Antenna Families & Selection

Before you begin

Bring antenna parameters from 06.1, real transmission-line structures and matching that survives reality. Here the decision is which physical implementations deserve investigation. Exact synthesis, full-wave solver operation, installation experiments, array design, measurement execution and legal limits belong to later material.

By the end, classify current and field behavior; calculate wavelength and electrical size with a defensible boundary; and retain two candidates while rejecting two supplied implementations for explicit reasons. No family name or geometry check will establish product performance.

01 / 10

Failure: copying a catalogue antenna without its evaluation ground

The ceramic part is identical. Why is the antenna no longer the same?

Our illustrative engineering case is a condition-monitoring node near 2.45 GHz. It must eventually work inside plastic, in free space, on a metal machine, near a hand, and in two mounting orientations. A catalogue picture shows a tiny component, so the mechanical team reserves only its body. The reference board that supported the catalogue result is much larger. Which conductors did the picture persuade us to ignore?

Start at the feed and trace both terminal currents. A chip implementation may excite currents on the board, ground edge and attached conductors. The ceramic package can set loading and coupling without containing the entire radiator. Copying its footprint while changing the board can change the excitation, stored fields and radiating current distribution.

Think about itRemove the evaluation ground but keep the same chip and matching parts. Which original claim survives?

Answer

The component identity survives. The original input impedance, radiation efficiency and angular response do not transfer without evidence. Even a recovered S11 trace would leave radiation and coverage unknown. The return may now involve a cable or another unintended conductor.

The hidden conductor is still an antenna part. The evaluated chip and its board form one current-bearing structure. Removing board length changes that structure even if the purchased ceramic part is identical. The node's ground is a supplied mechanical constraint, not measured antenna performance. Original schematic, not to scale; blue arrows are qualitative. Feed planes and construction conditions must be specified in a real build.

The first-party comparison in TI AN058 / SWRA161B, §5.1.2 places the same antenna board alone and on the SmartRF04EB. It illustrates changes in the ground-dependent pattern. It supports preserving evaluation conditions; it does not supply any dimension or performance number in our four-candidate fixture.

Annotated vendor-condition audit · what the comparison actually permits
Item to audit	What was consulted	Decision for the node
Ground and assembly	AN058 §5.1.2 compares standalone and evaluation-board-mounted configurations.	Require the exact board outline, current return, mounting and connection drawing before transferring a result.
Feed and measurement plane	The note discusses feed cable mounting and calibration in §§6.2.1–6.2.3.	Request the real reference impedance, connector/fixture plane and loss removal. A cable-included trace is not automatically an R2 result.
Pattern and polarization	A plotted angular response belongs to its stated antenna coordinate frame and polarization.	Request absolute co-/cross-polar data and orientation registration. A normalized cut does not prove full-sphere or two-orientation coverage.
Our synthetic chip condition	C-CHIP requires an invented 80 × 40 mm ground.	The 60 mm node ground length is incompatible with this supplied implementation. This is neither a TI specification nor a theorem about all chip antennas.

Common misconceptionA chip antenna saves product volume without a ground or layout price.

The purchased body, its clearance and its current-bearing surroundings are separate envelopes. Include all three before comparing product cost or space.

Go deeperWhat must remain identical to call it the same configuration?

Record the board stackup and copper, ground interruptions, feed and short locations, component BOM, enclosure and battery, connector, cable route and mounting state. A different mechanical state is a named variant. Do not silently relabel catalogue data as installed-node evidence.

That failure gives us a better starting question: what physical behavior does the structure support?

02 / 10

Classify antennas by physical behavior

Would “printed antenna” tell you where the current returns or which way it radiates?

Printed describes how conductors are made. Dipole, loop, slot and aperture describe different useful physical models. A printed structure could belong to any of them. Classify along several axes, because none replaces the others: the current path, balance, resonance or traveling-wave behavior, electrical extent, field orientation, and counterpoise.

Classify behavior before selecting construction
Physical question	Useful distinction	What it changes in a product
Where do currents flow?	An open-ended arm, circulating loop, slot-edge currents, or an illuminated aperture.	Include every conductor supporting the mode; retain feed and return in the drawing.
How is the feed balanced?	Equal/opposite terminal excitation versus a single-ended signal and counterpoise.	An unbalanced cable can create an additional common-mode radiator. A balun has a bandwidth and loss budget.
What happens along the structure?	Resonance emphasizes stored energy and standing-wave behavior; a traveling-wave structure has progressive phase.	Resonance, feed coupling, taper, truncation and termination each limit usable bandwidth in different ways.
Which spatial field is intended?	Electric-dipole, magnetic-dipole or aperture descriptions; linear or circular polarization in a stated direction.	The receiver must occupy a useful coverage region with a compatible polarization.
How large is the participating structure?	Electrical extent relative to λ0 and complete enclosing radius a.	The smallest purchased part may not be the smallest current-bearing antenna system.

A traveling-wave example is a tapered slot. Its feed launches a field between opposing metal edges; the opening gradually becomes a radiating aperture. It can support a useful broad band with suitable taper and extent, but a finite outline still imposes limits. “Broadband” is not proof that its pattern, efficiency and polarization satisfy our node over a requested band.

A traveling field can radiate along a taper. A tapered-slot example is excited at its narrow balanced slot-line feed. Opposing metal edges carry currents while the field expands toward the aperture, with end-fire linear-polarization intent across the opening. Termination, taper and truncation still limit useful bandwidth. Traveling-wave is a current-behavior description; printed is a manufacturing description. Original schematic, not to scale; blue arrows are qualitative. Feed planes and construction conditions must be specified in a real build.

Go deeperElectric versus magnetic is a model emphasis, not a different kind of wave

Both E and H exist in the radiated field of either family. The small electric dipole model emphasizes separated charge and longitudinal current; the small loop model emphasizes circulating current and magnetic moment. These descriptions help predict orientation and coupling without claiming that one antenna radiates only E or only H.

For the node, “broad azimuth, linear polarization” is a requirement intent. The family name cannot establish that intent in both mounting orientations. We will first look at two particularly common current paths.

03 / 10

Dipoles, monopoles, and the non-optional counterpoise

A dipole has two arms. Why does a monopole seem to need only one?

A symmetric centre-fed dipole excites two conductor arms. In a balanced terminal convention their currents are equal and opposite, so the feed does not need to recruit the outside of a coax shield as an intended third arm. A coax connection alone does not enforce that balance; the transition and common-mode control are part of the feed plan.

A monopole replaces the visible second arm with a conducting counterpoise. In the ideal infinite perfect-conductor model, an image below the surface reproduces the upper-half-space fields of a corresponding dipole. A finite PCB has edges, resonances and current crowding; it is not an infinite image plane. The shield-to-board connection is therefore an electromagnetic boundary, not merely a mechanical accessory.

Two arms, or an arm and its counterpoise. Left: a balanced wire or flex dipole, with equal and opposite terminal currents referred into its two terminals. Right: a single-ended monopole over a finite conducting ground. A z-directed thin-wire mode has linear Eθ far-field intent and broad azimuth coverage with axial nulls; the product can disturb it. Original schematic, not to scale; blue arrows are qualitative. Feed planes and construction conditions must be specified in a real build.

$\lambda _{0} = \frac{c}{f}$ Derived free-space reference. f is in Hz; λ0 is in m. c = 299792458 m/s exactly.

Worked dimension 1 · vacuum starting references at 2.450 GHz
Calculation	Checked value	Permitted inference
299792458 / 2450000000	λ0 = 122.364268571 mm	One vacuum wavelength; no substrate or loading correction.
λ0 / 2	61.182134286 mm	Half-wave scale for an approximately resonant thin dipole; not a final conductor length.
λ0 / 4	30.591067143 mm	Quarter-wave scale for a monopole with a specified counterpoise; not a floating 30.6 mm part.

A real resonant length depends on conductor diameter, bends, end fields, nearby conductors and dielectrics, loading and feed geometry. The 31 mm external candidate in this lesson is an invented envelope, not a synthesized quarter-wave design. Our flex candidate reserves 65 mm for both arms, clearance and feed allowance; that number is likewise a supplied mechanical condition.

