Path 06 · Module 03

Antennas in Real Products

The antenna worked until the product was assembled. Follow the current beyond the copper shape, separate retuning from recovery, and choose the experiment that tells you what changed.

Before you begin

Bring 06.1 antenna parameters, 06.2 antenna families, 03.3 real transmission-line structures and 03.6 matching that survives reality. The outcome here is a defensible placement/feed/tuning plan and a controlled integration experiment.

By the end, name the complete radiating configuration; separate detuning, dissipation, angular redistribution and common mode; and specify evidence across use states and units. Detailed PCB execution belongs to Path 10.3; arrays to 06.4; chamber/VNA execution to 06.6 and Path 08; exposure and certification decisions to Path 09. No full-wave solver or product validation is implied.

01 / 10

Failure: the open-board antenna collapses after final assembly

The same antenna and matching parts are fitted. Why did the installed link change?

Our illustrative engineering case is a battery-powered condition-monitoring node near 2.45 GHz. The open board looks promising. Final assembly adds plastic, a battery, fasteners and a mounting assembly. A technician leaves a programming cable attached during a repeat test. The product now has several physical configurations, not one context-free “antenna result.”

Before interpreting a graph, say the unit and mechanical revision, the feed/calibration plane, tune, cable route, surrounding object, orientation and environment. A lower reflection can mean more accepted power. It cannot tell us how much is dissipated or where the radiation goes.

The specimen boundary includes its returnAn antenna arm and feed share the board with a battery, shield, fasteners and an enclosure. Ground and attached conductors can carry RF current. Product x/y lie in the board; z points out toward the viewer.BatteryShieldGroundEnclosureAntenna armR2 feedReturn pathSpecimen x → · y ↑ · z out of board
The specimen boundary includes its return. An antenna arm and feed share the board with a battery, shield, fasteners and an enclosure. Ground and attached conductors can carry RF current. Product x/y lie in the board; z points out toward the viewer. Original qualitative schematic; arrows identify candidate current paths, not measured amplitudes or a solved field map.
Six frozen configurations · p06-m03-integration-v1 · single-frequency illustrative results
Named stateZin at R2 (Ω)Signed S11 (dB)ηrad,R2ηtot,R2
Open board35.000 + j20.000 Ω-10.863598 dB85.714286%78.688525%
Plastic enclosure35.000 − j10.000 Ω-13.529243 dB80.000000%76.450512%
Wall assembly35.000 + j10.000 Ω-13.529243 dB82.857143%79.180887%
Machine mount30.000 − j40.000 Ω-6.020600 dB66.666667%50.000000%
Hand-like proximity50.000 + j0.000 Ωideal match40.000000%40.000000%
Programming cable on open board35.000 + j20.000 Ω-10.863598 dB85.714286%78.688525%

All rows use IFA-like, ground 60 × 40 mm, clearance and object distance 5 mm, bypass, orientation A, matched real 50 Ω source and 1 mW incident at R2. b = 0.1 except the cable row, b = 0.6. Temperature validity is unknown. The wall row uses the battery/conductor proxy for an invented mounting assembly. It is not a wall-material prediction. Full per-state metadata appears in the evidence map.

The enclosed row improves S11 relative to open board while total efficiency falls slightly. The hand-like row has ideal match yet radiates only 40%. In explanatory notation its signed S11 is −∞ dB, ideal model; data uses “ideal match” and a null logarithm rather than a serialized nonfinite number.

Common misconceptionVendor evaluation-board data transfers directly into our enclosure.

It belongs to its evaluation configuration. A repeated part number preserves neither current distribution nor surrounding fields. Carry the board, ground, feed, match, cable, fixture and environment with the claim, then collect product-specific evidence.

The case is frozen as p06-m03-integration-v1. It does not continue measured performance of 06.1’s candidates or select an IFA/flex winner from 06.2. To interpret these independent teaching numbers, first expand the antenna boundary.

02 / 10

The antenna includes the product current distribution

If RF current flows on the board, why would the board be outside the antenna?

The designated antenna conductor launches one current distribution together with its return. An IFA-like arm can excite the finite ground and chassis. The feed location determines how strongly it couples to those available current distributions. Battery metal, a shield bond or a mounting plate can redirect or extend them. “Ground” names a circuit reference; it does not make every point on a finite GHz structure the same potential.

Think of the drawing as a boundary-condition record. If a ground edge is cut, a bond moves, or the chassis becomes connected through a screw, the allowable current paths change. This can change radiation resistance, stored energy and pattern without simply adding heat. A balanced two-arm radiator still interacts with its surroundings even when its intended return is on the other arm.

Current-boundary review · same specimen x/y/z frame
Part of the configurationQuestion to askNext evidence
Antenna conductor + ground/chassisWhere does each feed-terminal current return?Registered current/near-field view and impedance of a controlled reference build.
Ground seam, shield bond, fastenerDoes the connection change RF current continuity?Paired open/bonded or torque-controlled comparison, keeping other metal fixed.
Cable outside the intended returnDid the test create another radiating path?Cable-route/choke perturbation plus current and pattern, not S11 alone.
Common misconceptionThe antenna is only the visibly designated copper shape.

A package or etched arm may excite a much larger structure. Define the whole relevant conductor and field boundary before claiming that two builds contain “the same antenna.”

Go deeperRadiation resistance is a port representation of radiated power

With RMS current I at the chosen equivalent-circuit plane, Prad = |I|²Rrad and Ploss = |I|²Rloss. Rrad accounts for power leaving as radiation; it is not a hot physical resistor. The representation changes with current normalization and plane. A solved current-to-field relation is needed to connect actual geometry to these values. Our coefficients are deliberately supplied instead.

MIT’s Electromagnetics and Applications, Chapter 10, §§10.2–10.3 develops current-to-radiation and radiation-resistance foundations. It does not assign the product sensitivities in this lesson. Once the boundary is named, locate the plane at which its port is being described.

03 / 10

Feed placement, reference plane, matching, and return current

Was the improved match measured ahead of a loss, or at the antenna itself?

R1 is the component/package RF port. R2 is the product antenna-feed reference plane. In this lesson R2 sits immediately before an optional series teaching tuner; R2-A is its bare-antenna side. State this local mapping whenever reporting efficiency. A physical feed between R1 and R2 needs its own characterized transformation.

Move the plane with the network attachedR1 is the component port. A characterized feed connects R1 to R2. The optional series tuner lies between R2 and bare antenna plane R2-A. S0 is radiation; tuner heat stays in the R2 power ledger.R1R2R2-AS0Feedtwo-portRt + jXtseries tunerRrad + Rloss+ jXPinc = 1 mWPacc → radiation + antenna heat + tuner heate^(+jωt) · real 50 Ω reference · f = 2.450 GHz
Move the plane with the network attached. R1 is the component port. A characterized feed connects R1 to R2. The optional series tuner lies between R2 and bare antenna plane R2-A. S0 is radiation; tuner heat stays in the R2 power ledger. Original qualitative schematic; arrows identify candidate current paths, not measured amplitudes or a solved field map.
Zin,R2=Zantenna,R2A+Rt+jXtZ_{\mathrm{in,R2}}=Z_{\mathrm{antenna,R2-A}}+R_{\mathrm{t}}+jX_{\mathrm{t}}One frequency, e^(+jωt), all impedances in Ω. Rt and Xt are the series tuner’s real and reactive contributions.

Place the tuner with a defined return and a documented antenna-side plane. Moving it along an electrically significant feed changes the impedance it sees. A fixed compensation that cancels open-board reactance may reinforce the error in another state. Matching-network topology and physical realization remain the subject of 03.6.

Think about itDetune only: hold Rrad = 30 Ω, Rloss = 5 Ω and the pattern fixed. What changes when X goes from +20 Ω to 0 Ω?
Answer

The mismatch factor improves, so more incident power is accepted and radiated. Bare and composite radiation efficiency remain 30/35 = 6/7; the shape and b remain fixed. Compare complex impedance to confirm the reactive change, and independently check efficiency/pattern to rule out a hidden loss or geometry change. A real material causing only this change remains unestablished.

