HPR4382: Understanding Antenna Gain and the Decibel scale
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Power Measurement and Antenna Gain
HPR show by Paulj, May 2025.
1.0 Power expressed in dB (also written as dBW)
Power PdB = 10 . log10P
Where P is the power expressed in Watts.
2.0 Power expressed in dBm
Power PdBm = 10 . log10P
Where P is the power expressed in milliwatts.
1W = 1000mW
Power PdBm = 10 . log101000mW
Power PdBm = 30
dBm
so:
0 dB = 30 dBm
3.0 Power expressed relative to an isotropic antenna - dBi
An Isotropic antenna is an theoretical ideal antenna which
radiates equally in all directions. Imagine the antenna is at the
centre of a sphere, the signal strength at the surface of the
sphere is equal at all points. The gain of an isotropic antenna is
defined as 1, meaning:
10 dB = 10 dBi
4.0 Power expressed relative to a half wave dipole antenna - dBd
The simplest practical antenna is a half wave dipole antenna,
where each of the two legs is a quarter wave length long. The feed
is at the centre, and the two legs are generally horizontal, and
aligned away from the feed point 180 degrees apart. The dipole
antenna exhibits gain perpendicular to the legs. The maximum gain
is 1.64 times the isotropic antenna - a gain of approximately
2.15dBi. The gain off the ends of the dipole is much lower - the
total power radiated by the antenna can not exceed the power being
input, so if there is more radiation (gain) in one direction,
there must be a corresponding reduction in a different direction.
So:
2.15 dBi = 0 dBd
5.0 Effective Radiated Power - ERP and EIRP
ERP and EIRP are both used to indicate the power achieved using
an antenna.ERP compares the antenna performance with a dipole, and
EIRP compares the performance with an isotropic antenna. So, the
ERP is the power which would need to be fed into a dipole antenna,
to get the same effect in the direction your antenna is pointing.
EIRP is the power required for an isotropic antenna to gain
equivalence.
Practical example: My KX3 can transmit 15W. using the formula
above, this is 11.77 dB. If I attach a Yagi-Uda antenna with a
gain of 10dB, the ERP is 21.77 dB. Using the formula
above, from this number you can calculate that this is the
equivalent of 150.3142 Watts ERP. To understand the EIRP, we need
to add 2.15 to the 21.77 dB value, giving 23.92 dB EIRP.
Again, converting to actual power gives 246.515 Watts EIRP.
If you are comparing antennas, make sure the same units are
being used in all cases (either EIRP or ERP) - some sellers will
use EIRP, because the values are higher!
Check your licence conditions. Power output limits are often
at the antenna, and don't include antenna gain. You can set your
transmitter to output sufficient power to overcome any feed line
losses, and present up to the power permitted to the antenna. A
good antenna can then be used to get the transmitted power out
and across the world. For feedline loses, the value is given in
dB per 10 metres. For example, RG58 is 2dB / 10 metres (at
100MHz - choose the right feeder coax for your target
frequency!). If you have 15 metres, then you will have 3 dB
feeder loss, so half of your transmitter power will be lost in
the feed line. If you know this and your transmitter can output
more, then you can increase the transmitter power accordingly.
So for 25W at the transmitter, with 3dB loss in the feeder, you
can set the output to 50W.
Some transmit power limits are set in ERP or EIRP, so you will
need to calculate back from the antenna to see the maximum
allowable transmitter power, to stay within the rules.
6.0 Combining values
One result of the use of dB is that you can add the values
together to understand the whole system gain. So, with our example
above, if we have 11.77 dB of output power, then -1 dB insertion
loss for a bandpass filter, -3 dB loss for the feeder, and 5dB
gain on the antenna, the overall ERP is 12.77 dB. You can convert
this back to Watts, to get 18.92W ERP.
7.0 Links
Dipole
information
Yagi-Uda
information
Wikipedia
information on Decibels
Wikipedia
information on ERP and EIRP
Wikipedia
information on Antenna Gain
ERP
& EIRP calculator from M0UKD
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