Basic Wireless Communication for Microcontrollers
Chapter 2 - Design Project 1: Crystal Radio Receiver
Basic Noise Overview: What is Noise and Can We Avoid It?
In a crystal receiver, the amount of signal power received is of prime importance because there are no amplification stages. The output power must necessarily be slightly less than the input. Since your ear needs a minimum amount of power to hear something clearly, you need to design the receiver to deliver at least that amount of power to your ear.
Most receivers, however, have no shortage of gain. There are usually long chains of amplifiers with a total gain of a million or more in voltage, and a trillion or so in power. To obtain more gain, we can just add more stages of amplification. Contrary to popular belief, the limit of a receiver's sensitivity is not determined by absolute signal level since raising that is not a problem. The real problem is noise.
First of all, let me preface this by saying that your experience in maximizing absolute signal level in the crystal receiver is a valuable exercise and will still be applicable to receivers with gain. Except in some rare cases of very strong signals, it is never to your advantage to purposely or sloppily loose signal power in a receiver, and you will learn the concepts of impedance matching and filtering along the way. It is important to talk about noise now so that by the end of project one, you will have a good overview of the main concepts facing a receiver designer.
Any undesired signal could be considered noise, but usually signals which are intended to be received by other receivers, but which prevent you from clearly hearing the signal you want, are called interference. The term "noise" is usually limited to random or semi-random signals which arise from many sources: thermal interactions among molecules, uncoordinated current flow, internal semiconductor effects, fluctuating resistor value, lightning, the sun, planets, and even warm ground, digital circuitry, electric appliances (especially with electric motors) operated near the receiver, and other causes.
Noise can be divided into two categories: internal noise and external noise. Internal noise is that which comes from your own equipment (antenna, feedline, and receiver). Thermal noise and semiconductor effects would be examples of this. External noise is that which is caused elsewhere and received through your antenna just like the desired signal, such as lightning and electric motor noise.
When working below VHF frequencies (below 30 MHz), noise from external natural and man-made sources usually dominates over that generated by components in the radio. In the VHF, UHF, and microwave region, it is possible to achieve such "quiet" from outside noise sources that the receiver's internal noise is the main noise source. Man-made noise is even more broad-band than the natural noise but is still usually more of a problem for HF frequencies than at higher ones due to inductance and capacitance in the motors and other devices limiting the bandwidth of emissions.
Why is noise the limiting factor on sensitivity? Why can't we just filter it out somehow? In some cases, we can. In fact, decreasing bandwidth will always decrease noise. The problem is, though, that the bandwidth cannot be smaller than that required by your signal. So, it is best to tailor your receiver's filtering to closely match the spectrum of your desired signal.
Even if your filter only allows the desired signal bandwidth through, there will still be some amount of noise present. Noise starts out with varying degrees of randomness, which is exhibited by its frequency spectrum. The more random, the broader and flatter the spectrum. Over a narrow bandwidth, however, almost any noise source starts to look the same as a random one. In other words, even if the overall spectrum of the noise varies significantly, when you look at only a small chunk of it, it will look fairly flat over that small bandwidth.
If your signal uses bandwidth very efficiently, it, too, will have a fairly flat spectrum within its bandwidth. Obviously, if there is some part of the bandwidth that it is not using, then it could be re-organized so that it uses that part and the overall width decreased. This means that very efficient signals are technically random, too, in the purest mathematical sense. In this sense, random means that the listener cannot predict what comes next based upon what came before. After all, if the listener could predict what came next, it wouldn't need to be transmitted in the first place. Efficiency means transmitting only what is necessary to convey the information. It is important to bear in mind that random does not mean "containing no meaning".
Herein lies the reason why noise is a problem: if you have a signal which is very efficient and essentially mathematically random, it will be indistinguishable from random noise. So, we cannot hope to remove noise from such a signal in any way, the noise will definitely alter the information contained in the signal.
Another way to look at this is that as you reduce the bandwidth of noise, it begins to look more and more like a signal. You can actually try this using a sharp bandpass filter and an oscilloscope. If you look at random noise, you will see that it is all over the place and doesn't look periodic. However, if you feed it through the filter and then look at it, it will look like a rough sine wave. The reason is simply that you are forcing it to look that way by filtering it. After all, an infinitely sharp bandpass filter would make anything look like a sine wave.
Typically, a balance is struck whereby the efficiency of a signal is decreased to make it more distinguishable from noise. Such schemes usually add a small amount of redundant information (such as a CRC(Cyclic Redundancy Check) or checksum) to enable decoders to detect errors and possibly correct them. It turns out that there is a limit to this, called the Shannon limit, after the information theorist Claude Shannon. This states that for a given bandwidth with a certain signal to noise ratio, there will be a maximum information transfer rate. For digital communications, it is clear how to apply this theorem and schemes exist which come very close to the Shannon limit. This concept applies even to voice, but in that case it is your brain which is using the redundant information in the voice signal to extract the information despite noise, whether it be over a radio link or in a crowded room. The mathematical relationship, called the Shannon-Hartley Theorem, is C=W*log2(1+S). C is information transfer rate in bits/second, W is bandwidth in Hertz, and S is the signal to noise ratio (in power). Log2 means the base 2 logarithm. Note that this expression is really only valid for white (flat-spectrum) noise and has to be modified for other cases.
So, what can we do about noise? First, if we are working in a frequency range where natural noise is dominant, we can use directive antennas which receive only in the desired direction, to get more signal and less noise and interference. If we are working in the VHF,UHF, or microwave region, we can not only use such antennas, but we can also improve the receiver system itself to decrease its internal noise. This will be dealt with further in the next project. In some unusual cases, reducing receiver internal noise can also help in the HF region, because man-made noise may be particularly low in a certain area or natural noise may be reduced due to certain atmospheric conditions.
Secondly, we can use filtering and other special techniques to remove the noise outside of our signal bandwith. Finally, we can design encoding schemes which strike a good balance between bandwidth efficiency and information redundancy to approach as closely as possible the Shannon limit. This will all be more pertinent in the next project but for now, we can maximize the power delivered from the antenna to the ear so that it will enable your ear to hear it over the noise sources it has to contend with, like typical household noises.
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