Detune-only comparison · same pattern β = 1/6, b = 0.1, A, bypass
Bare reactanceZin at R2Signed S11ηrad,R2ηtot,R2
X = 20 Ω35.000 + j20.000 Ω-10.863598 dB85.714286%78.688525%
X = 0 Ω35.000 + j0.000 Ω-15.066553 dB85.714286%83.044983%
Go deeperA plane change can rotate and shrink reflection

For a uniform matched line of length ℓ and propagation constant γ = α + jβline, ΓR1 = ΓR2 e−2γℓ. The round trip rotates phase and, if α > 0, reduces reflection magnitude. Only a lossless matched line preserves |Γ|. An arbitrary feed/fixture requires its two-port network, not a universal subtraction in dB. The interactive ledger begins at R2 and includes no such upstream feed loss.

TI AN058, §6.2 describes feed-point connection and cable calibration in its development-kit context. Its magnitude-preservation shortcut must be restricted to a lossless matched line. IEEE 370-2020’s public scope covers interconnect data quality; no inaccessible de-embedding clause is used here. A correct plane still does not prove a balanced excitation.

04 / 10

Balanced antennas on unbalanced lines

Can the port look matched while the outside of the coax radiates?

Yes. Define both conductor currents in the same longitudinal direction. Opposite signs then describe the intended differential mode. Their shared part describes common mode. Reversing one current’s reference arrow without changing the equations would erase the meaning of this comparison.

A shared current reference reveals common modeBoth conductor currents are defined along +x. Equal and opposite currents give zero common mode. The outside surface of a coax shield can carry a third current distinct from the intended coaxial mode; a choke is placed around that path and must be evaluated in position.Both reference arrows: +x →I1 = +II2 = −ICoax / surrounding chokeOuter-surface current →Idiff = (I1−I2)/2Icm = (I1+I2)/2
A shared current reference reveals common mode. Both conductor currents are defined along +x. Equal and opposite currents give zero common mode. The outside surface of a coax shield can carry a third current distinct from the intended coaxial mode; a choke is placed around that path and must be evaluated in position. Original qualitative schematic; arrows identify candidate current paths, not measured amplitudes or a solved field map.
Idiff=I1I22Icm=I1+I22\begin{aligned}I_{\mathrm{diff}} &= \frac{I_{1} - I_{2}}{2} \\ I_{\mathrm{cm}} &= \frac{I_{1} + I_{2}}{2}\end{aligned}I1 and I2 are RMS phasors in amperes, both referenced along +x. Idiff and Icm may be complex; the following sample is in-phase real arithmetic.

In a supplied algebra example, I1 = +12 mA and I2 = −8 mA give Idiff = 10 mA and Icm = 2 mA. With +10 and −10 mA, Icm = 0. These are invented current inputs, entirely separate from the explorer’s dimensionless C. No equation converts its C to these milliamperes.

The intended coax mode uses the inner conductor and shield’s inner surface. Shield outer-surface current is a different path. A balun provides a balanced/unbalanced transition; a suitably placed choke can impede an unwanted common-mode path. Their frequency response, loss, impedance, orientation and physical placement require evidence. A choke can also change the impedance environment it was meant to stabilize.

Think about itAttach the programming cable: S11 and efficiency are unchanged in the toy. Must the pattern cut stay unchanged?
Answer

No. The fixture holds the entire circuit ledger fixed and changes only b: 0.1 → 0.6. β changes 1/6 → 6/11 and C changes 1/11 → 3/8. Compare a controlled cable route/choke perturbation with current/field and absolute pattern evidence to distinguish redistributed radiation from detuning or dissipation. The real cable’s current, polarization and effect on impedance remain unknown.

Common misconceptionA balun is a magic matching component, and low S11 proves balance.

Balance, impedance transformation and dissipation answer separate questions. Inspect and measure each. A matched port can coexist with an unintended cable radiator, and a well-balanced port need not be 50 Ω.

TI AN058, §§6.2.1–6.2.3 explicitly treats cable attachment, fixed routing and ferrite placement as setup variables. Next, apply that same configuration discipline to conductors inside the product.

05 / 10

Batteries, displays, shields, cables, fasteners, and mounting metal

A metal mounting plate is added. Which result should we expect to change first?

There is no universal ordering. Induced currents can couple to the radiator, alter the return, change stored energy or redirect radiation. A conductor may serve as a useful reflector or counterpoise in one arrangement and produce a poor coverage direction in another. Its conductivity, spacing, size, bonds and orientation matter.

Predict mechanisms before assigning a numerical penalty
Controlled changeCandidate mechanismDiscriminating observation
Battery can or display backplate addedCoupled conductor changes current distribution and reactive loading.Hold spacing and wiring fixed; compare complex Z, efficiency and registered pattern.
Shield seam or fastener torque changedChanged bond impedance redirects return current; contact loss may also change.Document bond/contact condition, repeat assembly, inspect current and loss separately.
Programming cable routed differentlyCommon-mode path and coupling change; cable also has ordinary feed loss when in the RF path.Name which cable is a feed versus a programmer, then compare current, Z and absolute pattern.
Wall assembly versus machine mounting plateMechanical boundary/coupling changes; no universal “metal loss.”Record plate outline, material, spacing, fasteners and product axes; pair the same unit.

In our synthetic machine state Rrad = 20 Ω, Rloss = 10 Ω and X = −40 Ω. These supplied changes identify a teaching problem; they do not predict a plate’s electromagnetic behavior. A ground-size edit changes two coefficients in this toy, while a real ground edit may also change the pattern and loss in ways the toy omits.

Common misconceptionNearby metal only causes loss, and a programming cable is invisible to RF.

Both can participate in currents and coupling. Separate loss from redistribution and mismatch. Do not assign every link decrease to absorption or every resonance change to the antenna arm.

Go deeperKeep mechanical change separate from observation direction

Rotating a complete radiator in homogeneous free space merely changes which product direction points at a fixed receiver. Bringing a mounting plate into its near environment changes the radiator-plus-environment problem itself. Rotating the product relative to a fixed plate also changes that physical problem; it is not the rigid rotation used in orientation B.

Conductors change boundary currents. Materials that appear electrically insulating can change the fields just as consequentially.

06 / 10

Enclosures, adhesives, coatings, tissue/water, and tolerances

Can adding loss make S11 look better?

A dielectric changes electric-field storage through its material response. A lossy dielectric also converts some accepted RF energy to heat. An enclosure, adhesive thickness, coating, moisture or hand-like object can therefore change reactance, dissipation and current distribution at once. The resonance shift is geometry/material specific; “plastic always shifts down” is not a rule.

Think about itHold Rrad = 30 Ω, X = 0, b and pattern fixed. Increase Rloss from 5 Ω to 20 Ω. Which metric improves?
Answer

The total resistance moves from 35 Ω to 50 Ω, so reflection falls to zero. Radiation efficiency falls from 6/7 to 3/5; total efficiency falls from 83.044983% to 60%. Only the loss resistance changed in this constructed comparison. Match plus calibrated radiation evidence distinguishes added dissipation from reactive detuning; the physical origin of that resistance remains unknown.

Loss-only circuit comparison · A, bypass, β = 1/6, Pinc = 1 mW
Changed resistanceZinSigned S11ηrad,R2Prad (mW)
Rloss = 5 Ω35.000 + j0.000 Ω-15.066553 dB85.714286%0.830450
Rloss = 20 Ω50.000 + j0.000 Ωideal match60.000000%0.600000

The canonical hand-like preset is a different comparison: it changes Rrad, Rloss, X and the pattern coefficient together. One menu selection is not one physical-factor experiment. Its perfect match comes with 0.6 mW antenna dissipation and 0.4 mW radiation.

Luomaniemi and colleagues, IEEE TAP 69(7), 2021, include a phone and hand together in their characteristic-mode analysis and distinguish radiated, reactive and loss power. That study supports including the user in the design problem. Its handset geometry, material model and excitation cannot calibrate this node’s coefficients or guarantee performance for a different grip.

Common misconceptionPlastic cannot affect an antenna because it is not metal.

Field storage and dielectric loss can change even without a conducting return. Specify material grade, thickness, placement, moisture and temperature; a familiar trade name alone is insufficient evidence.

