A Chebyshev-Response Step-Impedance Phase-Inverter Rat-Race Coupler Directly on Lossy Silicon Substrate and Its Gilbert Mixer Application

Abstract

This paper focuses on the analysis and the design methodology of the step-impedance phase-inverter rat-race coupler on a silicon-based process. The issues of impedance limitation and bandwidth are discussed in detail. Our proposed concept utilizes a high silicon dielectric constant, phase-inverter structure, step-impedance technique, and Chebyshev response to make the rat-race coupler more compact ( <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\sim \!{\hbox {64}}\%$</tex></formula> reduction) and highly balanced over a wide operating bandwidth. Moreover, the inter-digital coplanar stripline used in the step-impedance section effectively reduces the characteristic impedance of the transmission line for large size shrinkage and insertion-loss reduction. The demonstrated step-impedance rat-race coupler directly on silicon substrate has <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\hbox {6-}}\sim {\hbox {7-}}{\hbox {dB}}$</tex></formula> insertion loss from 5 to 15 GHz and small variations in amplitude/phase balance. Compared with our previous work, the proposed rat-race coupler achieves a 3-dB improvement in the insertion loss. Thus, a 0.13- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu{\hbox {m}}$</tex></formula> CMOS Gilbert down-converter with a miniature phase-inverter rat-race coupler at the RF path for wideband single-to-differential signal conversion achieves a noise figure of 16 dB.