How noise limits performance; types of internal noise

How noise limits system performance

Noise is unwanted random energy added to the signal. It sets the basic limits of every communication system:

• Reduces SNR and fidelity: in analog systems the output becomes noisy (hiss, snow) and quality is poor.
• Causes bit errors in digital systems; the bit error rate depends on $E_b/N_0$.
• Limits range (sensitivity): a receiver cannot detect signals much weaker than its noise floor, so distance between repeaters is limited.
• Limits channel capacity: $C = B\log_2(1 + S/N)$; with finite SNR the data rate is limited.
• Forces more power or bandwidth: to overcome noise we need higher transmit power, bigger antennas, or wideband modulation, which increases cost.
• Noise in cascaded amplifiers accumulates (measured by noise figure), so the first stage must be low-noise.

Four types of internal noise

1. Thermal (Johnson / Nyquist) noise

• Cause: random motion of free electrons in any resistor or conductor due to heat (above 0 K).
• Noise power available: $P_n = kTB$; rms voltage $V_n = \sqrt{4kTBR}$, with $k = 1.38\times10^{-23}$ J/K, $T$ in kelvin, $B$ in Hz.
• It is white (flat PSD $N_0/2$ up to very high frequencies) and Gaussian. Reduced by lowering bandwidth, resistance or temperature.

2. Shot noise

• Cause: current in diodes, BJTs and vacuum tubes is a flow of discrete charges whose arrival times are random, so the current fluctuates around its average.
• rms noise current $I_n = \sqrt{2qI_{DC}B}$, where $q = 1.6\times10^{-19}$ C.
• Also white; sounds like lead shot falling on a metal sheet, hence the name.

3. Partition noise

• Cause: random division of current between two or more electrodes, e.g. emitter current splitting between base and collector in a BJT, or between screen grid and anode in a pentode.
• Larger in multi-grid tubes and BJTs than in diodes or FETs.

4. Flicker (1/f or excess) noise

• Cause: fluctuations in carrier density due to surface states, crystal defects and contamination in semiconductors and carbon resistors.
• PSD varies as $1/f$, so it is important below about 1 kHz (audio and DC amplifiers) and negligible at RF.

(Other internal noise: transit-time noise, which grows at very high frequencies when carrier transit time is comparable with the signal period.)