Go deeperTolerance belongs to the configuration, not a generic ±dB allowance

Antenna placement, ground outline, adhesive stack, battery position, fastener contact and matching-part tolerances may interact. Do not add assumed independent variances when the assembly process couples them. Separate measured variation across identified units from reconnect and reassembly variation on one unit. The toy has no tolerance distribution or temperature law.

A candidate clearance must also protect the receiver from fields produced inside its own product.

07 / 10

Clearance, keepout, and coupling to noisy circuits

The passive antenna evidence looks stable. Why does reception worsen when the display turns on?

The antenna is also a coupling path into a receiver. A clock, display interconnect or switching supply can couple through fields or a shared return, raising self-noise or creating a spur near the wanted channel. Passive S11 says little about that operating-state disturbance. Keepouts reserve a controlled electromagnetic region; they are not decorative empty rectangles.

Placement review · explain the purpose of each reserved region
ReservationPhysical questionControlled test
Near the feed and return junctionWill routing or a bond change intended current continuity?Record both current paths and compare the same feed/calibration fixture.
Near strong electric fields / antenna endsDoes nearby material load stored fields or dissipate energy?Change one spacer/adhesive thickness on the same build; retain efficiency evidence.
Near current maxima / shared returnCan nearby conductors couple or create another return path?Use current/near-field evidence with explicit probe location; no universal clearance distance.
Clock/display/power circuitryDoes a working radio ingest self-generated noise?Hold wanted signal and RF configuration fixed; toggle one operating mode and compare noise/sensitivity.

As a first-party implementation example, Antenova’s flexiiANT Integration Guide (2 September 2021) makes cable placement, orientation and surrounding circuitry part of FPC integration. Use the selected antenna’s own evaluation conditions; its routing advice is not a universal keepout specification. In this lesson the clearance coefficient is an arbitrary 5 Ω/mm teaching slope, not a PCB rule.

Think about itA display-on test worsens receiver sensitivity but leaves passive match unchanged. Is antenna efficiency known to have fallen?
Answer

No. A self-noise hypothesis is compatible with those observations. Hold hardware, wanted signal, tune and cable fixed, then compare operating-state noise or sensitivity with the display on/off. Efficiency and coupling mechanisms remain separate questions; no noise value is generated by our circuit model.

Record placement intent now; defer detailed stack-up, via, routing and grounding execution to Path 10.3. Next we organize all these changes into states a tuning policy can actually support.

08 / 10

Multiple user/mechanical states need a tuning strategy

Should one tune cover every state, or should the product recognize different states?

First decide which states are normal use, which are corners and which belong only to the test setup. Open board is a correlation reference; enclosed, wall and machine are installation states; hand-like proximity is a use/corner hypothesis; a programming cable is a debug state unless the product ships with it. None of these labels establishes how often a user encounters a state.

Rotate the specimen without changing itOrientation B is a rigid +90 degree rotation about world y. World +z is product −x and world +x is product +z. A fixed receiver samples a new direction. In homogeneous free space the total radiated power is unchanged; adding a hand or mounting plate changes the physical configuration.AB+z+x+z product+x product+90°about yWorld +z ↑ · world +x → · y perpendicular to this view
Rotate the specimen without changing it. Orientation B is a rigid +90 degree rotation about world y. World +z is product −x and world +x is product +z. A fixed receiver samples a new direction. In homogeneous free space the total radiated power is unchanged; adding a hand or mounting plate changes the physical configuration. Original qualitative schematic; arrows identify candidate current paths, not measured amplitudes or a solved field map.
Think about itCancel the machine state’s −j40 Ω perfectly. Have radiation loss and pattern recovered?
Answer

Only net reactance is cancelled. Reflection falls from 25% to 6.25% and total efficiency rises from 50% to 62.5%, but radiation efficiency stays 2/3 and β stays 1/2. Add a 2 Ω tuner loss and composite efficiency becomes 62.5%, with total efficiency 1000/1681 ≈ 59.488400%. Bare efficiency is still 2/3. Hold geometry, b and direction fixed; independent efficiency and pattern evidence distinguish better port acceptance from recovered radiation. Real tuner bandwidth, loss and stress remain unknown.

Machine mount · identical mechanics, A, b = 0.1; tuner-only comparison
Series tunerZin at R2Reflected fractionηrad,R2-A / R2ηtot,R2
Bypass30.000 − j40.000 Ω0.25000066.666667% / 66.666667%50.000000%
Ideal cancellation at 2.450 GHz30.000 + j0.000 Ω0.06250066.666667% / 66.666667%62.500000%
Lossy cancellation · Rt = 2 Ω32.000 + j0.000 Ω0.04818666.666667% / 62.500000%59.488400%

Exact machine fractions: bypass reflection 1/4, ideal cancellation 1/16, lossy cancellation 81/1681. Tuner heat in the lossy row is 100/1681 mW, antenna heat 500/1681 mW and radiation 1000/1681 mW. Add reflected 81/1681 mW to recover exactly 1 mW.

Conditional tuning strategies · no topology chosen by a single S11 point
StrategyWhat must be trueAdditional evidence/burden
Fixed production tuneA common setting meets match, loss and coverage across required states.Band/corner data, BOM tolerance, repeatable manufacturing and service access.
Switched settingsA small known state set benefits from separate settings.Switch loss, state detection, transitions and a correct setting in ambiguous states.
Adaptive tuningUseful changes can be sensed and corrected in operation.Convergence, sensing, tuning range, stability, current use and added loss; sensed match cannot prove efficiency.
Per-unit production adjustmentAdjustment fixes permitted variation under a specified reference condition.Calibration time, measurement uncertainty, locked configuration and retention across temperature/use.
Common misconceptionRetuning S11 restores lost efficiency and pattern.

Reactive compensation changes port acceptance. It does not remove dissipative material or restore a former current distribution. A finite-loss tuner adds another power destination; its loss must remain visible.

Follow the integration experiment

Predict first, then compare open/enclosed → hand-like proximity → machine with ideal/lossy cancellation → cable on open board → rigid orientation B. Finally select a suspected mechanism and reveal its evidence request. Return to the named open-board reference after each comparison; never silently replace it with the last edited state.

Predict → compare → request evidence

Integration Perturbation Map

Illustrative circuit/pattern teaching model — no product prediction.

antenna-integration-perturbation/2.0 · p06-m03-integration-v1. Fixed: f = 2.450 GHz, matched 50 Ω source, Pinc = 1 mW at R2. Series tuner inside R2; no upstream feed loss. This single-frequency toy cannot produce a frequency sweep or validate temperature/material behavior.

Each preset restores every physical field, orientation A and its metadata. Reset restores plastic enclosure and world +x. The open-board comparison always stays fixed.
Physical configuration · apply edits together
Toy baselines; no typical family performance claim.
One aggregate object; this menu changes several circuit/pattern coefficients.
20100; step 1; default 60.
20100; step 1; default 40.
120; step 0.5; default 5.
0.550; step 0.5; default 5. With object none, distance has no effect.
01; step 0.05; default 0.1. Dimensionless parameter, not measured current.
Bypass / fixed Xt = −20 Ω / cancellation with Rt = 0 or 2 Ω. No broadband tuning model.
Inverse rotation: world +z → product −x; world +x → product +z. Power integral is unchanged.

Viewing a direction changes no circuit value, preset or physical orientation.
enclosed · canonical configuration

Plastic enclosure · mechanical M3-E; PCB P3 / antenna A3 / BOM B3 teaching identifiers. IFA-like; ground 60 × 40 mm in product x/y; clearance 5 mm; Plastic at 5 mm; b = 0.1; Bypass; orientation A. Battery/display/shield/fastener/adhesive: absent from the circuit except the selected aggregate object proxy. Cable: absent from named case; residual b = 0.1 is an invented baseline. Temperature/material validity unknown. R2 at tuner input, R2-A at antenna; no R1 feed loss in this ledger. S0 scalar power, no polarization basis.

