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# Understanding Noise – Part 2: Sources of Noise

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# Sources of Noise

## Thermal Noise

The first major contributor to noise inside electronic components comes in the form of Thermal or Johnson-Nyquist Noise.  This noise is present even when there is no current actually passing through any component.  It is present even when the device is turned off!

Thermal noise is caused by the random movements of electrons inside resistive electrical components.  A perfect capacitor or perfect inductor should exhibit no thermal noise as they have no resistance.  As we add up the random movements of all of the electrons, the net result of the random movements do not add up to zero.  In fact, at any given time, we will find a net movement of charge (a net electrical current) in some direction through the component.

As the temperature of the electrical component is increased, the electrons gain more kinetic energy and the energy of their random movements increases resulting in a higher net movement of charge and a higher noise level!  Johnson-Nyquist Noise is independent of frequency and can usually be modeled as white noise.

Thermal Noise does not account for ALL of the noise in a system.  Rather, it represents the minimum amount of noise that will be found in an ideal system.  There are many other sources of noise present in electronic and optical communication systems that must be accommodated!

### Boltzmann Constant

Before we can go any further, we have to look at something called the Boltzmann constant.  This physical constant is the result of dividing the Gas constant R by Avogadro’s Constant NA and defines the linear ratio between the average kinetic energy of particles in a gas and the temperature of the gas.  If the temperature of the gas increases, the average kinetic energy of the particles of the gas increases by a linearly proportional amount!

“What on earth are we talking about gases for?” you might ask.  As it turns out, electrons inside a metallic conductor can be modeled as a gas!  The Boltzmann constant is defined in Joules per degree Kelvin and has a value of:

k =1.38064852 × 10-23 Joules/Kelvin

Going very much further into this topic is not for the faint of physics and is really beyond the scope of this post.

### Calculating Thermal Noise:

The video above has a great description of where thermal noise comes from and how we derive the formula:

P = kTB

where:

P = Thermal Noise Power in expressed in dBm (Decibels above a milliwatt)
k = Boltzmann Constant
T = Temperature in Kelvin (0° Celsius = 273° Kelvin)
B = System Bandwidth in Hz

## Non-ideal Filters

Remember that some systems do not use very high order filters.  This means that when we are looking at a band-limited system, it may be necessary to take into account the additional noise power introduced to the system by noise in the transition bands of the filters.  This information is referred to as the “Equivalent Noise Bandwidth“.

Thankfully, the filters used in modern digital communication systems are generally designed to have very small transition bands for the sake of spectral efficiency, and so we can generally treat this contribution as negligible.

### Problems:

1. Calculate the expected Thermal noise power for a Wi-Fi receiver, using a 20MHz wide channel at a temperature of 300° Kelvin.
2. Do the same calculation for the same Wi-Fi receiver, but using a 160MHz wide channel.
3. Do the same calculation for a standard GSM channel of 200kHz
4. Do the same for a LoRa channel (125MHz) and a Sigfox channel (100 Hz).

Completing the above calculations should tell you something about the Noise floor for each of these Radio technologies.

## Shot Noise

Shot noise is a result of the fluctuation in the rate of flow of individual electrons/photons in a system.  Shot Noise can only exist if there is an electrical current flowing in a device or in the case of an optical sensor, if there is a stream of photons arriving at the detector.  I really like the analogy to a series of raindrops falling on a tin roof given by Frank Rice in the American Journal of Physics.  The intervals between the arrival of the raindrops is actually random, thus the total water flowing onto the tin roof actually fluctuates around an average rate!

Shot noise can be naturally suppressed in some electronic components.  As noted in the article above, electrons tend to repel each other and obey the Pauli Exclusion principle.  This implies that it is unlikely to get large groups of electrons moving together through a system, and thus the noise currents due to shot noise will be naturally limited.  It is worthwhile to note from the article above, that photons do not have the same repulsive effect on each other and correlations between their movements can cause much higher shot noise.