# Interference of Spread-Spectrum EMI and Digital Data Links under Narrowband Resonant Coupling
## 1 Introduction  
Due to the widespread diffusion of highly integrated information and communication technology (ICT) systems like smartphones, tablets and intelligent sensor nodes, digital communication modules operate in a more and more harsh electromagnetic environment, in which electromagnetic interference (EMI) from digital integrated circuits (ICs) and switching mode power converters can be easily coupled to the nominal signal path via the silicon substrate, the IC package and the power distribution network of ICs and printed circuit boards (PCBs), resulting in a degraded bit error rate (BER) and possibly in a complete communication failure [1; 2; 3; 4; 5; 6; 7]. As a consequence, the effects of EMI need to be addressed adopting specific countermeasures as early as possible in the design of circuits and systems and/or by limiting the coupling mechanisms so that to assure the proper operation with no penalty in terms of costs, time-to-market and performance, and also in order to meet the stringent Electromagnetic Compatibility (EMC) regulations [8; 9; 10; 11]. For this purpose, several approaches have been proposed in recent years to mitigate EMI [12; 13; 14; 15; 16]. Among them, _Spread-Spectrum (SS) techniques_, which consist in the modulation of the frequency of switching signals around the nominal value, so that to spread their spectral energy over a wider bandwidth [17; 18], are often adopted in clock oscillators [19; 20; 21; 22; 23] and DC-DC converter controllers [24; 25; 26; 27] since they give rise to a significant (10-20 dB) reduction of EMI spectral peaks measured following EMC standards [8; 9; 10; 11] and make it possible to meet EMC requirements at low cost. In this field, chaos-based random SS-modulations have proven to achieve the best spectral characteristics [28; 29; 30]. While SS techniques help in complying with EMC regulations, their effectiveness in reducing the interfering potential of switching signals is more controversial and has been sometimes put in question [31; 32; 33; 34]. Moreover, SS-modulations have found to bring no BER reduction in an \(I^{2}C\) link operating in the presence of EMI generated by a power converter [35] and a worse interfering potential of SS-modulated compared to non-modulated EMI in Wireless Local Area Networks (WLAN) is reported in [36]. In this scenario, focusing on the effects of SS EMI on digital communications, the impact of random SS-modulated interference on baseband digital data lines has been described in [37] in terms of an equivalent channel capacity loss and compared with non-SS-modulated EMI in practical application scenarios, revealing that SS-modulated EMI can show a worse interfering potential compared to non-modulated EMI in a digital link featuring advanced channel coding. The analysis presented in [37], however, was carried out assuming frequency-independent EMI coupling in the victim channel bandwidth. This assumption conveniently describes low frequency inductive and capacitive coupling scenarios in baseband data links but could not be valid in general in the presence of radiated and conducted EMI resonant coupling mechanisms [38; 39; 40; 41; 42], which affect high-frequency EMI propagation and can be therefore relevant when interference with radio-frequency (RF) digital communications are considered. Generally speaking, in the presence of resonant coupling, the adoption of SS-modulations may lead to a more significant reduction of the EMI power which is actually coupled to the victim equipment compared with the case of wideband coupling considered in [37], as illustrated in Figure 1, where \(B\) and \(W\) are the channel and the EMI bandwidth, respectively. From the figure, it can be observed that under the same resonant coupling mechanism \(G(f)\), the coupled EMI power can be reduced of more than 50% by adopting SS-modulations compared to the non-SS-modulated case.