An antenna is composed of pieces of conductive metal, which are geometrically tuned in ways that radio waves hitting the metal and electric current flowing through the metal can interact: when radio waves generate current the antenna is receiving, and when current generates radio waves the antenna is transmitting. Antennas exhibit geometric gain, in which they have higher sensitivity to signals coming from some directions than from others. Antennas can be broad-band, in which case they are tuned to pick up signals from a broad portion of the electromagnetic spectrum, or they can be narrow-band, in which case they will reject everything but small segments of the spectrum that they are sensitive to.
Electromagnetic signals (composed of photons) range from high-energy gamma rays & X-rays of short bandwidth, to ultraviolent, optical, and near infrared light of medium bandwidth, to far infrared thermal radiation, microwaves, and radio waves of long bandwidth. Is is these last bands, with frequencies from 10^7 Hz to 10^10 Hz, that radio control typically uses.
 Basic: Isotropic Radiator
An isotropic radiator pushes out signal in all directions at once with the same intensity. Due to geometrical physics a true isotropic radiator is impossible, but it provides a useful reference for intensity to illustrate radiation patterns against.
 Basic: Gain
For a given antenna at a given distance, gain is typically the peak degree to which the signal strength is greater than an isotropic radiator. Gain is measured in decibels of signal. High-gain antennas rob part of their radiation pattern to pay other parts; Any segment with above-isotropic signal strength corresponds to a lowering of other segments below an isotropic signal strength. +3db represents a doubling of effective power, and +6db offers a quadrupling of effective power, which corresponds to the same effective power at twice the range.
 Basic: Equivalence
One principle of radio transmission is that the antenna of the reciever and the antenna of the transmitter are both equally important, and commutative: +15db of gain on one and +15db of gain on the other would be functionally equal to +0db of gain on one and +30db of gain on the other. So long as the same antennas are used at the same distance and orientation, one can switch the reciever location for the antenna location with no difference in received signal strength. This holds true in all situations where there is not a noise source in proximity to one of the antennas.
 Basic: Wavelength
The frequency of electromagnetic radiation is inversely proportional to its wavelength: Shorter wavelength, higher frequency. The fixed speed of light = wavelength * frequency. A useful rule of thumb is Freq. in Mhz = 300 / Wavelength in meters.
There are all sorts of peculiarities about particular bands, atoms which preferentially absorb only a narrow part of the spectrum, but to generalize in the extreme, EM tends to 'pass through' obstacles that are substantially smaller than wavelength, and be blocked by obstacles that are substantially greater. To continue the generalization, in a gas medium like atmosphere, even when the particles are much smaller than wavelength, some scattering does occur, and it occurs more with shorter bandwidth EM than with longer bandwidth.
At the same time, though, plausible antenna designs tuned for a longer wavelength are proportionately larger. Antenna makers may compensate by tuning for a weaker 'harmonic' of the wavelength in question (like 1/2 or 1/3 the wavelength), which reduces gain: this is how a lot of dual-frequency antennas (for example 2.4Ghz/5Ghz) are made.
 Advanced: Radiation Pattern
The basic conceptual antenna gain geometries are isotropic, omnidirectional, and directional. For all but the simplest designs, this is an oversimplification There exist 'side-lobes' where a directional antenna is more sensitive off its primary axis, and omnidirectional sensitivity may look more like a star than a circle. It's important to know the radiation pattern of the antenna you're using. Software tools to model antenna designs are well-advanced.
 Advanced: Linear Polarization
It's a big step to go from imagining that light & EM radiation is a density wave, like sound, to the notion that it is oscillating in a direction perpendicular to its line-of-sight path; This physical fact can be demonstrated with a micro-mesh of parallel wires, however. The naive view of linear polarization is simply that EM has an 'axis', and these axes have to match up or the signal goes to shit. When dealing with a linearly polarized antenna like an omnidirectional, is is precisely what happens: not only do you have to make sure that the antennas are facing each other, you have to ensure that they are close to parallel, something that can be very difficult on an aircraft maneuvering in three dimensions.
 Difficult: Circular Polarization
Circular polarization adds another layer of complexity onto what you thought you understood about linear polarization: light/EM can oscillate with two degrees of freedom, not one. Linear polarization is just a minimal-width subset of the general case of elliptical polarization. On the other end of the continuum is the special case of circular polarization. Circular polarization can be thought of as a helical screw twisting along the axis of transmission. Circular polarization can avoid the dropouts associated with linear polarization's poles going into unfortunate positions, although the radiation pattern of the antennas still have to be sufficient (they have to be pointed at each other).
Circular polarization comes in right-handed and left-handed, and trying to match them will indeed cause problems just like off-axis linear polarity... but line of sight circular polarization will always be the same. The polarity mismatch is considered a feature rather than a bug, because it reduces multipath problems in high-frequency data streams (a right-handed polarization beam that hits a reflector like the ground will become a left-handed polarization beam that overlays the primary signal, causing interference).
 Difficult: Interference
Generally requiring the assistance of a directional antenna with attached wide-band spectrum analyzer, tracking down the industrial microwave at the lumbermill down the street that's destroying your 2.4Ghz signal, or figuring out which one person is using the obnoxiously high power transmitter and spiking everyone else's controls, is a skill that requires knowledge of everything that tends to go on at the specific band in question, the equipment to track it down, and the legal knowledge to know who's in their rights to be using that spectrum.