Common misconceptionA quarter-wave monopole needs no other conductor.

The other conductor is the counterpoise. If it is not controlled, board, chassis and cable currents can supply it unpredictably. Restoring match alone cannot establish that those currents radiate into the required directions.

Go deeperBalance, impedance and efficiency are three separate questions

A balanced antenna need not have a 50 Ω differential impedance. A balun can transform balance and sometimes impedance, but its insertion loss and usable band require evidence. At the declared R2 plane, ηrad = Prad/Paccepted, ηtotal = Prad/Pincident, G = ηradD and realized gain includes mismatch. Upstream feed loss must be assigned once at its actual plane.

Antenna Basics, §§4.1–4.2, supplies dipole/monopole context. The next families change the current path or the opening in the conductor; they do not eliminate the need to define it.

04 / 10

Loops and slots

If the same wire is closed into a loop, does it remain a bent dipole?

In an electrically small loop, current is approximately in phase around a perimeter much smaller than a wavelength. Its magnetic moment is normal to the loop plane. This gives a useful orientation model: an ideal loop has a null along its normal and radiates toward directions in its plane. The far-field electric polarization is tangential around that normal. The antenna still radiates both E and H.

A resonant full-wave loop has perimeter on the order of a wavelength and substantial current phase variation. The small-loop approximation cannot predict its pattern or feed impedance. At 2.450 GHz a vacuum wavelength is about 122.36 mm, but folding that perimeter into a product does not preserve the isolated-wire environment or automatically create a useful resonant loop.

Circulating current and an excited opening. Left: a small wire loop in the x/y plane with a feed gap and circulating current; its magnetic dipole moment points along z. Its ideal far-field Eφ is linear in each direction, with a null on the loop normal. A resonant full-wave loop has substantial current phase variation. Right: a y-directed slot in a finite conductor, fed across its width; the broadside electric polarization is across the slot (x). Screen currents close around the opening. Original schematic, not to scale; blue arrows are qualitative. Feed planes and construction conditions must be specified in a real build.

A slot excites an opening in a conducting surface. The electric field across a narrow slot and currents around its edges provide a useful aperture description. For the illustrated long slot, broadside electric polarization is across its long direction. Cutting it into a finite machine panel introduces that panel’s edges, seams and feed arrangement into the problem.

Go deeperUse duality to ask a question, not to copy a numerical product result

Ideal complementarity interchanges electric and magnetic roles for paired structures in an infinite, thin, perfectly conducting screen under corresponding excitations. Finite metal, substrate loading, cavities and a real feed break those simplifying conditions. Our duality sketch supplies orientation intuition; it supplies no impedance, efficiency or bandwidth conversion for the node. MIT Chapter 10, Example 10.3D, treats the small-loop receiving model under its explicit electrically small assumption.

Common misconceptionA loop shape or slot label guarantees the final polarization and coverage.

The realized current distribution, feed and surrounding conductor determine the field. A small loop and a resonant loop are different models; a slot in a finite product is not the infinite-screen ideal.

For a metal-mounted node, a slot may turn an existing conductor into part of the antenna, but it also makes that conductor’s mechanical specification an RF dependency. Next, consider families deliberately built around a ground and a thin product envelope.

05 / 10

Patch, PIFA, IFA, and planar product antennas

Why can two flat antennas need very different clearances and mounting directions?

A microstrip patch places a conductive plate above a ground plane with a dielectric region between them. A useful resonant-mode description follows currents on the plate and ground and fringing fields at its edges. A conventional patch often aims broadside to its surface, with linear polarization tied to its mode. Two appropriately excited orthogonal modes can support circular polarization, which still needs axial-ratio evidence over angle and frequency.

An inverted-F antenna, or IFA, has an arm with a short to ground and a nearby feed; bending or loading reduces a physical dimension while changing current and stored energy. A planar inverted-F antenna, or PIFA, uses a plate above ground with short and feed structures. Height, plate/arm geometry and the participating board change the available modes. Similar projected size does not imply similar coverage or bandwidth.

Similar packaging, different field boundaries. Side views: a patch has a conducting plate over dielectric and ground, with radiating fringing edges. A PIFA uses an elevated plate with a short to ground and a nearby feed. An IFA uses a narrower bent arm, short and feed with a current-bearing board. These are resonant structures; feed position changes coupling and input impedance. Patch broadside coverage and IFA/PIFA coverage are design intentions, not promised product patterns. Original schematic, not to scale; blue arrows are qualitative. Feed planes and construction conditions must be specified in a real build.

For a concrete geometry cross-check, MathWorks’ PIFA example, Design Parameters and Vary Antenna Feed Location, identifies the grounded plate, height and feed offset. Its particular dimensions and simulated matching result are not copied into the node fixture.

Substrate properties, height and loss affect stored fields and radiation. Increasing dielectric loading can reduce a resonant physical scale but can also concentrate energy in the material. Fringing fields sample the surrounding enclosure and adhesive. Feed and short placement change coupling and input impedance, so an apparently harmless connector or keepout change can invalidate a reference tuning.

Think about itThe chip body is smaller than the IFA arm. Must its complete current-bearing structure have smaller ka?

Answer

No. This chip implementation calls for an 80 × 40 mm ground; the IFA calls for 50 × 30 mm. At the canonical 60 × 40 mm ground, the supplied IFA clears that condition and the supplied chip does not. The body-only comparison omits the very conductor carrying part of the current.

Common misconceptionPhysical length alone fixes resonance.

Electrical mode, end and fringing fields, conductor/ground geometry, loading, substrate and construction all matter. A matching component can move a port condition without restoring the original radiation behavior.

Go deeperWhy there is no universal εeff shortening slider

A relation resembling λ0/√εeff can describe a particular guided or resonant mode under a defined effective-medium model. Bulk εr is not automatically that mode’s εeff. A patch cavity, IFA arm, slot and chip use different field distributions. This lesson applies no numerical permittivity correction and offers no finished layout recipe; a sourced model and its validity range are needed first.

For our node, the IFA’s 40 × 10 × 5 mm reservation fits the 70 × 12 × 8 mm internal allocation. Its 50 × 30 mm minimum ground fits too. That earns an investigation, not a claim of 40% radiation efficiency. Polarization-specific structures make that distinction still clearer.

06 / 10

Helical and circular-polarization options

Does winding the conductor into a spring make the antenna circularly polarized?

A compact normal-mode helix combines the behavior of a short electric dipole along its axis with loop-like magnetic contributions. It is often used as a loaded, predominantly linear radiator. Its circumference and pitch are small compared with a wavelength; radiation is generally broadside to the axis in that model. The word “helix” alone does not fix the relative electric and magnetic contributions.

An axial-mode helix uses a different geometric scale and progressive current phase to form an end-fire beam. A circumference near a wavelength is a mode-scale cue, not a complete design condition. Pitch, turns, ground/reflector and feed matter. Under suitable excitation it can provide circular-polarization intent near its beam axis, at the cost of volume and directionality that may be incompatible with a flat node.

A winding does not specify the radiation mode. A compact normal-mode wire helix behaves as a combination of short electric and magnetic dipoles, often used as a loaded linear radiator. An axial-mode helix has a traveling current progression and a wavelength-scale circumference, producing end-fire circular-polarization intent under suitable geometry and ground conditions. Both show a feed and counterpoise; the arrows do not specify a solved phase distribution. Original schematic, not to scale; blue arrows are qualitative. Feed planes and construction conditions must be specified in a real build.

The MathWorks helix model description distinguishes axial and normal modes and explicitly includes a ground plane. The illustration here transfers no solver result or default geometry.

$|E_{1}| = |E_{2}|, \Delta \phi = \pm 90^{\circ}$ Definition in a specified transverse basis and observation direction: equal component magnitudes with ±90° phase difference describe circular polarization.

