# Classical Noise Analysis of a Two-Port Network 1 comment

A noisy two port network can be represented by a noiseless two port network along with noise sources referred to input. Figure 1 illustrates the noiseless two port network with noise sources referred to input.

• The input is represented by it’s Norton equivalent – current source( ) in parallel with source admittance ( )
• Input referred noise sources and have correlated components
• is uncorrelated with and The noise factor for this two port network can be expressed as

(1) By splitting the input referred noise into uncorrelated and correlated components, . Now we can related the correlated component ( ) to with correlation admittance as .

Substituting in Eq-(1), we get

(2) These noise sources are now uncorrelated, can be treated as thermal noise sources with equivalent thermal noise resistance given by

(3) Substituting Eq-(3) in Eq-(2),

(4) The noise factor of the two-port network (from Eq-(4) ) characterized by , , and is also a function of source admittance( and ). So the noise factor of network is minimized by right selection of source admittance .

The noise factor as a function of is minimum when .

The condition for minimizing noise factor w.r.t is given by (5) The solution for minimum noise figure is

(6) The minimum noise figure is given by

(7) If source impedance , then noise factor is given by

(8) For maximum power transfer , but for minimum or optimum noise figure . Therefore the noise match does not correspond to the power match, and thus a compromise is necessary to find the best performance.

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## One thought on “Classical Noise Analysis of a Two-Port Network”

• ShihHsing Chen