Antennas Q&A

Directivity measures how focused the radiation pattern is relative to an isotropic radiator, considering only the radiated power. It is a purely geometric property of the pattern shape — an antenna with a narrower beam has higher directivity.

Gain includes all losses (conductor ohmic loss, dielectric loss, mismatch loss if included in the definition). It measures what you actually get relative to an isotropic radiator when driven with real input power.

Practical examples:

• Half-wave dipole: D = 2.15 dBi. A real dipole with resistive losses might have G = 1.5–2.0 dBi
• Patch antenna: D ≈ 7–9 dBi, G ≈ 5–7 dBi (losses in the substrate and copper)
• Yagi (10 elements): D ≈ 13 dBi, G ≈ 12 dBi (small ohmic losses)

VSWR (Voltage Standing Wave Ratio) describes the impedance mismatch between a transmission line and its load (the antenna). When an antenna is not 50 Ω, some of the transmitted power is reflected back toward the transmitter.

Acceptable VSWR values:

• VSWR 1.5:1 (RL = 14 dB, 4% reflected) — typical minimum for base station antennas
• VSWR 2.0:1 (RL = 9.5 dB, 11% reflected) — marginal but used in some wideband systems
• VSWR 3.0:1 (RL = 6 dB, 25% reflected) — generally unacceptable for TX (25% of power wasted, PA may be damaged)

Why it matters for transmit systems:

• Reflected power returns to the PA. If the PA's output stage cannot handle the reflected power, it can overheat or fail (especially solid-state PAs and tube finals).
• High VSWR can cause voltage standing waves with peaks 2× the normal voltage — breakdown risk in high-power systems.
• Some PAs have built-in VSWR protection that folds back power when VSWR exceeds a threshold, reducing TX power.

Polarisation describes the orientation of the electric field vector as the wave propagates. For maximum power transfer, the transmit and receive antenna polarisations must match.

Practical polarisation types:

• Linear (vertical or horizontal): The E-field points along a fixed axis. Vertical dipole, horizontal Yagi.
• Circular (RHCP / LHCP): E-field rotates. 3 dB loss against any linear antenna — useful when polarisation angle is unknown (GNSS satellites).
• Elliptical: Between linear and circular — most real-world antennas are slightly elliptically polarised.

Real-world impact:

• A horizontally-polarised Yagi receiving from a vertically-polarised base station: PLF → 0, link fails
• Indoor Wi-Fi: multipath scattering rotates polarisation — a nominally co-polarised system may lose only 0–3 dB in rich scattering
• GNSS: satellites transmit RHCP. A linear patch receives GNSS but with a 3 dB penalty vs. RHCP patch

The Friis equation gives the received power in a free-space line-of-sight link:

Terms: Pt = transmit power, Gt = TX antenna gain, Gr = RX antenna gain, R = range, λ = wavelength (= c/f). The (λ/4πR)² term is the free-space path loss (FSPL).

Link budget example — 2.4 GHz Wi-Fi at 50 m:

• Pt = +20 dBm (100 mW), Gt = 2 dBi (dipole), Gr = 2 dBi
• FSPL = 32.44 + 20·log(2400) + 20·log(0.05) = 32.44 + 67.6 − 26 = 74 dB
• Pr = 20 + 2 + 2 − 74 = −50 dBm
• Wi-Fi sensitivity ≈ −90 dBm → link margin = 40 dB (excellent)

Antenna bandwidth is the frequency range over which the antenna meets its specifications (usually VSWR < 2:1 or gain within 3 dB). Two distinct types:

• Impedance bandwidth: Range where S11 < −10 dB (VSWR < 2:1). The primary spec for most commercial antennas.
• Pattern / gain bandwidth: Range where gain stays within 3 dB of peak and pattern shape is acceptable. Usually wider than impedance bandwidth.

What limits bandwidth — the Chu limit:

The Chu-Harrington limit says: for a given antenna size (sphere of radius a), there is a minimum radiation Q (and therefore a maximum achievable bandwidth). Smaller antennas are inherently narrow-band.

Practical implications:

• A small Bluetooth antenna (a ≈ 5 mm at 2.4 GHz, ka ≈ 0.25) has very limited achievable bandwidth — you can match it at 2.4 GHz but broadband multi-band operation is fundamentally limited.
• Wideband antennas must be physically large relative to the wavelength.
• Matching networks and active antenna techniques can change the operating frequency but cannot overcome the Chu limit for a given physical size — they always trade off efficiency for bandwidth.

The three-antenna method determines the gain of three unknown antennas without needing a reference antenna — the gain of each is derived purely from transmission measurements between pairs.

Procedure:

• Label antennas A, B, C. Set up a far-field range (R > 2D²/λ)
• Measure S21 for all three pairs: S21_AB, S21_AC, S21_BC (keeping range distance R constant)
• Apply Friis to each pair:
  S21_AB = G_A + G_B + 20·log(λ/4πR)
  S21_AC = G_A + G_C + 20·log(λ/4πR)
  S21_BC = G_B + G_C + 20·log(λ/4πR)
• Three equations, three unknowns → solve:
  G_A = (S21_AB + S21_AC − S21_BC)/2 − 20·log(λ/4πR)

Why preferred over standard gain horn:

• Standard gain horns have calibration uncertainties of ±0.3–0.5 dB. Their gain is affected by the aperture size tolerance and the feed waveguide transition.
• Three-antenna method is self-referencing — the accuracy depends only on the range geometry and the S21 measurement (typically ±0.1 dB on a good VNA)
• No dependency on a traceable reference artifact that could be damaged, aged, or incorrectly applied