Zin at R2 · 2.450 GHz / 50 Ω
35.000 − j10.000 Ω
|Γ| · signed S11 / positive RL
0.210639 · -13.529243 dB / 13.529243 dB
Radiation efficiency · bare R2-A / composite R2
80.000000% / 80.000000%
Total efficiency · Prad / Pinc at R2
76.450512%
Absolute realized gain · S0 world +x
0.849450 linear · -0.708621 dBi
C = b/(1+b) · uncalibrated proxy
0.090909 dimensionless · no amperes
R2 power ledger · mW · Pinc = 1.000000 mW
Power destination / transformationCurrentOpen-board A reference
Reflected · Pinc |Γ|²0.0443690.081967
Accepted · Pinc (1−|Γ|²), subtotal0.9556310.918033
Antenna dissipation · Pacc Rloss / Rsum0.1911260.131148
Tuner dissipation · Pacc Rt / Rsum0.0000000.000000
Radiated at S0 · Pacc Rrad / Rsum0.7645050.786885

Conservation: reflected + antenna loss + tuner loss + radiated = 1 mW. Accepted power is a subtotal, never an extra destination. Residual: 0.000000000000 W.

World x/z normalized power cut, orientation ASolid blue is the current configuration, dashed navy is the fixed open-board reference in orientation A. Linear radius is q divided by the peak in this cut, not field amplitude or dBi. The adjacent table supplies absolute realized gain and all six directions. Current beta 0.259259, reference beta 0.166667.+z world+x−x−z world0.251S0 · q / peak in cut · linear power
Illustrative circuit/pattern teaching model — no product prediction. antenna-integration-perturbation/2.0. Solid: current; dashed: open board A. α starts at world +z and turns toward +x; y = 0. Each cut is normalized to its own peak, max(β, 1−β). ±y is outside this cut and has D = 1.5. Scalar mixture only: no polarization, phase addition, measured current, or product coverage prediction.
Absolute scalar direction samples · S0 / incident power at R2
World directionD (linear)Greal (linear)Greal (dBi)Open-board A (dBi)
+x1.1111110.849450-0.708621 dBi-0.071786 dBi
−x1.1111110.849450-0.708621 dBi-0.071786 dBi
+y1.5000001.1467580.594717 dBi0.720027 dBi
−y1.5000001.1467580.594717 dBi0.720027 dBi
+z0.3888890.297308-5.267941 dBi-7.061486 dBi
−z0.3888890.297308-5.267941 dBi-7.061486 dBi

What changed relative to the open board?

With Pinc fixed, Prad ratio = mismatch-factor ratio × composite-radiation-efficiency ratio = 1.040956 × 0.933333 = 0.971559. In world +x, multiply by D ratio 0.888889 to obtain realized-gain ratio 0.863608. These are arithmetic factors, not identified physical causes.

Ground and clearance change circuit coefficients here; b changes only β and C. The object menu changes several coefficients together. Tuning changes port acceptance and possibly dissipation, while β and C stay fixed. Orientation changes directional readings while the entire scalar power ledger stays fixed.

Inspect every circuit and pattern contribution
Exact evaluated contributions · resistance/reactance in Ω
QuantityValueWhere it belongs
Rrad / Rloss / X28.000000 / 7.000000 / -10.000000Bare antenna R2-A
Rt / Xt0.000000 / 0.000000Series transformation from R2-A to R2
a_d / g / ΔXclear1.000000 / 0.000000 / 0.000000First two unitless; final quantity Ω
β / C0.259259 / 0.090909Unitless shape weight / uncalibrated proxy

Rsum = Rrad + Rloss + Rt. Bare efficiency uses Rrad/(Rrad+Rloss); composite R2 efficiency includes Rt once. Cancelling reactance does not transform the remaining real resistance to 50 Ω. Temperature response, actual material validity, vector polarization, measured common-mode current, and product uncertainty remain unknown.

Choose the next discriminating experiment

Reactance / detuning: Same unit, cable, R2 plane and tune; change only the named geometry or material. Controlled complex impedance over a declared frequency grid; retain separate loss and pattern questions.

The complete teaching model

Illustrative circuit/pattern teaching model — no product prediction. Model antenna-integration-perturbation/2.0, fixture p06-m03-integration-v1. IFA-like baseline (Rrad0, Rloss0, X0) = (30, 5, 20) Ω; flex-like = (60, 5, 20) Ω. These are hypothetical circuit parameters, not typical antenna-family values.

Pinned object coefficients · no material-property fit
Object proxyΔRrad (Ω)ΔRloss (Ω)ΔX (Ω)p (unitless)
None0000
Plastic-22-300.15
Battery / conductor-11-100.1
Machine metal-105-600.8
Hand-like lossy-1025-200.5
ad=10d+5g=12[60Lg60+40Wg40]ΔXclear=5(5clearance)Ω\begin{aligned}a_{d} &= \frac{10}{d + 5} \\ g &= \frac{1}{2}[\frac{60 - L_{g}}{60} + \frac{40 - W_{g}}{40}] \\ \Delta X_{\mathrm{clear}} &= 5(5 - \mathrm{clearance}) \Omega\end{aligned}d, Lg, Wg and clearance are numerical millimetres in these interpolation laws; a_d and g are dimensionless. No term is a universal proximity law.
Rrad=Rrad0+adΔRrad+4gΩRloss=Rloss0+adΔRlossX=X0+adΔX+20gΩ+ΔXclear\begin{aligned}R_{\mathrm{rad}}&=R_{\mathrm{rad0}}+a_d\Delta R_{\mathrm{rad}}+4g\,\Omega\\R_{\mathrm{loss}}&=R_{\mathrm{loss0}}+a_d\Delta R_{\mathrm{loss}}\\X&=X_0+a_d\Delta X+20g\,\Omega+\Delta X_{\mathrm{clear}}\end{aligned}Rrad0, Rloss0, X0 and object increments are in Ω. The ground coefficients are 4 Ω and 20 Ω.

Permitted controls: ground length/width 20–100 mm in 1 mm steps; clearance 1–20 mm and distance 0.5–50 mm in 0.5 mm steps; b = 0–1 in 0.05 steps. Default is 60 × 40 mm, clearance/distance 5 mm, b = 0.1, plastic, IFA-like, bypass, A. A rigid orientation and the key-direction view are different controls. Object “none” has zero coefficients, so distance cannot change its result.

Tuner choices are bypass (Xt = Rt = 0); fixed open-board compensation (Xt = −20 Ω, Rt = 0); ideal cancellation (Xt = −X, Rt = 0); and lossy cancellation (Xt = −X, Rt = 2 Ω). These are series demonstrations at one frequency, not synthesized L/C or adaptive networks. Cancelling X leaves real mismatch whenever Rrad + Rloss + Rt differs from 50 Ω.

Γ=Zin50Zin+50ηrad,R2=RradRrad+Rloss+Rtηtot,R2=(1Γ2)ηrad,R2\begin{aligned}\Gamma&=\frac{Z_{\mathrm{in}}-50}{Z_{\mathrm{in}}+50}\\\eta_{\mathrm{rad,R2}}&=\frac{R_{\mathrm{rad}}}{R_{\mathrm{rad}}+R_{\mathrm{loss}}+R_{\mathrm{t}}}\\\eta_{\mathrm{tot,R2}}&=(1-|\Gamma|^2)\eta_{\mathrm{rad,R2}}\end{aligned}Real Z0 = 50 Ω, matched source; Zin includes tuner. ηrad,R2 includes tuner dissipation, while ηrad,R2-A = Rrad/(Rrad+Rloss) does not.
Pacc=Pinc(1Γ2)[Prad,Ploss,Ptuner]=Pacc[Rrad,Rloss,Rt]Rsum\begin{aligned}P_{\mathrm{acc}} &= P_{\mathrm{inc}}(1 - |\Gamma|^{2}) \\ [P_{\mathrm{rad}}, P_{\mathrm{loss}}, P_{\mathrm{tuner}}] &= \frac{P_{\mathrm{acc}} [R_{\mathrm{rad}}, R_{\mathrm{loss}}, R_{t}]}{R_{\mathrm{sum}}}\end{aligned}All powers in W; Pinc = 0.001 W. Every resistance shares the same series RMS current at this single frequency.

