Spectral shaping by generalized transfer function design in frequency modulation ΣΔ synthesizers

A new straightforward ΣΔ-fractional-N modulation-loop design methodology is proposed in this paper. In contrast to present design approaches the closed loop transfer function can be used for pulse forming. An algorithm is presented which allows loop filter design based on the desired transfer function shaping. Using this technique, a closed loop modulation with low reference frequency for Bluetooth can be achieved without the need for predistortion. Using a 5^th order loop filter, the ΣΔ modulator of order three will maintain the required noise specifications for the commonly used 13 MHz reference frequency. The resulting simulated total phase noise is as low as -111 dBc/Hz at 1.5 MHz and -132 dBc/Hz at 2.5 MHz.