A Unity Feedback Length-Extend Delta-Sigma Modulator for Fractional-N Frequency Synthesizer

A unity feedback length-extend multistage noise-shaping (MASH) delta-sigma modulator (DSM) is presented in this paper. The proposed length extension technique adds a feedback path, like HK-MASH, and fixes the feedback factor to unity. In this way, only one additional register is needed, which decreases the operating time and the hardware cost of DSM, and achieves maximum sequence length of M-1 ($M = {2^{{n_0}}}$, n
0
is input word length). Using this structure, MASH DSMs are optimized with maximum sequence length extending to (M-1)
^l
( l is the order of the MASH DSM) and the minimum extending to N(M-1)
^l-1
( N is the smallest prime number of M-1). This paper proves that the output sequence length is exponentially increased, regardless of the input value. Compared with classical structure, the proposed MASH 1-1-1 structure shows a spur-free performance at the expense of limited hardware cost.