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Noise match is used for minimizing "Noise Factor" of an amplifier and gain match is used for maximizing the gain of an amplifier. However, for achieving a good noise factor for a multistage amplifier, you should you should consider noise match and gain match simultaneously. Power match is totally different from noise match and gain match in amplifiers and is used only for power amplifiers. You can learn matching details in the "Microwave Transistor Amplifiers" By Guillermo Gonzalez.
Yes, it is possible. You need to “modify” the transistor with a series or parallel feedback. Usually for the purpose the series feedback technique is used because the parallel one will bring much worse instabilities. You have to use an inductor (or a high characteristic impedance line) in the common node of the transistor (emitter or source). You can also use parallel feedback with a resistor in it but that will worsen the NF. It depends on what you want to achieve. Is you use the series feedback still watch for instabilities at higher frequencies though in the working band the k-factor will improve. Adding a inductor in the common node is a very good way to produce an oscillator. You can plot in a simulator the noise circles and the simultaneous match circles and you see and you add and increase the inductor that the optimum noise match will start moving towards the match circle and to the centre of the Smith Chart. Same applies for a parallel feedback. If you have to design amplifiers on a regular bases then I’ll recommend a specialized software – go to www.ampsa.com.
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