I fell like I have to write a couple of lines regarding the setup where the popular RTL dongles are used together with the external LNA to improve the reception, despite the fact that this was already explained many times and the radio signals theory can be found on the web, books, white papers etc.
The most common question that can be found through the various posts on the forums is:
I add the LNA but my reception is not improving, more over it is even worst then without the LNA ! What is wrong !?
To make a long story short I can use the old classic children approach where the stork always bring the baby. In our situation we can say, just use the LNA and do not ask further, it will work better then without it.
As we grew up we are not buying the stork and the baby stories any more so here I will try to elaborate as simple as possible what is going on when the LNA is connected just between the antenna and the RTL dongle, or any other receiver. I will try to make the things really simple not using the fancy NASA language and just one formula, but hey, no calculation at all.
Just to mention, what you already know, the LNA stands for the Low Noise Amplifier. So the first question that may arose is how much low is low enough for the LNA, where is limit when the LNA is not any more the low noise amplifier but rather a signal amplifier ? Is this number 1, 2, 3 or 5dB ? Well, this is a kind of who's first, egg or chicken question. But to simplify, if you have the receiver that has the NF 10dB, any amplifier that has the lower NF than 10dB (let say 5dB) will be a low noise amplifier for that receiver. The NF stands for Noise Figure and this will be explained soon.
On the Picture 1. we can see the standard signal shape on the well known SDR# screen. We can clearly distinguish the signal from the noise. We can read on the side axis the level represented in dB for the each, the noise floor and for the signal. Simply, the difference between this two values will give us the signal to noise ratio, SNR or S/N. This is a measure of signal strength relative to background noise. Of course, we want to have this ratio as higher as possible.
If you look now the Picture 2. you will barely notice any difference comparing to the Picture 1. Most of you will think that this is wrongly posted picture or the same as the first one. Looking carefully you can notice that the signal on Picture 2. is a bit higher, stronger than the first one, exactly for 3dB. So “only” 3dB which can be barely seen on the screen ? The S/N in this case is improved for 3dB. This improvement sometimes make a difference in decoding the signals from not decoding the signals at all.
Increasing the S/N for “only” 3dB may be done “simply” by increasing the transmitter power by other party for double, so let say you are listening some FM broadcast station and to have this small increase on your screen the guy need to double the power from 1 kilowatt to 2 kilowatts.
Or, you can increase the gain of the antenna, if you are using one yagi antenna 2 meters long, roughly for 3 db you will have to use one 4m long, or pair another same size antenna with that existing one. Maybe you finally assemble you 8' dish, but for 3db increase you will have to look for another one 12' in diameter.
In terms of free space path loss the 3db gain may be obtained if the distance is shorter. Plain transmitting ADS-B on 1 GHz on 140km from the listener will increase the signal for 3db when closer, just on 100km from the same listener location.
It is obvious that all this measures are not possible, simple, nor cheap for the user armed with the 10$ DVB-T dongle acting as SDR receiver. What can be done fairly simply is to add the extra LNA. S/N can be increased by decreasing receiver contributed noise. What does it mean? It you simple decrease the overall system noise figure, the S/N will be increased, roughly for the same amount expressed in dB. So here is the place where we should explain terms like noise figure, noise factor and relationship with the S/N ratio.
The noise factor Fn of the system is the input S/N divided by the output S/N. Noise figure is then noise factor expressed in dB NF=10xlog(Fn). Sometimes it is convenient to express the noise as temperature (K), when using the antenna temperature Ta and the temperature of galactic sky background in the calculations but we will not go so deep in this guide.
It is important to say that once the signal is delivered from the antenna to the receiver, the S/N will deteriorate. This is why there is the saying that the best amplifier you can get is your antenna. We can not increase the S/N higher than one delivered from the antenna using analog techniques. Any LNA, even ultra low noise LNA will contribute with the internal noise degrading S/N ratio. So how the heck we can then improve the S/N at the end with the LNA?
The best way is to explain that with the practical example. Of course we will use our cheap 10$ DVB-T dongle. We can find different informations where the noise figure (NF) of the dongle is from 4dB up to 10dB. Let's stay in the middle and assume that the DVB-T NF is 7db, at the maximum gain, (the same stated from the Leif-SM5BSZ, and this is the guy we can trust). Higher up we mentioned that S/N can be increased by decreasing the receiver contributed noise. In this case the receiver contributed noise is 7dB. If we add the extra LNA with the noise figure NF=1db delivering 20dB of the gain the overall resulting noise figure will be now only 1.04dB which is receiver contributed noise. It is 6dB lower then without the LNA and roughly this is the amount that S/N will be improved. So adding the simple LNA we can improve the S/N ratio for 6dB. If you remember the earlier comparison where we use the 8' dish antenna, this will be equal as using the 16' diameter dish antenna, just by adding the LNA.
Not clear enough? Lets try to use the formula that I mentioned at the beginning. You do not need the calculator for this :-) The following formula determines the lowest signal that can be received by our receivers :
Smin = kT x B x Fn x S/Nmin
Smin – minimum signal
kT – Boltzman's constant
B – receiver noise bandwidth
Fn – noise factor
S/Nmin – minimum SNR required for the receiver to decode the signal
From all upper factors, the only one that is not a kind of constant is the noise factor. All the rest are constants. It should be clear enough that lowering the noise factor the level of the Smin is also lower, so simple. One can say, hey, but narrowing the bandwidth B we can also improve the minimum signal level. That is true, but this may be the material for another guides for dummies. Should I challenge somebody to write it ? Meantime, just check and compare the following two pictures.
I use the weak signal from the signal generator and on the first picture the signal is clearly seen, some 5db over the noise. On the second picture there is no sign of any signal present. Same frequency, same signal level injected, same gain on the same E4000 tuner but different bandwidth – sample rate used.
So when you tune to the desired signal, use the minimum required bandwidth, you can improve your reception.
The final word that is spread all over the guide is that the purpose of the LNA in tandem with the DVB-T dongle is not amplifying the signal (as we have enough gain in the dongle) but rather lowering the noise figure, hence improving the signal to noise ratio.
So have fun with your cheap dongles....