For the scalar pattern, x and z are components of a unit observation direction in the product frame. θ is measured from +z and φ from +x toward +y. t below is a dimensionless mixing variable, not time. Both shape terms integrate to 8π/3, so the same normalization applies to every mixture.

t=adp+2b,β=t1+tq=(1β)(1z2)+β(1x2)D=1.5q,Greal=ηtot,R2D\begin{aligned}t&=a_dp+2b,\quad\beta=\frac t{1+t}\\q&=(1-\beta)(1-z^2)+\beta(1-x^2)\\D&=1.5q,\quad G_{\mathrm{real}}=\eta_{\mathrm{tot,R2}}D\end{aligned}β is a convex weight. The uncalibrated common-mode proxy C = b/(1+b) is dimensionless and never a physical current.

∫D dΩ = 4π and q ≥ 0. This is a mixture of power shapes, not coherent vector-field addition. It cannot produce polarization, axial ratio, cable-current radiation, SAR, or a measured efficiency. For B apply the inverse +90°-about-y rotation to a world direction before evaluating q: (xproduct, yproduct, zproduct) = (−zworld, yworld, xworld). The integral and power ledger stay unchanged.

No-script / print direction reference · absolute Greal, linear, at S0
Canonical state±x in A±y in A or B±z in A±x in B±z in B
Open board0.9836071.1803280.1967210.1967210.983607
Plastic enclosure0.8494501.1467580.2973080.2973080.849450
Wall assembly0.9136261.1877130.2740880.2740880.913626
Machine mount0.3750000.7500000.3750000.3750000.375000
Hand-like proximity0.3529410.6000000.2470590.2470590.352941
Programming cable on open board0.5365131.1803280.6438150.6438150.536513
Go deeperCheck the model before interpreting a control sweep

Across the full domain, −13/12 ≤ g ≤ 7/12 and 2/11 ≤ a_d ≤ 20/11. The smallest Rrad is 247/33 Ω ≈ 7.484848 Ω, with IFA-like, machine/hand object, closest distance and largest ground. Rloss ≥ 5 Ω. The largest t is 38/11, so 0 ≤ β ≤ 38/49 < 1. All resistance fractions are positive, tuner loss is nonnegative, and ηtot ≤ ηrad ≤ 1. These are model-validity proofs, not bounds on product performance.

The map tells you which observables to request. A reproducible build and a correlation plan turn that request into an engineering experiment.

09 / 10

Coupons, prototypes, simulation correlation, and configuration control

What does a simulation-to-measurement discrepancy mean if the cable or mechanical build changed?

It may mean the two sides describe different experiments. Freeze a reference build before fitting parameters. A coupon can isolate a feed launch, material stack or matching part, but it does not establish the final chassis current distribution. A representative prototype contains the physical boundaries needed for the question. Keep both kinds of evidence and label which one they provide.

One reproducible correlation reference

Proposed correlation reference REF-M3: unit U01, PCB P3, antenna A3, mechanical M3-O, BOM B3; IFA-like teaching configuration, 60 × 40 mm ground, 5 mm clearance, open board, bypass. Battery/display/shield/adhesive/fasteners absent for the reference coupon. Characterized 50 Ω R2 fixture at tuner input; actual cable C1 route, connector launch and choke CH1 position require drawings before execution. A aligned with world axes; requested chamber ambient 25 °C. These are proposed identifiers, not built or measured specimens.

The measured reference will include its actual fixture and its uncertainty. The mathematical open-board preset is cable-free; do not silently relabel a cabled measurement as that preset. Correlate the as-measured configuration first, then justify any transformation to a cable-free quantity.

Configuration control and parameter ownership
OwnerFreeze before comparisonEvidence that tests the assumption
RF / antennaAntenna revision, feed location, ground/return, tuner BOM and reference-plane map.Complex impedance plus accepted/radiated power at compatible planes.
Mechanical / materialsCAD, enclosure and adhesive grade/thickness, battery/display/shield, fasteners/torque, mount and phantom position.As-built dimensions/photos and material characterization with frequency/temperature.
Test / metrologyCable/connector/choke route, fixture, instrument/method revision, calibration, coordinates, grids, uncertainty.Begin/end reference and reconnect repeats; traceable calibration and stable setup.
ManufacturingU01/U02/U03 identities, component lot, placement and assembly records.Across-unit variation separated from repeated reassembly of one unit.
System / firmwareSupply, radio mode, clock/display/power state, receiver criterion and wanted signal.Noise/sensitivity comparison with a frozen passive RF configuration.

Correlate complex impedance, efficiency and absolute directional gain; matching a resonance point alone is weak evidence. Use held-out states or units to test a model adjustment. If several material or geometric parameters can explain one trace, preserve that ambiguity and choose another observable. An uncalibrated field image can suggest a current path, but it does not become an ampere reading.

Common misconceptionOne golden unit proves manufacturability.

Repeatedly measuring one well-tuned unit tests repeatability, not population variation. Three identified units improve the experiment but still do not establish a production distribution or yield. Record component, placement and assembly differences instead of hiding them in one margin.

Go deeperCorrelation needs an uncertainty-aware decision

Differences contain model discrepancy, material/configuration error and measurement uncertainty. State the acceptable residual for each quantity before fitting. A broad match can conceal loss; a normalized pattern can conceal absolute power error. Compare absolute units at the same planes and retain unresolved nulls below the measurement floor. An agreement goal is an original project requirement, not a standard limit.

Now choose the smallest set of paired observations that can distinguish these competing explanations.

10 / 10

Define node integration variants and acceptance evidence

Which comparison would make you change the integration decision?

Write the hypothesis before the test. Preserve one complete reference and change an identified factor or a deliberately named bundle. Record mechanical revisions, ground and return, battery/display/shield/fastener/adhesive configuration, feed/tune/cable/choke, object geometry/material/distance, orientation, frequency grid, unit, temperature, instrument/method owner, uncertainty and intended comparison.

Completed integration DOE · requirements, no observed results
StageFactor matrix / countRequested conditionsDecision supported
DOE-SCREEN6 states × 2 orientations × U01/U02/U03 = 36 observations25 °C requested; Bypass in all 36 observationsPaired integration screening. The wall state is a conductor mounting-assembly stand-in, not every wall material. Cable state pairs with the open board.
DOE-FOLLOWWall assembly and machine mount × 2 tunes × 2 temperatures × 2 orientations × U01/U02/U03 = 48 observations0 °C and 50 °C requested; Bypass and one documented fixed production candidateConditional follow-up if both mounting assemblies remain actual finalists. Reopen geometry if radiation/coverage misses; do not choose the winner from S11. No synthetic temperature result exists.

One “observation” here is the complete planned frequency/angular evidence set for a unit/state/orientation, not one independent population sample. The 36-row screen is six mechanical/use states × A/B × U01/U02/U03. The conditional 48-row follow-up explicitly selects wall assembly and machine mount as the two actual installation finalists, bypass and one physically documented fixed tune, 0/50 °C, A/B and the same three units. If those installations cease to be finalists, revise the plan and count before testing.

The local requested band is 2.401–2.499 GHz, matching 06.2’s 4% symmetric request; it does not replace 06.1’s separate 2.400–2.500 GHz and five-unit proposal. The toy calculates only 2.450 GHz. A temperature such as 0 °C or 50 °C is a requested test condition, never a hidden model input or a measured pass.

Hypotheses → paired comparison → observable
HypothesisHold and changeEvidence needed
Reactance / detuningSame unit, cable, R2 plane and tune; change only the named geometry or material.Controlled complex impedance over a declared frequency grid; retain separate loss and pattern questions.
Dissipative lossSame geometry and power plane; compare matched acceptance and integrated radiation.Calibrated radiation efficiency plus S11, uncertainty and both polarizations; a better match cannot identify absorption.
Pattern redistributionSame physical build; compare registered sphere/cuts, then repeat rigid orientation A/B.Absolute directional gain and integrated power with compatible coordinates; a cut cannot determine total power.
Cable common modeCable-free reference versus cable route C1/C2 and a specified choke position, same unit and plane.Outer-surface current or calibrated near-field evidence, plus S11 and pattern. C supplies neither amperes nor cable EIRP.
Receiver self-noiseSame antenna/mechanics, radio receive state and wanted signal; toggle one clock/display/power mode.Input-referred noise or operating-state sensitivity/PER with interference and receiver conditions. The toy has no noise calculation.

