Noise transfer characteristics and design techniques of a frequency synthesizer

This paper presents an exact method for the loop parameters’ calculation. The noise transfer functions of PLL based synthesizers are derived in the z-domain analysis. Through the comparison of the s-domain model with the z-domain model, we show that the noise peak from inherent sampling behaviors always exists in the loop, and the loop filter with the wide loop bandwidth doesn’t suppress it. Such a noise peak causes instability to the system. A stability limit of the wide loop bandwidth frequency synthesizer is extracted by the behavioral simulation using the z-domain model, which depends on the phase margin and the ratio between the reference frequency and the loop bandwidth.