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Following the trend in portable wireless communications, this dissertation explores new approaches to designing of power-critical building blocks in the elementary circuit level. Specifically, the work focuses on designs of baseband continuous-time Gm-C filter, LC-resonator quadrature oscillators, transistor-only quadrature oscillators and LC-resonator frequency dividers. The established circuits share a common design objective of low-power and low-voltage operation, where the simplicity of the demonstrated topologies serves as a basis. The dissertation is separated in two parts. The first part is dedicated for the baseband section where a 3rd-order Bessel filter is designed and fabricated. The filter comprises a set of linear transconductors, which each one is based on the operation of triode-biased transistors. According to the operation in this region and to the simplicity of the transconductor, high dynamic range can be achieved for a supply voltage as low as 1.2 V. In the other part, attempts in reducing the power consumption of two critical building blocks in a frequency synthesizer, namely, the quadrature oscillator and the first-stage frequency divider, are introduced. For the oscillators, two quadrature oscillators based on LC resonators are presented, in conjunction with a transistor-only quadrature oscillator. Quadrature signal generations in these designs are achieved by making use of the principles of ring oscillator and coupled oscillator. The last building block that is designed in this part is the LC-based injection-locked frequency divider. The single-ended Colpitts oscillator topology is used as the core circuit of the divider due to its simplicity and low-voltage property. Detailed analysis concerning the phase relationship between the input and the output leads to the implementations of differential and quadrature divider configurations. Although a silicon integration is done only for the baseband filter, the concept, the operation and the theories developed for the quadrature oscillators and the frequency dividers have been verified against simulations and measurements employing low-frequency discrete prototypes. As they are illustrated in each chapter, the established theories match closely to the measurements.