10 dBm CW, 1000 Hz IFBW and one sweep average. Establish the actual small-signal range, receiver reserve, bias, settling, thermal equilibrium and connector state before a physical run. Take ten complete repeat sweeps and a separate controlled remating series; do not confuse the populations.
Verification and decision. Use an unused characterized attenuator/line appropriate to both directions before and after DUT acquisition, including the fixture operation. Quantify standard, thru/line, match, receiver, remating and fixture-model covariance. Reject incompatible metadata and unstable inverses. Reverify after cable, connector, power-state or thermal changes. No actual DUT limit or complete uncertainty is supplied; the plan cannot close product acceptance.
Plan B · Antenna feed through a cable and launch
Planes and method. Prefer a feasible characterized SOL at R2-FEED. If calibration ends at M-CAL/F-IN instead, use an independently characterized cable/launch ending at F-OUT/R2-FEED. Apply its removal once. Verify standard gender, offsets, loading and actual access; do not silently replace a launch with a matched line.
Fixtures and acquisition. Freeze antenna mounting, enclosure, nearby objects, cable route and any common-mode suppression, plus supply and thermal state. The local 150 Ω resonant load proxy uses the same stepped CW grid and context as Plan A. Begin with an unused reflection reference at the intended feed plane, preserve ungated complex sweeps, and collect ten stable repeats plus separately labelled remating/route perturbations.
Verification and decision. Compare the independent reference before/after correction, then a direct feed-plane calibration when practicable. Include standard, mismatch, loss/delay, launch, drift and connection uncertainty. Cable-loss improvement alone cannot establish antenna improvement. Hand qualified R2 impedance evidence to the antenna evidence architecture; radiation efficiency, pattern and S0/OTA claims require their own measurements.
Complete static measurement records
These two p08-measurement-record-v1 snapshots are illustrative plans, independent of previous visits and custom explorer edits. “Unknown” fields require evidence; they do not mean zero or pass. Raw IDs remain immutable.
M08-04-FILTER-PLAN-A · full record
| Record field | Fixed illustrative snapshot |
|---|---|
| id | M08-04-FILTER-PLAN-A |
| parentIds | M08-03-SPUR-PLAN-A · M08-02-TX-PLAN-B · M08-01-RAW-A |
| owner | 08.4 · fictional RF measurement engineer |
| question | Does a shift in the node filter response belong to the component or its launch fixtures? |
| hypotheses | H1: component resonance changed. H2: incorrect fixture model. H3: calibration/connector drift. H4: receiver or DUT is outside its small-signal state. |
| requirement | REQ-VNA-EVIDENCE-v1: coherent four-Sij data at R1-DUT over 2.0–3.0 GHz; synthetic independent max |ΔSij| ≤ 0.01, all 101 samples. No product insertion-loss limit supplied. |
| decisionRule | p08-m04-verification-rules-v1: compatible identity, planes, ports, Zref and grid; valid state; invertible model; independent verification ≤0.01 inclusive. Unknown actual uncertainty prevents real acceptance. |
| specimen | SYN-FILTER-RLC-v1 / p08-m04-fixture-cascade-v1; R=10 Ω, L=10 nH, C=1/[(2π·2.45 GHz)²L]; one analytic network, not a commercial filter. |
| configuration | CFG-VNA-FILTER-A; HW-SYN-A1; FW-SYN-1.0 retained as parent identity; radio transmit disabled, unpowered passive component test. New local swept-CW mode, not portfolio QPSK or a named wireless standard. |
| state | Unbiased passive RLC, 3.300 V parent node supply disconnected from RF path, illustrative 298.15 K; fixed left/right 20 mm fixtures, supported cables, stable enclosure state. |
| timestamp | Frozen illustrative plan 2026-09-09T00:00:00Z; no physical acquisition timestamp. |
| environment | Stable 25 °C assumption; actual temperature record, humidity and external coupling unknown. |
| stimulus | SYN-VNA-CW-v1: stepped coherent CW from 2e9 to 3e9 Hz, 1e7 Hz spacing, 101 points; forward and reverse source directions. No PRBS/seed applies to CW. |
