Tuesday, June 22, 2010

I have two towers of different heights ...

Q Ray, WX3A, asks, “I have two towers of different heights: one with a 2-meter beam above an HF tribander, and the other with a 440-MHz Yagi above a 6-meter-beam. I’d like to determine what my ERP would be at:

Frequency Power Antenna Height

Is there a simple way to do this?”

AEffective Radiated Power (ERP) is actually fairly easy to calculate, as long as you know the gain figures of your antennas and can live with a few (supportable) approximations. ERP is related to the gain of a dipole in free space. To calculate ERP, you simply multiply the power at the antenna by the gain of the antenna, referenced to a dipole. The actual gain of an antenna over ground is about 4 dB higher than the “published” gain of the antenna, due to ground reflections.

Let’s start with the HF calculation. To determine the RF power radiated by the antenna, we must reduce the transmitter power in the shack by the amount of loss in the feed line, then boost that by the gain of the antenna. Assume that your HF tribander has 6.5 dBi of gain at 29 MHz in free space, with a transmission-line loss of 1.5 dB. This is about the loss that can be expected for 100 feet of RG-213 coax at this frequency for a low SWR. This is a net gain of 6.5 – 1.5 = 4.0 dBi. Next, you must reference the net gain to a dipole (dBd), not an isotropic radiator (dBi), so subtract 2.15 dB. This gives a net gain of 1.85 dBd, but this is in so-called “free space.”

You’re obviously going to be placing the antenna over ground rather than in theoretical free space, so there will be some “ground gain,” at a peak angle determined by how high the antenna is located over ground. The exact angle isn’t important for this discussion, since we’re looking for the peak radiated power. EPA documentation assumes that reflection from typical ground will give another 4 dB over the net gain in free space. So, now we’ve got 1.85 + 4.0 = 5.85 dBd, due to ground gain. Convert this to a numerical ratio by raising 10 to the power of 5.85 divided by 10 = 105.85/10 = 3.85. This is the number we now use to multiply the transmitter output power to give the ERP: 3.85 × 1500 W = 5775 W = 5.78 kW.

For VHF, let’s assume that you have a high-gain Yagi with 15 dBi gain in free space on 432 MHz. Here, the feed line loss will be more significant than on HF. Assume that you are using 100 feet of high-quality Belden 9913 coax, which will have about 2.8 dB of loss on 70 cm. The net gain, in dBd over ground is: 15.0 – 2.8 + 4.0 - 2.15 = 14.05 dBd, which is a numeric ratio of 25.41. Thus the ERP at 432 MHz would be 1.5 × 25.41 = 38.11 kW, a very substantial number indeed.

Now, there is another term in use, EIRP, or Equivalent Isotropically Radiated Power. This term is not referenced to a reference dipole in free space but to an isotropic radiator in free space. You can get EIRP by multiplying ERP by 1.64, the equivalent of 2.15 dB.

From QST March 1999