4th Order LC-Based Sigma Delta Modulators

Due to the characteristic of narrow band conversion around a central radio frequency, the Sigma Delta Modulator (ΣΔM) based on LC resonators is a suitable option for use in Software-Defined Radio (SDR). However, some aspects of the topologies described in the state-of-the-art, such as noise and nonlinear sources, affect the performance of ΣΔM. This paper presents the design methodology of three high-order LC-Based single-block Sigma Delta Modulators. The method is based on the equivalence between continuous time and discrete time loop gain using a Finite Impulse Response Digital-to-Analog Converter (FIRDAC) through a numerical approach to defining the coefficients. The continuous bandpass LC ΣΔM simulations are performed at a center frequency of 432 MHz and a sampling frequency of 1.72 GHz. To the proposed modulators a maximum Signal-to-Noise Ratio (SNR) of 51.39 dB, 48.48 dB, and 46.50 dB in a 4 MHz bandwidth was achieved to respectively 4th Order Gm-LC ΣΔM, 4th Order Magnetically Coupled ΣΔM and 4th Order Capacitively Coupled ΣΔM.