JNTU B.Tech II PRINCIPLES OF COMMUNICATIONS Previous Question Paper (November/December - 2020 - R13)

Effective noise temperature (T_e) is a hypothetical temperature that, when assigned to the input of a noiseless version of a system, would produce the same noise power at the output as the actual system. It is defined by the relationship P_n = k T_e B G, where k is Boltzmann's constant, B is bandwidth, and G is gain. It provides a convenient way to quantify the noise performance of components like antennas and amplifiers.

Noise figure (F) is a measure of the degradation of the signal-to-noise ratio (SNR) as a signal passes through a system. It is defined as the ratio of the input SNR to the output SNR: F = (S_i/N_i) / (S_o/N_o). Expressed in decibels, the noise figure is NF = 10 log₁₀(F). A noiseless system has a noise figure of 1 (0 dB). The relationship between noise figure and effective noise temperature is given by T_e = T₀(F - 1), where T₀ is the standard reference temperature (typically 290 K).

Noise in linear systems is calculated by modeling the system as a cascade of stages, where each stage contributes its own noise. For a single linear component, the output noise power is calculated as N_o = G N_i + N_add, where G is the available gain, N_i is the input noise, and N_add is the noise added by the system itself.

For a cascade of n stages, the total effective noise temperature (T_e) is determined by the Friis formula for noise temperature:

Similarly, the total noise factor (F_total) of a cascaded system is calculated using the Friis formula for noise factor:

These formulas demonstrate that the noise performance of a cascaded system is dominated by the first stage, as its noise contribution is not attenuated by any preceding gain, while the noise contributions of subsequent stages are reduced by the gains of the stages preceding them.