Electronics/Noise in electronic circuits

Electrical Noise

any unwanted form of energy tending to interfere with the proper and easy reception and reproduction of wanted signals.

Classification

Based on Origin

1. External noise
   1. Atmospheric
   2. Extraterrestrial
      1. solar
      2. Cosmic
   3. Industrial
2. Internal noise
   1. Thermal Agitation Noise
   2. Shot Noise
   3. Transit Time Noise
   4. Flicker Noise
   5. Miscellaneous Sources

Thermal noise

Thermal Agitation Noise

Also known as Johnson noise or White noise.

$P_{n}\propto \ T\;\delta \!f=k\,T\;\delta \!f$

where k = Boltzmann's constant = 1.38x10^-23J/K

T = absolute temperature, K = 273 + °C

δ f = bandwidth of interest

P_n = maximum noise power output of a resistor

$P_{n}={\frac {V^{2}}{R_{L}}}={\frac {\left({\frac {V_{n}}{2}}\right)^{2}}{R}}={\frac {V_{n}^{2}}{4R}}$
$V_{n}^{2}=4RP_{n}=4RkT\;\delta \!f$
$V_{n}={\sqrt {4kT\;\delta \!f\;R}}$

Shot Noise

$i_{n}={\sqrt {2ei_{p}\;\delta \!f}}$

where i_n = r.m.s. shot-noise current

e = charge of an electron = 1.6x10^-19C

i_p = direct diode current

δ f = bandwidth of system

Noise Calculations

Addition due to several sources

noise voltages:

$V_{n}1={\sqrt {4kT\,\delta \!f\,R_{1}}}$, $V_{n}2={\sqrt {4kT\,\delta \!f\,R_{2}}}$...and so on, then

$V_{n,tot}={\sqrt {{V_{n}1^{2}}+{V_{n}2^{2}}+...}}={\sqrt {4kT\,\delta \!f\,R_{tot}}}$

where R_tot = R₁+R₂+...

Addition due to Cascaded Amplifier stages

R_eq = R₁+R'₂
$R_{eq}=R_{1}+{\frac {R_{2}}{A_{1}^{2}}}+{\frac {R_{3}}{{A_{1}^{2}}{A_{2}^{2}}}}$

Analog Noise Models

Methods of reducing noise

Differential signaling

Differential signaling is a method of transmitting information electrically by means of two complementary signals sent on two separate wires. The technique can be used for both analogue signaling, as in some audio systems, and digital signaling, as in RS-422, RS-485, PCI Express and USB.

Good grounding

An ideal signal ground maintains zero voltage regardless of how much electrical current flows into ground or out of ground.

When low-level signals travel near high currents, their return currents shouldn't be allowed to flow in the same conductor. Otherwise, noise such as AC ripple on the high current will modulate the low-level signal.

References

Kennedy, George 'Electronic Communication Systems' , 3^rd Ed. ISBN 0-07-034054-4