With our e^+jωt convention, handedness also requires a viewing/propagation convention. For a wave traveling +z, Ex = A and Ey = −jA gives a real E vector rotating from +x toward +y; this is the IEEE RHCP propagation-view convention recalled from 06.1. Reversing the viewing direction reverses the apparent rotation. An axial ratio is a directional field property, not a construction label.

Common misconceptionEvery helix is circularly polarized.

Normal and axial modes support different behavior. Even a design intended for circular polarization needs handedness, axial ratio, direction, band and mounting conditions attached to the claim.

Go deeperCircular polarization is not a universal orientation cure

Rotation around a common line of sight is different from moving the receiver out of the antenna’s beam. Ideal linear-to-circular coupling has a polarization factor of one half under the corresponding plane-wave assumptions; multipath and real elliptical fields require vector evidence. A coiled antenna cannot eliminate an axial null or a blocked direction merely by acquiring a circular-polarization label.

The node asks for broad azimuth and linear polarization in two orientations. That is no basis for rejecting all helices, but it gives an axial directional design a clear burden: explain the useful angular region before proposing one.

07 / 10

Horns, reflectors, arrays, and aperture scaling

Why does a high-gain aperture often bring a pointing problem with it?

An extended aperture can arrange the phase of fields across space so they add strongly in a chosen direction. Elsewhere the path differences reduce that addition. A horn expands a guided wave into an opening; a reflector redirects a feed’s illumination using induced surface currents. Both require their feed and polarization to illuminate the useful region well.

An array offers several spatially separated excitations. Its element behavior and feeding network remain part of the antenna; more elements do not by themselves prove a wider useful field of view. Array-factor, coupling, diversity and beamforming design are deferred to 06.4. Here the shared selection question is whether the physical aperture, feed, pointing and mounting can fit the intended use.

Use an extended region to control relative phase. A horn feed expands a guided field into an aperture; conducting walls carry return currents. A reflector redirects a feed's illumination through induced surface currents; feed support and blockage matter. An array supplies multiple feeds and returns over a spatial extent. All three aim for directional coverage, with polarization set by excitation. Outgoing arrows indicate beam intent, not measured gain or beamwidth. Original schematic, not to scale; blue arrows are qualitative. Feed planes and construction conditions must be specified in a real build.

MIT Chapter 11, §§11.1.1–11.1.3, connects aperture extent and illumination to the angular field, including the limits of a large-aperture approximation.

$G \approx \eta_{\mathrm{ap}}\frac{4\pi A_{\mathrm{phys}}}{\lambda_0^2}$ Conditional scaling for a well-defined, electrically large aperture. Aphys is physical area in m²; λ0 is in m; G is a dimensionless gain referenced to accepted feed power.

Here ηap is defined as Ae/Aphys using the effective receiving area corresponding to gain under matched, polarization-aligned reciprocal conditions. With that definition it already accounts for aperture illumination, phase, spillover/blockage and dissipation that reduce gain at the chosen feed plane. Do not multiply radiation efficiency into the same gain again. It excludes mismatch at that plane and any upstream feed loss not included in the antenna boundary.

For geometrically comparable, similarly illuminated large apertures, increasing the electrical extent narrows a characteristic beam scale, roughly λ0/D in radians for a named aperture dimension D; the constant and sidelobes depend on illumination. At a fixed frequency, doubling aperture area approximately doubles gain only if ηap remains unchanged. This is a conditional scaling relation, not an output of the node feasibility tool.

Common misconceptionThe highest catalogue gain is automatically the best antenna for the node.

A narrow useful beam may miss the gateway in one mounting orientation. Coverage, pointing and polarization constraints can disqualify the proposal before its peak value becomes useful.

Go deeperAperture efficiency is not simply radiation efficiency

Radiation efficiency asks what fraction of accepted power radiates. Aperture efficiency asks how effectively a specified physical opening produces the chosen gain/effective area. A low-loss aperture can have poor illumination or phase coherence. State each denominator and whether the quoted efficiency already contains a dissipative term. MIT §10.3.4 derives the reciprocal gain–effective-area relationship; aperture scaling additionally requires an appropriate large-aperture model.

The node has a small mechanical allocation. To discuss what “small” means electromagnetically, we must stop measuring only the visible antenna part.

08 / 10

Electrically small antennas

Small compared with what—and around which complete structure?

Electrical size compares a length scale with wavelength. For antenna-bound discussions, a is the radius of an enclosing sphere around the declared complete current-bearing structure. A convenient estimate for a rectangular box is half its space diagonal. This need not be the smallest possible sphere for an arbitrary geometry, and a board box does not enclose an external arm or radiating cable.

The bounding sphere must enclose the participating currents. Left: a chip body alone omits current paths. Middle: chip and board need a larger enclosing sphere. Right: an external arm or exterior cable can extend beyond the product box. Circle outlines represent sphere projections, not radiation patterns; sketches are not to scale. Use half the box diagonal only for the complete declared box boundary. Original schematic, not to scale; blue arrows are qualitative. Feed planes and construction conditions must be specified in a real build.

$\begin{aligned}a &= \frac{1}{2}\sqrt{L^{2} + W^{2} + H^{2}} \\ k a &= \frac{2\pi a}{\lambda _{0}}\end{aligned}$ Definition and bounding construction. Use L, W, H, a and λ0 in the same length units. ka is dimensionless; k = 2π/λ0.

Worked dimension 2 · the boundary changes the answer at 2.450 GHz
Declared box	a, mm	ka	What the boundary includes
Product: 80 × 50 × 25 mm	48.798053240	2.505692346	Declared enclosure box; complete current containment must still be established.
Internal allocation: 70 × 12 × 8 mm	35.735136770	1.834935058	Reserved internal antenna region; does not include a separate participating board automatically.
Chip body: 10 × 4 × 3 mm	5.590169944	0.287045181	Only the chip. Incomplete for the supplied chip-plus-board implementation.

“Electrically small” is often used for ka below one, with the exact boundary and theorem assumptions stated. The chip-only value looks small, but it cannot support a bound for the entire chip-plus-board radiator. The larger box values do not prove high efficiency either. They expose a boundary error, not a ranking.

Think about itHold the product geometry fixed and double frequency from 2450 to 4900 MHz. What changes, and what stays unknown?

Answer

Vacuum wavelength halves to 61.182134286 mm. The product a stays 48.798053240 mm and ka doubles to 5.011384691. Half-/quarter-wave references halve too. The four frozen candidates have no established RF applicability at 4900 MHz; moving a calculator control does not retune hardware.

A small radiator can store substantial reactive energy near itself compared with the energy it radiates per cycle. Tuning can cancel input reactance at a chosen frequency, but the underlying fields and loss do not disappear. Attempts to reduce size, widen useful bandwidth, retain radiation efficiency and reduce sensitivity compete for the same physical design freedom.

$\eta _{\mathrm{rad}} = \frac{R_{\mathrm{rad}}}{R_{\mathrm{rad}} + R_{\mathrm{loss}}}$ A simple single-mode equivalent circuit at a declared current reference. Rrad represents radiation and Rloss dissipation, both in Ω; it is not a general synthesis formula.

Adding a tuning inductance may improve port acceptance while adding Rloss. A broad, shallow S11 response can reflect dissipation rather than useful radiation. Manufacturing or nearby material changes can shift a narrow useful region; a nominal match at one frequency supplies no tolerance distribution.

Common misconceptionAny small antenna can be tuned into efficiency.

A tuner can improve transfer into an antenna, but it cannot convert dissipation into radiation. Re-measure efficiency and pattern after tuning; do not declare success from return loss alone.

Go deeperWhy this map does not calculate a universal Chu Q or bandwidth

Q relates stored energy to energy loss per radian under a particular modal/resonant definition. A conversion from Q to bandwidth depends on match threshold, resonance structure and loss. It is not generally Q = 1/FBW. Gustafsson, Sohl and Kristensson (2007) discuss shape-dependent limitations and comparisons with spherical Chu limits. The consulted public abstract establishes that scope; the full derivation was unavailable. No theorem value, exact Q limit or efficiency bound is implemented here.

A good shortlist therefore needs both geometry and a manufacturing/evidence plan. The construction choice tells us how that plan might fail in production.

