Simple Inexpensive Range Expectations

So, what can be expected from these rigs in terms of range?

In free space

We don't often operate in free space, but it is easy to calculate and provides a useful metric.

• TX power (conducted)
• TX cable loss
• TX antenna gain (versus theoretical isotropic antenna)
• path loss (function of distance and frequency)
  • not really a function of frequency, but seems like it because we are calculating in terms of isotropic RX antenna instead of capture area [directivity or gain versus isotropic of an antenna is a function of its size in wavelengths]
• RX antenna gain
• RX cable loss
• RX sensitivity (at required SNR)

Link margin is how much more signal is received than is required.

Path loss is square law.

| change in distance |change in link margin |
+--------------------+----------------------+
| 2X                 | -6 dB                |
| 40% more           | -3 dB                |
| 1/2                | +6 dB                |
| 70%                | +3 dB                |

Range factors of 2 with 6 dB margin steps are easy to work with.

• 2X --> 6 dB
• 4X --> 12 dB
• 8X --> 18 dB
• 16X --> 24 dB
• 32X --> 30 dB
• 64X --> 36 dB
• 128X --> 42 dB
• 256X --> 48 dB
• 512X --> 54 dB
• 1024X --> 60 dB

Path loss formula: Friis transmission equation

Example: Yaesu FT-60 - in free space

From the specifications:

• RX sensitivity: 0.16 uV for required SNR
• TX power: 5W
• antenna: ?

Antenna is a rubber duck, so call it 0 dBi. With 5W conducted, this is 37 dBm EIRP.

0.16 uV into 50 ohm receiver is 1.5e-16 W or -123 dBm.

Free space path loss for 1 m range @ 146 MHz per Friis is 16 dB. So, link margin at 1 m is 37 - 16 - -123 = 144 dB.

From table above, this is about 1000 km.

Not in free space, with Yaesu FT-60 example

We never work that kind of range. Why? Terrain and atmosphere.

Standing on the (spherical) planet, we have a planet blocking the way. Or in shorter terms, horizon, hills, mountains, buildings, etc.

The atmosphere can work for us or against us. (ducting, scattering)

The atmosphere fluctuations can cause fading as can multipath, so additional link margin is useful.

From someplace not interesting, a few miles is normal. From mountain top to mountain top, > 100 miles isn't unusual. Sometimes a duct forms between CA and HI.

Example - SIMR 1296 whip to whip

ADF4350 TX power: +5

RTL-SDR RX sensitivity: good question

Let's call the whip antennas about 0 dBi.

Path loss for 1 m at 1296 MHz is 35 dB.

Let's guestimate the RX senstitivity as a noise figure of 10 dB above the thermal noise floor of -174 dBm/Hz. And let's use a channel bandwidth 4000 Hz. So, the sensitivity is -128 dBm. Or -118 dBm for 10 dB SNR.

So, the 1 m link margin is 5 - 35 - -118 = 88 dB. Not bad!

From the chart above, that's about 26 km.

Add antenna gain to get more margin. +10 dBi is easy. And this adds to both ends!

Example - SIMR 10 GHz open ended waveguide to LNB

ADF4350 TX power: -20 dBm

open ended waveguide antenna: approx 5 dBi

RX sensitivity: data sheets say 0.1 or 0.5 dB NF

Path loss for 1m at 10.368 GHz is 53 dB.

RX antenna gain for LNB is unknown. For the approximately 50 mm aperture at this frequency, 10 dBi is a reasonable guesstimate.

Using 1 dB NF and -174 dBm/Hz thermal noise floor and 4000 Hz channel width, the senstivity is -137 or with 10 dB SNR -127 dBm.

So, the 1 m link margin is -20 + 5 - 53 + 10 - -127 = 69 dB.

From the chart above, that's about 3 km.

Add antenna gain to get more margin. 10 to 30 dB more isn't hard at this frequency! And this adds to both ends!