Effect of Periodicity in Frequency Responses of Networks From Conducted EMI

In this paper, we consider different types of networks, and investigate the characteristics of the frequency responses of loads, which are distributed in the networks. Without loss of generality, both frequency-independent and frequency-dependent loads are discussed, respectively. Beginning with a transmission-line (TL) network with frequency-independent loads, via the TL theory and Baum-Liu-Tesche equation, we demonstrate that the frequency responses are periodic in the frequency domain, where the periodicity is derived and verified. Subsequently, our study is extended to the complex networks that consist of multiple junctions and branches. By using the statistical method, we generate random loads with different attributes, i.e., resistive, inductive, or capacitive, and mainly study the effect of the number of branches and junctions on the frequency response of targeted load in various networks. From the perspective of protections for the targeted load in networks, results indicate that, for lossless and good dielectric (i.e., low-loss) media, it is crucial to consider the frequency responses at the critical frequencies in a periodical manner, rather than at a single frequency. Furthermore, it is worth noting that, the frequency response of targeted load behaves differently when varying the attributes of other loads in the network. The variation of network topology, i.e., increasing the number of junctions or branches, also influences the frequency response.