Net\vork Realization 

 of Optimum Amplifier 

 Noise Performance 



In Chap. 6 we have shown that the excess-noise figure of an amplifier 

 with a high gain cannot be less than Me,opt, 



^.,ope = ^^ (6.32) 



where Xi is the smallest positive eigenvalue of the characteristic-noise 

 matrix. We also showed that an arbitrary lossless or passive interconnec- 

 tion of two-terminal-pair amplifiers, which leads to a new two-terminal- 

 pair amplifier, yields an excess-noise figure at high gain that is higher than, 

 or at best equal to, the ikfg, opt of the best ampHfier used in the inter- 

 connection. These proofs established the quantity Me,opt as a lower 

 bound on the noise performance of a two-terminal-pair amplifier. 



In this chapter we shall show that the lower bound Me, opt on the excess- 

 noise figure at high gain can always be realized. Specifically, we shall 

 show that the minimum positive noise measure Me,opt of any two- 

 terminal-pair amplifier can be achieved by suitable external network 

 operations, which, however, do not usually result in an amplifier with a 

 high gain. Nevertheless, the source impedance, and the ampHfier output 

 impedance with the source connected, will always have positive real parts 

 in the realizations of Me,opt presented. It follows that an amplifier with 

 an arbitrarily high gain can be constructed by cascading identical, 

 optimized amplifiers that have appropriate impedance-transformation 

 networks between the stages. By an adjustment of the transformation 

 networks, the optimum noise measure of the cascade can be made equal 

 to the Me,opt of the individual amplifiers in the cascade, as explained in 



58 



