Preamble

While searching for an answer to how different frequencies propagate from my home QTH, I came across a program called Splat!. To compare the 2 m, 70 cm, and 35 cm (868 MHz) bands. Since I already had a good idea of how 2 m and 70 cm signals propagate, I was curious to see how 868 MHz would perform. Here are the results:

Installation

As I am running Ubuntu, it was easy: 

sudo apt install splat

Since I’m located in Finland, I needed to obtain the terrain files used by Splat for its calculations. I found a site providing elevation data that can be downloaded based on your location, simply click a square on the map and download the ZIP file.

After unzipping, you’ll find .sdf files that must be converted to .hgt format using the srtm2sdf tool. Since there are many files, I used a simple one-liner to process them all:

for f in *; do srtm2sdf "$f"; done

and placed all the .hgt files in a data directory. 

Configuration

Splat requires a few files to run. The first is the.qth file, which defines your QTH configuration. Edit a file tx1.qth which in my case looks like this:

Home ; Just a name
60.4294 ; GPS coordinates
-24.1450
15m ; Antenna height

Also a rx1.lrp file is required, with the following info:

15.000 ; Earth Dielectric Constant (Relative permittivity)
0.005 ; Earth Conductivity (Siemens per meter)
301.000 ; Atmospheric Bending Constant (N-units)
868.000 ; Frequency in MHz (20 MHz to 20 GHz)
5 ; Radio Climate (5 = Continental Temperate)
1 ; Polarization (0 = Horizontal, 1 = Vertical)
0.50 ; Fraction of situations (50% of locations)
0.90 ; Fraction of time (90% of the time)
0.5 ; Effective Radiated Power (ERP) in Watts (optional)

Computing

Using the following command the output should look something like this:

splat -t (transmitter .qth file)  \
      -L (Height of receiver antenna)  \
      -R (max distance to calculate in km) \  
      -s (name of city file) \                 
      -d (directory for sdf files) \
      -o output_filename.ppm    

Comparing 145, 433, 868MHz

Disregarding  all  variables,  so assuming  same antennas,  same  power  etc. How  does  the  signal  differ, purely based  on frequency. 

RX antenna 2m above  surrounding  

commands:

splat -t tx1.qth -s cities.dat -dbm -db -L 2m -metric -o 145.ppm -R 150 -f 145 -d data/sdf/
splat -t tx1.qth -s cities.dat -dbm -db -L 2m -metric -o 433.ppm -R 150 -f 433 -d data/sdf/
splat -t tx1.qth -s cities.dat -dbm -db -L 2m -metric -o 868.ppm -R 150 -f 868 -d data/sdf/

result:

Notes

I have some experience with signals between my home QTH and the OH2RCH Espoo repeater. A direct one-to-one comparison isn’t perfect, as the 2 m antenna at the repeater is higher than the 70 cm one. However, the 70 cm antenna seems to have slightly more gain, so for simplicity, let’s compare them directly.

Reaching the 2 m repeater from my QTH is easier, I practically need only 1 W, while the 70 cm signal would require around 10 W for a good signal at the repeater. Assuming my antenna setup is otherwise equal, this implies I need roughly 10 dB more signal to reach the repeater (1 W → 10 W = 10 dB).

Now, let’s calculate this using Splat:

splat -t tx1.qth -r  rx1.qth -s cities.dat -d data/sdf/  -f 145  -H -l  -metric
splat -t tx1.qth -r  rx1.qth -s cities.dat -d data/sdf/  -f 433  -H -l  -metric
splat -t tx1.qth -r  rx1.qth -s cities.dat -d data/sdf/  -f 868  -H -l  -metric

result:

The path loss values align well, suggesting that:

• From 145 to 433 MHz, about 10 dB more path loss can be expected.
• From 433 to 868 MHz, about 5 dB more path loss can be expected.

Calculating LoRa link-budget

Calculating (a simplistic) link budget:

Link budget = Perp - Receiver sensitivity

• In EU the Max  Effective Radiated Power (e.r.p.) = 500mW -> 27dBm,
  This will be achieved by calculating the antenna gain, estimating the losses and adjusting the output power of the radio. 
• Now assuming the RX path has 0 gain.
• LoRa RX sensitiviy is around -136dBm (SF:8,BW:62.5kHz)
• Assuming we have a (very) low noise-floor at the RX (-116dB or better)

163dBm = 27dBm - (-136dBm)

Calculating the (theoretical) range of my LoRa signal:

• RX antenna 2m above average ground (on top of a roof)
• Added my Yagi parameters

Conclusion

Based on this short study, 868 MHz indeed propagates less effectively than 443 MHz, but not as poorly as I expected. With well-placed antennas and a low noise floor, very good ranges are still achievable thanks to LoRa’s excellent receiver sensitivity.

The calculations above assume good antennas,  definitely not the tiny “black stick” antennas. At 868 MHz, the wavelength is about 35 cm, so a quarter-wavelength antenna still needs to be around 9 cm.

That said, the 868 MHz band can be quite crowded,  especially in urban areas,  and the maximum allowed ERP imposes limits. Expectations should therefore remain realistic, as the numbers assume properly installed antennas in relatively quiet locations.