09 / 10

Printed, stamped, ceramic, cable, and external implementations

Which cost are you comparing: the antenna part, the occupied product space, or a repeatable assembled result?

Construction changes repeatability, assembly and validation work without uniquely determining electromagnetic behavior. A printed dipole and a printed IFA share a fabrication method but not an intended return. A stamped arm may avoid substrate loading yet depend strongly on formed height and fixture location. A ceramic part can make the purchased element repeatable while leaving board and matching sensitivity unresolved.

Construction decisions · qualitative engineering burdens, no vendor quotes
Implementation	Manufacturing and cost drivers	Evidence / integration burden
Printed copper	No separate radiator assembly; board area, keepout, stackup and copper tolerances consume product resources.	Control board geometry and substrate; test populated-board currents and match/efficiency/pattern variation.
Stamped or wire	Forming tools, height, spring-back, contact pressure and placement become variables.	Control mechanical datum, bonding and conductor clearance; compare representative formed parts.
Ceramic / chip	BOM and assembly cost plus ground and clearance; solder and dielectric variation affect the installed condition.	Request the exact reference board, land pattern, tuning network and unit-to-unit evidence.
Flex / adhesive dipole	A movable conductor pair can use enclosure space; placement, bend and adhesive thickness need control.	Investigate feed balance, cable route, nearby metal and production placement repeatability.
Cable and external	Connector, cable loss, common mode, seal, torque, impact and service requirements can dominate.	Specify R1/R2 loss ownership, counterpoise, exterior clearance, mounting and environmental tests.

For the two orientations, define a specimen-fixed x/y/z frame. Use O1 with +z upright and O2 rotated 90° about +y. The antenna’s polarization and pattern rotate with the product; any board, battery, metal plate or hand state must be named with the data. Comparison under incompatible planes or mounts is not a fair trade study.

Think about itKeep the geometry fixed but widen the requested useful band while retaining efficiency and coverage criteria. Is the same match plot enough?

Answer

No. The intersection of acceptable match, efficiency, pattern and polarization must cover the wider request. New band edges need corresponding thresholds and sweeps. Widening a requirement supplies no new evidence; the map retains unknown performance instead of inventing a bandwidth penalty.

$\mathrm{FBW} = \frac{f_{H} - f_{L}}{f_{c}}$ Definition with arithmetic centre fc = (fH + fL)/2. The edges belong to a named property and threshold, in a named configuration.

A symmetric 4% request at 2.450 GHz spans 2.401–2.499 GHz. In this local example the match screen is signed S11 ≤ −10 dB at real 50 Ω R2; radiation efficiency must remain at least 40%. Broad-azimuth coverage and linear-polarization intent still need quantitative angular and co/cross limits. Match, total efficiency, radiation efficiency and axial ratio can impose different edges.

Common misconceptionMatching bandwidth is the same as useful antenna bandwidth.

An antenna can accept power at a frequency where too much is dissipated, its useful direction has a null, or its polarization misses the requirement. Specify the acceptable intersection and retain unsampled frequencies as unknown.

Go deeperAsk for the assembled population, not a golden sample

Specify a unit population, board/part lots, mechanical variants, temperature range, tuning policy and uncertainty treatment. Do not turn one typical sample into a guaranteed worst case. Cost and validation effort remain qualitative here because no quotations, manufacturing distribution or measured units were supplied.

We can now declare the complete mechanical constraints and make a deliberately limited selection.

10 / 10

Build the node shortlist and disqualifier matrix

Which two implementations deserve the next experiment—and what stops the other two?

This is local variant M02-NODE, extending the shared fictional case. The product is 80 × 50 × 25 mm; the internal allocation is 70 × 12 × 8 mm; board ground is 60 × 40 mm. Candidate allocations already reserve their stated clearance and feed allowance. No external protrusion is allowed. R2 is a real 50 Ω single-ended interface with balun provision. The target is 40% radiation efficiency across 4% useful FBW, broad azimuth and linear polarization in O1/O2.

These are requirements and invented dimensions. The 06.1 analytic power and pattern fixtures are not measurements of these four implementations. Its 2.400–2.500 GHz proposed test plan keeps its earlier identity; the symmetric 2.401–2.499 GHz band here is an explicitly named local requirement variant.

Frozen candidates · p06-m02-candidates-v1 · fixed axis order L × W × H
ID / supplied implementation	Envelope, mm	Ground, mm	Canonical geometry / feed decision
C-IFA · PCB IFA implementation	40 × 10 × 5 internal	50 × 30	Retain: envelope and ground fit.
C-CHIP · Ceramic chip implementation	10 × 4 × 3 internal	80 × 40	Reject this implementation: 80 mm ground length required, 60 mm available.
C-FLEX · Flex dipole implementation	65 × 10 × 2 internal	No minimum in this fixture	Retain: 65 mm length fits; balun provision exists.
C-EXT · External monopole implementation	31 × 8 × 8 external	50 × 30	Reject: external protrusion required and prohibited.

The worked selection brief: retain C-IFA and C-FLEX for investigation. The IFA uses the board as part of its return; the flex provides two intended arms but requires feed/common-mode control and installation space. Reject this C-CHIP implementation for its supplied ground-length requirement and C-EXT for the exterior condition. Rejecting a fixed implementation does not reject its entire family.

The hardest known constraints are the failed ground length and prohibited protrusion; no arbitrary ranking breaks that tie. For the retained pair, the controlling uncertainty is evidence that useful efficiency and coverage survive the required band and mounting states. No winner is supported yet.

Illustrative engineering case · feasibility rules

Antenna Family Feasibility Map

Change one constraint, evaluate, then explain which condition changed. Retained means worthy of further investigation. No gain, efficiency, tuning or bandwidth is predicted.

Guided comparisonEach comparison starts from the canonical node and changes only its named input. All other controls and evidence conditions reset.

1 · Frequency and physical boundaries

Frequency (MHz)100–30000 MHz · step 1 · default 2450

Product length · x (mm)1–1000 mm · step 1 · default 80

Product width · y (mm)1–1000 mm · step 1 · default 50

Product height · z (mm)1–1000 mm · step 1 · default 25

Internal allocation length · x (mm)1–1000 mm · step 1 · default 70

Internal allocation width · y (mm)1–1000 mm · step 1 · default 12

Internal allocation height · z (mm)1–1000 mm · step 1 · default 8

Board ground length · x (mm)1–1000 mm · step 1 · default 60

Board ground width · y (mm)1–1000 mm · step 1 · default 40

Allocation includes clearance and feed allowance. L/W/H follow x/y/z. Ground lies in x/y. Each allocation and ground dimension must fit its product axis; this is a bounding check, not a component-placement solver.

2 · Requirements, never achieved values

Requested fractional bandwidth (%)0.1–50 % · step 0.1 · default 4

Bandwidth metricDefault: combined useful band. Required choice; no achieved performance is inferred.

Required efficiency threshold (%)1–90 % · step 1 · default 40

Efficiency definitionDefault: radiation. Required choice; no achieved performance is inferred.

Required patternDefault: broad azimuth. Required choice; no achieved performance is inferred.

Required polarizationDefault: linear. Required choice; no achieved performance is inferred.

Band edges are a symmetric request about the arithmetic centre. Match uses signed S11 ≤ −10 dB at real 50 Ω R2. Efficiency uses its selected threshold and denominator. A combined useful band requires all selected criteria together; quantitative pattern and polarization limits still need definition.

3 · Integration and construction

Mounting / environmentDefault: plastic enclosure. Required choice; no achieved performance is inferred.

Feed plan at R2Default: single-ended with balun provision. Required choice; no achieved performance is inferred.

External protrusionDefault: prohibited. Required choice; no achieved performance is inferred.

Construction preference · annotation onlyDefault: none. Annotates all four rows; never removes a rejection.