Total antenna radiation efficiency (η_total) accounts for all loss mechanisms between the input port and radiated power. It is the product of three efficiencies:

Loss mechanisms:

• Impedance mismatch: Power reflected back from antenna. Recovered if a circulator/isolator is used; otherwise wasted.
• Conductor (ohmic) loss: In the antenna elements (especially copper plating, thin PCB traces). Worst for electrically small antennas where resistance/radiation-resistance ratio is high.
• Dielectric loss: Power absorbed in substrate material (tanδ). FR4 (tanδ ≈ 0.02) is lossy — a patch on FR4 can have 30–50% power dissipated in the substrate. Rogers RO4003C (tanδ ≈ 0.0027) is far better.
• Surface wave loss (patch/PCB antennas): Power trapped in substrate propagates along the surface and never radiates from the intended aperture.
• Near-field absorption: Conducting objects (phone chassis, human body) near the antenna absorb radiated power.

Measurement — Wheeler cap method: Place a small metal cap ("Wheeler cap") over the antenna. The cap terminates the radiation resistance but leaves the loss resistance unaffected. Measure Q with and without the cap. Radiation efficiency = (Q_open − Q_cap) / Q_open.

Measurement — 3D pattern integration: Measure gain in all directions in an anechoic chamber. Integrate over the sphere and compare to directivity from pattern shape. Requires a full spherical scan (360° azimuth × 180° elevation).

A patch antenna resonant frequency is primarily set by its length (L ≈ λ_eff / 2) and the substrate's effective permittivity. Resonating 150 MHz too low means the effective electrical length is too long.

Most likely causes:

• Substrate εr higher than modelled: εr is frequency-dependent (dispersive) and varies between PCB lots. If εr is 4.5 instead of 4.2, λ_eff is longer → f_r is lower. Δf/f ≈ Δεr/(2εr) → 0.3/(2×4.2) ≈ 3.6% shift. At 2.45 GHz, 3.6% = 88 MHz — plausible for part of the discrepancy.
• Substrate thickness thicker than specified: Thicker substrate → larger fringing fields → larger effective length extension → lower frequency. Each ΔL extension due to fringing ≈ 0.412h((εr_eff + 0.3)(W/h + 0.264)) / ((εr_eff − 0.258)(W/h + 0.8)).
• Patch dimensions cut too large: If the PCB etching was under-etched (less copper removed than designed), the patch is physically longer → lower frequency.
• Ground plane too small: A finite ground plane modifies the fringing fields and effective permittivity, shifting frequency.
• Nearby conductor or metallic enclosure: Loading the near field of the patch with metal increases effective capacitance → lowers resonant frequency.

Corrections:

• Trim the patch length (reduce L) — a 3–5% length reduction shifts frequency up by 3–5%
• Cut slots in the patch — reduces effective length without requiring a new board spin
• Measure εr from a test resonator fabricated on the same board lot, update the model, re-spin
• Add a small capacitor in the feed to tune the resonant frequency electronically (active tuning)

A phased array steers its beam by applying a linear phase progression across its elements so that wavefronts add coherently in the desired direction.

How it works physically: At angle θ, there is a path length difference of d·sin(θ) between adjacent elements. Applying phase −Δφ to each successive element pre-compensates this delay, making all element contributions arrive in phase at θ → constructive interference → beam peak at θ.

Trade-offs with scan angle:

• Gain drop with scan (element pattern × array factor): Each element radiates as a cos(θ) pattern (for a flat aperture). At 60° scan, the projected aperture is halved → gain drops by cos(60°) = 3 dB. The array factor also narrows in the projected direction.
• Grating lobes: When d > λ/2, the array factor repeats and a grating lobe (second main beam) appears. For d = λ/2, grating lobes only appear at θ = ±90° (endfire). For larger d, grating lobes intrude into visible space at smaller scan angles.
• Impedance variation with scan (scan blindness): The mutual coupling between elements changes with scan angle. At certain angles, the active element impedance becomes reactive and VSWR rises sharply — "scan blindness." Array designers use element spacing and mutual coupling analysis to avoid this.

An antenna's impedance is not a fixed property — it is determined by the interaction of the near-field currents with all surrounding conductors and dielectrics. Nearby objects modify the boundary conditions of the electromagnetic fields, changing both the radiation resistance and the reactive part of the impedance.

Ground plane effect (image theory): A quarter-wave monopole above a ground plane behaves as a half-wave dipole through the image effect. Its resonant length, impedance, and pattern all depend on the ground plane size. A finite ground plane <λ/4 causes the resonant frequency to shift and radiation pattern to distort. The feed impedance can change by 10–30 Ω.

Human body effect (handset antennas): Human tissue (εr ≈ 40–60, tanδ ≈ 0.3 at 1.8 GHz) heavily loads an antenna. A 2.4 GHz PCB antenna free in air may show S11 = −20 dB; when held in a hand, the resonant frequency shifts down by 5–15% and S11 may degrade to −5 dB. This is the #1 challenge in handset antenna design.

PCB chassis as radiator: At frequencies where the PCB chassis is close to λ/2 in length, the chassis itself becomes the dominant radiator. A small antenna acts more as a "coupling element" exciting currents on the chassis. This is actually desirable — it means even a small antenna can drive a larger effective aperture.