 Omnidirectional Antennas
Omni antennas have a quasi-toroidal radiation pattern: there is an axis where they do not get any signal at all (on simple whips/dipoles, this corresponds to the direction the antenna line is pointing, the opposite of what many people assume), but on a plane perpendicular to that axis, they reach their highest signal strength.
Whip, dipole, or a compact helical are cheap to build and typically come standard on wireless gear with gains of +3 to +9db
Considered the simplest baseline antenna against which to measure, and building block from which several other types of antennas are constructed.
In a 'Normal Mode', or an 'Broadside' helix, the radiation pattern is omnidirectional and the dimensions are large relative to the wavelength.
 Cloverleaf / Skew Planar Wheel
Very popular DIY option in RC for UAV-mounted FPV transmitter. The SKP antenna performs the unusual design requirement of being extremely low gain, with a design that is not far off from isotropic, and since it's circularly polarized, does not have any problems with polarization dropouts either. An SKP on the aircraft coupled with a high gain CP antenna on the ground allows this design, which was initially promoted by RC user IBCrazy, to create a highly reliable connection regardless of the changing orientation of the plane.
 Directional Antennas
Directional antennas offer a radiation pattern whose signal strength is greatest in whichever direction they are pointing, and decays with the number of degrees off that axis the signal is measured.
A patch antenna is a large array of tiny dipoles, cut out of a sheet of conductive material and mounted in a thin, usually rectangular plastic case. Popular commercial option in RC. Can be CP or LP.
A Yagi-Uda antenna, or simply 'yagi', uses a small array of tuned dipoles arranged in a long, end-fire triangular pattern. Theoretical gain increases with the number of elements: a single element (essentially a dipole) at 2.2dbi, 3 elements at 7dBi, and 15 elements at 14dBi.
- Yagi-Uda Antennas - David Jefferies
A biquad uses two side by side rectangular wire elements in front of a reflector. Very popular DIY option in RC due to its ease of construction with solid-core wire. 8-11db
- Biquad - Trevor Marshall
 Double Biquad
The double biquad extends the quad elements out into figure 8's, and adds 2-3db of gain onto the biquad without much additional construction difficulty.
 Biquad Array
Some have attempted to squeeze a few more decibels of gain out of the biquad design using an array of driven elements.
Very popular DIY option in RC
 Slotted Waveguide
 Short Backfire
Short backfire antennas can use compact, mechanically easy to build annular & plate reflectors to achieve moderate gains if tuned for a particular band.
- 2.4Ghz Short Backfire Antenna - Carl Rabe
 Archery Target
- An Archery-Target Antenna - Microwave Journal
A parabolic reflector is the 'maxi' option for wide-band, high-gain applications, being much larger than the wavelengths in question, and works on the same principle as a reflecting telescope does in the much higher frequency optical-NIR bands. May require a significant degree of build precision. Larger antennas in a given dimension allow larger gain, on up to 60-100db with things the size of Arecibo, or more for phased arrays at low frequencies. It's common to see long, narrow slices of a parabola used when the signal should be a 'line' instead of a 'spotlight'.
Popular commercial option in RC. When dish diameter is sufficiently larger than wavelength, parabolic reflectors are essentially broadband in nature, so re-purposing other antennas for a particular frequency is common.
A parabolic reflector is not the whole antenna: there is a driven element composed some type of lower-gain directional antenna which is reflected by the dish. The optimal position of the driven element is dictated by the frequency, the size and curvature of the reflector, and the gain of the driven element.
 Satellite TV
Satellite television dishes, whether the huge 2-4m C-Band, the medium 75-125cm Ku-band, or the smaller 50-100cm Ka-band off-axis dishes, are all plausible parabolic reflectors for 2.4-5.8ghz work.
In a pinch, a small section of a sphere is rather close to a parabola, and the Chinese cooking pans known as woks are one of the easiest places to find a large-radius metal spherical surface to act as a reflector. A related cooking implement is the Chinese fryer basket, which also works despite the holes (since they are much smaller than wavelength). A flexible strainer may also be used if shaped to the appropriate form.
- Wifi Signal Strainer - WokFi - Instructables
In 'Axial mode' or an 'End-fire' helix, the radiation pattern is directional, the signal is circularly polarized, and the dimensions are comparable to the wavelength.
 Log-Periodic Array
 Franklin / Sector
Franklin antennas are tall, thin arrays of repeating elements which achieve a radiation pattern with a beam that is vertically narrow, but with significant horizontal spread. Sector antennas, which are usually Franklin-type, are an application rather than a design, and they involve putting separate antennas on different directions of transmission to achieve an effectively high-gain omnidirectional, but multichannel pattern at high frequencies. These are ubiquitous for cellular networks, and for municipal wifi, and may be appreciated for RC applications that are some range from the user, but have a cross-country swath that tracks all on one direction of a user. If the plane's position relative to the user for most of the flight is from several kilometer's northwest to several kilometers northeast, a sector antenna may be useful to avoid requiring a tracker.
Electromagnetic waves are not perfectly analogous to things like sound pressure waves: EM waves have not only amplitude and frequency, but transverse polarity in two dimensions. Grokking the physics of even simple wave dynamics can be difficult, and polarization should be considered an advanced topic (particularly due to that second dimension).
The practical effects are that radio waves are somewhere between perfectly "linearly polarized" and perfectly "circularly polarized", depending on the design of the antenna. A linearly-polarized antenna will recieve at full sensitivity if the axis of the transmitter's polarization is parallel, but sensitivity will fall off-axis, by the function abs(cos(angle)), with zero sensitivity at 90 degrees off axis (perpendicular). A circularly polarized antenna will not do this.