As with the development of the wireless telecommunications technologies, the demands of mobile applications by consumers and the robust network bandwidth management by supplier increases explosively, speeds up the adoption and deployment of 4G network in recent years, which benefits from its high speed, relative low cost and high security. To catch up with such requirements of 4G, the most important interface, analog-to-digital converter, inside the 4G network is constantly being improved. One most suitable type of ADCs for such high speed is sigma-delta modulator, with the attractive property of noise shaping performance. In this thesis, I will focus on this property to improve, meanwhile to overcome some limitations of the old methods. The first part is based on the zero optimization method. One new loop filter structure is designed with the relaxed zero shifting feedback coefficient. This proposed structure couples one local positive feedback with 2 negative feedbacks to balance the NTF. The same zero optimization performance is achieved with a more comfortable value of feedback by several times, which makes the circuit realization much easier. The second part is based on the order increasing method. To release the power budget, VCO-based SDM for multi-bit quantization is selected. In case of high resolution, The proposed structure with VCO-assisted VCO-based quantizer is designed for reducing the nonlinearity of VCO itself, while maintaining the implicit DEM function and intrinsic additional first order noise shaping performance of VCO-based quantizer.