S4-2.1 Antenna Basics & Parameters
Standard antennas and propagation theory — written August 2026
What this is and why it exists
An antenna is the one component that converts a circuit quantity into a field in space, and this unit is the vocabulary for talking about that conversion honestly. Every later discussion — dipoles, arrays, patches, whole link designs — assumes you can read a radiation pattern, keep gain and directivity apart, and run the Friis equation. The Friis equation in particular is the formula you will still be using decades from now, in every wireless job there is.
The vocabulary
- Retarded potential — the field at a distance reflects what the charge did earlier, delayed by the travel time of light; the mathematical reason accelerating charge radiates.
- Isotropic radiator — the fictional antenna radiating equally in all directions; the reference everything real is compared against.
- Radiation pattern — the map of radiated strength versus direction, with its main lobe, side lobes and nulls.
- Directivity — how much the pattern concentrates power in its best direction compared with an isotropic spread.
- Gain — directivity times efficiency: concentration with the antenna's own losses included.
- Polarization — the orientation traced by the electric field; a receiving antenna aligned wrongly collects almost nothing.
- Effective aperture — the equivalent collecting area a receiving antenna presents to a passing wave.
- Friis transmission equation — received power from transmitted power, both gains, wavelength and distance; the whole link in one line.
The mental model
A torch bulb and a torch. The bare bulb is the isotropic radiator: light everywhere, weak everywhere. Put the same bulb in a reflector and nothing about the total light changes — it is concentrated into a beam. That concentration factor is directivity. If the reflector also absorbs some light, the beam is dimmer than geometry promises: that shortfall is efficiency, and the honest brightness of the real beam is gain. A radiation pattern is the photograph of the beam: the main lobe is where the power went, side lobes are leakage in unintended directions, nulls are the dark seams between them. Near the antenna the field structure is still assembling (the near-field regions); far enough away the pattern settles into its final shape, and all pattern statements are far-field statements.
Why does anything radiate at all? A charge moving steadily carries its field along; a charge that accelerates leaves the distant field behind for a moment, because updates travel at light speed — the retarded potential. The kink between old field and new tears off and propagates. No acceleration, no radiation.
Reception is the same story reversed: an antenna presents an effective aperture to a passing wave and collects the power flowing through that area. Friis chains it together — transmitted power, concentrated by transmit gain, diluted by the sphere of radius equal to the distance, collected by the receive aperture. Run once with real numbers: one watt at 2.4 gigahertz through modest antennas across one kilometre delivers roughly a ten-billionth of a watt — and receivers work happily at that level. Link budgets live in decibels because the numbers span that range.
What you should now be able to explain or do
Read a radiation pattern: main lobe, side lobes, nulls, beamwidth. Distinguish gain from directivity in one sentence and say which one a datasheet owes you. Explain in two sentences why acceleration of charge radiates. Compute a received power with Friis and state why polarization mismatch would reduce it.
Check yourself
Gain and directivity of one antenna differ. What is the difference telling you?
Losses. Directivity is pure geometry — how concentrated the pattern is. Gain multiplies that by efficiency, so the gap between them is power lost in the antenna itself.
Why does a charge moving at constant velocity not radiate, while an accelerating one does?
The distant field is a delayed copy of the charge's state — the retarded potential. Constant motion needs no field update; acceleration creates a mismatch between old and new field that propagates outward as radiation.
In the Friis equation, what does doubling the distance do to received power, and why?
Divides it by four. The radiated power spreads over a sphere whose area grows with distance squared, so the power density through the receiving aperture falls by the square.
A vertically polarized wave arrives at a horizontally polarized antenna. What is received?
Almost nothing — the electric field drives no useful current along a conductor at right angles to it. Matching polarization is a link requirement, not an optimisation.
Where do all standard pattern measurements and statements apply?
In the far field — beyond the region where the field structure is still assembling, where the pattern shape no longer changes with distance.
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