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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 (~ 64% 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 6- ~ 7-dB 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-μm 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.