Committed conditions

2450 MHz · product 80 × 50 × 25 mm · internal allocation 70 × 12 × 8 mm · ground 60 × 40 mm.

plastic enclosure; O1 (+z upright) and O2 (90° about +y); single-ended with balun provision; protrusion prohibited; construction preference none. The single-ended R2 interface is real 50 Ω; a balanced plan needs its actual differential impedance specified. R1 is upstream; no R1-to-R2 loss has been supplied.

Canonical node: two retained candidates, two rejected supplied implementations. All RF performance remains unknown.

Derived vacuum wavelength λ0: 122.364269 mm
Starting references λ0/2 / λ0/4: 61.182134 / 30.591067 mm
Product box a / ka: 48.798053 mm / 2.505692346
Internal allocation a / ka: 35.735137 mm / 1.834935058
Chip-body-only a / ka · incomplete boundary: 5.590170 mm / 0.287045181
Ground Lg/λ0 / Wg/λ0: 0.490339220 / 0.326892813

Derived: λ0 = c/f; c = 299792458 m/s exactly. a = √(L² + W² + H²)/2; ka = 2πa/λ0. The three box boundaries are different questions, not efficiency rankings. Product a encloses the declared box only: exterior conductors or cable currents require a larger boundary. Chip dimensions omit its current-bearing board. No effective-permittivity shortening is applied.

Requested versus evidenced performance

Requested 4% combined useful band: 2.401000–2.499000 GHz. Arithmetic centre 2.450000 GHz. FBW = (fH − fL)/fc.

Required radiation efficiency ≥ 40% across that band; broad azimuth with linear polarization in both orientations. The local match criterion is signed S11 ≤ −10 dB at real 50 Ω R2. Quantitative angular and polarization limits still need agreement. Evidenced band, efficiency, absolute gain, vector pattern, tolerance distribution and production yield: unknown for every candidate. Radiation efficiency divides S0 radiated power by R2 accepted power; total efficiency divides by R2 incident power and includes mismatch once.

p06-m02-candidates-v1 · compatibility map · supplied constraints, no RF solver
Candidate	Envelope	Ground	Protrusion	Feed	RF evidence
C-IFA	✓ clears	✓ clears	✓ clears	✓ clears	? Unknown F05–F08 conditions below
C-CHIP	✓ clears	× fail	✓ clears	✓ clears	? Unknown F05–F08 conditions below
C-FLEX	✓ clears	· not applicable	✓ clears	✓ clears	? Unknown F05–F08 conditions below
C-EXT	· not applicable	✓ clears	× fail	✓ clears	? Unknown F05–F08 conditions below

✓ clears only the named supplied condition; × is an explicit disqualifier; · means not applicable or further integration work; ? means evidence is absent. Preference never hides a row or changes a rule.

Shortlist and controlling constraints

Retain for investigation: C-IFA, C-FLEX. Reject this supplied configuration: C-CHIP, C-EXT.

The controlling constraints are every failed dimension or feed/protrusion condition listed below. No priority or probability is invented between simultaneous failures. For a retained row, the controlling uncertainty is the unestablished useful band, efficiency and coverage in the product.

C-IFA · retain for investigation

PCB IFA implementation. Shorted resonant arm plus current-bearing board; single-ended feed. Envelope 40 × 10 × 5 mm internal; ground 50 × 30 mm.

Integration / manufacturing burden: Preserve edge keepout, short and feed positions, stackup and board return; plan installed tuning and PCB-tolerance samples.

F01-envelope · clears. 40 × 10 × 5 mm fits the declared internal axes, including reserved clearance/feed allowance.
F02-ground · clears. Supplied ground meets 50 × 30 mm minimum; RF performance remains unknown.
F03-external · clears. Internal implementation needs no protrusion.
F04-feed · clears. Single-ended plan is consistent with the supplied implementation.
F05-frequency · clears. 2450 MHz is the supplied reference centre, not measured operating-band evidence.
F06-performance · unknown. Requested 4% combined useful band; 40% radiation efficiency; broad azimuth; linear polarization. Achieved band, efficiency, gain, pattern and polarization: unknown.
F07-mount · burden. Compare open board with closed enclosure, battery and adhesive in place. O1: +z upright; O2: 90° about +y. Measure R2 match plus independent S0 efficiency and vector pattern across the requested band.
F08-evidence · unknown. Missing ground; Missing feedPlane; Missing band; Missing mounting; Missing metric in any supporting RF dataset. The dimensional teaching fixture is not such a dataset.

C-CHIP · reject this supplied configuration

Ceramic chip implementation. Loaded element plus the specified evaluation ground; chip body is an incomplete current boundary. Envelope 10 × 4 × 3 mm internal; ground 80 × 40 mm.

Integration / manufacturing burden: Obtain the exact land pattern, 80 × 40 mm evaluation ground, clearance, matching BOM and ceramic/assembly tolerances.

F01-envelope · clears. 10 × 4 × 3 mm fits the declared internal axes, including reserved clearance/feed allowance.
F02-ground · fail. ground L / x needs 80 mm; supplied 60 mm
F03-external · clears. Internal implementation needs no protrusion.
F04-feed · clears. Single-ended plan is consistent with the supplied implementation.
F05-frequency · clears. 2450 MHz is the supplied reference centre, not measured operating-band evidence.
F06-performance · unknown. Requested 4% combined useful band; 40% radiation efficiency; broad azimuth; linear polarization. Achieved band, efficiency, gain, pattern and polarization: unknown.
F07-mount · burden. Compare open board with closed enclosure, battery and adhesive in place. O1: +z upright; O2: 90° about +y. Measure R2 match plus independent S0 efficiency and vector pattern across the requested band.
F08-evidence · unknown. Missing ground; Missing feedPlane; Missing band; Missing mounting; Missing metric in any supporting RF dataset. The dimensional teaching fixture is not such a dataset.

C-FLEX · retain for investigation

Flex dipole implementation. Two conductor arms provide the intended return; balanced antenna terminals. Envelope 65 × 10 × 2 mm internal; ground no minimum in this fixture.

Integration / manufacturing burden: Reserve the conductor pair and adhesive location; verify balun loss, cable routing/common mode, bending and assembly repeatability.

F01-envelope · clears. 65 × 10 × 2 mm fits the declared internal axes, including reserved clearance/feed allowance.
F02-ground · not applicable. No minimum ground pair in this fixture. The conductor pair is the intended return; environmental independence is unknown.
F03-external · clears. Internal implementation needs no protrusion.
F04-feed · clears. Balanced feed or balun provision clears the feed-plan restriction; balance, loss and common-mode evidence remain unknown.
F05-frequency · clears. 2450 MHz is the supplied reference centre, not measured operating-band evidence.
F06-performance · unknown. Requested 4% combined useful band; 40% radiation efficiency; broad azimuth; linear polarization. Achieved band, efficiency, gain, pattern and polarization: unknown.
F07-mount · burden. Compare open board with closed enclosure, battery and adhesive in place. O1: +z upright; O2: 90° about +y. Measure R2 match plus independent S0 efficiency and vector pattern across the requested band.
F08-evidence · unknown. Missing ground; Missing feedPlane; Missing band; Missing mounting; Missing metric in any supporting RF dataset. The dimensional teaching fixture is not such a dataset.

C-EXT · reject this supplied configuration

External monopole implementation. External resonant arm with board/counterpoise return through the connector. Envelope 31 × 8 × 8 mm external; ground 50 × 30 mm.

Integration / manufacturing burden: Reserve exterior clearance and counterpoise connection; investigate connector, seal, mounting torque, handling and weather exposure.

F01-envelope · not applicable. Exterior envelope is assessed only when protrusion is allowed.
F02-ground · clears. Supplied ground meets 50 × 30 mm minimum; RF performance remains unknown.
F03-external · fail. External protrusion is required and prohibited.
F04-feed · clears. Single-ended plan is consistent with the supplied implementation.
F05-frequency · clears. 2450 MHz is the supplied reference centre, not measured operating-band evidence.
F06-performance · unknown. Requested 4% combined useful band; 40% radiation efficiency; broad azimuth; linear polarization. Achieved band, efficiency, gain, pattern and polarization: unknown.
F07-mount · burden. Compare open board with closed enclosure, battery and adhesive in place. O1: +z upright; O2: 90° about +y. Measure R2 match plus independent S0 efficiency and vector pattern across the requested band.
F08-evidence · unknown. Missing ground; Missing feedPlane; Missing band; Missing mounting; Missing metric in any supporting RF dataset. The dimensional teaching fixture is not such a dataset.

