Noise, interference, distortion; thermal and high frequency noise

Definitions

• Noise: random, unwanted electrical signals (from natural or electronic sources) that add to the wanted signal, e.g. thermal noise in resistors, shot noise in transistors, atmospheric static.
• Interference: contamination by unwanted signals from other man-made sources, usually other transmitters or electrical machines, e.g. a neighbouring radio station, power-line hum, crosstalk between wires.
• Distortion: alteration of the signal waveform caused by the imperfect response of the system itself (channel, amplifier, filter), e.g. clipping in an amplifier, unequal attenuation of frequencies in a cable. It disappears when the signal is switched off.

Effects in communication

• Noise lowers the signal-to-noise ratio, causing hiss in analog systems and bit errors in digital systems; it sets the minimum detectable signal and limits range and channel capacity ($C=B\log_2(1+S/N)$).
• Interference produces crosstalk, whistles and unwanted programmes; it limits frequency reuse and needs filtering, shielding and frequency planning.
• Distortion changes the waveform shape, causes intersymbol interference (ISI) in digital links and poor fidelity in audio; it can be reduced by equalizers.

Thermal noise

Thermal (Johnson or Nyquist) noise is produced by the random motion of free electrons in any conductor or resistor above absolute zero. Its power is proportional to absolute temperature and bandwidth, and its spectrum is flat (white) up to very high frequencies:

$$P_n=kTB,\qquad V_{n(rms)}=\sqrt{4kTBR}$$

where $k=1.38\times10^{-23}$ J/K, $T$ in kelvin, $B$ in Hz. Example: $R=1\ \text{k}\Omega$, $T=290$ K, $B=10$ kHz gives $V_n\approx0.4\ \mu\text{V}$.

High-frequency (transit-time) noise

At very high frequencies, the time taken by carriers (electrons or holes) to travel from input to output of a device, e.g. emitter to collector of a transistor, becomes comparable to the period of the signal. Some carriers then diffuse back toward the input, producing an input admittance whose conductive part grows with frequency and creates random noise currents. This transit-time noise increases rapidly above a cut-off frequency, which is why every active device has an upper usable frequency and why microwave receivers use special low-noise devices.