We will not introduce the subject of noise. Noise is a type of signal generated by the device itself. It is normally a non desirable signal that can interfere with the processing of desirable signals, for example, in amplification or reception. If one looks very carefully at the current of a real ms transistor, with perfect voltage sources. And this is instead the state, he or she finds the current, instead of being constant with respect to time, contains minute variations shown here. These variations are due to noise. So, the actual current, i capital DS sub t, can be written as the DS value, which is what we've been trying to predict with our DC models, plus a very small component, i sub n of t. That is called the current noise. This is a random process. It doesn't make much sense to talk about what is it's value at one specific instant in time, so rather we use certain measures for the noise. The mean square value of the current noise, or the square root of that, which is the root mean square, or RMS value, of the noise. We also talk about the power spectral density of the noise, and this is defined rigorously in mathematically oriented books on, on stochastic processes as they fully transform of the auto-correlation function. But instead of that, I will give you an intuitive understanding of power spectral density, which actually coincides with the way we measure power spectral density. So if you look at the noise within a certain band with, and lets call it delta f. And you could take the amount of mean square value that you get for the spectral components correspond to that band with and divide by that band with delta f. And, to allow delta f to go to zero, then you get what is called a power spectral density. And in general, this will be a function of frequency. From here, you can see that it will be measured in amps squared per hertz. Sometimes you to the square root of that and measure it in amps per square root of hertz. Similarly, you do. you can define the prospect of density for voltage noise. If you want the total mean squared value of the noise current in the bandwidth between frequencies f1 and f2, then you take the prospect of density then you integrate it over that interval. Now, white noise, white noise is very wide band noise that has constant power spectral density up to extremely high frequencies. Not infinite frequencies, because quantum effect start entering, but this is about the frequencies we're normally interested in, so we call it a white noise. There are two types of white noise. One is thermal noise that is due to random thermal motion of carriers, because of thermal vibration of the crystal lattice. And it is also called Johnson noise, or Nyquist noise. When we have an ideal resistor R it is supposed to be noiseless. But the real resistor, which is what I'm showing you here, if you look across its terminals, because of this thermal noise, shows a minute voltage. So you can represent a real resistor in other words a noiseless resistor when the noiseless resistor in series with a noise voltage short v sub t, t standing for thermal. The prospect authenticity of this source can be shown to be 4kTR. There are references for that in the book. K is the Boltzmann constant, T is absolute temperature, R is the resistance value. Instead of having a resistor in series with a voltage source, you can take the thevenin equivalent of that and have a noise resistor is in parallel with the current noise source. So now from the Thevinin Norton transformation, you know that i sub t must be V sub t over R. And therefore when you square both sides and you take their mean value You get this result. If you take the amount of mean square value over a bandwidth delta f and you divide by delta f, you divide both sides by delta f, you get the corresponding relation for sparse spacial densities that looks like this. I have used this in the process. And therefore the final result is 4kT times the conductance of the resistance. There is another type of white noise called Shot noise, and this is associated with DC current. It has to do with carriers crossing a potential barrier, and you get some noise because of the discreetness of the arriving charges. so since charges are individual electrons that pass, you can understand that they appear a discrete charge packets. So you can represent that as a DC current plus a minute noise, which is called Shot noise. It can be shown that the par-spectral density of that type of noise is 2qi, again references are in the book. Now, these two processes appear in nMOS transistors, but more generally for an nMOS transistor, if you plot the par-spectral density, you get the region where you have White noise, where the par-spectral density is constant. But then you get another region. A region where the par-spectral density goes up as you decrease the frequency. And in fact, it turns out to be proportional to approximately 1 over f. So this is called Flicker noise, or 1 over f noise,ah, it looks like a straight line here because both the vertical and horizontal axis are logarithmic. Now, if you extrapolate here and there, where the two asymptotes cross, we get that's what called corner frequency. So, well above the corner frequency, we have White noise. Well below the corner frequency we have Flicker, or one over f noise. The total par-spectral density for the noise current, is given by that for White noise plus the corresponding one for Flicker noise. And in the log log plot, you can show that this plus this gives you the solid line like this. So in this very brief video we introduced noise in very simple terms, of course this is a very subject. We just mentioned the minimum we need to understand in order to able to follow the videos that will be presented next. We talked about two types of noise, White noise and 1 over f noise. And now we will start discussing each of these processes seperately as they apply to nMOS transisstors.
