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:

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:

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) |

radius:

(2.23) |

with

(2.24) |

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