Design approaches:

• Simulate the antenna always in its final context (with full PCB model and representative chassis)
• Prototype on the actual PCB — never evaluate a handset antenna in free space
• Use frequency tuning (variable capacitor, RF MEMS) to re-tune when the environment changes
• Diversity (multiple antennas at different locations on the device) — use whichever shows best impedance at a given moment

OTA testing evaluates a complete wireless device — including its antenna, RF circuits, and firmware — as it actually operates in free space. Unlike conducted tests (where a cable connects to the device), OTA tests measure real radiated performance.

TRP — Total Radiated Power: The total RF power radiated by the device in all directions when transmitting. Accounts for mismatch loss, conductor and substrate loss, and body effect.

TIS — Total Isotropic Sensitivity: The average sensitivity of the device across all angles and both polarisations. It combines antenna gain pattern, receiver NF, and matching — the overall receive performance.

Measurement setup: Full-anechoic chamber + positioner (3-axis) + calibrated reference antenna. Device-under-test is placed on a positioner and measured at every (θ, φ) combination. For TX: measure radiated power. For RX: inject known signal from reference antenna and step until device just receives correctly (BER/PER threshold).

OTA requirements (examples):

• 3GPP LTE Category 4 handset: TRP ≥ +23 dBm (with antenna gain)
• TIS is typically specified as a minimum sensitivity (e.g. −95 dBm for LTE Band 4)
• Wi-Fi 6 certification requires TRP and TIS measurements in both vertical and horizontal orientations

Mutual coupling occurs when the near-field currents of one antenna element induce currents in an adjacent element, changing its radiation pattern, impedance, and the correlation between the two elements' received signals.

Effects of mutual coupling:

• Impedance change (active element impedance): When both elements are excited simultaneously, the active impedance seen at each port includes the mutual impedance. This shifts resonant frequency and mismatch, reducing efficiency.
• Pattern distortion: The near-field coupling modifies the radiation pattern of each element — the patterns are no longer independent. In compact MIMO (e.g. two antennas 10 mm apart at 2.4 GHz = 0.08λ), patterns can become nearly identical → no diversity gain.
• ECC (Envelope Correlation Coefficient): Quantifies how correlated the received signals are at two antennas. ECC = 0 means perfectly uncorrelated (ideal MIMO). ECC = 1 means identical received signals (no MIMO benefit). For spatial diversity, ECC < 0.5 is the target.

Reducing mutual coupling:

• Increase element spacing (>λ/4 typically sufficient; λ/2 is ideal)
• Add a parasitic decoupling element (e.g. slot or stub cut between elements)
• Use orthogonal polarisations (one vertical + one horizontal → >25 dB isolation even at close spacing)
• Neutralisation line: a coupling path designed to cancel the mutual coupling with opposite amplitude/phase

An electrically small antenna (ESA) is one whose maximum dimension is much smaller than λ (specifically ka << 1 where a is the radius of the smallest sphere enclosing the antenna). Examples: loop antennas in IoT devices, RFID tags, implantable medical device antennas.

Fundamental properties of ESAs:

• High Q, narrow bandwidth: Chu limit. ESAs store much more reactive energy than they radiate → high Q → BW = f₀/Q. A ka = 0.1 antenna has Q_min ≈ 1000, BW ≈ 0.1%.
• Low radiation resistance: A short dipole (L << λ) has R_rad = 80π²(L/λ)². For L = λ/10, R_rad ≈ 8 Ω. The loss resistance of the conductor may be comparable → low efficiency.
• High reactance: An electrically short dipole looks strongly capacitive (−jX >> 50 Ω). A small loop looks inductive.

Matching to 50 Ω:

• L-network (inductor-capacitor): Cancel the reactive part with the opposite reactance, then transform R_rad to 50 Ω. But the matching network Q adds to the total Q → further narrowing bandwidth.
• Helical loading / top loading: Increase radiation resistance by coiling or top-loading the antenna without physically enlarging it. A helical monopole has higher R_rad and better efficiency than a straight monopole of the same height.
• Lossy matching: Adding a series resistor can widen impedance bandwidth (at the cost of drastically reduced efficiency). Acceptable for receive-only applications where sensitivity is not critical.
• Matching at a narrowband point: For IoT (LoRa, BLE, Zigbee) with narrow modulated signals, match at the exact centre frequency — the narrow bandwidth is acceptable.

mmWave (24–100 GHz) enables multi-gigabit wireless links and is the cornerstone of 5G FR2 (n257/n258/n260/n261 bands at 24/26/28/39 GHz). The physics at mmWave introduces challenges absent at sub-6 GHz.

High path loss: FSPL increases as f². At 28 GHz vs. 2.8 GHz, FSPL is 20 dB higher for the same distance. This demands either high antenna gain (directional beams) or very short links. 5G mmWave NR is primarily used for <300 m coverage.

High atmospheric absorption: At 60 GHz, oxygen absorption is ~15 dB/km — limits range to indoor use but prevents inter-cell interference (used in 802.11ad/WiGig). At 28 GHz, absorption is modest (0.1 dB/km). Rain attenuation (above 10 GHz) scales with frequency — at 28 GHz, heavy rain (50 mm/hr) adds ~8 dB/km.

Antenna size and fabrication tolerance: At 28 GHz, λ = 10.7 mm → λ/2 = 5.4 mm. A 64-element array fits in 40 mm × 40 mm — small enough for a handset. But dimensional tolerances become critical: a 50 μm PCB etching error on a 1 mm trace is 5% — significant at mmWave. Requires tight PCB tolerances (≤25 μm).

