## A theory of noisy two-port networksIN ORDER TO OVEROME THE LAC OF SPECIFIC INFORMATION ABOUT THE NOISE PROPERTIES OF ACTIVE ELEMENTS, A STUDY OF NOISY ELECTRICAL NETWORKS IS PRESENTED, WHICH USES A MODEL THAT DESCRIBES THE TOTAL NETWORK NOISE BY MEANS OF EQUIVALENT NOISE GENERATORS AT THE SEVERAL ACCESSIBLE TERMINAL-PAIRS. The parameters of the generators are shown to be obtainable by measurements performed at these terminal pairs. Both time- and frequency-domain representations are given. A frequency-domain correlation function is introduced, which is shown to provide a complete description of the correlation between equvalent noise generators, and an experimental procedure for determining this function is presented. Two performance criteria for assessing the degree to which noise disturbs the desired operation of a network are discussed. The noise measure, which is related to the conventional noise figure, is shown to be a useful gauge of network performance when the applied input signal is not noisy. Minimizing the noise measure at each frequency of a frequency band is not always possible, so that it use is restriced to single-frequency amplifiers. Use of the meansquare error of the network as a performance criterion is discussed. (Author). |

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### Contents

SPECIFICATION OF NOISE PROPERTIES OF LINEAR | 4 |

PERFORMANCE MEASURES FOR LINEAR NOISY SYSTEMS | 24 |

MEANSQUARE ERROR OPTIMIZATION PROCEDURE | 30 |

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### Common terms and phrases

active elements actual network admittance matrix cascaded system CD CD CD CO CD Chapter compensation network comPlex correlation condition constant multiplier constraint CORRELATED NOISE defined denotes determined domain driving-point and transfer ed(t eigenvalues eQ(t equivalent noise expression filter input Fourier transform frequency-domain correlation function G(jw given gives gQ(r hence impedance matrix independent Lagrange multipliers left-half-plane poles LINEAR NOISY NETWORK mean-square error criterion minimal minimum error minimum mean-square error n-terminal-pair network network synthesis noise behavior noise figure noise matrix noise measure noise power noise properties noise sources noise temperature NOISY AMPLIFIER noisy two-port network obtained oo oo oo optimum network functions output parameters performance criterion phase shift positive real power spectra problem quantities random signals rational function representation result shown in Figure spectrum standard network stationary values substitution of Equation terminal pairs transfer characteristic transfer functions unilateral voltage yields zero