Distributed Matching Network Design

OBJECTIVE:

BUILD MATCHING NETWORKS FOR A NE$661$MO$4$ DEVICE AT $3$GHZ BY REPLACING THE ATF$551$M$4$ DEVICE. RETAIN THE TL AND STUB CONFIGURATIONS. REPORT THE MAXIMUM UNILATERAL, MAXIMUM AVAILABLE, AND MAXIMUM STABLE GAINS.

FOR THE DISTRIBUTED MATCHING NETWORKS YOU ARE ASKED TO DETERMINE: TRACE WIDTHS, L$1,$ S$1,$ L$2,$ S$2,$ AND THE $\frac{}{4}$ LENGTH.

Note: Please detail all computational steps, and substantiate the design by verifying your results in the Smith Chart. Make reasonable, engineering approximations $($for instance, use the unilateral design for the matching network layout$).$

GIVEN:

A$)$ The active device involves an RF npn BJT device by NEC $($NE$661$M$04)$ with a transition frequency $f_T$ of $25$ GHz and a power gain rating that is listed at $3$ GHz as $G_0=13\mathrm{.}6dB$ at a collect emitter voltage $V_{CE}=2V,$ collector current $I_C=5mA.$ The goal of this design is to develop matching networks such that maximum gain can be achieved while maintaining stability. The data sheet for the packaged device $($SOT$-343)$ and for the above $V_{CE},I_C,$ and f lists the following S$-$parameters:

$S_{11}=0\mathrm{.}345$exp$(-j{124\mathrm{.}2}^0),S_{21}=4\mathrm{.}809$exp$(j{67\mathrm{.}8}^0),$

$S_{12}=0\mathrm{.}050$exp$(j{34\mathrm{.}7}^0),S_{22}=0\mathrm{.}649$exp$(-j{68}^0)$

B$)$ The board material is FR$4$ with $30$mil$(0\mathrm{.}762mm)$ thickness and relative dielectric constant of ${}_r=4\mathrm{.}4.$