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We report a systematic investigation and design optimization of CMOS-compatible on-chip ferrite-integrated inductors, including a detailed quantitative analysis by simulation and circuit modeling, new ferrite material fabrication and characterization, and ferrite-integrated-inductor design, characterization, and optimization. A new ferrite nanopowder-mixed-photoresist spin-coating/inkjetting technique is discussed. The design and characterization of ferrite-integrated inductors with various ferrite-filling structures are presented. Measurement shows substantial improvement of up to +160% in inductance (L) and + 220% in quality factor (Q) across the multigigahertz frequency spectrum with a self-resonance frequency (f 0) of over 20 GHz for the new ferrite-integrated inductors. This paper clearly suggests that the new ferrite-integrated-inductor technique is a potentially viable solution to the realization of radio-frequency systems-on-a-chip requiring high-performance compact on-chip inductors. This work is presented in two parts. This paper is Part I, discussing the design and simulation of ferrite-integrated inductors. Part II discusses the experimental work, including material research and device implementation.