The Structure Spuriousness of MASH Model in Σ-Δ Modulation

Σ-Δmodulation fractional division frequency synthesizer moves the spectrum of quantization noise to the high frequency using noise shaping technology and suppresses the high frequency noise using the low-pass characteristic of phase-locked loop. This technology has not only realized the fine stepping of phase-locked loop output frequency, but also solved the mantissa modulation problems of the fractional division. However, all Σ-Δmodulators are finite state machines. In some specific input case, a unique hybrid spread spectrum, also known as Σ-Δmodulator structure spuriousness, will be created. This paper introduces structure spuriousness of MASH model in Σ-Δmodulation, deduces the output sequence length relations of 1st order, 2nd order and 3st order MASH model in detail. It reveals that the sequence length is closely related to the input value and the initial value of accumulators. An effective method is achieved to avoid short sequence length, which effectively eliminate structure spuriousness. The study provides a theoretical basis for the design of high performance Σ-Δ modulation fractional N frequency synthesizer. The analytical method adopted is also suitable for the analysis of the spuriousness analysis of other new modulator structures, and is of great significance.