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.