How much improvement in range if I replace the 2dBi antenna with a 3.1 dBi antenna on the ground module only of my 915 MHz radio?

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For comparison purposes, I'll assume no antenna cable loss and 100mW transmit power.

In terms of transmit (and this will give a general idea of receive also):

2dBi antenna is effectively 158mW EIRP

3.1dBi antenna is effectively 204mW EIRP

What does this mean? I've run some calculations. The theoretical range for both 2dBi antennas is about 2783 meters. In reality, it will be much less (because of loss in the connectors, orientation, and low signal quality.) But we can compare between the other values:

2 dBi to 2 dBi will be 2783m

3.1 dBi to 2 dBi will be 3029m
Of course, you will not get anywhere near these distances, but the ratio should be useful. Consider the distance you get now, you can add about 8% distance. Add 3.1 antennas on both sides, you might get distance + 18%, or a theoretical range (for comparison only, you will not get anywhere *near* this range in useful signal) 3295m.
If I did the math right, that is. 

These are calculated with -121dBi receiver sensitivity (spec on the radio) for 915Mhz DSS transmissions. But remember, while these max distances are theoretically possible to "hear" the signal, you cannot pass high speed data (or any data) as that is where the signal is lost, never mind noise, and never mind being a useful signal. 

It also assumes an unobstructed space between the radios, and across rural areas with no lakes or fence lines or metal buildings. 

But 8% distance gain is a better way to estimate it. Again, if I did the math right, and it is always possible that I messed it up. 

Thanks for the information that’s exactly what I wanted to know.

I always try to figure things with ERP instead of EIRP.

Here's a quote from another post I made...

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I got two of these 3.5dBi antennas...

http://www.ebay.com/itm/290362347165?ssPageName=STRK:MEWNX:IT&_...

100mw * 2 dBi = 158 mw EIRP, 97 mw ERP = -3%

100mw * 3.5 dBi = 224 mw EIRP, 137 mw ERP = +37%

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I can't vouch for the online calculator I used, but ERP is what actually matters as far as what you receive.  The stock 2 dBi antennas give you about your rated power.  3.5 dBi antennas will give you quite a boost.  They're also quite a bit larger and you can't always trust that the specs are true.

I wish I had both to compare actual range, but I couldn't wait for the "kit" to be in stock so I ordered air and ground modules separately from 3DR and bought my own antennas.

 

Are there any other higher gain antennas available that would worth looking at?

You could put something like this on an antenna tracker: http://www.zdacomm.com/900-mhz-grid-paraboilc-dish-antenna-high-gai...

Or if you want an omni, you might look into the cloverleaf antennas that are popular with FPV systems. 

I don't know if it will work well, but it will certainly make for nice photos to share here :)

Sure, but they start getting expensive pretty quick.  Any 900 mhz GSM antenna should work.  You want 900mhz only, some antennas are de-tuned to cover a wider frequency range and I don't suggest these.

I also got a cheap 900mhz yagi off of ebay. (~$20)

It was something like this...

http://www.ebay.com/itm/NEW-900Mhz-GSM-Yagi-an-enna-13-dBi-N-female...

You'll need to find one with a RP-SMA connector on it or get the connector.  You'll also want a usb extension cable since you'll be using at least a short pole with this antenna.  Yagi antennas are highly directional, so you'll want it to be pointed within around 30 degrees of the actual plane.

100mW @ 13 dBi = 1.217 Watt ERP

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