Link Budget - Are there any restrictions in the formula?

Depending on the parameters used in the link budget formula it seems that one may come up with a received power (dBm) larger than the transmitter output power (dBm).

For example:
Frequency: 50 MHz
Distance: 100 m
Free-Space Path Loss (FSPL): 49.95 dB
Tx Power: 10 dBm
Tx Gain: 25 dBi
Rx Gain: 25 dBi

Link Budget (dBm) = Tx Power + Tx Gain - FSPL + Rx Gain

Result: 13.57 dBm which is higher than Tx Power and should not be possible. (EIRP - Conservation of energy)

I could not find any restriction to the usage of the link budget formula to avoid "impossible" results. Am I missing something?

Thanks,

• where does tx gain come from? is it possible to focus the light of a candle into a point that shines brighter than the candle itself? i'm guessing tx gain comes from the antenna, which "focuses" some of the energy (25 dBi is a lot). Oct 8 '21 at 19:45
• Yes your assumption is correct, "TX Gain" is the gain of the Tx antenna (dBi). Regarding the candle example, yes it would be brighter if we focus it, the "intensity" (energy / area) would be higher, but the total energy would be the same. Oct 8 '21 at 20:59
• I edited your question to clarify that "FSPL" is free-space path loss, and linked to the Wikipedia article. I hope you don't mind! Oct 9 '21 at 19:39

The Antenna Gain in the formula is the far field gain - at an infinite distance, or at least far enough that the antenna is indistinguishable from an isotropic source or a dipole.

When you're close to the antenna, gain is not really a relevant concept, we would use something called Antenna Factor. AF is the field strength in V/m, for each 1 V applied to the antenna terminals. This is valid everywhere. Far away from the antenna, AF can simply be calculated from gain and distance. Near to the antenna, gain isn't a relevant concept.

We use a rule of thumb for when you're in the far field: $${2D^2}\over{\lambda}$$ Where D is the width of the antenna. This is the position at which fields from all parts of the antenna are within 45 degrees of phase from each other, i.e. all parts are roughly at the same distance, as they would be at an infinite distance.

So the flaw in your calculation is assuming that an antenna of 25 dBi, at 50 MHz, has a far field of only 50 metres. Here are the actual numbers:

$$\text{Effective area} = {{G\lambda^2}\over{4\pi}} = 906 \text{ m}^2$$

Which assuming a circular aperture is a diameter of $$34 \text{ m}$$. (and, by the way, requires a yagi length of about $$45\lambda$$ or $$270 \text{ m}$$). The far field distance from this is $$385 \text{ m}$$.

This applies to both ends of the link, so if you have two 25 dBi antennas, you'll need to put them 750 m apart before the free space path loss equation starts to make sense.

Another way I like to look at Gain and EiRP of low and high gain antennas is this:

From far away,
. a 0 dBi antenna fed with 316 W, and
. a 25 dBi antenna fed with 1 W,
look exactly the same. The power density is just $$EiRP/\pi r^2$$.

But close the antenna something different happens.

• The power density of the isotropic antenna gets stronger and stronger as you move closer, until you're 3 m away and the 316 Watts starts to warm you up.
• But the power density of the high gain antenna stops going up. Imagine standing right in front of this 34 m diameter horn antenna. The 1 watt power is evenly distributed over the whole aperture. So the power density never gets to more than $$1/900 \text{ W/m}^2$$. And this region of low density lasts for several times the diameter, so putting a receive antenna too close doesn't capture any more power.
• Awesome! You helped me to understand why not taking the far field in consideration is a problem and also the energy conservation. Oct 8 '21 at 22:28
• @377ohms it's roughly the same reason why you can't use the inverse square law to conclude that it's infinitely bright at the center of a light bulb :) Oct 8 '21 at 23:35