Read all eight rules and their provenance

F01-envelope. Each internal L/W/H must fit its corresponding allocation. Equality clears that axis. Exterior reservation is considered only if protrusion is allowed; no exterior clearance limit was supplied. Geometric derivation + supplied synthetic constraint.
F02-ground. Ground L/W must meet both supplied minima. No minimum is not a measurement of zero. This is not a general RF cutoff. Supplied synthetic constraint.
F03-external. Reject C-EXT when exterior protrusion is prohibited, regardless of preference. Supplied synthetic constraint.
F04-feed. Reject the C-FLEX feed plan if a single-ended feed has no balun provision. Clearing this rule does not establish balun performance. Supplied synthetic constraint; balance principle.
F05-frequency. A centre other than 2450 MHz has unknown RF applicability for all frozen candidates. Geometry remains reportable. Supplied synthetic fixture scope.
F06-performance. No compatible band, efficiency, pattern or polarization evidence exists. All are unknown, never zero, a pass or a measured failure. Evidence absence.
F07-mount. Request configuration-specific integration tests. No automatic dB penalty is assigned to an environment. Sourced physical principle · TI AN058 §5.1.2.
F08-evidence. Missing ground, feed plane, band, mounting or metric metadata makes vendor-like data unqualified. Incompatible definitions cannot be ranked. Evidence discipline · IEEE 149 public scope / TI AN058.

Model antenna-family-feasibility/2.0; rules p06-m02-rules-v1; fixture p06-m02-candidates-v1; coordinates p06-m02-coordinates-v1; display p06-m02-display-v1. IEEE-style spherical coordinates: θ from +z; φ from +x toward +y. Linear co/cross basis and allowed pattern/axial-ratio limits must be supplied before evidence can establish S0 coverage. No persistence, scoring or antenna validation is performed.

The canonical results, inputs and four-candidate evidence matrix are available above. Interactive edits require JavaScript; all lesson predictions and model answers use native disclosures.

Follow the controlled comparisons

Canonical defaults plus one explicit override · static/no-script comparison
Local comparison	Changed condition	What clears or fails	What remains unknown
Ground extended	Ground L = 80 mm, within product L = 80 mm	C-CHIP clears its ground rule; C-EXT remains rejected.	Chip efficiency, useful band, pattern and mounting evidence.
Allocation shortened	Internal L = 64 mm	C-FLEX fails its 65 mm longitudinal envelope. At L = 65 mm, equality clears this axis.	The 1 mm mechanical change proves no RF trend.
Balun unavailable	Single-ended without balun	C-FLEX fails the feed plan; C-IFA remains retained.	A different balanced feed could change this result; actual balance and loss are unmeasured.
External allowed	Protrusion allowed	C-EXT clears prohibition and the supplied ground pair; reserve 31 × 8 × 8 mm outside.	Exterior clearance, connector and installed RF behavior. Internal allocation is not an exterior clearance limit.
Frequency doubled	4900 MHz; identical geometry	Wavelength references halve; ka doubles. Mechanical decisions remain the same.	Every frozen candidate’s RF applicability at this new frequency.

Request the evidence before trusting a catalogue comparison

Mechanical and current boundary: exact evaluation-board dimensions, copper and stackup; antenna/ground/clearance drawings; short and feed placement; battery, enclosure and mounting hardware.
Feed reference: actual impedance and balanced/single-ended definition, balun and matching BOM, calibration/de-embedding plane, cable routing, and losses included between R1, R2 and the radiating structure.
RF definitions: band edges and thresholds for match and each efficiency definition; absolute co-/cross-polar pattern with coordinates, direction, normalization, uncertainty and polarization/axial-ratio conditions.
Population: specimen IDs, unit/lot distribution, mechanical and environmental conditions, component/placement tolerances, tuning policy and repeatability. No such data have been acquired by this lesson.

For 06.3, plan a correlation reference in free space with a controlled cable/balun, then compare closed plastic, the specified metal plate and a specified hand condition. Repeat O1/O2; change one mechanical factor at a time; retain both match and independent radiation/vector evidence. Agree the plate, phantom, spacings and acceptance thresholds before execution. This is a test request, not measurement evidence.

Think about itAlternative brief: shorten the enclosure and internal allocation to 64 mm, or mandate metal mounting. Defend the changed shortlist.

Answer

With both lengths 64 mm, C-FLEX fails the fixed 65 mm reservation. C-IFA remains provisional; the supplied chip and external constraints still fail. A new fold, feed, ground or enclosure would be a new implementation needing its own fixture. Metal mounting alone adds defined integration tests, not an invented dB penalty or automatic rejection. Keep both geometrically compatible alternatives until evidence distinguishes them.

Antenna and channel evidence map

This complete local snapshot of p06-evidence-map-v1 preserves the earlier unknown installation row and adds the node requirement, bounding calculations and four decisions. It works without a previous visit or saved workbook. R2-TX/R2-RX, if introduced later, both map to portfolio R2; R3 remains the receiver detector/decision boundary. S0 quantities require direction and polarization. Incident, accepted, available receive, delivered receive, EIRP and TRP are distinct; none is synthesized by these selection rules.