Blockage sensitivity: At mmWave, the human body and hand are nearly opaque — a full hand blockage can cause 20–40 dB additional path loss. This drives the need for beam diversity (multiple antenna panels on different faces of the handset) and fast beam steering to find a clear path.

Connector and PCB loss: RG58 cable has >10 dB/m loss at 28 GHz. Even high-quality SMA connectors add 0.5 dB each. PCB traces on FR4: 5–10 dB/cm. Everything must be done on-chip or on low-loss substrate (PTFE, Rogers) with very short interconnects.

Beam tracking latency: In mobile scenarios, the beam must track the user. 5G NR mmWave beam management (SSB, CSI-RS, beam reporting) allows <10 ms beam switching — insufficient for fast-moving vehicles without predictive tracking algorithms.

A single-mode patch antenna should show one clean S11 resonance. A double dip indicates two resonant mechanisms are present simultaneously.

Cause 1 — Dual-mode excitation (degenerate modes): A square (or nearly square) patch has two degenerate TM10 and TM01 modes at the same frequency. If the feed point breaks the symmetry, both modes are excited with slightly different impedances and coupling — two separate resonances appear very close together. Perturbation (a small corner cut, a notch, or an asymmetric feed point) splits these modes. This is intentional in circular polarisation patch design but unintentional here.

Cause 2 — Feed probe resonance: The SMA probe pin (or through-hole via) feeding the patch has its own resonant length. If the probe is too long (electrically), it resonates near the patch resonance, coupling energy from the probe resonance into the S11 response → two dips.

Cause 3 — Higher-order mode: The TM20 mode of a patch resonates at exactly twice the TM10 frequency. If the intended frequency is in between, and fringing fields push the modes, one higher-order mode of a different patch dimension could appear near the fundamental.

Cause 4 — Coupling to nearby structure: A ground slot, a metallic enclosure edge, or another conducting element near the patch can act as a second resonator coupled to the patch, forming a coupled-resonator pair with two split resonances.

Fixes:

• For asymmetric feed / dual mode: symmetrise the feed point (move to exact centre of a side) or change the patch to rectangular (make L ≠ W) to separate the two modes in frequency
• For probe resonance: shorten probe length or add a small cap on the probe to adjust its electrical length
• For nearby structure coupling: increase separation from the surrounding metal by λ/4 minimum or add an absorber

SAR (Specific Absorption Rate) quantifies the rate at which RF energy is absorbed per unit mass of biological tissue, expressed in watts per kilogram (W/kg). It is a regulatory safety limit, not a performance metric.

How antenna placement affects SAR:

• Distance from body: SAR falls with distance as approximately 1/r² to 1/r⁶ depending on geometry. Moving the antenna from 2 mm to 10 mm from the tissue can reduce SAR by 10–20 dB.
• Antenna type and orientation: A patch antenna with backside ground plane radiates primarily away from the body — much lower SAR than a dipole or monopole which radiates toward the body as well.
• Feed current distribution: Surface currents near the antenna (especially on the PCB chassis) that flow close to the body contribute significantly to SAR. Baluns or ferrite beads can break these currents.

Regulatory testing: SAR is measured by probing the E-field inside a liquid phantom (a shell filled with tissue-simulating liquid) with a calibrated probe while the device transmits at maximum power on each certified band. The measurement is done in "cheek" (held flat against the phantom) and "tilt" (angled) positions.

Design mitigations:

• Place antennas at the bottom of the handset (far from ear during voice call)
• Use power control — reduce TX power when close to body while maintaining link (proximity sensor)
• Use directional antennas (patch) biased to radiate away from head
• Use ferrite backing to block radiation into body (parasitic absorber)

The space around an antenna is divided into three regions with distinct field behaviours:

1. Reactive Near-Field (Fresnel inner): Distance r < 0.62√(D³/λ). Fields are dominated by reactive (stored) energy — inductive and capacitive fields that don't propagate. E and H fields are not in phase. Objects placed in this region load the antenna and change its impedance and resonant frequency. This is why nearby conductors detune antennas.

2. Radiating Near-Field (Fresnel outer): 0.62√(D³/λ) < r < 2D²/λ. Radiation fields dominate but the amplitude and phase distribution is not yet plane-wave. The pattern shape depends on the observation distance — the antenna cannot be described by a single direction-independent gain value. Near-field scanning and holographic measurements are done in this region.

3. Far-Field (Fraunhofer region): r > 2D²/λ. Fields are plane waves, E and H are in phase and perpendicular. The radiation pattern is independent of distance (only its magnitude scales as 1/r). All gain and pattern specifications apply in the far field.

Impact on measurements:

• All antenna range measurements must be in the far field — measuring gain or pattern inside 2D²/λ gives erroneous results
• Compact antenna test ranges (CATRs) use a shaped reflector to create a simulated plane wave (far-field illumination) at a short physical distance — enabling far-field measurement without a large range
• Near-field scanning (NFS) measures the complex near field on a surface, then applies an NF-FF transformation to compute the far-field pattern mathematically
• For small antennas (ka << 1), D is small and R_ff = 2D²/λ is very short — you can measure in the far field at close range, making small antenna testing easy

In a planar antenna array, the feed network distributes signal from a single input port to all elements. There are two main distribution topologies:

Series-fed (travelling wave) array:

• A single transmission line passes by each element in sequence. Each element taps off a fraction of the signal as it propagates.
• The element excitation phase naturally increases from one end to the other by k·d (one free-space wavelength of spacing per element), resulting in a fixed progressive phase shift.
• Beam squint: As frequency changes, the electrical length of the feed line changes → phase shift changes → beam pointing angle changes with frequency. A 10% bandwidth change can cause >10° of beam squint in a series-fed array.
• Advantages: Simple layout, no power dividers, low-loss (no combiner losses), easy to fabricate on PCB.
• Best for: Fixed-frequency (narrowband) applications such as 77 GHz automotive radar (ISM channel, narrow bandwidth) or ISM-band microstrip Yagi.

