This post will not make you an expert. This post points you to things to research on your own.

The speed of radio waves is the speed of light. 299,792.8 kilometers per second.

YRB: Yeah, Right, Buddy. The speed of light is 300,000 kilometers per second. nobody has a ruler accurate enough to measure the difference.

The sine wave that depicts a radio wave is shown as a 2 dimensional voltage:

but that is actually a two dimensional representation of a three dimensional phenomenon. Best illustrated with an everyday object:

A sine wave is a screw thread, or the path of the tip of a propeller.

By mutual agreement, one cycle of a sine wave starts at the point where the signal crosses the midpoint going positive, which is 0 degrees. the positive peak is 90 degrees. the next negative going midpoint is 180 degrees. the most negative point is 270 degrees. the next cycle starts at the point where the signal crosses the midpoint going positive again. One cycle is one wave.

The Half Wave DipoleOn an unmodulated carrier, the maximum voltage difference is between any two points 180 degrees apart. The maximum voltage is one half of one cycle: a half wave. This maximum voltage developed across an antenna transfers maximum RF energy.

Given the fixed speed of radio waves, 300 km/sec, standard scientific designation c, the wavelength can be calculated simply:

c / frequency = wavelength.

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c is expressed as 300 km/sec, which is 300 million meters per second. If the frequency is expressed in mHz - millions of cycles per second - we can toss the millions out and come up with:

Wavelength = 300 / Frequency in megaHerz

at 433 mHz, 300 / 433 = .693 meters, commonly expressed as 70 CM.

Half of that wavelength; the length that results in peak transfer of RF power from transmitter to sky, or from sky to receiver at 433 mHz, is .346 meters.

Divide that in half, to get a quarter wave dipole and a quarter wave ground plane, and the optimum length for the antenna elements is .173 meters. Multiply that by 95% because the end of the wire creates a capacitive effect: .173 X .95 = .164 meters = 6.47 inches

The Isotropic Radiator

The isotropic radiator is a theoretical construct. An infinitely small point in infinitely empty space which radiates equally in all directions. The Big Bang would be an isotropic radiator. It exists only as a reference p[oint. Any antenna design can be compared to an isotropic radiator. A half wave dipole, or it's close relative, the quarter wave dipole, have a gain of 2.14 db over an isotropic radiator.

The Quarter Wave Dipole, AKA the Marconi antenna

The quarter wave dipole is a half wave dipole with the radiating element at a right angle to the ground plane. The antennas on your car are Marconi antennas. The ground plane should be at least a quarter wave, it can be larger.

Radiation pattern and antenna gainThe half wave dipole is directional: it sends more energy along a line at a right angle to the antenna leads than it sends off the ends. The Marconi antenna is omnideirectional in the horizontal plane.

There is a type of antenna known as a collinear array. It is a series of half wave elements, stacked a half wavelength apart. How it works is: The radiation patterns of the stacks of radiating elements repel each other vertically. This pushes the patern out horizontally. The same amount of energy goes in, but it is delivered farher horizontally and less vertically. If you coul;d see the radiation pattern of a quarter wave dipole it would look like a bagel. If you could see the radiation pattern of a collinear, it would look like a panceke. Same quantity of dough, distributed differently. Anyone who claims that more than 15 db of gain from a colinear knows laws of physics he is not sharing.

The YagiA yagi is a directional antenna. It is a half wave dipole with directors and reflectors added on both ends of a boom. You can find many websites with more detail. A thing worth knowing: you can build a stealth yagi between two sheets of plywood with copper or aluminum strips. Useful info if youi have a bossy HOA.

ReciprocityGain at either end of an RF link bestows its blessings on both ends of that link. If you have a quarter wave dipole on both ends, and you substitute a 9 db yagi on one end, the link is 7 db better in both directions.

Helical antennasThe name helical applies to two entirely different types of antennas: the pathetic little spring antennas that come with modules, and vast coils a foot across and a yard long. The puny coil is a quarter wave dipole in a compact form. It is a clever trick: get a module certified as Part 15 ( see the other RF module tl;dr about Part 15 ) so the combination of transmitter and antenna produces maximum legal power. If the end user chooses to use an illegal ( for that module ) better antenna, he gets the maximum possible range.

The other variety of helical antenna is "circularly polarized" Do yourself a favor, assume that anyone who extols the virtues of circularly polarized antennas never actually built one. They are, in fact, a superior design, but the talking to doing ratio is probably lopsided.