Antenna basics

 VSWR
VSWR is a measure of impedance mismatch between the transmission   line and its load. The higher the VSWR, the greater the mismatch. The   minimum VSWR, i.e., that which corresponds to a perfect impedance    match, is unity.
To understand the definition above we must understand what impedance   is. Impedance in antenna terms refers to the ratio of the voltage to   current (both are present on an antenna) at any particular point of the    antenna. This ratio of voltage to current varies on different parts of the   antenna, which means that the impedance is different on different spots   on the antenna if you could pick any spot and measure it.
As stated before, the impedance for the entire chain from the radio to the   antenna must be the same, and almost all radio equipment is built   for an impedance of 50 ohm.
If any part of this chain fails to show a 50 ohm impedance due to e.g. bad   connections, incorrect antenna length, etc., the maximum power   will not be radiated from the antenna. Instead part (or all) of the wave is   reflected back down the line. The amount of the wave reflected back   depends on how bad the mismatch is.
The combination of the original wave traveling down the coaxial cable   (towards the antenna or opposite during receive) and the reflecting wave   is called a standing wave. The ratio of the two above described   waves is known as the Standing Wave Ratio.
The result is presented as a figure describing the power absorption of the   antenna. A value of 2.0:1 VSWR, which is equal to 90 % power   absorption, is considered very good for a small antenna: 3.0:1 is   considered acceptable (-6dB) which is equal to 75 % power absorption. 
 

Smith Chart  
One common way of visualizing the VSWR is a polar plot called Smith   chart. From this plot the VSWR value, the return loss and the impedance   for the different frequencies can be derived. Therefore it is an important   instrument for understanding antennas. To learn more about the SMITH   chart, see e.g. http:///smith.html
Retrun Loss
 
This is basically the same thing as VSWR.
If 50 % of the signal is absorbed by the antenna and 50 % is reflected   back, we say that the Return Loss is -3dB. A very good antenna might   have a value of -10dB (90 % absorbed & 10 % reflected).
When studying a graph showing Return Loss/VSWR, a deep and wide dip   of the curve is good since this shows an antenna with good bandwidth   (spreadband). Consequently, the narrower the dip is, the bigger risk that   also desired channels will be reflected away (narrow band).
 
Return Loss Chart  

Note: To be able to compare figures from different manufacturers, you   must be aware of the conditions under which the measurement was   made. Was impedance matching used or not?
  
Conversion table VSWR / Return Loss

Bandwidth
Normally a radio needs to work on multiple frequencies. For example, the   2.4 GHz ISM band used by Bluetooth/Wi-Fi/Zigbee/WiMedia devices   has a range from 2400-2483 MHz. In this band PAN   communication uses 78 channels for its frequency hopping technique, 1 MHz between each channel.
 This means that the antenna must perform well over a range of   frequencies. So, the goal must be to make it resonant in the middle of   that band. The term that is important here is bandwidth or how much   band your antenna works well over. One method of judging how well   (efficiently) your antenna is working is by measuring VSWR. 
Typically, bandwidth is measured by looking at SWR, i.e., by finding the   frequency range over which the SWR is less than 2.

Efficiency
Efficiency is a figure showing the ratio of the total radiated power to the   total input power . Efficiency has no unit and the ideal figure is 1.
Efficiency =radiated power /input power
It is essential to know how the measurement was performed before   comparing figures from different manufacturers: was a matching network   used? Was the measuring point as close to the antenna as   possible or was the transmission line included? Often, the figure for   efficiency will dramatically decrease when the antenna is built into a   device.
Note: This is a good figure of merit, especially for small antennas.  

Efficiency

 
Gain & 3D Pattern
Antenna gain is a measure of directivity. In order to explain this better,   we must first have a look at the different antenna types and their radiation patterns.
Basically there are only two types of antennas: The dipole antenna   (Hertzian) and the vertical antenna (Marconi). All antennas can be   broken down to one of these types (although some say that there is only   one - the dipole). In addition to this we have a theoretical perfect   antenna (non-existent) that radiates equally in all directions with 100%   efficiency. This antenna is called an isotropic radiator.

Basic Antenna types 
 
  
Antenna Radiation Patterns  
  
This is similar to gain but the heat losses (i.e. the efficiency) are  disregarded. We will then get a pattern as the dotted line shown in the   figure. Point “d” refers to directivity,point “a” to gain and point “b” to the   isotropic reference. 

