# 4 th Order LC-Based Sigma Delta Modulators
## 4 Discussion  
Regarding the pole positioning in Gm-LC and the capacitive coupling architectures present, respectively, none and low dependency on the coupling device. In these architectures, the individual positioning of the poles can be easily done. On the other hand, poles positioning in magnetic coupling are extremely dependent on the coupling factor, creating a forbidden zone where the poles cannot be placed. This coupling depends on the distance between the two inductors and cannot be trimmed, which makes this architecture not robust to process variations if a low coupling coefficient value is needed.  
Capacitive coupling uses a linear device, and magnetic coupling is modeled as one. The Gm-LC is naturally non-linear, due to the transistors that operate in saturation. Ideally, the power consumption for passive coupling architectures is zero, as well as their noise contribution.  
Regarding 4 th order \(\Sigma\)AMs presented here, Figure 12a shows the comparison of the PSD for all three designed modulators and their equivalent DT for maximum SNR and Figure 12b the magnification of the image around the center frequency. All designed \(\Sigma\)AMs had a good agreement with their DT equivalent as shown in, validating the proposed methodology.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**FIRDACs** & **Coefficient 0** & **Coefficient 1** & **Coefficient 2** & **Coefficient 3** \\ \hline FIRDACm & \(-0.82\) & \(1.19\) & \(-0.60\) & \(0.97\) \\ FIRDACc & \(-0.90\) & \(0.72\) & \(-0.15\) & \(0.00\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Coefficients for the 4 th order capacitively coupled \(\Sigma\)AM.  
Figure 11: Output spectrum of the designed capacitively coupled \(\Sigma\)AM.  
Advances in highly integrated wireless communication transceivers provide applications for integrated RF bandpass filters. Active filters have a poor dynamic range when operating at high frequencies [22]. Passive LC filters can achieve high dynamic range at very low power consumption, but on-chip inductors have very low-quality factors, Q. Active LC filters are a good compromise between these two types of filters [23]. In active LC filters, the quality factor is enhanced by adding a negative resistance to compensate for the losses of the reactive devices. Active LC filters are not only used to realize integrated RF bandpass filters but they are also used in the design of RF bandpass SDMs. The methodology to design high-order LC-Based SDM introduced opens the door to unexplored filter topologies such as high-order passively coupled LC filters and Microelectromechanical Systems (MEMS) filters.  
In Table 5, a comparison between the present work with other RF SD implementations is presented. This table shows that the proposed architecture achieves good performances, to the state of the art.  
The oversampling technology and noise shaping make Sigma Delta modulation have many potential applications, as demonstrated in [27], where an optical sigma-delta modulation theory is presented along with calculation and design issues for optical system implementation. It is demonstrated that Delta Sigma Modulation is a powerful technique for optical signal processing due to its high bandwidth, noise immunity, and cost. The Delta-Sigma modulation concept is also used by [28] in a system to resolve the influence of the reflecting surface of the deflection and the large-scale traction mobile feed system on the astronomical signal received by the feed-in FAST. Experimental results show that, when compared to traditional solutions, the quantization noise generated by the transmission end of the analog signal to the digital signal is reduced.