Pair cable-attached and cable-free open-board states on the same unit. For a hand-like phantom, record material properties and their source, shape, spacing, side, fixture and contact pressure if applicable. For wall/machine fixtures, record dimensions, electrical bonds, fasteners and whether orientation rotates the whole assembly. Do not treat A/B relative to a stationary mounting plate as rigid free-space rotation.

Proposed thresholds and acceptance logic · original illustrative requirements
Rule IDQuantity / limitConditions and decision
TH-MATCHSigned S11 ≤ −10 dB at real 50 Ω R2Each sample 2.401–2.499 GHz, 1 MHz spacing (99 points); worst per unit/state. Upper expanded-uncertainty bound must meet the limit.
TH-EFFComposite ηrad,R2 ≥ 40% including tuner lossAt 2.401, 2.450, 2.499 GHz, full sphere with both polarizations; lower expanded-uncertainty bound must meet 40%. Also report bare R2-A efficiency.
TH-COVERCo-polar realized gain ≥ −6 dBi in the requested world sectorWorld θ 60°–120°, all φ on a 5° grid; co=eθ, cross=eφ; both A/B. Same three frequencies. Lower bound meets limit including justified interpolation uncertainty; otherwise grid-only evidence.
TH-CORRELATE|ΔRe Z| and |ΔIm Z| ≤ 2 Ω; |Δηrad| ≤ 3 percentage points; |ΔGreal| ≤ 1 dBProposed simulation/measurement agreement goals at common planes, frequencies and states. Compare gain only at declared samples above −25 dBi measurement floor; null depth remains unresolved below floor. Include combined uncertainty in each bound.
TH-REPEATReconnect spread ≤ 1 Ω per impedance component; ≤ 0.5 dB directional gainProposed setup-stability goals for repeated REF-M3 before/after/reconnect. If exceeded, investigate fixture/cable/drift before assigning change to product. Physical current threshold still unknown; RF/test owners must agree one.

All thresholds are proposed engineering requirements, not achieved values or regulatory limits. Report expanded uncertainty with k = 2 and its justified coverage. If the relevant bound fails, investigate/redesign; if uncertainty, material validity or measurement coverage is missing, the decision remains unknown. A numeric toy output never passes a physical requirement. Common-mode current and receiver self-noise need application-specific limits agreed by their owners.

Keep the experiment identifiable

Repeat REF-M3 at run start/end and after reconnecting; add these checks beyond the 36/48 counts. Randomize unit/state order within practical blocks. Block temperature when thermal settling makes random switching impractical, then counterbalance unit and tuner order within each block. Record order and dwell so temperature drift is not mistaken for tuner benefit. Cable changes, mechanical reassembly and tuner changes made together are confounded unless separately paired.

Compare repeated readings and reconnects on one unit for setup repeatability; compare U01–U03 for unit variation. A conditional fixed tuning strategy survives only if the uncertainty-bounded match, radiation and coverage requirements all hold in the named states. If good match hides loss, reopen material/placement/current paths. If only a repeatable state-dependent mismatch remains, investigate switched/adaptive tuning with its detection and loss burden.

Antenna and channel evidence map

This is a complete local p06-evidence-map-v1 snapshot, available without an earlier visit or saved state. It preserves M01-INSTALL-UNKNOWN and adds six local synthetic rows plus the proposed plan. R2-TX and R2-RX, when used elsewhere, map to portfolio R2; R3 stays the detector/decision boundary. Incident, accepted, available receive, delivered receive, directional EIRP and integrated TRP are different quantities. No receive power, channel success or product certification is inferred here.

p06-evidence-map-v1 · complete static 06.3 snapshot
ID / owner / labelQuestion, specimen, quantityConfiguration / basisDecision / next evidence
M01-INSTALL-UNKNOWN

Owner 06.1

Illustrative

Will the node work in its intended states?

Fixture: N1 product requirement; no specimen evidence supplied

Frequency: 2.400–2.500 GHz requirement band

Quantity/unit: Match, efficiency, gain, vector pattern, and channel/link performance: unknown

Plane/losses: R2: real 50 Ω, matched source; S0: radiation. No upstream feed loss. Realized gain includes mismatch and antenna dissipation once.

Configuration: Free space, metal-machine plate, plastic enclosure, hand phantom; O1 +z upright, O2 rotated 90° about +y. Drawings/phantom specification still required.

Coordinates/polarization: Right-handed specimen x/y/z; θ from +z, φ from +x toward +y. Total scalar power; vector co/cross/AR unknown.

Population/statistic: Five proposed prototypes; no observed population or uncertainty yet.

Source: Illustrative engineering case / proposed evidence plan

Assumptions/uncertainty: Gateway may use two antennas; no diversity or channel benefit assigned. Missing evidence is unknown.

Decision: No installed antenna, channel, or product compliance decision.

Next evidence: Freeze mechanics and coordinates; family selection in 06.2, installation in 06.3, channel in 06.5, measurement execution in 06.6.

M03-OPEN

Owner 06.3

Illustrative

Which mechanisms could explain the open board comparison?

Fixture: p06-m03-integration-v1

Frequency: 2.450 GHz model only

Quantity/unit: Zin 35.000 + j20.000 Ω; composite ηrad 85.714286%; ηtot 78.688525%; β 0.166667; C 0.090909 (unitless).

Plane/losses: Real 50 Ω R2 at tuner input; R2-A bare antenna; R2 includes Rt once; upstream R1 feed absent. S0 integrated/scalar directional power.

Configuration: Open board · mechanical M3-O; PCB P3 / antenna A3 / BOM B3 teaching identifiers. IFA-like; ground 60 × 40 mm in product x/y; clearance 5 mm; None at 5 mm; b = 0.1; Bypass; orientation A. Battery/display/shield/fastener/adhesive: absent from the circuit except the selected aggregate object proxy. Cable: absent from named case; residual b = 0.1 is an invented baseline. Temperature/material validity unknown. R2 at tuner input, R2-A at antenna; no R1 feed loss in this ledger. S0 scalar power, no polarization basis.

Coordinates/polarization: Right-handed product x/y/z; θ from +z, φ from +x toward +y. A unrotated; B +90° about world y. Scalar total power; vector co/cross/AR unknown.

Population/statistic: Deterministic synthetic case, one configuration; no physical units or population observed.

Source: antenna-integration-perturbation/2.0; independent integration-golden.json

Assumptions/uncertainty: Circuit/pattern teaching parameters, not measured material properties. Temperature, physical current and physical uncertainty unknown.

Decision: Choose paired impedance, radiation and current evidence; installed performance remains unknown.

Next evidence: Freeze mechanics/cable and compare calibrated complex impedance, full-sphere efficiency and absolute vector pattern.

M03-ENCLOSED

Owner 06.3

Illustrative

Which mechanisms could explain the plastic enclosure comparison?

Fixture: p06-m03-integration-v1

Frequency: 2.450 GHz model only

Quantity/unit: Zin 35.000 − j10.000 Ω; composite ηrad 80.000000%; ηtot 76.450512%; β 0.259259; C 0.090909 (unitless).

Plane/losses: Real 50 Ω R2 at tuner input; R2-A bare antenna; R2 includes Rt once; upstream R1 feed absent. S0 integrated/scalar directional power.

Configuration: Plastic enclosure · mechanical M3-E; PCB P3 / antenna A3 / BOM B3 teaching identifiers. IFA-like; ground 60 × 40 mm in product x/y; clearance 5 mm; Plastic at 5 mm; b = 0.1; Bypass; orientation A. Battery/display/shield/fastener/adhesive: absent from the circuit except the selected aggregate object proxy. Cable: absent from named case; residual b = 0.1 is an invented baseline. Temperature/material validity unknown. R2 at tuner input, R2-A at antenna; no R1 feed loss in this ledger. S0 scalar power, no polarization basis.

Coordinates/polarization: Right-handed product x/y/z; θ from +z, φ from +x toward +y. A unrotated; B +90° about world y. Scalar total power; vector co/cross/AR unknown.

