Advanced Frequency Synthesis by Phase Lock

CHAPTER 4

DEFECTS IN ΣΔ SYNTHESIZERS

In this chapter, we consider the effects of some of the imperfections that can occur in the implementation of a ΣΔ frequency synthesizer. To do this, we will first create theoretical noise models, adding quantization noise to sources such as those that we studied in Sections F.3.8 and F.3.9 and combining them all in several synthesizer loops in order to study how they affect the output PPSD. This is similar to what we did in Section F.3.10, except for the addition of quantization noise. We will also use noise levels here that are appropriate for available ICs. Then, we will consider how additional noise sources that are related to ΣΔ synthesis affect the closed loop performance of our models.

4.1   NOISE MODELS

4.1.1   VCO Noise

Figure O.1 (Appendix O) is a plot of oscillator spectrums. It joins the plots of Fig. F.3.38a–e. Recall that the plots are normalized in the way they are because they tend to fall −20 dB/decade to a noise floor with the break at

where f_osc is the oscillator's frequency and Q is the loaded Q. Therefore, if we plot against f_m/f_osc, oscillators with similar noise floors and Q’s will have similar S_φ in their −20 dB/decade regions, regardless of the value of f_osc. This helps us scale the curves for different frequencies.

Curves 1a and 10 bracket most of the noise curves in Fig. F.3.38a–e and form “points-of-reference” between ...