Antennas & Radiation

30-second intuitionAn antenna is the transition between a guided electromagnetic mode and a radiated free-space mode. Its geometry controls the current distribution; the current distribution controls the radiated field; the field pattern determines where power goes and how efficiently another antenna can receive it.

1. Radiation from time-varying current

Radiation ultimately comes from accelerating charge and time-varying current. In the far field, electric and magnetic fields become approximately transverse and locally related by the free-space impedance,

\[\frac{|E|}{|H|}\approx\eta_0\approx377\ \Omega.\]

The radiated power density is described by the time-average Poynting vector,

\[\langle\mathbf S\rangle=\frac12\operatorname{Re}\{\mathbf E\times\mathbf H^*\}.\]

2. Near field, Fresnel region and far field

For an antenna with largest dimension $D$, a commonly used far-field criterion is

\[R_{FF}\gtrsim\frac{2D^2}{\lambda}.\]

The exact boundary is application dependent. In the reactive near field, stored electric/magnetic energy dominates; in the radiating near field (Fresnel region), the angular field distribution still changes with distance; in the far field, angular dependence is effectively independent of range and fields scale approximately as $1/R$.

Common misconception“A few wavelengths away” is not a universal far-field rule. Electrically large apertures can require many wavelengths of separation.

3. Radiation pattern, directivity and gain

Radiation intensity is

\[U(\theta,\phi)=r^2S_r.\]

Directivity is

\[D(\theta,\phi)=\frac{4\pi U(\theta,\phi)}{P_{rad}},\]

and gain includes radiation efficiency,

\[G=\eta_{rad}D.\]

Important pattern quantities include main-beam direction, half-power beamwidth, sidelobe level, front-to-back ratio and cross-polarization.

4. Effective aperture

A receiving antenna converts incident power density into available power through its effective aperture,

\[A_e=\frac{G\lambda^2}{4\pi}.\]

This relation is one of the cleanest bridges between transmit and receive antenna concepts.

5. Polarization

Polarization describes the trajectory of the electric-field vector: linear, circular or elliptical. For two linearly polarized antennas with relative angle $\psi$, ideal polarization mismatch contributes

\[\eta_p=|\hat e_t\cdot\hat e_r|^2=\cos^2\psi.\]

Circular polarization adds handedness; axial ratio is a common quality metric.

6. Common antenna families

Antenna	Strength	Typical use
Dipole	simple reference radiator	communications, calibration
Monopole	compact over ground plane	mobile/vehicle systems
Loop	magnetic-field coupling	LF/HF, RFID, sensing
Patch	low profile, PCB integration	phones, GNSS, arrays
Horn	broadband, predictable pattern	microwave links, ranges, feeds
Reflector	very high gain	satellite, radio astronomy, radar
Helix	circular polarization	satellite/space links
Phased array	electronic steering	radar, 5G/6G, satellite terminals

7. Arrays and beamforming

For a linear array,

\[AF(\theta)=\sum_{n=0}^{N-1}w_ne^{jn(kd\sin\theta+\beta_s)}.\]

Changing progressive phase $\beta_s$ steers the beam. Element spacing, element pattern, mutual coupling and scan angle determine grating lobes and scan loss. See AESA & Phased Arrays.

8. Link equation

For two matched, polarization-aligned antennas in free space,

\[P_r=P_tG_tG_r\left(\frac{\lambda}{4\pi R}\right)^2.\]

This is a far-field power-transfer equation, not a complete channel model.

Worked example — aperture of a 20 dBi antenna at 10 GHz

At 10 GHz, $\lambda\approx0.03$ m. A 20 dBi gain corresponds to $G=100$:

\[A_e=\frac{100(0.03)^2}{4\pi}\approx7.2\times10^{-3}\ \text{m}^2.\]

That is about $72\ \text{cm}^2$ of effective receiving area.

9. How antennas are measured

VNA: impedance, return loss and mutual coupling.
Anechoic range: gain, pattern, polarization and sidelobes.
Near-field scanner: measure near field and transform to far field.
Reverberation chamber: efficiency/diversity/statistical OTA quantities.
OTA chamber: complete device performance including enclosure and beamforming.

Antenna measurement is strongly affected by reference antenna calibration, chamber reflections, cable movement, positioner accuracy and polarization alignment.

10. Engineering reality

What ideal equations missConnector launches, finite ground planes, radomes, housings, hands/heads, battery placement, cable currents, mutual coupling, manufacturing tolerance, substrate loss and nearby metal can shift resonance and reshape the pattern.

11. Design questions worth asking

What bandwidth and matching criterion are actually required?
Is realized gain more important than raw directivity?
What is the polarization environment?
Does the platform alter the installed pattern?
Is the antenna operating in someone’s near field?
How sensitive is performance to manufacturing tolerance?
What quantity will be measured to validate the design?

References

C. A. Balanis, Antenna Theory: Analysis and Design.
W. L. Stutzman and G. A. Thiele, Antenna Theory and Design.
R. F. Harrington, Time-Harmonic Electromagnetic Fields.
MIT OpenCourseWare, Electromagnetics and Applications.

Related: RF & Microwave · Wireless & MIMO · AESA · Measurements