p06-evidence-map-v1 · complete 06.2 snapshot; static canonical case
ID / owner / label	Question, fixture, quantity	Conditions and population	Decision and 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 Band: 2.400–2.500 GHz requirement band Quantity/unit: Match, efficiency, gain, vector pattern, and channel/link performance: unknown	Planes/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. Basis: Right-handed specimen x/y/z; θ from +z, φ from +x toward +y. Total scalar power; vector co/cross/AR unknown. 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.
M02-REQ-BAND Owner 06.2 Requirement	Which useful band must the retained configuration demonstrate? Fixture: p06-m02-candidates-v1 Band: Local mechanical / requirement variant M02-NODE: 2.450 GHz; symmetric requested band 2.401–2.499 GHz. Quantity/unit: 4% FBW about arithmetic fc 2.450 GHz = 2.401–2.499 GHz; radiation efficiency ≥ 40%; broad azimuth, linear polarization, two orientations.	Planes/losses: R2 real 50 Ω single-ended feed with balun provision. R1 upstream; no feed/balun loss supplied. S0 radiation and vector pattern unknown; no loss assigned or counted twice. Configuration: 80 × 50 × 25 mm plastic product; internal allocation 70 × 12 × 8 mm; ground 60 × 40 mm. Free-space, specified metal-machine and hand states are future tests. O1 +z upright; O2 rotated 90° about +y. Basis: Specimen right-handed x/y/z; L/W/H along x/y/z; ground x/y. θ from +z, φ from +x toward +y. Linear, broad-azimuth intent; co/cross basis, exact coverage and thresholds still to be agreed. Statistic: One deterministic geometry fixture, no observed units. Proposed five-unit follow-up inherits the M01 test-plan intent, not measurement evidence.	Source: Builder-supplied synthetic constraints; antenna-family-feasibility/2.0; p06-m02-rules-v1. Geometry arithmetic independently checked in feasibility-golden.json. Assumptions/uncertainty: All candidate envelopes include clearance/feed allowance and are invented constraints. No statistical tolerance or physical uncertainty data. No ranking by ka, size or family name. Decision: Requirement only; compatible efficiency, pattern, match and polarization sweeps unknown. The 2.400–2.500 GHz M01 plan remains a separate requirement snapshot. Next evidence: Agree S11 ≤ −10 dB for the local match screen, absolute co/cross coverage thresholds, polarization criterion, sweep grid and between-point uncertainty; acquire installed results.
M02-BOUNDARY Owner 06.2 Derived	Which enclosing boundary belongs in ka? Fixture: p06-m02-candidates-v1 Band: Local mechanical / requirement variant M02-NODE: 2.450 GHz; symmetric requested band 2.401–2.499 GHz. Quantity/unit: Product a 48.798053240 mm, ka 2.505692346; allocation a 35.735136770 mm, ka 1.834935058; chip-body-only a 5.590169944 mm, ka 0.287045181 (incomplete).	Planes/losses: R2 real 50 Ω single-ended feed with balun provision. R1 upstream; no feed/balun loss supplied. S0 radiation and vector pattern unknown; no loss assigned or counted twice. Configuration: 80 × 50 × 25 mm plastic product; internal allocation 70 × 12 × 8 mm; ground 60 × 40 mm. Free-space, specified metal-machine and hand states are future tests. O1 +z upright; O2 rotated 90° about +y. Basis: Specimen right-handed x/y/z; L/W/H along x/y/z; ground x/y. θ from +z, φ from +x toward +y. Linear, broad-azimuth intent; co/cross basis, exact coverage and thresholds still to be agreed. Statistic: One deterministic geometry fixture, no observed units. Proposed five-unit follow-up inherits the M01 test-plan intent, not measurement evidence.	Source: Builder-supplied synthetic constraints; antenna-family-feasibility/2.0; p06-m02-rules-v1. Geometry arithmetic independently checked in feasibility-golden.json. Assumptions/uncertainty: All candidate envelopes include clearance/feed allowance and are invented constraints. No statistical tolerance or physical uncertainty data. No ranking by ka, size or family name. Decision: Different boundaries cannot rank efficiency. The box sphere is usable only if the complete relevant current structure fits within it. Next evidence: Identify board, chassis, feed cable and external current extent from controlled geometry/current evidence before applying any antenna-size bound.
M02-C-IFA Owner 06.2 Illustrative	Is this supplied PCB IFA implementation compatible with the declared product? Fixture: p06-m02-candidates-v1 Band: Local mechanical / requirement variant M02-NODE: 2.450 GHz; symmetric requested band 2.401–2.499 GHz. Quantity/unit: Envelope 40 × 10 × 5 mm internal; ground 50 × 30 mm. Shorted resonant arm plus current-bearing board; single-ended feed. Required radiation efficiency 40%, useful FBW 4%; achieved values unknown.	Planes/losses: R2 real 50 Ω single-ended feed with balun provision. R1 upstream; no feed/balun loss supplied. S0 radiation and vector pattern unknown; no loss assigned or counted twice. Configuration: 80 × 50 × 25 mm plastic product; internal allocation 70 × 12 × 8 mm; ground 60 × 40 mm. Free-space, specified metal-machine and hand states are future tests. O1 +z upright; O2 rotated 90° about +y. Basis: Specimen right-handed x/y/z; L/W/H along x/y/z; ground x/y. θ from +z, φ from +x toward +y. Linear, broad-azimuth intent; co/cross basis, exact coverage and thresholds still to be agreed. Statistic: One deterministic geometry fixture, no observed units. Proposed five-unit follow-up inherits the M01 test-plan intent, not measurement evidence.	Source: Builder-supplied synthetic constraints; antenna-family-feasibility/2.0; p06-m02-rules-v1. Geometry arithmetic independently checked in feasibility-golden.json. Assumptions/uncertainty: All candidate envelopes include clearance/feed allowance and are invented constraints. No statistical tolerance or physical uncertainty data. No ranking by ka, size or family name. Decision: retain for investigation. Envelope and feed-plan restrictions clear; useful-band / coverage evidence controls the next decision. Next evidence: Preserve edge keepout, short and feed positions, stackup and board return; plan installed tuning and PCB-tolerance samples. Obtain band and efficiency definitions, calibrated feed plane, absolute co/cross pattern, unit population, tolerances and installation comparisons.
M02-C-CHIP Owner 06.2 Illustrative	Is this supplied Ceramic chip implementation compatible with the declared product? Fixture: p06-m02-candidates-v1 Band: Local mechanical / requirement variant M02-NODE: 2.450 GHz; symmetric requested band 2.401–2.499 GHz. Quantity/unit: Envelope 10 × 4 × 3 mm internal; ground 80 × 40 mm. Loaded element plus the specified evaluation ground; chip body is an incomplete current boundary. Required radiation efficiency 40%, useful FBW 4%; achieved values unknown.	Planes/losses: R2 real 50 Ω single-ended feed with balun provision. R1 upstream; no feed/balun loss supplied. S0 radiation and vector pattern unknown; no loss assigned or counted twice. Configuration: 80 × 50 × 25 mm plastic product; internal allocation 70 × 12 × 8 mm; ground 60 × 40 mm. Free-space, specified metal-machine and hand states are future tests. O1 +z upright; O2 rotated 90° about +y. Basis: Specimen right-handed x/y/z; L/W/H along x/y/z; ground x/y. θ from +z, φ from +x toward +y. Linear, broad-azimuth intent; co/cross basis, exact coverage and thresholds still to be agreed. Statistic: One deterministic geometry fixture, no observed units. Proposed five-unit follow-up inherits the M01 test-plan intent, not measurement evidence.	Source: Builder-supplied synthetic constraints; antenna-family-feasibility/2.0; p06-m02-rules-v1. Geometry arithmetic independently checked in feasibility-golden.json. Assumptions/uncertainty: All candidate envelopes include clearance/feed allowance and are invented constraints. No statistical tolerance or physical uncertainty data. No ranking by ka, size or family name. Decision: reject this supplied configuration. F02-ground: ground L / x needs 80 mm; supplied 60 mm Next evidence: Obtain the exact land pattern, 80 × 40 mm evaluation ground, clearance, matching BOM and ceramic/assembly tolerances. Obtain band and efficiency definitions, calibrated feed plane, absolute co/cross pattern, unit population, tolerances and installation comparisons.
M02-C-FLEX Owner 06.2 Illustrative	Is this supplied Flex dipole implementation compatible with the declared product? Fixture: p06-m02-candidates-v1 Band: Local mechanical / requirement variant M02-NODE: 2.450 GHz; symmetric requested band 2.401–2.499 GHz. Quantity/unit: Envelope 65 × 10 × 2 mm internal; ground no minimum in this fixture. Two conductor arms provide the intended return; balanced antenna terminals. Required radiation efficiency 40%, useful FBW 4%; achieved values unknown.	Planes/losses: R2 real 50 Ω single-ended feed with balun provision. R1 upstream; no feed/balun loss supplied. S0 radiation and vector pattern unknown; no loss assigned or counted twice. Configuration: 80 × 50 × 25 mm plastic product; internal allocation 70 × 12 × 8 mm; ground 60 × 40 mm. Free-space, specified metal-machine and hand states are future tests. O1 +z upright; O2 rotated 90° about +y. Basis: Specimen right-handed x/y/z; L/W/H along x/y/z; ground x/y. θ from +z, φ from +x toward +y. Linear, broad-azimuth intent; co/cross basis, exact coverage and thresholds still to be agreed. Statistic: One deterministic geometry fixture, no observed units. Proposed five-unit follow-up inherits the M01 test-plan intent, not measurement evidence.	Source: Builder-supplied synthetic constraints; antenna-family-feasibility/2.0; p06-m02-rules-v1. Geometry arithmetic independently checked in feasibility-golden.json. Assumptions/uncertainty: All candidate envelopes include clearance/feed allowance and are invented constraints. No statistical tolerance or physical uncertainty data. No ranking by ka, size or family name. Decision: retain for investigation. Envelope and feed-plan restrictions clear; useful-band / coverage evidence controls the next decision. Next evidence: Reserve the conductor pair and adhesive location; verify balun loss, cable routing/common mode, bending and assembly repeatability. Obtain band and efficiency definitions, calibrated feed plane, absolute co/cross pattern, unit population, tolerances and installation comparisons.
M02-C-EXT Owner 06.2 Illustrative	Is this supplied External monopole implementation compatible with the declared product? Fixture: p06-m02-candidates-v1 Band: Local mechanical / requirement variant M02-NODE: 2.450 GHz; symmetric requested band 2.401–2.499 GHz. Quantity/unit: Envelope 31 × 8 × 8 mm external; ground 50 × 30 mm. External resonant arm with board/counterpoise return through the connector. Required radiation efficiency 40%, useful FBW 4%; achieved values unknown.	Planes/losses: R2 real 50 Ω single-ended feed with balun provision. R1 upstream; no feed/balun loss supplied. S0 radiation and vector pattern unknown; no loss assigned or counted twice. Configuration: 80 × 50 × 25 mm plastic product; internal allocation 70 × 12 × 8 mm; ground 60 × 40 mm. Free-space, specified metal-machine and hand states are future tests. O1 +z upright; O2 rotated 90° about +y. Basis: Specimen right-handed x/y/z; L/W/H along x/y/z; ground x/y. θ from +z, φ from +x toward +y. Linear, broad-azimuth intent; co/cross basis, exact coverage and thresholds still to be agreed. Statistic: One deterministic geometry fixture, no observed units. Proposed five-unit follow-up inherits the M01 test-plan intent, not measurement evidence.	Source: Builder-supplied synthetic constraints; antenna-family-feasibility/2.0; p06-m02-rules-v1. Geometry arithmetic independently checked in feasibility-golden.json. Assumptions/uncertainty: All candidate envelopes include clearance/feed allowance and are invented constraints. No statistical tolerance or physical uncertainty data. No ranking by ka, size or family name. Decision: reject this supplied configuration. F03-external: External protrusion is required and prohibited. Next evidence: Reserve exterior clearance and counterpoise connection; investigate connector, seal, mounting torque, handling and weather exposure. Obtain band and efficiency definitions, calibrated feed plane, absolute co/cross pattern, unit population, tolerances and installation comparisons.

