










  +50    dBm   power output
 +  2.15 dBi   transmitter antenna gain
 -102    dB    propagation loss, 20 km at 150 MHz
 +  2.15 dBi   receiver antenna gain
  -47.7  dBm   signal strength at receiver


   +8    dBm   power output
 +  2.15 dBi   transmitter antenna gain
 -102    dB    propagation loss, 20 km at 150 MHz
 +  2.15 dBi   receiver antenna gain
  -89.7  dBm   signal strength at receiver



  • ＋ Transmitter output power
  • ＋ Transmitter antenna gain in the direction of the receiver
  • － Propagation loss in free space
  • － Attenuation due to absorption in atmospheric gases
  • － Margin for attenuation due to rain
  • － Margin for attenuation in tree foilage
  • － Margin for attenuation due to reflection against walls etc.
  • － Margin for signal fading
  • ＋ Receiver antenna gain in the direction of the transmitter



That's a pretty good answer but I can add some more details.

The exact formula for path loss is $$ 20 \times \log_{10}\left( 4 \times \pi \times \frac{d}{\lambda{}} \right) $$ $ 20 \times \log_{10}\left(4\times\pi{}\right) \approx 21.98$, and that's where the '22' comes from.

If your receiver specs give a minimum signal strength, then the analysis above is pretty much all you need. But in a more general link budget you have to compute the required receive power yourself from the data rate, the type of modulation and coding, and the receiver system noise temperature.

The most power-efficient modulation/coding method in use is rate 1/6 turbo coding over BPSK (binary phase shift keying). This is a very popular deep space signal; it's being used by New Horizons at Pluto, for example. This particular signal requires a minimum $E_b/N_0$ of about 0 dB.

What is $E_b/N_0$? It's the received energy per bit divided by the received noise power spectral density in watts/Hz. This also has units of energy, so the ratio is dimensionless. It's usually expressed in decibels. The famous Shannon Limit says it's impossible to make a system operate error-free at an $E_b/N_0$ below -1.6 dB even if you can use infinite bandwidth. So you can see that we're pretty close to the theoretical limit.

Then you add the data rate, also expressed in decibels (with respect to 1 bps). For example, 1000 b/s would be 30 dB(bps), so your New Horizons signal would require a $P/N_0$ of at least 0 + 30 = +30 dB, where P is received power.

That just leaves us with $N_0$. In space communications, noise is usually expressed as a temperature T since everything above absolute zero generates thermal noise. The big 70m dish at the NASA Deep Space Network sites has a noise temperature of 17.5 kelvins (I looked it up). To get N0, you multiply T by Boltzmann's constant, 1.38e-23 J/K or -228.6 dBW/Hz-K. So 17.5K is an $N_0$ of -216.2 dBW/Hz (or dBJ, same units).

Now you have what you need to compute P, the required receive power. It is simply -216.2 dBW/Hz + 30 dB-Hz = -186.2 dBW or -156.2 dBm. That's not much, but it's still hard to generate all the way from Pluto!

  • $\begingroup$ Phil Karn KA9Q?? $\endgroup$
    – Scott Earle
    Nov 15 '18 at 14:29
  • $\begingroup$ Yup, that's me. $\endgroup$
    – Phil Karn
    Nov 17 '18 at 5:46

Let me take the later question out of the title.

how do I make one?

By using a tool, such as

This is a free tool, and will work for Amateur Radio frequencies.

Once you get started, in order to display a "Link", you do the following

  • Use "New Site" from the main menu to setup both TX location and RX location
  • Use "New Link" from the main menu to setup a new link.

This will get you a nice graphical representation of your link, and accompaning data which was used for its calculation.



A practical solution to examine the performance of a terrestrial radio link doesn't require the consideration of very small contributors to that performance.

Link performance that considers the major factors such as frequency, radiated power, receive system sensitivity, free space LOS path loss, added losses due to direct path and Fresnel zone obstructions/reflections from the earth, etc can be calculated usefully by allowing sufficient "fade margin" to account for temporal path loss variations.

Below is one example of software using this approach to evaluate the expected performance of an FM broadcast station for the conditions shown there. The analysis includes the effects of terrain elevations along the great circle path between the transmit and receive antennas.

Note that despite a significant obstruction to the LOS path and Fresnel zones, the fade margin calculated for this application exceeds 20 dB — which would permit very high link reliability.

Longley-Rice Path Analysis.


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