Abstract-A compact microstrip rat-race coupler is proposed with a new phase inverter which is realized by a modified Lange coupling structure with a slotted ground plane and a floating-potential conductor. Based on the even-and odd-mode theory, its parameters are generally synthesized. In order to further miniaturize the rat-race coupler, a T-shaped line is utilized. A prototype operating at 2.0 GHz is designed and fabricated for verification. The circumference of our proposed rat-race coupler is only 0.52λ. Its in-phase and out-of-phase bandwidths are also enhanced, with reasonable agreement obtained between its simulated and measured S-parameters.

Abstract-Electrothermal effects in various through silicon via (TSV) arrays are investigated in this paper. An equivalent lumped-element circuit model of a TSV pair is derived. The temperature-dependent TSV capacitance, silicon substrate capacitance and conductance are examined for low-, medium-, and high-resistivity silicon substrates, respectively. The partial-element equivalent-circuit (PEEC) method is employed for calculating per-unit-length (p.u.l.) resistance, inductance, insertion loss and characteristic impedances of copper and polycrystalline silicon (poly-Si) TSV arrays, and their frequencyand temperature-dependent characteristics are treated rigorously. The modified time-domain finite-element method (TD-FEM), in the presence of a set of periodic differential-mode voltage pulses, is also employed for studying transient electrothermal responses of 4-and 5-TSV arrays made of different materials, with their maximum temperatures and thermal crosstalk characterized thoroughly.