These are brief (over-simplified) summary notes on noise as it pertains to electronic circuits (for personal future reference only).

Content credits include (use these as factual references instead):

## What is noise?

Spontaneous “random” fluctuations – statistical fluctuations – that give rise to electrical noise in a circuit.

Spectral densities are commonly used to specify noise parameters in a circuit or electronic component.

Voltage noise is usually provided in a voltage-spectral-density graph, and is usually expressed as noise-voltage per root Hz `nV/sqrt(Hz)`.

Current noise is usually provided in a current-spectral-density graph, and is usually expressed as noise-current per root Hz `nA/sqrt(Hz)`.

Alternatively, a single noise-voltage or noise-current can be provided together with the frequency bandwidth of operation for the circuit/component.

## Power Spectral Density (PSD) or Spectrum of Noise

We can provide a PSD to provide a measure of circuit noise in function/graphical form.

In general, the power spectral density (PSD) tells us how much power the signal carries in a small bandwidth around each frequency, or loosely the power at every frequency for our noise signal.

## Integrated Noise

To specify a single noise figure of merit: We can provide a noise-voltage or noise-current, but we must also specify a frequency bandwidth of operation for the circuit.

This is because noise adds-up (integrates) over frequency (a larger bandwidth will lead to a greater noise figure). In practice the characteristic equations that identify noise sources are always integrated over frequency.

To determine the noise of a circuit over a given frequency band, the beginning and ending frequencies are used as the integration limits for the PSD integral.

## External Noise Sources

### Thermal Noise: Resistors

All resistances act as noise sources due to the thermal movement of charge carriers (Brownian Motion), This is called “Johnson Noise” or “Thermal Noise”.

This noise increases with resistance, temperature, and bandwidth.

For an ideal resistor (constant resistance over bandwidth):

Voltage Thermal Noise

``````Vn = Sqrt(4*K*T*B*R)
``````

This agrees with practical experience, e.g:

• In low-power circuit design greater resistance values are often desirable (to limit current consumption), however this leads to a degradation in voltage noise figures. (as can be seen above)

• The same can be said of circuits operating at higher temperatures (which is sometimes necessary) or over a very large frequency range (which is sometimes desirable).

Current Thermal Noise

``````In = Sqrt(4*K*T*B/R)
``````

Where:

``````K = Boltzmann Constant (Joules/Kelvin)
T = Temperature (Kelvin)
B = Bandwidth (Hz)
R = Resistance (Ohms)
``````

Keep in mind: All resistors in a circuit generate noise. However, in practice, only resistors in the input and feedback paths (typically in high gain configurations) are likely to have an appreciable effect on total circuit noise.

## Internal Noise Sources

Taking amplifier circuits as a reference example

Noise appearing at the amplifier’s output is usually measured as a voltage. However it is generated by both voltage and current sources.

### Input-referred Noise

All internal sources are generally referred to the input: treated as uncorrelated or independent random noise generators in series (or in parallel) with the inputs of an ideal noise-free amplifier.

It is a little complex concept to grasp, but here is an example:

Assume you have a noisy amplifier: It adds some noise to the signal (which itself might have some initial noise on it).

You measure the total output noise V_no.

Now, imagine the amplifier being noiseless.

What is the amount of noise V_ni that should be present at the input of this noiseless amplifier to get the same output noise V_no?

This is called input-referred-noise

It is a useful metric to be able to compare noise figures among different circuits/components.

Schematic Drawing here.

Internal noise sources are:

• Randomly distributed and/or
• Exhibit Gaussian distribution behavior

Amplifiers’ noise falls into 4 different categories:

• Input-referred voltage noise (nV/sqrt(Hz))
• Input-referred current noise (nA/sqrt(Hz))
• Flicker noise
• Popcorn noise

#### Flicker Noise

The noise of Op Amps is in general Gaussian with constant spectral density (white noise) over a wide range of frequencies.

However, as frequency decreases, the spectral density starts to rise at a rate of about 3dB per octave for CMOS amplifiers. This is due to the fabrication process,the IC device type and layout.

This “low-frequency-noise” characteristic is known as flicker noise. It is also called 1/f noise because the noise PSD goes inversely with frequency – it has a -1 slope in a log plot.

The frequency at which an extrapolated -3dB per octave spectral density line intersects the broadband constant spectral density value is known as the 1/f corner frequency: This is a figure of merit for the amplifier.

#### Popcorn Noise

Minor source of noise (not usually advertised)

An abrupt shift in offset voltage/current lasting for several milliseconds with amplitudes from uV to hundreds of uV. This “burst” or “pop” is random in nature.

Low temperature and high source resistances usually produce the most favourable conditions for popcorn noise.

Although the root cause of popcorn noise is not absolute, both metallic contamination and internal or surface defects in the silicon lattice can cause popcorn noise in ICs.

In modern semiconductor processes, considerable work has been done to reduce the onset of popcorn noise.