Gain presented as 3D gain

 
The gain can also be presented as a 3D gain. The radius of the spheriod is   proportional to the antenna gain.
Gain in theory Since all real antennas will radiate more in some directions   than in others, you can say that gain is the amount of power   you can reach in one direction at the expense of the power lost in the   others. When talking about gain it is always the main lobe that is   discussed.
Gain may be expressed as dBi or dBd. The first is gain compared to the   isotropic radiator and the second gain is compared to a half-wave dipole   in free space (0 dBd=”2″.15 dBi).
It may be worthwhile considering the fact that instead of doubling your   amplifier output, you could alternatively use an antenna that has 3db   more gain than your current antenna and achieve exactly the same  effect.
Note: Small antennas usually have low gain, often between 0 and 2dBi.
Note: Regarding efficiency and radiation patterns - what is  true for  transmission is generall also true for  reception.
 
Directivity
This is similar to gain but the heat losses (i.e. the   efficiency) are disregarded. We will then get a pattern as   the dotted line shown in the  figure. Point “c” refers to   directivity, point “a” to gain and point “b” to   the   isotropic reference.

 Polarization
Radio waves are built by two fields, one electric and one magnetic. These   two field are perpendicular to each other. The sum of the fields is   the electromagnetic field. Energy flows back and forth from one field to   the other - This is what is known as “oscillation”.
The position and direction of the electric field with reference to the   earth’s surface (the ground) determines wave polarization. In general,   the electric field is the same plane as the antenna’s radiator.
Horizontal polarization —— the electric field is parallel to the ground.  
Vertical polarization — the electric field is perpendicular to the ground. 

There is one special polarization known as Circular polarization. As the   wave travels it spins, covering every possible angle. It can either be   righthanded or lefthanded circular polarization depending on which way   its spinning.
Note: Small antennas have no clear polarization.

Polarization chart

 

Impedance matching
An ideal antenna solution has an impedance of 50 ohm all the way from   the transceiver to the antenna, to get the best possible impedance   match between transceiver, transmission line and antenna. Since ideal   conditions do not exist in reality, the impedance in the antenna   interface   often must be compensated by means of a matching network,   i.e. a net   built with inductive and/or capacitive components.   The VSWR result is   optimized by choosing the proper layout and   component values for the   matching net and the maximum potential of   the antenna is shown.
dB units
Decibel (dB) is a mathematical expression showing the relationship   between two values.

The RF power level at either transmitter output or receiver input is   expressed in Watts, but it can also be Expressed in dBm. The relation   between dBm and Watts can be expressed as follows:

P dBm = 10 x Log P mW

For example: 1 Watt = 1000 mW; P dBm = 10 x Log 1000 = 30 dBm 

100 mW; P dBm = 10 x Log 100 = 20 dBm
 
 
Conversion table dBm / Watt
 

The following definitions are taken from IEEE Standard Definitions of   Terms for Antennas, IEEE Std 145-1983.

Adaptive (smart) antenna: An antenna system having circuit elements   associated with its radiating elements such that one or more of the   antenna properties are controlled by the received signal.

Antenna polarization: In a specified direction from an antenna and at a   point in its far field, is the polarization of the (locally) plane wave which is   used to represent the radiated wave at that point.

Antenna: That part of a transmitting or receiving system which is   designed to radiate or to receive electromagnetic waves.
 
Coaxial antenna: An antenna comprised of a extension to the inner   conductor of a coaxial line and a radiating sleeve which in effect is   formed by folding back the outer conductor of the coaxial line.

Collinear array antenna: A linear array of radiating elements, usually  dipoles, with their axes lying in a straight line.

Co-polarization: That polarization which the antenna is intended to  radiate

Cross-polarization: In a specified plane containing the reference  polarization ellipse, the polarization orthogonal to a specified reference  polarization.

Directional antenna: An antenna having the property of radiating or  receiving electromagnetic waves more effectively in some directions  than others.

Effective radiated power (ERP): In a given direction, the relative gain of a  transmitting antenna with respect to the maximum directivity of a  half-wave dipole multiplied by the net power accepted by the antenna  from  the connected transmitter.

E-plane: For a linearly polarized antenna, the plane containing the  electric field vector and the direction of maximum radiation. 

Far-field region: That region of the field of an antenna where the angular  field distribution is essentially independent of the distance from a  specified point in the antenna region.