Digital Delta Sigma Modulator (DDSM) is responsible for generation of spurious tones at the output of fractional n frequency synthesizer due their inherent periodicity. This results in an impure output spectrum of frequency synthesizer when they are used to generate the fractional numbers in the divider of Phase Locked Loop (PLL) based frequency synthesizer. This paper presents the design of Error-Output feedback modulator based third order Multistage noise Shaping (MASH) structure with lesser hardware and effective error compensation network to break the underlying periodicity of DDSM. The DDSM is also analyzed by using non-shaped, shaped and selfdithering mechanism to achieve a pure output spectrum and reduced quantization noise.