Go deeperWhat would justify changing the decision?

A different chip implementation with a compatible ground condition could re-enter the shortlist. A balanced source or an appropriate balun could repair the flex feed plan. An external mounting allowance could reopen the monopole. Each changes a specific disqualifier and may introduce another burden. Nonidentifying evidence should leave alternatives open; no weighted “best antenna” score is needed to state that.

Ungraded review

Check your understanding

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

01Classify an IFA and a tapered slot without using their manufacturing labels. What current path distinguishes them?
Model answer
An IFA is a resonant bent/loaded arm with a feed, short and current-bearing counterpoise. A tapered slot supports a progressive guided field toward an opening, with return currents on the opposing conductor. Both can be printed. Resonant/traveling-wave behavior, balance and field boundary are independent of the manufacturing label.
02At 2.450 GHz, calculate λ0/4 and ka for the 80 × 50 × 25 mm box. What does the chip-only result omit?
Model answer
With exact c = 299792458 m/s, λ0 = 122.364268571 mm and λ0/4 = 30.591067143 mm. Half the box diagonal gives a = 48.798053240 mm, so ka = 2.505692346. The 10 × 4 × 3 mm chip body gives ka = 0.287045181 but excludes board/chassis/cable currents. Neither result predicts efficiency; an exterior radiator changes the enclosing boundary.
03The external monopole is only one visible arm. Where did its other conductor go?
Model answer
It became the board/chassis/counterpoise and possibly unintended exterior cable currents. The feed shield must return current to a declared conductor. The ideal image construction is a model of an infinite perfect ground, not permission to remove the return from a product.
04Does a helical wire guarantee circular polarization in both mounting orientations?
Model answer
No. Normal and axial modes have different current progression and geometry scales. A compact loaded helix is often used for linear polarization; axial-mode geometry can give circular-polarization intent along its axis. Actual handedness, axial ratio and co/cross response require frequency- and direction-specific evidence. Moving the product can move the gateway outside that useful angular region.
05A lossy miniature antenna has a wide S11 band after tuning. Has it met a 40% radiation-efficiency target over 4% useful FBW?
Model answer
Unknown. Loss can broaden a match response while diverting accepted power into heat. A tuner changes port acceptance and adds its own loss; it does not manufacture radiation efficiency. Useful band requires the named match, efficiency, pattern and polarization conditions together. Q is not universally 1/FBW, and a chip-body ka is not a product bound.
06Defend the two-retained/two-rejected canonical shortlist. Then shorten the product and its allocation to 64 mm, or require metal mounting.
Model answer
Retain C-IFA and C-FLEX for investigation. Reject this C-CHIP implementation because its 80 mm minimum ground length exceeds 60 mm; reject C-EXT because protrusion is prohibited. With product L = allocation L = 64 mm and other canonical fields unchanged, C-FLEX also fails its 65 mm length. C-IFA remains provisional. At allocation L = 65 mm the flex length condition clears if the product contains it. Mandatory metal mounting alone supplies no numeric penalty or hard rejection: keep compatible alternatives and request specified plate/spacing/fastener tests in O1/O2. Ground, feed or enclosure redesign can change these fixed-implementation decisions; none rejects a whole family.

References and further reading

Separate principles from the invented constraints

Access and status checked 7 September 2026. All diagrams are original qualitative schematics. Definitions and geometric derivations are explicit; candidate sizes and targets are Illustrative/Requirement entries, not vendor data. Phasors use e^+jωt; voltages/currents are RMS when used for power; power ratios use 10 log10 and dBm references 1 mW. No measured result or normative product limit is asserted.

C. A. Balanis, Antenna Theory: Analysis and Design, 4th edition, Wiley, 2016. Official publisher edition and contents consulted; family/current, loop, broadband/helical, aperture, patch and array chapters are further reading. Full book and sample chapter were not accessible in this review; no invented page or theorem citation is used.
IEEE 145-2025, IEEE Standard for Definitions of Terms for Antennas. Active; published 31 March 2026, supersedes 145-2013. Public identity, scope and status consulted; normative full text not accessed.
IEEE 149-2021, IEEE Recommended Practice for Antenna Measurements. Active; published 18 February 2022. Public scope for passive, linear, reciprocal antenna measurements consulted. Full text not accessed; this lesson supplies no measurement procedure or conformity claim.
Texas Instruments, AN058 Antenna Selection Guide, SWRA161B, 5 October 2010. §§3.1–3.3, 4, 5.1.2, 6.2 and document-history entry consulted for feed/ground and configuration context. Its implementation examples do not establish this lesson’s synthetic minima; its general range statements are not used.
D. H. Staelin, MIT Electromagnetics and Applications, Spring 2009, Chapter 10. §§10.2–10.3, small-loop Example 10.3D and array orientation in §10.4 consulted. Used for current/field, radiation resistance, receive-area and phase-addition foundations with the stated assumptions; no numerical family performance is transferred.
M. Reckeweg and C. Rohner, Antenna Basics, Rohde & Schwarz, 8GE01_1e, March 2015. §§3.6–3.9, 3.11 and 4.1–4.2 consulted for aperture/impedance, bandwidth and wire-antenna cross-checks. Its older “practical gain” language is mapped to mismatch-inclusive realized gain.
D. H. Staelin, MIT Chapter 11: Common Antennas and Applications (2009). Aperture derivation and examples in §§11.1.1–11.1.3 consulted; used only for conditional electrical-aperture scaling, illumination and blockage.
MathWorks, Design PIFA for WLAN Wi-Fi Applications (Design Parameters / Vary Antenna Feed Location) and helix (Description). Online documentation accessed 7 September 2026; no dated revision displayed. Geometry and mode descriptions consulted; no MATLAB model or numerical result is reused.
M. Gustafsson, C. Sohl and G. Kristensson, Physical limitations on antennas of arbitrary shape, Proceedings A 463, 2589–2607 (2007), DOI 10.1098/rspa.2007.1893. Author-institution abstract and bibliographic record consulted. Supports the scope of shape-dependent bounds; the full derivation could not be retrieved, so no exact bound is claimed or calculated.

Model antenna-family-feasibility/2.0; rule set p06-m02-rules-v1; fixture p06-m02-candidates-v1; evidence p06-evidence-map-v1. Equations retain full precision internally and round only for display. Exact enclosure synthesis, EM solution, final tuning, installed performance, array design, measurement execution and regulatory/exposure conclusions are intentionally outside this lesson.