| statistic | Complex normalized wave ratios, real positive 50 Ω at both ports. Source available CW mean −10 dBm at exterior M-CAL, not accepted DUT power, PSD, dBc, PEP or a burst-period average. |
| population | One synthetic specimen/state, one deterministic sweep each direction; practical plan takes 10 unchanged complete sweeps and 5 separately labelled disconnect/reconnect sequences, with before/after verification. No synthetic repeatability variance supplied. |
| acquisition | Configure band, source power, IFBW and bias first; warm up per selected manual; inspect interfaces; calibrate; verify unused device; DUT forward/reverse; verification again. Actual settling and duration unknown until measured. |
| planes | M-CAL1 = left F-IN → left F-OUT = R1-DUT port1 → component → R1-DUT port2 = right F-IN → right F-OUT = M-CAL2. Currents into ports. R2 antenna feed, S0 OTA and R3 decision boundary not measured. |
| chain | Two independent known uniform fixtures: each l=.020 m, v=2e8 m/s, one-way matched loss 1 dB, Zc=50 Ω baseline /55 Ω named mismatch variant; no protection pad, bias tee or external loss silently inherited. All unused RF ports terminated in stated 50 Ω. |
| instrument | SYN-VNA-04 / SIM-004 / firmware SIM-1, two source directions and reference/test receivers. Actual make/model/options/firmware and safe ratings unknown; teaching sources do not supply a physical operating authorization. |
| settings | −10 dBm source available CW, 1000 Hz IFBW, averaging1, linear 101-point grid. Plan power repeat at −20 dBm and confirm unchanged S within evaluated uncertainty; settle bias/thermal state independently. |
| calibration | Plan full two-port SOLT at coax M-CAL with characterized connector-compatible SOL and thru, both directions/load match; independently characterize fixture models. If same-stackup TRL standards at DUT planes exist, compare that alternative over validated line bands instead of removing those launches twice. Commercial solve not implemented. |
| rawEvidence | SYN-VNA-FILTER-RAW-v1: immutable analytic exterior S from left × DUT × right; SYN-VNA-VERIFY-2P-v1: independent matched device S12=S21=.8, S11=S22=0. Parent raw and fixture IDs retained. Actual Touchstone files/certificates absent. |
| processing | vna-error-plane-explorer/2.0; p08-m04-fixture-cascade-v1: T_DUT=T_left⁻¹ T_exterior T_right⁻¹; no raw rewrite, smoothing, gating or renormalization. Derived record M08-04-FILTER-DERIVED-A refers to raw and both box IDs. |
| uncertainty | Real standard-model, connection, drift, source/load match, receiver noise, fixture-parameter covariance, bias and thermal contributions unknown. κF and 1e−10 tests are numerical checks, not measurement uncertainty or confidence. |
| result | Exact known models recover S11=S22=1/11, S21=S12=10/11 at 2.450 GHz; transmission −0.827853703165 dB. Synthetic verification residual is roundoff. A wrong 50 Ω removal model for the 55 Ω fixture fails independent verification. |
| inference | Supported only for the named synthetic inverse problem; passive-looking recovered curves cannot override failed verification. No real filter pass, commercial SOLT/TRL solve, accredited calibration or radiation claim. |
| unresolved | Actual standards/fixtures, method covariance, reference-device characterization, connector repeatability, instrument limits and state evidence are required before using hardware data. |
| next | Measurement engineer: acquire a connector-compatible unused attenuator/line and check four complex Sij across the band; compare independent fixture characterization. Hand qualified vector data and residual uncertainty to planned 08.5. |
| review | Invalidate on cable movement, reconnect, changed fixture/port mapping, power/gain switching, bias, temperature, firmware or frequency grid; reverify and recalibrate as the cause requires. |
M08-04-FEED-PLAN-A · full record
| Record field | Fixed illustrative snapshot |
|---|---|
| id | M08-04-FEED-PLAN-A |
| parentIds | M08-03-BURST-PLAN-A · M08-02-TX-PLAN-B · M06-E1 |
| owner | 08.4 · fictional RF measurement engineer |
