# Extra Class question of the day: Effective radiated power

Effective radiated power is a widely misunderstood concept. Effective radiated power is the term that describes station output, including the transmitter, antenna and everything in between, when considering transmitter power and system gains and losses. (E9H04)

The effective radiated power, or ERP, is always given with respect to a certain direction. Let’s think about this for a second. If your transmitter has an output of 100 W, the maximum power that the antenna can radiate is also 100 W. Transmitting antennas are, after all, passive devices. You can’t get more power out of them that you put into them. In reality, the total power output will be even less than 100 W because you will have losses in the feedline.

An antenna can, however, concentrate the power in a certain direction. The power being radiated in that direction will be more than the power radiated in that direction by a reference antenna, usually a dipole or an isotropic antenna, which is an antenna that radiates equally in all directions.

When an antenna concentrates power in a certain direction, we say that it has gain in that direction, and we specify the amount of gain in dB. If the reference antenna is an isotropic antenna, then the unit of gain is dBi. If the reference antenna is a dipole, then the unit of gain is dBd.

With that in mind, let’s take a look at an example. In this example, a repeater station has 150 watts transmitter power output, there is a 2-dB feed line loss, 2.2-dB duplexer loss, and the antenna has 7-dBd gain. To calculate the system gain (or loss), you add the gains and losses, so

Gain = 7 dBd – 2 dB – 2.2 dB = + 2.8 dB

 dB Ratio 1 1.26:1 2 1.585:1 3 2:1

Now, if you recall, 3 dB is close to a gain of 2, as shown in the table at right, so in this example, to calculate the effective radiated power, you multiply the transmitter’s output power by a factor slightly less than two. This makes the effective radiated power slightly less than 15o W x 2, or 300 W. The closest answer to 300 W is 286 W. (E9H01)

Let’s look at another example. The effective radiated power relative to a dipole of a repeater station with 200 watts transmitter power output, 4-dB feed line loss, 3.2-dB duplexer loss, 0.8-dB circulator loss and 10-dBd antenna gain is 317 watts. (E9H02) In this example, the gain is equal to 10 dB – 8 dB in lossses or a net gain of 2 dB. That’s equivalent to a ratio of 1.585:1. The ERP is then 200 W x 1.585 = 317 W.

Now, lets look at an example using an isotropic antenna as the reference antenna. The effective isotropic radiated power of a repeater station with 200 watts transmitter power output, 2-dB feed line loss, 2.8-dB duplexer loss, 1.2-dB circulator loss and 7-dBi antenna gain is 252 watts. (E9H03) In this example, the gain is equal to 7 dB – 2 dB – 2.8 dB – 1.2 dB = 1 dB. That’s equivalent to a ratio of 1.26:1, so the ERP is 200 W x 1.26 = 252 W.