Numerical Analysis of a Transmission Line Illuminated by a Random Plane-Wave Field Using Stochastic Reduced Order Models

A novel nonintrusive statistical approach, known as the stochastic reduced order model (SROM) method, is applied to efficiently estimate the statistical information of the terminal response (i.e., the induced current) in transmission lines excited by a random incident plane-wave field. The idea of the SROM method is conceptually simple, i.e., to represent the uncertain input space dimensioned by random variables using the SROM-based input model. This input model consists of a very small number of selected samples with assigned probabilities. Thus, only these input samples in the model need to be evaluated using the deterministic solver. The SROM-based output model can be constructed to approximate the propagated uncertainty to the real output response with elementary calculation. The efficiency and accuracy of the SROM method to obtain the statistics of the induced current are analyzed using two examples, where the complexity of the uncertain input space gradually increases. The performance of the SROM method is compared with that of the traditional Monte Carlo (MC) method. The stochastic collocation (SC) method based on sparse grid sampling strategy computed via the Smolyak algorithm is also implemented to fairly evaluate the SROM performance. The result shows that the SROM method is much more efficient than the MC method to obtain accurate statistics of the induced current, and even shows a faster convergence rate compared with that of the SC method in the examples considered. Therefore, the SROM method is a suitable approach to investigate the variability of radiated susceptibility in electromagnetic compatibility problems with a random incident wave

Efficient Computation of Cable Electromagnetic Compatibility Problems with Parametric Uncertainty

Cables are heavily used to transmit power and signals in various systems. However, due to the susceptibility of cable to conducted and radiated emissions, unintended response could be provoked in the cable, and therefore, degrade the system operation. This is referred to as the cable electromagnetic compatibility (EMC) problems. Deterministic simulations based on the nominal values of system variables are usually performed to predict the possible malfunction. However, the variables characterising the cable system are naturally random due to, e.g. manufacturing tolerance. As a result of the systemic uncertainty, the induced interference in the cable also becomes a random observable. Therefore, the statistical description of the cable interference is a more reasonable outcome for assessing the system risk. Accordingly, stochastic approaches are needed to produce the required statistical outcome. The conventional statistical approach to quantify the uncertainty of the system response is the Monte-Carlo (MC) method. However, the computational cost of the MC method could become overly expensive when dealing with a large number of random variables. Thus, the cable EMC problems in large platforms with multiple uncertainty sources cannot be efficiently solved using the MC method. Clearly, an efficient statistical approach needs to be sought to solve the challenging cable EMC problems in the real world. Very recently, the stochastic reduced order model (SROM) method was proposed in the field of mechanical engineering, and is known to have merits such as the non-intrusiveness feature and superior efficiency. Therefore, the potential of applying the SROM method for cable EMC problems is very promising, and thoroughly investigated in this thesis. This thesis presents a comprehensive study of the cable EMC problems. The contributions of this thesis are mainly twofold, comprising the investigation of cable interference caused by: (1) the conducted emission (mainly at intra-system level), and (2) the radiated emission when exposed to incident electromagnetic fields. In the case of parametric uncertainty, the statistical analysis of the induced interference is efficiently performed using the SROM method. Specifically, the first main contribution of this thesis is dedicated to the study of crosstalk phenomenon, i.e., the inference induced to a wire by nearby wires in the cable. A parametric study is performed to investigate the effect (i.e., by increasing or decreasing) of the cable configurational changes on the crosstalk variation. The result can also be used to suggest factors causing excessive crosstalk. Under the cable parametric uncertainty, the statistics of crosstalk is successfully predicted using the SROM method. The efficiency of the statistical analysis using the SROM method and its ease of implementation are clearly demonstrated, compared to the conventional MC method and another state-of-the-art statistical approach referred to as the stochastic collocation (SC) method. The sensitivity of crosstalk to different cable variables is efficiently quantified using the SROM method, and then ranked. With this ranking, the feasibility of reducing the complexity of stochastic EMC problems by ignoring weak parametric uncertainties is explored. The second significant contribution of this thesis is the efficient uncertainty quantification of the interference in the cable caused by random electromagnetic field illumination. The most complex scenario where the incident electromagnetic wave is assumed to be fully random is chosen for investigation. As a response to the random illumination, the statistics of the interference (i.e., the induced current) in the cable is efficiently obtained using the SROM method. The computational cost of the SROM method is shown to be significantly reduced by orders of magnitude, compared to those of the MC and SC methods. The result demonstrates the potential of the SROM method for the general problems of the cable system response to the random radiation field. Overall, the research presented in this thesis has successfully advanced the uncertainty propagation techniques for EMC problems, especially in the case of the cable interference. Based on the performance discussion, this thesis has also provided an in-depth knowledge about the merits and disadvantages of different stochastic methods, which helps EMC engineers perform the efficient statistical analysis for their specific problems

Design of Multioctave High-Efficiency Power Amplifiers Using Stochastic Reduced Order Models

This paper presents a novel general design method of frequency varying impedance matching. The method is applied to design of a broadband high-efficiency power amplifier (PA). The proposed method defines the optimal impedance regions of a PA at several frequency sections over the operational frequency band. These regions contain the impedances that can achieve a high output power and a high-power added efficiency (PAE) simultaneously. A low-pass LC-ladder circuit is selected as the matching network (MN). The element values of the MN can be obtained using a synthesizing method based on stochastic reduced order models and Voronoi partition. The MN provides desired impedance in the predefined optimal impedance region at each frequency section. Thus, optimal output power and PAE of the PA can be achieved. To validate the proposed method, two eighth-order low-pass LC-ladder networks are designed as the input and output MNs, respectively. A gallium nitride (GaN) HEMT from Cree is employed as the active device. Packaging parasitic of the transistor has been taken into account. A PA is designed, fabricated, and measured. The measurement results show that the PA can achieve P1 dB PAE of better than 60% over a fractional bandwidth of 160% (0.2-1.8 GHz). The output power is 42-45 dBm (16-32 W), and the gain is 12-15 dB. The performance of the PA outperforms existing broadband highefficiency PAs in many aspects, which demonstrates the excellence of the proposed method

Uncertainty Quantification of the Responses of Transient Electromagnetic Disturbance Coupling to Transmission Lines Based on Stochastic Models

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