| question | Is the apparent antenna-feed match a load property or round-trip cable attenuation? |
| hypotheses | H1: feed impedance changed. H2: cable loss hides reflection. H3: wrong standard model. H4: common-mode cable coupling invalidates a two-port line model. |
| requirement | REQ-FEED-EVIDENCE-v1: complex Γ at R2-FEED, same product state, 2.0–3.0 GHz; synthetic independent |ΔΓv|≤.01. No antenna efficiency or product return-loss limit supplied. |
| decisionRule | p08-m04-verification-rules-v1: compatible one-port identity, plane, real 50 Ω and grid; valid state and inverse; unused reflection reference residual ≤.01 inclusive. Actual residual uncertainty is unknown; no real DUT acceptance. |
| specimen | SYN-ANT-LOAD-RLC-v1 / p08-m04-one-port-v1: Z=150+j(ω·10 nH−1/(ωC)) Ω; C shares 2.450 GHz resonance; impedance-only proxy. |
| configuration | CFG-VNA-FEED-A; parent HW-SYN-A1/FW-SYN-1.0; radio disabled for passive swept-CW feed test. Physical plan names enclosure, mounting, cable support and antenna tune state before comparison. |
| state | Passive unbiased load; parent 3.300 V supply disabled for RF test; 298.15 K teaching state; no spatial/OTA model. Connector mating/torque follows actual interface procedure. |
| timestamp | Frozen illustrative plan 2026-09-09T00:00:00Z; no physical acquisition timestamp. |
| environment | Stable 25 °C assumption; actual temperature record, humidity and external coupling unknown. |
| stimulus | SYN-VNA-CW-v1: one-port stepped CW, 2e9–3e9 Hz in 1e7 Hz steps, 101 samples. No PRBS/seed applies; no transmission-direction observation is inferred. |
| statistic | Complex incident/reflected wave ratio Γ at real positive 50 Ω R2-FEED after correction. Source available CW mean −10 dBm at M-CAL; actual power delivered to the mismatched load is not assumed equal to that available power. |
| population | One synthetic load/state and deterministic sweep. Physical plan: 10 fixed-setup sweeps, then 5 separately identified controlled remating/route sequences; independent verification before/after. No statistical confidence from the synthetic repeats. |
| acquisition | Freeze mounting, enclosure, route and thermal state; establish actual safe/linear source level; calibrate SOL at named plane; check unused reference; acquire one-port DUT sweep; recheck reference; retain route/remating controls separately. Actual settling and duration unknown. |
| planes | M-CAL = F-IN before cable; F-OUT = R2-FEED. Fixture-free anchor calibrates directly at R2-FEED. R1 component port and R3 decision boundary retain their portfolio meanings. |
| chain | One cable/launch, 20 mm, 100 ps one-way, 1 dB one-way matched loss, Zc50 Ω baseline; full known fixture transformation required for mismatch. No pad or protection network from TX-PWR-A is copied into this new topology. |
| instrument | SYN-VNA-04 / SIM-004 / firmware SIM-1, two source directions and reference/test receivers. Actual make/model/options/firmware and safe ratings unknown; teaching sources do not supply a physical operating authorization. |
| settings | −10 dBm source available CW, 1000 Hz IFBW, averaging1, linear 101-point grid. Plan power repeat at −20 dBm and confirm unchanged S within evaluated uncertainty; settle bias/thermal state independently. |
| calibration | Plan one-port SOL at feed if compatible standards can physically reach it. Otherwise SOL at M-CAL using correct open/short/load definitions, then remove independently characterized cable/launch once. Independent Γv=−.2 load is excluded from fit; repeat it before and after each controlled reconnect. |
| rawEvidence | SYN-VNA-SOL-RAW-v1; SYN-VNA-WRONG-LOAD-RAW-v1 preserves actual load Γ=.02 and assumed0; SYN-VNA-FEED-RAW-v1; SYN-VNA-VERIFY-1P-v1 Γv=−.2. These immutable simulated definitions are not measurements. |
| processing | vna-error-plane-explorer/2.0; p08-m04-one-port-v1: solve [1,Γi,miΓi]·[d,q,s]=mi, t=q+ds; Γ=(m−d)/(t+s(m−d)); then inverse fixture transformation. M08-04-FEED-DERIVED-A references raw and cable model; no double correction. |