Corporate-fed (parallel / tree) array:

• A binary tree of power splitters distributes the signal symmetrically to all elements simultaneously. All elements see identical electrical path length → identical phase (broadside array by default).
• No inherent beam squint: Since all elements have equal path lengths, frequency changes do not change the relative phase → beam stays broadside. Phase shifters can be inserted in each branch for beam steering.
• Higher insertion loss: Each power divider junction introduces ~0.3 dB insertion loss. A 1→64 corporate feed requires log₂(64) = 6 splitter stages = ~1.8 dB combining/splitting loss.
• Best for: Wideband phased arrays, electronically steered arrays (radar, 5G), any application where frequency tuning or scan stability is required.

Effective aperture (Ae) is the equivalent collecting area of an antenna for a plane wave arriving from the direction of maximum gain. It relates received power to incident power density:

Why larger antennas have higher gain: The effective aperture scales with physical aperture area A_phys: Ae = η_ap · A_phys, where η_ap ≈ 0.5–0.7 for well-designed aperture antennas. Since G = 4π·Ae/λ², and Ae ∝ A_phys, then G ∝ A_phys / λ². Doubling the physical aperture doubles the gain (3 dB). Halving the wavelength (doubling frequency) quadruples the gain for a fixed aperture size.

Practical implication (Friis equation): In a satellite downlink, if you move from 1 m to 3 m dish on the ground (9× area increase → 9.5 dB gain increase), and simultaneously move from 1 GHz to 3 GHz (9× higher FSPL), the larger dish at 3 GHz has the same effective aperture as the 1 m dish at 1 GHz — received power is unchanged. This is why Ka-band (26 GHz) VSAT terminals can use a 45 cm dish and match the performance of a Ku-band (12 GHz) 90 cm dish.

Beamforming is the spatial processing technique that shapes the radiation pattern of an antenna array to direct energy toward desired users (transmit beamforming) or to enhance signal reception from a desired direction while rejecting interference (receive beamforming).

Analogue beamforming:

• Phase shifters and attenuators in the RF/analog domain adjust element weights before a single ADC/DAC
• Only one beam can be formed at a time per RF chain
• Lower hardware cost (one ADC per panel, not per element)
• Cannot simultaneously serve multiple users at different directions
• Used in: 5G FR2 (mmWave) handsets and early 5G base stations; 802.11ad WiGig

Digital beamforming:

• Each antenna element has its own RF chain, ADC/DAC
• Beamforming is done in software via complex multiplication of element samples
• Can form unlimited simultaneous beams in any direction — enables MU-MIMO (multi-user MIMO)
• Full channel state information at the transmitter (CSIT) enables maximum capacity
• High hardware cost and power (each ADC draws 10–100 mW; 64 elements = 640 mW just for ADCs)
• Used in: 5G FR1 (<6 GHz) massive MIMO base stations (64T64R); research systems

Hybrid beamforming (most practical massive MIMO):

• Groups of elements share one RF chain; analogue phase shifters steer within the group
• Multiple RF chains → multiple simultaneous analogue beams → digital processing combines/steers them
• Balance of hardware cost and spatial multiplexing capability
• 5G NR Rel-15/16 supports hybrid beamforming with up to 32 digital ports on a 64-element array

Polarisation describes the orientation of the electric field vector of the radiated wave. For a vertical dipole, the E-field oscillates vertically — the antenna is vertically polarised.

Polarisation Loss Factor (PLF):

Types of polarisation:

• Linear: E-field oscillates in one plane. Vertical dipole=vertical polarisation.
• Circular (CP): E-field rotates — one full revolution per wavelength. Produced by two orthogonal LP fields with 90° phase difference. CP antennas suffer only −3 dB loss with any linearly-polarised antenna at any rotation angle.
• Elliptical: General case between linear and circular — the field traces an ellipse.

Practical consequence: A GPS satellite uses RHCP. A vertical dipole receiving GPS sees −3 dB polarisation loss, but is immune to Faraday rotation of the ionospheric path (which would cause complete signal loss with a linearly-polarised satellite).

Radiation resistance R_rad is the equivalent resistance that, if placed at the feed point, would dissipate the same power as the antenna radiates. It allows us to model radiation as a power dissipation in a circuit element.

Why small antennas have low efficiency: For an electrically small dipole (L<<λ), R_rad is very small (a few ohms or less). The loss resistance R_loss of the conductor may be comparable: η = R_rad/(R_rad+R_loss). A 1 Ω R_rad with 1 Ω R_loss gives only 50% efficiency.

Improving small antenna efficiency:

• Use high-conductivity materials (silver, copper) and large conductor cross-sections to minimise R_loss
• Use loading coils to increase effective electrical length (but coil Q must be high)
• Use a ground plane to increase effective R_rad (image theory doubles it)

The total radiation pattern of an antenna array equals the product of the individual element pattern and the array factor (AF) — this is the pattern multiplication principle.

