 Power and power-gains are two main considerations in the design of a microwave transistor amplifier. To derive power and power-gains using traveling waves concept, we need to determine the reflection coefficients in the form of traveling waves and S parameters.

 the source and the load reflection coefficient in a Z 0 system are  For the transistor, the input and output traveling waves measured in a Z 0 system are related by

 The concepts of a reflection coefficient and traveling waves can be used even if there are no transmission lines at port 1 and port 2.  We can show that the input reflection coefficient

 For the output reflection coefficient:

and can be shown in terms of S parameters as and where

 The power available from the source is equal to the input power when  IN =  S * and can be expressed as  We can also express P IN in the form or P IN = P AVS M S

where M S is the source mismatch factor which is equal to

 The power delivered to the load Z L is and can be shown in terms of S parameters as and where

 The power available from the network P AVN is equal to the power delivered to the load when  L =  OUT * and can be expressed as  We can also express P L in the form or P L = P AVN M L

where M L is the load mismatch factor which is equal to

 The power gain G P is given by  The transducer power gain G T is given by

Manipulating the denominator, G T can be also written in the form  The unilateral power gain G TU is an often employed approximation for the transducer power gain. G TU which neglects the feedback effect of the amplifier (S 12 = 0) can be expressed as

 The available power gain G A can be expressed in the form

,the input side of the amplifier is connected to a voltage source with E 1 = 10 V and source impedance Z S = 50 . The output is connected to a load which also has an impedance Z L = 50 , given find the following quantities: a) transducer power gain G T, unilateral transducer gain G TU, available power gain G A, and operating power gain G P. b) power delivered to the load P L, power available from the source P AVS, and input power P IN.

 In a two-port network, oscillations are possible when either input or output port represents a negative resistance. This occurs when or  For a unilateral device (S 12 = 0), the oscillations occur when or.

 The two-port network is unconditionally stable if the real parts of Z IN and Z OUT are greater than zero for all passive load and source impedances. (1) (2) (3) (4) Note: all coefficients are normalized to the same characteristic impedance Z 0.

 This happens when some passive source and load terminations (some but not all values of  S and  L ) produce input and output impedances having a negative real part.

 The graphical analysis is useful in the analysis of potentially unstable transistors. First, the regions where values of  S and  L produce and are determined, respectively. The solutions for  S and  L lie on circles (called stability circles) whose equations are given by and

 The radii and centers of the circles where and in the  L plane and  S plane, respectively, are obtained, namely  L values for (Output Stability Circle): radius center

  S values for (Input Stability Circle): radius center where  = S 11 S 22 -S 12 S 21.

(a)  L plane (b)  S plane

 The region where values of  L (where ) produce are the stable regions.

 The region where values of  S (where ) produce are the stable regions.

K > 1 where and. or K > 1 and

 From practical point of view, most microwave transistors produced by manufacturers are either unconditionally stable or potentially unstable with 0< K < 1 and. Conditions for unconditionally stability for  L plane and  s plane.

Determine the stability. If the transistor is potentially unstable at a given frequency, draw the input and output stability circles. f (GHz)S 11 S 12 S 21 S

 Even when the selection of  S and  L produces or, the circuit can be made stable if Re(Z S +Z IN ) > 0 and Re(Z L +Z OUT ) > 0  A potentially unstable transistor can be made unconditionally stable by either resistively loading the transistor or by adding negative feedback. These techniques are not recommended in narrowband amplifiers.