# Noise

We’ve talked enough about analyzing signals. It’s now time to talk about the signal’s arch-enemy, noise. Why do I say noise is the signal’s arch enemy?  Well it is because noise is the factor that limits the information capacity of the signal. Look what happens to the Shannon limit if the noise is zero:

$I = 3.32B \times log_{10}(1+\frac{S}{N})$

• If the noise is zero, the S/N will approach infinity
• If S/N approaches infinity, then so does (1+S/N), so does log(1+S/N), and so does $3.32B \times log_{10}(1+\frac{S}{N})$
• In other words, the information capacity of the channel approaches infinity

With no noise, the only limiting factor to the information capacity would be how much information you can pump into the system at a time.

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Noise is any undesirable electrical energy that falls within the passband of the intended signal.  For example in all electronic systems in North America, there is 60 Hz noise due to the nature of the AC power delivered by the electric companies. This can affect an audio system because we can hear 60 Hz signals, therefore 60 Hz falls in the passband of an audio system. The 60 Hz “hum” would not affect a WLAN network because those signals are in the GHz range.

Noise can fall into one of two general categories – correlated noise which only exists when the signal exists and uncorrelated noise which exists whether there is a signal or not.  It is good to have an understanding of these different noise sources so that if you are setting up a communication system, you can eliminate, or at least reduce many of the sources of noise.

## Uncorrelated Noise

Uncorrelated noise is always present in a system, and it can come from sources external to the system or from devices or circuits inside the system.

### External Sources

1. Atmospheric Noise – This is commonly called static, and is due to electrical disturbances that occur in the atmosphere. A common source is lightning.  This source of noise is relatively insignificant above 30MHz.
2. Extraterrestrial Noise – This is noise generated outside of the earth’s atmosphere, and as such, the atmosphere often shields the earth from this type of noise. Satellites can be affected by it though. The two primary sources of this noise are the sun (sun spots and solar flares) and cosmic background noise
3. Man-Made Noise – These are noises generated by humankind, and comes from everything from electric motors, to AC circuits, to fluorescent lights, to radio and television stations

### Internal Sources

1. Thermal Noise – is the noise generated by the thermal agitation of electrons inside an electrical conductor. This kind of noise is sometimes called Brownian Noise (after an early researcher), Johnson Noise (after another researcher), random noise or white noise (because it is due to random movement).  Thermal noise is constant across the entire frequency spectrum which makes it a source of noise for any and all systems.
Thermal noise can be predicted mathematically by:
$N = KTB$
N = noise power in Watts
K = Boltzmann’s Constant:  $1.38\times 10^{-23} \frac{joules}{Kelvin}$
T = Temperature in Kelvin (to convert Celsius to Kelvin, add 273)
B = the bandwidth in Hertz
2. Shot Noise – occurs in semiconductors and is noise generated by random fluctuations in electric current due to the fact that electric current occurs from flow of electrons, and sometimes electrons take different paths as they flow through a semiconductor.

## Correlated Noise

Correlated noise is noise that is somehow related to the signal.  If there is no signal, there is no correlated noise.  This type of noise is produced because of some effect the system has on signals passing through it. A good example of this type of distortion is non-linear amplification which occurs when a signal is amplified but is distorted somehow. The most extreme case is when the amplifier is overdriven and the peaks of the signal get clipped as shown in the circuit below. The input signal is a 10V peak sine wave, but the amplifier circuit is only powered by +/-10V, so the output is clipped:

The output signal is still periodic, but is no longer sinusoidal which means the new signal will have added harmonics. This added non-linearity is called harmonic distortion.

Amplifiers will always create some amount of harmonic distortion in a signal, the situation does not have to be as extreme as the example above.

## Noise Calculations

### Signal to Noise Ratio (S/N or SNR)

The signal to noise ratio is just what you would expect; it’s the ratio of the signal power to the noise power. It is often expressed in dB.

Example: If the strength of a received signal is 2mW and the noise power is 0.2mW, the SNR is:

$SNR = \frac{2mW}{0.2mW} = 10$

$SNR(dB) = 10log_{10}\frac{2mW}{0.2mW} = 10dB$

### Noise Factor (F) and Noise Figure (NF)

Noise factor and noise figure are useful for relating the amount of noise a device or stage of  a system adds to a signal going through it. Take this example block diagram:

The amplifier has an input signal and input noise enter into it. Both the signal and the noise get amplified in some manner, and then an amplified output signal and noise are driven out of the system. The amplifier may not affect the signal and the noise in the same manner, so in order to examine the relationship between input and output, we use the noise factor which is simply

$F = \frac{SNR_{in}}{SNR_{out}}$

Alternatively, we can use the noise figure which is:

$NF = 10log_{10}\frac{SNR_{in}}{SNR_{out}}$

If an amplifier is ideal and affects the signal and the noise exactly the same then the noise factor will be 1 and the noise figure will be 0. There is no ideal amplifier or system, therefore noise factor and noise figure give one indication of how non-ideal the amplifier (or other system component) is.

Example

The input signal to an amplifier is 10mW and the noise is $2\times 10^{-11} W$. The output signal is 100mW and the output noise is $3\times10${-8}W. What is the noise factor? What is the noise figure?

$SNR_{in} = \frac{10mW}{2\times 10^{-11} W} = 5.0\times10^8$

$SNR_{out} = \frac{100mW}{3\times 10^{-8} W} = 3.33\times10^6$

$F = \frac{5.0\times10^8}{3.33\times10^6} = 150.2$

$NF = 10log_{10}\frac{5.0\times10^8}{3.33\times10^6} = 21.8dB$