Population/statistic: Deterministic synthetic case, one configuration; no physical units or population observed.

Source: antenna-integration-perturbation/2.0; independent integration-golden.json

Assumptions/uncertainty: Circuit/pattern teaching parameters, not measured material properties. Temperature, physical current and physical uncertainty unknown.

Decision: Choose paired impedance, radiation and current evidence; installed performance remains unknown.

Next evidence: Freeze mechanics/cable and compare calibrated complex impedance, full-sphere efficiency and absolute vector pattern.

M03-WALL

Owner 06.3

Illustrative

Which mechanisms could explain the wall assembly comparison?

Fixture: p06-m03-integration-v1

Frequency: 2.450 GHz model only

Quantity/unit: Zin 35.000 + j10.000 Ω; composite ηrad 82.857143%; ηtot 79.180887%; β 0.230769; C 0.090909 (unitless).

Plane/losses: Real 50 Ω R2 at tuner input; R2-A bare antenna; R2 includes Rt once; upstream R1 feed absent. S0 integrated/scalar directional power.

Configuration: Wall assembly · mechanical M3-W; PCB P3 / antenna A3 / BOM B3 teaching identifiers. IFA-like; ground 60 × 40 mm in product x/y; clearance 5 mm; Battery / conductor at 5 mm; b = 0.1; Bypass; orientation A. Battery/display/shield/fastener/adhesive: absent from the circuit except the selected aggregate object proxy. Cable: absent from named case; residual b = 0.1 is an invented baseline. Temperature/material validity unknown. R2 at tuner input, R2-A at antenna; no R1 feed loss in this ledger. S0 scalar power, no polarization basis.

Coordinates/polarization: Right-handed product x/y/z; θ from +z, φ from +x toward +y. A unrotated; B +90° about world y. Scalar total power; vector co/cross/AR unknown.

Population/statistic: Deterministic synthetic case, one configuration; no physical units or population observed.

Source: antenna-integration-perturbation/2.0; independent integration-golden.json

Assumptions/uncertainty: Circuit/pattern teaching parameters, not measured material properties. Temperature, physical current and physical uncertainty unknown.

Decision: Choose paired impedance, radiation and current evidence; installed performance remains unknown.

Next evidence: Freeze mechanics/cable and compare calibrated complex impedance, full-sphere efficiency and absolute vector pattern.

M03-MACHINE

Owner 06.3

Illustrative

Which mechanisms could explain the machine mount comparison?

Fixture: p06-m03-integration-v1

Frequency: 2.450 GHz model only

Quantity/unit: Zin 30.000 − j40.000 Ω; composite ηrad 66.666667%; ηtot 50.000000%; β 0.500000; C 0.090909 (unitless).

Plane/losses: Real 50 Ω R2 at tuner input; R2-A bare antenna; R2 includes Rt once; upstream R1 feed absent. S0 integrated/scalar directional power.

Configuration: Machine mount · mechanical M3-M; PCB P3 / antenna A3 / BOM B3 teaching identifiers. IFA-like; ground 60 × 40 mm in product x/y; clearance 5 mm; Machine metal at 5 mm; b = 0.1; Bypass; orientation A. Battery/display/shield/fastener/adhesive: absent from the circuit except the selected aggregate object proxy. Cable: absent from named case; residual b = 0.1 is an invented baseline. Temperature/material validity unknown. R2 at tuner input, R2-A at antenna; no R1 feed loss in this ledger. S0 scalar power, no polarization basis.

Coordinates/polarization: Right-handed product x/y/z; θ from +z, φ from +x toward +y. A unrotated; B +90° about world y. Scalar total power; vector co/cross/AR unknown.

Population/statistic: Deterministic synthetic case, one configuration; no physical units or population observed.

Source: antenna-integration-perturbation/2.0; independent integration-golden.json

Assumptions/uncertainty: Circuit/pattern teaching parameters, not measured material properties. Temperature, physical current and physical uncertainty unknown.

Decision: Choose paired impedance, radiation and current evidence; installed performance remains unknown.

Next evidence: Freeze mechanics/cable and compare calibrated complex impedance, full-sphere efficiency and absolute vector pattern.

M03-HAND

Owner 06.3

Illustrative

Which mechanisms could explain the hand-like proximity comparison?

Fixture: p06-m03-integration-v1

Frequency: 2.450 GHz model only

Quantity/unit: Zin 50.000 + j0.000 Ω; composite ηrad 40.000000%; ηtot 40.000000%; β 0.411765; C 0.090909 (unitless).

Plane/losses: Real 50 Ω R2 at tuner input; R2-A bare antenna; R2 includes Rt once; upstream R1 feed absent. S0 integrated/scalar directional power.

Configuration: Hand-like proximity · mechanical M3-H; PCB P3 / antenna A3 / BOM B3 teaching identifiers. IFA-like; ground 60 × 40 mm in product x/y; clearance 5 mm; Hand-like lossy at 5 mm; b = 0.1; Bypass; orientation A. Battery/display/shield/fastener/adhesive: absent from the circuit except the selected aggregate object proxy. Cable: absent from named case; residual b = 0.1 is an invented baseline. Temperature/material validity unknown. R2 at tuner input, R2-A at antenna; no R1 feed loss in this ledger. S0 scalar power, no polarization basis.

Coordinates/polarization: Right-handed product x/y/z; θ from +z, φ from +x toward +y. A unrotated; B +90° about world y. Scalar total power; vector co/cross/AR unknown.

Population/statistic: Deterministic synthetic case, one configuration; no physical units or population observed.

Source: antenna-integration-perturbation/2.0; independent integration-golden.json

Assumptions/uncertainty: Circuit/pattern teaching parameters, not measured material properties. Temperature, physical current and physical uncertainty unknown.

Decision: Choose paired impedance, radiation and current evidence; installed performance remains unknown.

Next evidence: Calibrated radiation efficiency plus S11, uncertainty and both polarizations; a better match cannot identify absorption.

M03-CABLE

Owner 06.3

Illustrative

Which mechanisms could explain the programming cable on open board comparison?

Fixture: p06-m03-integration-v1

Frequency: 2.450 GHz model only

Quantity/unit: Zin 35.000 + j20.000 Ω; composite ηrad 85.714286%; ηtot 78.688525%; β 0.545455; C 0.375000 (unitless).

Plane/losses: Real 50 Ω R2 at tuner input; R2-A bare antenna; R2 includes Rt once; upstream R1 feed absent. S0 integrated/scalar directional power.

Configuration: Programming cable on open board · mechanical M3-C; PCB P3 / antenna A3 / BOM B3 teaching identifiers. IFA-like; ground 60 × 40 mm in product x/y; clearance 5 mm; None at 5 mm; b = 0.6; Bypass; orientation A. Battery/display/shield/fastener/adhesive: absent from the circuit except the selected aggregate object proxy. Cable: programming cable represented only by b = 0.6; physical route unmodeled. Temperature/material validity unknown. R2 at tuner input, R2-A at antenna; no R1 feed loss in this ledger. S0 scalar power, no polarization basis.

Coordinates/polarization: Right-handed product x/y/z; θ from +z, φ from +x toward +y. A unrotated; B +90° about world y. Scalar total power; vector co/cross/AR unknown.

Population/statistic: Deterministic synthetic case, one configuration; no physical units or population observed.

Source: antenna-integration-perturbation/2.0; independent integration-golden.json

Assumptions/uncertainty: Circuit/pattern teaching parameters, not measured material properties. Temperature, physical current and physical uncertainty unknown.

Decision: Choose paired impedance, radiation and current evidence; installed performance remains unknown.

Next evidence: Outer-surface current or calibrated near-field evidence, plus S11 and pattern. C supplies neither amperes nor cable EIRP.

M03-PLAN

Owner 06.3

Requirement

Which observations can support a conditional integration/tuning decision?

Fixture: REF-M3 proposed build and U01/U02/U03; not the M01 five-unit plan

Frequency: Local M03/M02 band request 2.401–2.499 GHz; model remains single-frequency

Quantity/unit: DOE-SCREEN 36 configurations; conditional DOE-FOLLOW 48. TH-MATCH −10 dB; TH-EFF 40%; TH-COVER −6 dBi. Proposed thresholds, no pass result.

