**Author details**

420 MATLAB – A Fundamental Tool for Scientific Computing and Engineering Applications – Volume 1

**Figure 22.** IBJN plots for the ΔƩ modulator in Figure 18 using different DAC types.

In this chapter, the effects of clock-jitter in the sampling-clocks of ΔƩ modulators are analyzed and studied in details. The critical sources of jitter induced errors in a ΔƩ loop are discussed for ΔƩ modulators with DT and CT loop filters. The comparison between DT and CT modulators showed that CT architectures are more sensitive to clock-jitter than DT counterparts due to PWJ in the feedback signal caused by clock-jitter in the DAC samplingclock. In essence, PWJ in the feedback waveform entails random phase-modulation that folds back high-pass shaped noise components over the desired channel bandwidth. Thus, a detailed analysis for the sensitivities of various signal waveforms provided by different types of CT DACs to clock-jitter is given thereafter. Also, efficient Matlab/Simulink models for additive errors induced by clock-jitter in the feedback DACs are shown so that to help designers characterize the sensitivities of various types of CT ΔƩ architectures to clock-jitter and obtain the specification requirement on the rms jitter of the sampling-clock for a given target performance. Furthermore, modeling of jitter induced errors is beneficial for systemlevel simulations adopted in the process of developing efficient solutions and modulator or DAC architectures that can remedy the effects of clock-jitter on the ΔƩ modulator performance. The robustness of these models is verified by CT simulations in Matlab/Simulink and simulations results show good agreement with the theoretical

10-3 10-2 <sup>10</sup>-1 <sup>100</sup> <sup>101</sup> <sup>102</sup> -160

*jitter / Ts, %*

.ࢠૢ Ǥ ൌ ,െ ൌ

**6. Conclusion** 




*IBJN, dBFS*




*RZ DAC NRZ DAC SCR DAC,* 

 *= 0.1 TS*


expectations.

Ramy Saad, Sebastian Hoyos, and Samuel Palermo *Department of Electrical and Computer Engineering, Texas A&M University, College Station, Texas, USA* 
