# 4 th Order LC-Based Sigma Delta Modulators  
[PERSON]  
1 Graduate Program in Electrical and Computer Engineering, Federal University of Rio Grande do Norte, Natal 59078-970, RN, Brazil 1  
* National Environmental Data System--\"Sistema Nacional de Dados Ambientais\" (SINDA) is the Brazilian data collection system, which has been built to collect environmental data such as temperature, pressure, and ultraviolet (UV) radiations from all Brazilian territory and provide this information to end users as hydroelectric power plants. * The Medical Implant Communication Service (MICS) is used for diagnostic and therapeutic purposes in implanted medical devices in the human body. For example, MICS devices include implanted cardiac pacemakers and defibrillators as well as a neuromuscular stimulator that help restore sensation, mobility, and other functions to limbs and organs. * Private Mobile Radio 446 (PMR446) is a part of the radio frequency range which is open and without licensing, used for business and personal use in most countries of the European Union. The implementation of SDR using a Nyquist rate analog-to-digital converter (ADC) has been challenging and with very high-power consumption, which makes it unsuitable for mobile applications [5]. Bandpass \(\Sigma\Delta\) modulators are well suited to SDR applications, since they are capable of converting a limited bandwidth centered on RF frequency. The center frequency \(f_{o}\) is usually chosen to be \(f_{s}/4\). This allows the multiplication to be performed with a simple exclusive-or gate, facilitating the design of the following down-conversion mixer and the decimation filter [6]. CT bandpass \(\Sigma\Delta\)M using LC resonators are well suited for SDR, as they can convert a narrowband around a Radio Frequency (RF) center frequency. In [7,8] RF LC-based 2 nd order bandpass SD ADC has achieved interesting performances with Figure of Merits, but \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Ref.** & \
\begin{tabular}{c} **Frequency Range** \\ **(MHz)** \\ \end{tabular} &
\begin{tabular}{c} **Channel Bandwidth** \\ **(kHz)** \\ \end{tabular} & **Application** \\ \hline ARGOS & 401.635–401.665 & 30 & Active RC \\ SINDA & 401.605–401.635 & 30 & Satellite \\ MICS & 401.0–406.0 & 300 & Medical \\ ISM-433 & 433.050–434.790 & 1840 & any \\ PMR-466 & 446.0–446.2 & 12.5 & Voice \\ KDR-444 & 444.6–444.975 & 16 & Voice \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Bands and standards in the 400–446 MHz range. Figure 1: 4 th receiver architecture: (**a**) Conventional RF. (**b**) SDR based on RF ADC. the obtained performances are not sufficient to be used in an RF transceiver for wireless communication standards. One way to increase the maximum achievable SNR of the SD ADC is by increasing the order of the loop filter of the SDM. In LC-based SDMs, increasing the order of the loop filter is usually done by cascading two or three LC resonators coupled using transconductance (Gm). Another important context that we can cite regarding the use of SDM is in the paradigm of edge computing (EC), which faces many challenges concerning energy efficiency, data quality, reliability, data and device security, and computational performance level. EC is an emerging data processing paradigm that processes data over local computing and communication infrastructure, such as sensors and mobile sensor networks, and only, if necessary, prepares the data and establishes a communication link with a data center or other CE [9]. In [10], a 4 th-order SDM, clocked at 3.6 GHz and centered at 900 MHz, was presented. The SDM ADC architecture was composed of 2 LC tank circuits with Q-enhancement, 3 transconductors, 1 single-bit comparator, and 3 single-bit NRZ feedback DAC. To tune and calibrate the Sigma Delta loop filter, a simple algorithm, suitable for integration, was presented. High-order LC-based \(\Sigma\)AM in the literature use the nodes between the LC tanks either for feedforward or feedback coefficients to obtain the desired Noise Transfer Function (NTF).