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 P_dB = 10 . log₁₀P

Where P is the power expressed in Watts.

2.0 Power expressed in dBm

Power P_dB = 10 . log₁₀P

Where P is the power expressed in milliwatts.

1W = 1000mW

Power P_dBm = 10 . log₁₀1000mW

Power P_dBm = 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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