Element pattern vs array factor:

• Element pattern: shape determined by the individual antenna element geometry (dipole, patch, horn)
• Array factor: shape determined by the array geometry (element spacing, number of elements, phase weights). Independent of what element type is used.
• Total pattern: their product — array factor sharpens the main lobe but element pattern determines whether energy can go in a given direction at all

Grating lobes: When element spacing d>λ/2, the AF produces additional main lobes (grating lobes) at angles θ_g where d·sinθ_g=nλ for integer n. These grating lobes have the same amplitude as the main lobe — they waste radiated power and cause ambiguity in radar/direction finding.

Prevention: Keep d≤λ/2 for full electronic scanning. For narrow-angle scanning (±30°), d up to 0.7λ is acceptable before grating lobes enter visible space.

The Friis equation gives the received power for a complete RF link:

5G NR 28 GHz link budget at 200 m:

• FSPL = 20·log₁₀(0.2) + 20·log₁₀(28000) + 32.44 = −14 + 88.9 + 32.44 = 107.3 dB
• TX power: +23 dBm (handset)
• TX beamforming gain: +24 dBi (8×8 phased array)
• RX beamforming gain: +24 dBi (base station)
• P_R = 23 + 24 + 24 − 107.3 = −36.3 dBm
• Receiver sensitivity (100 MHz BW, NF=7 dB, SNR=10 dB): −174+10+80+7+10 = −67 dBm
• Link margin = −36.3 − (−67) = +30.7 dB — healthy link even with atmospheric losses

Antenna radiation patterns are defined in the far field (Fraunhofer region, r>2D²/λ). For large antennas this distance can be enormous — a 1 m parabolic dish at 10 GHz needs r>2×1²/0.03=67 m. Testing this requires an outdoor range or a special indoor facility.

Far-field range testing:

• Antenna under test (AUT) placed far enough that the incident wave is effectively planar
• Requires large outdoor ranges or tall towers — expensive, weather-dependent, limited to below ~6 GHz due to atmospheric absorption
• Gold standard for accuracy

Near-field testing:

• Measure amplitude and phase of E-field on a surface close to the AUT (planar, cylindrical, or spherical scanner)
• Apply near-to-far-field transformation (NF-FF): a Fourier transform of the measured near-field data gives the far-field pattern
• Compact — fits in a laboratory. Full 3D spherical scan takes minutes with automated positioner
• Requires very accurate phase measurement — probe positioning to λ/100

Compact Antenna Test Range (CATR):

• Uses a large parabolic reflector to collimate a spherical wave from a nearby feed into a flat wavefront, simulating a far-field plane wave in a short distance (the "quiet zone" is typically 1/3 of the reflector diameter)
• Used when the antenna is too large for near-field scanning but indoor testing is required
• Essential for testing 5G base station antennas (30–60 cm aperture, 3.5/28 GHz) and satellite antennas in large anechoic chambers
• The reflector must be precisely shaped to λ/100 — edges must be serrated to minimise diffraction

Mutual coupling occurs when radiation from one antenna element induces a voltage in a neighbouring element. In an array, every element both radiates and receives, creating a complex network of electromagnetic interactions between elements.

Effect on impedance matching:

• The active input impedance of an element in an array differs from its isolated impedance, because currents in neighbouring elements create additional EM fields at the element under consideration
• Z_active(i) = Z_isolated + Σ Z_mutual(ij) × I_j/I_i for all neighbouring elements j
• As the beam is steered, the relative current phases change → active impedance varies with scan angle → matching degrades → scan blindness at some angles

Effect on radiation patterns:

• Embedded element patterns differ from isolated element patterns — each element's pattern is distorted by the presence of surrounding elements
• Can cause "scan blindness" — at certain scan angles, the array input impedance becomes purely reactive and S11→0 dB (all power reflected). Common in patch arrays with substrate-guided surface waves.
• Can also create unwanted sidelobes and tilt the main beam slightly

Mitigation:

• Full-wave EM simulation of the array (not just element isolation) to predict embedded element patterns
• Wideband matching network designed for the array's active impedance, not isolated element impedance
• Optimised element spacing to reduce coupling (but <λ/2 causes grating lobes — tradeoff)
• Meta-material EBG (electromagnetic band-gap) surfaces to suppress surface waves and reduce coupling

Omnidirectional antenna: Radiates uniformly in all directions in the azimuth plane (horizontal) while having some directionality in elevation. Gain is typically 0–8 dBi. Pattern is a toroid (donut shape).

Examples: Half-wave dipole (2.15 dBi), ground plane antenna, whip antenna, collinear array (higher gain, tighter elevation beam).

Directional antenna: Concentrates radiated power in one or more preferred directions. Gain ranges from 6 dBi (patch) to 50+ dBi (large parabolic dish).

Examples: Yagi-Uda, patch, horn, parabolic dish, phased array.

When to choose each:

• Omnidirectional: Broadcasting to all directions without knowing where receivers are (FM radio, cellular base station covering 360°, WiFi access point, IoT nodes). Cannot afford to miss receivers that move around unpredictably.
• Directional: Point-to-point links where both ends are fixed (microwave backhaul, satellite downlink, VSAT terminal). Concentrates power toward the target, increasing range or reducing required transmit power. Also used in radar where angular resolution matters.
• Phased array (steerable directional): When you need directionality but the target moves (5G beamforming handsets, radar tracking). Electronic steering replaces physical pointing.

