# Noise Parameters

Having the noise wave correlation matrix, one can easily compute the noise parameters [5]. The following equations calculate them with regard to port 1 (input) and port 2 (output). (If one uses an n-port and want to calculate the noise parameters regarding to other ports, one has to replace the index numbers of S- and c-parameters accordingly. I.e. replace "1" with the number of the input port and "2" with the number of the output port.)

Noise figure:

 (2.4)

 dB (2.5)

Optimal source reflection coefficient (normalized according to the input port impedance):

 (2.6)

With

 Re (2.7)

 (2.8)

Minimum noise figure:

 (2.9)

 (2.10)

Equivalent noise resistance:

 (2.11)

 With internal impedance of input port Boltzmann constant J/K standard temperature K

Calculating the noise wave correlation coefficients from the noise parameters is straightforward as well.

 (2.12)

 (2.13)

 (2.14)

with

 (2.15)

Once having the noise parameters, one can calculate the noise figure for every source admittance , source impedance , or source reflection coefficient .

 (2.16) (2.17) (2.18) (2.19) (2.20) (2.21)

Where and are the signal to noise ratios at the input and output, respectively, is the equivalent (input) noise temperature. Note that does not equal .

All curves with constant noise figures are circles (in all planes, i.e. impedance, admittance and reflection coefficient). A circle in the reflection coefficient plane has the following parameters.

center point:

 (2.22)