| uncertainty | Real standard-model, connection, drift, source/load match, receiver noise, fixture-parameter covariance, bias and thermal contributions unknown. κF and 1e−10 tests are numerical checks, not measurement uncertainty or confidence. |
| result | At 2.450 GHz actual ΓDUT=.5. Cable input −.396380404700−j.024938141268; phase-only .397164117362; exact loss-and-phase removal .5. Wrong-load calibration alone yields Γhat=.484848484848 and unused-load residual .019123505976, failing the .01 local criterion. |
| inference | An apparently improved match behind loss is not improved antenna performance. S11 supplies port evidence only; radiation efficiency, pattern, TRP/TIS and packet behavior require their own evidence. |
| unresolved | Actual standards/fixtures, method covariance, reference-device characterization, connector repeatability, instrument limits and state evidence are required before using hardware data. |
| next | Measurement engineer: check unused load through the same fixture, then compare direct feed-plane calibration if possible. Control cable route/choke effects; send qualified R2 impedance evidence to 08.5 and the Path06 spatial investigation. |
| review | Invalidate on cable movement, reconnect, changed fixture/port mapping, power/gain switching, bias, temperature, firmware or frequency grid; reverify and recalibrate as the cause requires. |
Hand both qualified port-measurement records to 08.5 Modulated Transmitter & Receiver Measurements. Preserve remaining uncertainty and validity conditions when moving from small-signal CW evidence to a modulated operating state.
Check your understanding
Answer each question in your own words, then reveal the model answer.
01What information does a three-term one-port solve add to open-response scaling?
Model answerThree independent known complex standards identify directivity d, reflection tracking t and source match s at each frequency. Scaling m by one open observation fixes one response but cannot identify three independent terms. Repeated standards make the solve singular; a complete two-port calibration also needs both source directions and load-match information.
02Why can the wrong load model produce a perfect calibration-standard fit?
Model answerThe solve matches the assumed standard definitions. An actual Γ = 0.02 load called zero changes the fitted terms. It maps all three fitted standards to those assumptions but recovers the separate −0.2 verification load as −0.219123505976. A small fit residual tests the equations, not the truth of the models.
03Does remeasuring the calibration load provide independent verification?
Model answerIt checks repeatability and some changes, but shares the definition and interface errors used in the fit. Use an unused, independently characterized device with reference values and uncertainty. Keep its observations out of the calibration solve; compare at compatible planes, ports, reference impedance, grid and state.
04Why does phase-only extension leave the cable example at |Γ| = 0.397164117362?
Model answerIt reverses the −176.4° round-trip phase, but leaves 2 dB of round-trip attenuation. The DUT is still Γ = 0.5. A justified matched loss-and-phase inverse restores it; a mismatched launch needs the full network model. Removing an already calibrated cable a second time is also wrong.
05Can a time gate prove a discontinuity no longer affects the DUT?
Model answerNo. It changes the finite-band transformed dataset. Windowing trades sidelobes for impulse width, close reflections overlap, and early reflections can mask later energy. Gating does not repair the hardware, recover missing frequencies or establish absolute calibration accuracy. Retain the ungated data and all transform/gate settings.
06A passive-looking trace clears the residual tolerance after a connection changed. Is the DUT result accepted?
Model answerNo. The unchanged-state validity condition failed. The local residual criterion is only one gate and does not replace uncertainty. Unknown verification is inspect; incompatible or changed evidence is blocked; a singular model or invalid small-signal state is invalid. None is a product pass.