MIMO (Multiple Input Multiple Output) uses multiple antennas at both TX and RX to transmit independent data streams simultaneously on the same frequency band, increasing spectral efficiency by a factor of min(N_TX, N_RX).

How it works: The multipath radio channel creates a matrix H of complex channel coefficients between each TX-RX antenna pair. If the columns of H are linearly independent (spatially uncorrelated channels), singular value decomposition gives min(N_TX,N_RX) independent parallel data channels — each adding ~log₂(1+SNR) bits/s/Hz.

Antenna requirements for 4×4 MIMO:

• Low mutual coupling: Isolation between any two antenna ports should be >15–20 dB. High coupling means the antennas see correlated channels — the MIMO capacity gain collapses to SISO levels.
• Low envelope correlation coefficient (ECC): ECC = |∫∫ F_i(θ,φ)·F_j*(θ,φ) dΩ|² / (∫|F_i|²dΩ · ∫|F_j|²dΩ). Target ECC <0.5, preferably <0.1. ECC depends on both mutual coupling and the radiation pattern correlation.
• Diverse radiation patterns: Antennas should cover different spatial directions or polarisations to exploit different multipath components.
• Sufficient gain: Each element must have adequate gain to maintain the per-stream SNR. Too low gain starves the MIMO streams.
• Compact size: 4 antennas must fit in a phone body <150 mm × 70 mm — challenging at sub-1 GHz (λ=33 cm). Common solution: use combination of dipoles, PIFA (planar inverted-F antennas), and chassis modes.

A PIFA (Planar Inverted-F Antenna) is a low-profile resonant antenna consisting of a flat rectangular patch connected to a ground plane at one edge (the short-circuit post) and fed at another point. It is the dominant handset antenna type for cellular frequencies.

Structure:

• Rectangular metal patch above the ground plane
• Short-circuit post: connects patch to ground at one end — this is the "inverted-F" geometry
• Feed point: typically 50 Ω coax or microstrip connected near the short-circuit post
• Resonant length: L+W ≈ λ/4 (quarter-wave resonance — the short circuit acts as a mirror, making a λ/4 long path equivalent to a λ/2 dipole)

Why PIFAs dominate handset design:

• Low profile: Height h is typically 5–10 mm above the ground plane. Total height << λ/4 — antenna fits inside a slim smartphone body.
• Ground plane as radiator: The handset PCB (ground plane) is a major part of the radiating structure. PIFA excites currents on the PCB ground plane that contribute to radiation — reducing the antenna size required.
• Wide bandwidth: Increasing h increases bandwidth (at the cost of height). Typical 50 MHz bandwidth at 900 MHz with 6 mm height.
• SAR control: The patch is placed against the handset back cover away from the user's head — the ground plane provides a degree of shielding, reducing SAR (Specific Absorption Rate) compared to a monopole.

SAR (Specific Absorption Rate) measures the rate at which radio frequency energy is absorbed by biological tissue. Units: W/kg (watts per kilogram of tissue).

Regulatory limits:

• FCC (USA): 1.6 W/kg averaged over 1 gram of tissue (head and body)
• ICNIRP (Europe, most countries): 2.0 W/kg averaged over 10 grams of tissue
• Handsets must be tested at maximum conducted power in all frequency bands with the device held against the head (ear) and body (chest pocket)

SAR constraints on antenna design:

• Antenna placement: antennas must be positioned as far as possible from the user's head — typically at the bottom of the phone (away from ear when in talk position)
• Maximum TX power may need to be reduced (power limiting) near the head to pass SAR limits — this directly reduces coverage range
• Antenna orientation: antennas with near-field radiation directed away from the body (using ground plane as shield) have lower SAR
• Frequency effects: lower frequencies penetrate tissue deeper but have lower absorption. Higher frequencies (5G mmWave) are absorbed in the skin only — SAR is lower per unit power but concentrated at the surface.

SAR measurement: A robotic arm scans a probe through tissue-simulating liquid adjacent to the phone, measuring the E-field. The measurement takes several hours per phone model per regulatory domain.

A retrodirective array automatically reflects an incoming signal back toward its source without knowing the source direction in advance and without any digital processing or phase control. It uses the phase conjugation property of a Van Atta configuration or a mixer-based phase conjugating array.

How it works (Van Atta array):

• Pairs of antenna elements are connected by transmission lines of equal length (symmetric cross-connections)
• When a signal arrives at angle θ, it accumulates phase delay across the aperture. The cross-connections swap elements so that the accumulated phase is reversed
• The re-radiated signal has the conjugate phase profile → it steers automatically toward the incoming direction
• No phase shifters, no feedback, no knowledge of incoming angle required

Phase conjugating array (mixer-based):

• Each element mixes the received signal with a 2×LO signal, producing a phase-conjugated copy
• This conjugated signal is re-radiated — the wavefront automatically returns to the source

Applications:

• Passive radar transponders — returning a radar pulse directly back to the interrogating radar
• Wireless power transfer — a transmit antenna can aim power at a moving target using retrodirectivity
• Passive RFID at microwave frequencies
• Self-phasing communication links — eliminates pointing error between two moving platforms

The Chu-Harrington limit establishes a fundamental relationship between antenna size (expressed as ka, where k=2π/λ and a is the radius of the smallest sphere enclosing the antenna), radiation efficiency, and bandwidth. No antenna design, regardless of its complexity, can exceed this limit.

