The dB or decibel is derived from a ratio as shown below:

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Where: Pi =the larger of two powers
P2 = smaller of two powers
Or:
Where: V1 =the larger of two voltages
V2 =the smaller of two voltages
Thus the dB value represents a gain of P1 or V1 over P2 or V2. So when one says 3 dB,
the question is 3 dB over what? In the above equations if the numerators are smaller than
the denominators, the dB value will be negative or a loss.
With antennas it has been common practice to compare the gain of an antenna in a
given direction with the gain of a dipole in free space or the gain of a quarter wavelength
vertical over perfect ground in the same direction. For example, the gain of a 5/8
wavelength vertical is commonly said to be 3 dB. This means that a 5/8 WL vertical has a
maximum radiation of about 3 dB over the maximum radiation of a
¼
WL vertical. The
trouble with these comparisons is simply that our antennas are not in free space or over
perfect ground. In the case of a dipole, the height above any kind of ground has a major
effect on the maximum gain in a given direction. So a more constant means of
comparison was needed. I don’t know who came up with the isotropic radiator but it’s
concept is simple and constant. Admittedly, an isotropic radiator exists in theory only.
Consider a sphere with a point radiation source at it’s center. The point source
radiates equally in all directions; therefore, the inside surface of the sphere receives an
equal amount of radiation on each square inch of inside surface. This point source is

Page 15
known as an isotropic radiator. If an antenna is placed in the center of the sphere, it will
not produce equal radiation on each square inch of inside surface. If the antenna causes
twice as much energy to fall on a given point on the sphere, compared to the isotropic
radiator, it is 3 dBi better than the isotropic radiator or has a gain in that direction of 3
dBi.
However, the total power radiated is constant. Therefore, if one spot is 3 dBi
better than other spots on the inside of the sphere, other spots must get lots less radiation
for the total to remain constant. Since so many commercial antennas are rated in dBd,
compared to a dipole in free space, the standard difference of 2.15 dB for a dipole over an
isotropic radiator seems to be agreed upon. Thus when reading specs on commercial
antennas whose gain is expressed in dBd, one needs to subtract 2.15 dBd to get dBi.
When looking at azimuth plots of two antennas in dBi, to compare two directions or the
same direction simply subtract the dBi gain in the direction of least gain from the larger
dBi gain. The difference will be in dBd. For example, let’s say that antenna 1 has a gain
at 35 degrees azimuth and 20 degrees elevation of 7 dBi. Antenna 2 has 4 dBi gain in the
same direction. Antenna 1 will have 3 dB higher gain in that direction over antenna 2.

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- Summer '19