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This paper introduces a novel statistical method, referred to as the stochastic reduced order model (SROM) method, to predict the variability of cable crosstalk subject to a range of parametric uncertainties. The SROM method is a new member of the family of stochastic approaches to quantify propagated uncertainty in the presence of multiple uncertainty sources. It is non-intrusive, accurate, efficient, and stable, thus could be a promising alternative to some well-established methods such as the stochastic Galerkin (SG) and stochastic collocation (SC) methods. In this paper, the SROM method is successfully applied to obtain the statistics of cable crosstalk subject to single and multiple uncertainty sources. The statistics of uncertain cable parameters are first accurately approximated by SROMs, i.e., pairs of very few samples with known probabilities, such that the uncertain input space is well represented. Then, a deterministic solver is used to produce the samples of cable crosstalk with the corresponding probabilities, and finally the uncertainty propagated to the crosstalk is quantified with good accuracy. Compared to the conventional Monte Carlo (MC) simulation, the statistics of crosstalk obtained by the SROM method converge much faster by orders of magnitude. Also the computational cost of the SROM method is shown to be small and can be tuned flexibly depending on the accuracy requirement. The SC method based on tensor product sampling strategy is also implemented to validate the efficacy of the SROM method.

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. Index Terms-Broadband power amplifier (PA), gallium nitride (GaN) high electron mobility transistor (HEMT), highefficiency PA, PA, stochastic reduced order model (SROM), voronoi partition, wideband matching network (MN). I. INTRODUCTION P OWER amplifiers (PAs) are essential devices of many communication systems. The features of a PA regarding the bandwidth, power gain, linearity, output power, and power added efficiency (PAE) could significantly affect the overall performance of the system. A high-power, high-efficiency broadband PA is in high demand by the industry and market. Consequently, a lot of research efforts have been made in this area to achieve better performance.

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Railways are electrified in many different ways. In this article, the main options for electrifying a high speed AC railway are reviewed from an electromagnetic compatibility (EMC) perspective. Firstly, the trend of increasing the usage of electrified trains to replace conventional diesel locomotives is pointed out. On this basis, the significance of considering EMC in the railway environment is explained, with a view to preventing the malfunction of the railway system. Secondly, different electrification options are introduced, namely the rail-return, boostertransformer and auto-transformer systems. The benefits and drawbacks of each electrification option are considered based on the interference level to the trackside railway signalling and telecommunication systems. The discussion of each electrification system is verified using electromagnetic simulations. By comparing the different electrification schemes, it is shown that the auto-transformer system has better EMC performance and delivers higher power to the train.