# I don't know how to choose an adequate antenna

I need to choose an antenna for a long range free space communication (~10km), and I currently have a receiving antenna, but I don't understand enough to be able to pick an adequate emitter.

The receiver is a 900Mhz antenna, with 14dBi gain. I learned about the Friis equation, but there are a few things which I do not understand.

1. Of course, if you increase the electrical power in your emitter, the signal will be stronger, but is there a direct link between those two values or is it different for each antenna ?

2. With this formula you can calculate what will be the theorical strength of the received signal, but what is the minimum required to have a correct transmission ?

Thank you

• I know the answer to your last question: it depends. The demands you put on your antenna and amplifier are tied directly to what you are trying to do with it. Trying to send Morse code in a Ham band requires much less power than sending video in the same band. Sending anything to the Voyager probe takes an immensely powerful antenna. Commented Dec 8, 2018 at 21:13
• Yeah I see what you're saying, my biggest problem is that with a given antenna, I can't manage to have a value of what will be the signal strength, and without it I can't pick my antenna :( Commented Dec 8, 2018 at 21:16
• Just need to add an important point: in most countries, there are limits on what you can do on each shared band, which may involve transmit power, EIRP, duty cycles, frequency hopping or frequency agility, LBT, spread spectrum, and so on. You can’t just pump up the power to achieve your needs in most of those bands (if you did you would just drown all the signals from other users of the band nearby). Commented Dec 9, 2018 at 10:39

What you are looking for is to build a "link budget". Here is a calculator. First consider the transmit strength and receiver sensitivity of your system. Then figure out all your losses. If your transmit strength + losses > receive sensitivity, then the system should work.

You will have at least 111dB of free space loss. calculator. I would also budget something like 30dB for margin due to multi-path loss, occlusion ect. Weather could become a big factor and stop your system from working as well if it's all outside.

Now your receiver antenna 14dBi of gain, so assuming it's aimed correctly you would need a receiver that is at least -127dBm sensitive (-111dB - 30dB + 14dB). If you have a transmit antenna with gain, or a transmitter with power above 0dBm then you can relax that requirement.

Typically RF settings are already in dB for transmit strength, but in general the relationship is the log relationship for power. A doubling of power will increase signal strength by 3dB. A 10x power increase, gets you a 10dB increase in power etc.

To design the system you have to pick you transmitter, receiver, transmitter antenna and receive antenna at the same time. Picking one without the other doesn't make much sense.

This paper may be a good read as well.

Also dBi, dBm, dB etc can get confusing so this is a worthwhile read too.

• I've started to process your answer, which is helping me a lot to understand. I have a small question about the free space loss, what gain do you set for the transmitter ? If I set 10km, 900Mhz and 14dBi for the receiver I get something like 95dB loss, is it just a margin added ? Commented Dec 8, 2018 at 21:54
• I realized it was 111dB for 10km not 114dB, so that was a typo by me. It's 111dB for an isotropic antenna (radiates evenly everywhere) across 10km of air. Or 97dB if you assume that the antenna has a gain of 14dBi due to directionality. I am pedantic and would always write free space loss and antenna gain separately...but for whatever reason the calculator chooses to add it. The end result should be the same. Commented Dec 8, 2018 at 22:06
• Ok I see, but then the calculator is not good, it gives me 95dB when the formula from the paper gives me 111dB, but it start to be clearer and clearer in my head Commented Dec 8, 2018 at 22:22
• Ohhh, ok no, my bad, the calculator calculates the loss with the gains applied, so it's correct, I just didn't realized if I just want FLS I should put 0 gains. Commented Dec 8, 2018 at 22:24

Assume the receiver is high up, so no multipathing.

Assume the radiated power, thru a vertical whip (8cm long)at 900 MHz, is only 1 microwatt (-30 dBm [dB milliwatt], or the energy of a toy car responding back to the human controller).

Can we provide 100 bits per second, from the 1uW Transmitter to the Receiver, over 10km?

Lets run some numbers

-174dBm/Hz the Boltsmann/Nyuist/Johnson random noise floor

+20 dB increase in system noise, with 100Hz BandWidth

+20 dB Signal Noise Ratio providing essentially NO Bit Errors

+4 dB easy receiver noise figure at 900MHz

+0 dB multipath, rain, foliage losses

-6 dB benefit of matching RX antenna into LNA

+6 dB nearby transmitters, desensing 900MHz receiver

========================================

-174 + 20 + 20 + 4 -6 +6 = -174 + 44 = -130dBm, which across 50 ohms is [(-120dBm = 0.623 microVolts PP) / sqrt(10)] ==> 0.20uVpp.

Now assume your TX produces 1uW (-60dBW, -30 dBm or dBmW) into a zero-gain vertical whip 8cm antenna.

What range can we expect? RX needs -130, TX produces -30.

Your antenna produces 14dB gain, so there is some beam-forming and the sensitive region is 360 degrees / 2^(14/3) or 360/20 or about 18 degrees field-of-view. We'll assume all this beamforming is in the horizontal axis.

Our link has 130 - 30 + 14 = 114dB.

Path loss is

22dB + 10*log10( distancedistance / wavelengthwavelength)

So we have about 92 dB to spend on distance between TX and RX.

Divide the 90 by 2 (to handle the D^2/W^2) and get 45.

Discard the 5 (gives more margin), and you have 40, indicating only 10^40/10 = 10,000 wavelengths; at 1/3 meter wavelength, you have 3,333 meters of communication distance. Or about 2 miles. With lots of margin, if your RX antenna is up high.

What does this mean? at 900MHz, you can slowly signal for several miles, using very low power, perhaps generated from a simple XTAL osc and a 90:1 prescalar and a PhaseLockLoop.

Can you send 100 bits/second over 10,000 meters? Not without more power or some TX antenna gain OR using (Error Correction) Coding of the data so the SNR can be dramatically reduced.

We need about 3X more range; given 4X more range will cost 6+6 = 12dB, the 3*3 will cost 10dB. Coding should let you drop the SNR from 20dB to 10dB. Standard Viterbi coding (easy said, hard to do) will provide this.

The fun comes from the narrow-band signal: only 100 Hertz, thus the receiver and transmitter need to track each other within 10Hertz???? or 1 part in 90,000,000. Or, as NASA does in acquiring signals of a narrow-band satellite transmission: slowly sweep the frequency region around the expected Transmission carrier.

And TX and RX phase noise become big deals, requiring skill and money and complexity and power-draw.