# What is Gain?

### Gain compared to a half wave dipole – dBD

The gain of an antenna is the relative increase in radiation at the maximum point expressed as a value in decibels (dB) above a standard.

The standard to which other antennas are compared is usually a ½-wavelength dipole. The standard antenna is given a reference gain of 0dBD (zero decibels referenced to a dipole). This comes from:

$\mbox{gain} = 10 \times \log \left( \frac {Pe}{Pi} \right)$

Where Pe is effective radiated power and Pi is input power

An antenna with the effective radiated power of three times the input power would therefore have a gain of:

Pe = 3, Pi = 1

$10\times\log\left(\frac {3}{1}\right) = 4.77\mbox{dBD}$

### Gain compared to an isotropic radiator = dBi

Anisotropic radiator is a theoretical “point source” antenna that radiates the same amount of energy in all directions. Although an isotropic antenna cannot be constructed, it is sometimes useful to compare actual antennas to it.

### Comparison of dBD and dBi

Graphically, the radiation patterns of isotropic and dipole antennas – for equal power inputs – can be represented thus:

The area between the isotropic radiator circle and the half wave circle radiator circle represents a gain difference of approximately 2.15dB

hence, $dBi = dBD + 2.15$

### Comparative gain of various antenna types

 Antenna Type dB gain over an isotropic radiator dB gain over half-wave dipole Isotropic radiator 0 -2.1 Ground plane +0.3 -1.8 half-wave dipole +2.1 0 5/8 wave dipole +3.3 +1.2 Quad loop single element +4.1 +2 2 element yagi +7.1 +5 3 element yagi +10.1 +8 4 element yagi +12.1 +10 2 element quad +9.1 +7 3 element quad +12.1 +10 4 element quad +14.1 +12

Adapted from Orr WL (W6SAI) and Cowan SD (W2LX), 1986, the Radio Amateur Antenna Handbook

### dBo Optical Gain

dBO is an unofficial term used by some amateurs working with the transmission of data using light. It refers to the apparent gain of an optical system compared to a point source of light.

### 3 thoughts on “What is Gain?”

1. It would be great if you said at the very beginning: before you can understand this explanation you need to know what the following means:
– radiation at the maximum point
– half-wave dipole
– this weird nomenclature: 10 \log_{10}\frac{P_A}{P_B}
– etc. etc. etc. (about 10 more terms and phrases)
Next it would be great if the writing were clearer.

Thanks for putting all this together. I know it was well-intentioned… just off the mark for your intended audience which, admittedly is mixed… so maybe start off simple and add the complex part at the end or with a link to another page. Instead of an electronics college professor writing it, try someone who has JUST got their tech license.