References and further study
Primary-source access: 2026-09-09. vna-error-plane-explorer/2.0; p08-m04-one-port-v1; p08-m04-fixture-cascade-v1; p08-m04-verification-rules-v1. Numerical validation uses 10⁻¹⁰ absolute complex error, 10⁻⁸ dB, 10⁻⁸ degrees for nonzero phase, and 10⁻⁹ relative normalized chain recovery. These are computation tolerances, not measurement uncertainty. IEEE 370 catalogue scope and its 2022 erratum were inspected; the full standard was not available. The two Keysight application-note URLs supplied asset introductions, not readable full PDFs. No unavailable clauses or normative thresholds are asserted.
- VNA-TIME · Keysight. Time Domain · M9485A help. Living documentation; no displayed revision/date. Consulted: Response resolution; alias responses; transform modes; gating and masking; window settings. Informative finite-band transform and gating limits; the original delay/window sketch is qualitative, not a computed transform.
- VNA-ERROR · Keysight. Measurement Errors · PXI VNA help. Living documentation; no displayed revision/date. Consulted: Random Errors; Systematic Errors; individual directivity, match, tracking and isolation descriptions. Informative instrument error orientation; not a complete implementation or specification.
- VNA-APP · Keysight. Applying Error Correction to Vector Network Analyzer Measurements · 5965-7709. Asset identity verified; PDF edition unavailable. Consulted: Accessible asset introduction only. Catalogue/introduction: SOLT, TRL and adapter scope. Full PDF was unavailable; no clause claims.
- VNA-KIT · Keysight. Calibration Standards · M9485A help. Living documentation; no displayed revision/date. Consulted: Standard Definitions; capacitance/inductance models; class assignments. Informative standard/offset model fields. No actual kit coefficients are assumed.
- VNA-KIT-APP · Keysight. Specifying Calibration Standards and Kits · 5989-4840. Asset identity verified; PDF edition unavailable. Consulted: Accessible asset introduction only. Document scope only. Accessible help supplies teaching; full PDF and kit-specific definitions remain unresolved.
- VNA-TRL · Keysight. TRL Calibration · PNA help. Living documentation; no displayed revision/date. Consulted: Cal Standards Used in TRL: THRU, REFLECT, LINE, MATCH. Method-specific line impedance, phase selection and band planning; not a universal phase-only validity rule.
- VNA-LRM · Anritsu. LRL/LRM Calibration Theory and Methodology · 11410-00492. Rev. C, printed January 2017, ©2016. Consulted: pp.1–4: algorithm choices, LRM, line lengths; p.10 revision. Historical informative method distinctions, match assumptions and line separation; not current option availability.
- VNA-EXT · Keysight. Port Extensions · PNA help. Living documentation; no displayed revision/date. Consulted: Why/How to use Port Extensions; data-flow note. Electrical plane motion and optional loss; this lesson explicitly distinguishes its phase-only operation.
- VNA-VERIFY · NIST authors / IEEE Microwave Magazine. Electronic Vector-Network-Analyzer Verification. Williams, Lewandowski, LeGolvan and Ginley; October 2009, pp.119–123. Consulted: Calibration comparison; quantifying verification; uncertainty/covariance discussion. Independent reference comparisons and residual uncertainty; no claim about current service/software availability.
- IEEE370 · IEEE SA. IEEE 370-2020 · Electrical Characterization of PCB and Related Interconnects up to 50 GHz. Active at access; published 2021-01-08. Consulted: Official catalogue identity, scope and errata link. Catalogue only. Full normative text not read; does not prescribe every antenna calibration.
- IEEE370-ERR · IEEE SA. IEEE 370-2020 correction sheet. 21 January 2022. Consulted: Complete two-page erratum; correction to Annex G equation G.1. Erratum identity reviewed; no normative algorithm implemented from the unavailable base text.
- MET-NIST · NIST. TN 1297 · §5 Combined Standard Uncertainty. 1994 guidance; web page updated 2023-03-01. Consulted: 5.1–5.5; combination, correlation and coverage conditions. Uncertainty is distinct from calibration residual and numerical tolerance; no uncertainty budget fabricated.
- MET-INDEX · BIPM / JCGM. Guides in Metrology publication index. Live listing: JCGM 100:2008 and Amd.1:2026. Consulted: GUM, nonlinearity amendment and GUM-6 listings. Current source identity only; inherited 08.1 owns detailed propagation.