Plane/losses: Real 50 Ω R2 at tuner input; R2-A bare antenna; R2 includes Rt once; upstream R1 feed absent. S0 integrated/scalar directional power.

Configuration: Proposed correlation reference REF-M3: unit U01, PCB P3, antenna A3, mechanical M3-O, BOM B3; IFA-like teaching configuration, 60 × 40 mm ground, 5 mm clearance, open board, bypass. Battery/display/shield/adhesive/fasteners absent for the reference coupon. Characterized 50 Ω R2 fixture at tuner input; actual cable C1 route, connector launch and choke CH1 position require drawings before execution. A aligned with world axes; requested chamber ambient 25 °C. These are proposed identifiers, not built or measured specimens.

Coordinates/polarization: Right-handed product x/y/z; θ from +z, φ from +x toward +y. A unrotated; B +90° about world y. Scalar total power; vector co/cross/AR unknown.

Population/statistic: Repeated observations on three identified units, two orientations; no production-yield inference. Reference repeats are additional to 36/48.

Source: Original illustrative requirements and experimental plan in this lesson; not a standard.

Assumptions/uncertainty: Temperature/material validity unknown. Record expanded uncertainty k=2 with justified coverage and between-point limitations. Baseline M01 band and five-unit proposal are preserved separately.

Decision: Conditionally compare fixed versus state-dependent tuning only after efficiency/pattern evidence; actual finalist geometry, temperature behavior, current limit and method capability require confirmation.

Next evidence: Freeze actual hardware BOM/CAD, phantom/material, cable/choke, frequency/angular grids, instrument/method ownership and thresholds before executing the paired DOE.

Think about itThe proposed temperature comparison has no material data yet. Should the evidence row contain zero loss or a failed result?
Answer

Neither. Mark temperature/material validity and the result unknown. Freeze the material specification and acquire the planned data. A missing observation cannot be converted into a zero, a failure measurement, or a pass by the synthetic model.

Go deeperWhat would make this plan smaller without weakening it?

A justified reduction could omit an installation the product will never support, or use screening evidence to remove a redundant factor. Preserve the paired cable comparison, representative/corner rationale and a common correlation reference. Record the reduced scope explicitly; do not silently present a smaller matrix as evidence for all six states.

Ungraded review

Check your understanding

Answer each question in your own words, then reveal the model answer.

  1. 01The hand-like state has ideal match but only 40% total efficiency. Diagnose the disagreement.
    Model answer

    At R2 all 1 mW is accepted, but Rrad = 20 Ω and Rloss = 30 Ω divide it into 0.4 mW radiation and 0.6 mW antenna loss. S11 measures reflection, not this split. Compare calibrated efficiency plus match at the same plane. Real hand material, placement and uncertainty remain unknown; the toy supplies no absorption measurement.

  2. 02The cable changes a pattern cut while S11 stays unchanged. Identify the setup risk and a discriminating experiment.
    Model answer

    The open and cable rows deliberately share Zin and the power ledger. Only b changes from 0.1 to 0.6; β changes from 1/6 to 6/11 and C from 1/11 to 3/8. Hold unit, tune, plane and orientation fixed, control cable route/choke position, and measure outer-surface current or field plus absolute pattern. C is not current. Real cables may also alter impedance and efficiency.

  3. 03Why are a mounting conductor and a lossy dielectric different hypotheses?
    Model answer

    A conductor changes boundary/return paths and induced currents; a dielectric changes field storage and may dissipate energy. Either can change resonance and pattern; metal does not only add loss and plastic is not electromagnetically invisible. Specify geometry, spacing, material and fixed factors, then compare impedance, independent radiation and current/field evidence. No universal shift direction or numeric distance rule follows.

  4. 04Choose representative and corner states for the node, and name a conditional tuning strategy.
    Model answer

    Screen open, enclosed, wall, machine, hand-like and cable on U01–U03 in A/B at 25 °C, bypass, with repeated reference states. A/B is rigid rotation; mechanics and hand are physical changes. Use wall/machine as conditional finalists only if the product must support them. Compare bypass to one documented fixed candidate at 0/50 °C. If loss or coverage fails, revisit integration; ideal reactance cancellation cannot repair radiation loss.

  5. 05Repair “the vendor board proves our enclosed node works at all temperatures.”
    Model answer

    Vendor data belongs to its exact board, ground, feed, tune, cable, enclosure, frequency, orientation, method and sample population. Request equivalent data for identified product revisions and units, with R2/S0 planes, vector basis, uncertainty and thresholds. Until supplied, installed and temperature performance are unknown. This lesson’s coefficients cannot fill the gap.

  6. 06Complete the DOE counts, correlation reference and decision rule without claiming production yield.
    Model answer

    Six states × two orientations × three identified units = 36 configuration observations at 25 °C/bypass. Two actual finalist states × two tunes × two temperatures × two orientations × three units = 48 conditional observations. Add REF-M3 at start/end and after reconnect; block temperature and randomize within feasible blocks. Record BOM/CAD, ground, battery/shield/fasteners/adhesive, cable/choke, R2 plane, phantom/spacing, A/B, grids, instrument owner and uncertainty. Use the displayed match, efficiency, coverage, correlation and repeatability thresholds with uncertainty bounds; unknown evidence cannot pass. These repeated observations on three units establish neither a population distribution nor yield.

References and further reading

Principles, access and model provenance

Access/status checked 7 September 2026. Schematics are original; all numeric product responses are deliberately invented. SI, RMS phasors and e+jωt apply. Coefficient laws are teaching choices; circuit conservation and scalar normalization are derived under the stated definitions.

  1. C. A. Balanis, Antenna Theory: Analysis and Design, 4th edition, Wiley, 2016. Official edition/contents record consulted. Current, feed and pattern chapters are further reading; the full book was not accessed and no unseen passage is cited.
  2. IEEE 145-2025, IEEE Standard for Definitions of Terms for Antennas. Official active status and public scope consulted; published 31 March 2026. Normative full text not accessed.
  3. IEEE 149-2021, IEEE Recommended Practice for Antenna Measurements. Active, published 18 February 2022; public scope for passive, linear, reciprocal antenna measurements consulted. No unseen procedure or compliance criterion is asserted.
  4. IEEE 370-2020, Electrical Characterization of Printed Circuit Board and Related Interconnects at Frequencies up to 50 GHz. Active public scope and linked errata consulted; normative full text not accessed. No corrected normative equation is implemented; our line transformation is explicitly derived and bounded.
  5. Richard Wallace, TI AN058, Antenna Selection Guide, SWRA161B, 5 October 2010. Ground comparison §5.1.2 and feed/cable/calibration/placement §§6.2.1–6.2.5 consulted. Hardware examples are tied to the development kit; no material coefficient is transferred. A lossy line does not preserve reflection magnitude.
  6. D. H. Staelin, MIT Electromagnetics and Applications, Spring 2009, Chapter 10. §§10.2–10.3 consulted for radiation, resistance and pattern foundations. The toy’s positive circuit, power ratios and shape integrals are separately shown and independently checked.
  7. R. Luomaniemi, P. Ylä-Oijala, A. Lehtovuori and V. Viikari, “Designing Hand-Immune Handset Antennas With Adaptive Excitation and Characteristic Modes,” IEEE TAP 69(7), 3829–3839, July 2021. Author-institution published reprint; introduction and §II consulted, DOI 10.1109/TAP.2020.3044640. Its combined handset/user analysis supports configuration-aware design; neither its performance nor material parameters are assigned to this node.
  8. Antenova, flexiiANT Integration Guide, 2 September 2021. Cable, orientation and connector/placement sections consulted as a first-party FPC implementation example. No vendor dimensional rule is generalized and no evaluation result is claimed for the node.

Model antenna-integration-perturbation/2.0; fixture p06-m03-integration-v1; control rules p06-m03-controls/1.0; coordinates p06-m03-coordinates/1.0; display p06-m03-display/1.0. Temperature/material calibration, physical common-mode current, polarization, full-wave prediction, measurement execution, exposure and certification remain outside this model.