# For example in low noise amplifiers noise depends

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For example in low noise amplifiers noise depends mostly on gamma S rather than gamma L so noise depends mostly on gamma S. Here the gamma L that is the Output impedance of the amplifier is already fixed but to (con) obtain the optimum noise figure we can modify gamma S. On the other hand if we consider power amplifiers for these amplifiers the source is already fixed so we can’t change anything in the source gamma S but gamma L cab be designed to obtain the appropriate power gain.
12 2 2 2 21 2 2 11 22 0 0 1 1 1 1 S L T S L S L S G S S S G G G     Now let us consider the case as I said even though GT is not useful for designing an amplifier we can consider some special cases one of them is what is known as the unilateral case. Unilateral case means S12 is equal to 0 and this assumption is not that par to S because most amplifiers the reverse transmission coefficient is indeed very low it has to be low otherwise power will keep flowing back we don’t want that we want power to always flow from input to Output. W e don’t want the power to flow back from the Output to the input so this is a somewhat valid somewhat valid assumption though in most amplifiers it is not so low it is not 0 but it is a low value. But then by making this assumption we get some very it makes our life of the designer much easier, how does it make it easier. Because see now the expression for GT becomes 1 minus S22 gamma SL whole square. As you can see it is now there is no gamma OUT or gamma IN term here it is purely a function of gamma S and gamma L and so these terms are can be considered as gain term. If you want in fact we can write it like this this is equal to GS multiplied by G0 multiplied by GL so his GS is the source gain gain due to the source network S21 is the gain due to the inherent or this S parameters of the network and GL is the gain due to the load network. * 11 * 22 2 21 2 2 11 22 when, 1 1 = 1 1 S L T TU S S G G S S S We see that when gamma S is equal to S11 conjugate and gamma L is equal to S22 conjugate then this GT which is its maximum value which I call GTU max. This U represents unilateral so this comes equal to I upon 1 minus S11 whole square, S21 whole square. So this is GS max and G Smax is equal to this value and GLmax is equal to this value.
12 2 2 2 21 2 2 11 22 0 0 1 1 1 1 S L T S L S L S G S S S G G G     So this is the unilateral design case and as we shall see later when we discuss about gain circles that we the locus of a (lo) of (G) of gamma S or gamma L which gives a constant value of this GS or GL will be circles so this is the equation that we just discussed GTU or unilateral gain and the locus of gamma S that gives a constant value of this GS is the circles similarly the locus of gamma L which gives the constant value of this GL will also be a circle. We shall discuss this when we are when we discuss about the amplifier gain circles.