Gain gradients applied to optimization of distributed‐parameter matching circuits for a microwave transistor subject to its potential performance

In this article, a rigorous design procedure is carried out for a microwave amplifier by employing the Feasible Design Space and simple analytical gain gradients of the matching circuits. Physical lengths and characteristic impedances of the transmission lines used in the matching circuits are chosen as the design variables and their lower and upper limits are bounded by the limits of the planar transmission line technology so that resulted microwave amplifier can be realized by this technology. Feasible Design Target Space is determined by the compatible performance [noise (F), input VSWR (V_i), gain (G_T)] triplets and their source Z_S(ω_i) and load Z_L(ω_i) terminations resulted from the performance characterization of the active device. These triplets take into account the physical limitations of the device and realization conditions so that F_req ≥ F_min, V_ireq ≥ 1, G_{T min} ≤ G_{T req} ≤ G_{T max}; and Z_S(ω_i) and Z_L(ω_i) terminations be taken place within the “Unconditionally Stable Working Area”. Design of the amplifier for the compatible performance triplets is reduced to the design of the Z_S(ω_i) and Z_L(ω_i), i = 1…N terminations, which is achieved by the gain optimization of the two passive, reciprocal matching two‐ports using the Darlington theorem. Analytical expressions of the gain gradients of the matching circuits are obtained by the two different methods: (i) chain sensitivity matrix approach; (ii) adjoint network approach. Gain gradients of the L‐, T‐, and Π‐types of distributed‐parameter matching circuits are obtained as worked examples. Then typical design examples are given with together the synthesized, target, simulated characteristics. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.