Physical meaning:

• As an antenna shrinks below λ/2Ï€ (ka<1), its minimum radiation Q increases rapidly as (ka)⁻³
• High Q means narrow bandwidth — a very small antenna can only be matched and efficient over a very narrow frequency range
• This is not a consequence of any particular technology — it is a fundamental electromagnetic limit derived from mode theory in spherical coordinates

Practical consequences:

• A 10 mm antenna at 900 MHz: ka=2π×0.01/0.333=0.189 → Q_min≈150 → BW≈0.5% (4.5 MHz) for VSWR<2
• This matches the observed difficulty of making wideband small antennas for IoT at sub-GHz frequencies
• Any antenna claiming to be very small AND wideband AND efficient simultaneously is violating fundamental physics — check the data carefully

Circumventing the limit (partially):

• Accept lower efficiency — fill the sphere with lossy material (absorber). Bandwidth improves but gain drops proportionally
• Accept lower VSWR limit — allow VSWR=3 instead of VSWR=2; bandwidth triples but 25% power is reflected
• Non-Foster matching (active negative capacitors/inductors): circumvents the passive network constraint at the cost of noise and stability

The Yagi-Uda (commonly called "Yagi") is a directional end-fire parasitic array antenna. It consists of one driven element (fed from the TX/RX chain), one reflector, and one or more directors — all parallel dipoles of different lengths on a common boom.

Each element's role:

• Driven element: Typically a half-wave dipole or folded dipole. This is the only element connected to the feedline. Current in the driven element radiates directly and inductively drives currents in all parasitic elements.
• Reflector: Positioned behind the driven element (away from the desired direction). Slightly longer than λ/2 — this makes it inductive, so its induced current lags the driven element's phase. The reflector re-radiates with a phase that reinforces the forward direction and cancels the backward direction. Gain from reflector: +3 dB. F/B ratio: 10–15 dB.
• Directors: Positioned in front of the driven element (toward the desired direction). Slightly shorter than λ/2 — capacitive, current leads the driven element. Each director re-radiates with a phase that further focuses energy forward. Adding directors increases gain by ~1.5–2 dB each, with diminishing returns after 6–8 directors.

Typical specs for a 6-element Yagi at 144 MHz: Gain ≈ 11 dBi, F/B ratio ≈ 20 dB, beamwidth ≈ 50°, boom length ≈ 1.3 m.

Antenna bandwidth is the range of frequencies over which the antenna meets a specified performance criterion. Different applications use different criteria, so "bandwidth" has multiple definitions — always clarify which one is being used.

Common bandwidth definitions:

• Impedance bandwidth (most common): Frequency range where S11 < −10 dB (VSWR < 2:1) or S11 < −6 dB (VSWR < 3:1). This is the most widely quoted number in datasheets.
• Gain bandwidth: Frequency range where gain is within 3 dB of the peak gain. For many wideband antennas, gain bandwidth is larger than impedance bandwidth.
• Radiation efficiency bandwidth: Range where efficiency exceeds a threshold (e.g. >50%). Important for small antennas where efficiency degrades steeply off-resonance.
• Pattern bandwidth: Range where the radiation pattern maintains its shape within a specified variation (e.g. <3 dB beamwidth change, or F/B ratio stays >10 dB). Relevant for directional antennas.
• Polarisation bandwidth: Range where the axial ratio (for CP antennas) remains <3 dB. A circularly-polarised patch may have narrow polarisation bandwidth even if impedance bandwidth is wider.

Fractional bandwidth: BW% = (f_high−f_low)/f_centre × 100. Used for comparison across frequency bands. A typical LTE band: BW%=(880−824)/852=6.6%. A UWB antenna: BW%≥100%.

A reconfigurable antenna can dynamically change its operating frequency, radiation pattern, or polarisation by altering its physical geometry or material properties through active control elements. This enables a single antenna to serve multiple bands or radiation requirements without switching between separate antennas.

Types of reconfigurability:

• Frequency reconfiguration: Change the resonant frequency — connect/disconnect capacitors or inductors to alter effective electrical length. Used in cognitive radio, software-defined radio (SDR), and multi-standard handsets.
• Pattern reconfiguration: Change the radiation pattern direction or shape. Connect/disconnect parasitic elements (directors/reflectors) to steer the beam electronically — like a switchable Yagi.
• Polarisation reconfiguration: Switch between linear and circular polarisation, or between RHCP and LHCP. Two orthogonal feeds with switchable 90° phase shift achieves this.

Switching technologies:

• PIN diodes: Switch between conducting and non-conducting states with DC bias current. Fast (<ns), compact, low cost. Loss: 0.5–1 dB per switch. Work up to ~30 GHz.
• RF MEMS switches: Micro-electromechanical systems — a metal cantilever electrostatically actuated. Very low insertion loss (0.1 dB), high isolation (>30 dB), but slow (10–100 μs) and require high control voltage (20–80 V). Limited lifetime (10⁸–10¹⁰ cycles).
• Varactor diodes: Voltage-controlled capacitance — continuous tuning rather than switching. Enables smoothly tunable resonant frequency. Loss: 0.3–0.8 dB per element. Used for continuously tunable matching networks.
• Liquid crystals / ferroelectrics: Tunable permittivity materials that change dielectric constant under applied voltage. Enable low-loss tunable patch antennas at mmWave frequencies.
• Optical switches / photoconductive switches: Illuminating a silicon island with light makes it conductive — creates a short circuit on the antenna structure. Used in research for high-isolation switching.