This paper deals with the frequency design of lossless passive electronic filters under magnitude constraints. With the huge increase in design complexity for mobile applications, new systematic and efficient methods are required. This paper focuses on the direct synthesis approach, an historical design approach that has not been recently updated. It consists in directly synthesizing the $LC$ values of a pre-specified circuit until the spectral mask is satisfied. While beneficial in practice, this approach typically leads to an important computational time and requires an initial guess to reduce it. Based on recent developments of the System and Control community, that led to efficient methods for system design, the direct synthesis approach is revisited. To achieve this, the port-Hamiltonian Differential Algebraic Equation (pHDAE) representation, that particularly fits the design problem, is introduced. A synthesis method is then developed, leading to solve an optimization problem of moderate complexity. For particular cases, this complexity happens to be remarkably low. Based on this observation, a second method reveals how to obtain such complexity for the more general case, using an original combination between the pHDAE and the LFT representations. Finally, a numerical example shows the validity and illustrates the benefits of this work.

中文翻译：

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无损无源电子滤波器的频率设计：直接合成方法的状态空间公式

本文讨论了在幅度限制下无损无源电子滤波器的频率设计。随着移动应用程序设计复杂性的大幅增加，需要新的系统和有效的方法。本文重点介绍直接综合方法，这是一种最近未更新的历史设计方法。它包括直接合成预先指定电路的 $LC$ 值，直到满足频谱掩码。虽然在实践中有益，但这种方法通常会导致重要的计算时间，并且需要初始猜测来减少它。基于系统和控制社区的最新发展，这导致了系统设计的有效方法，直接综合方法被重新审视。为了实现这一点，port-Hamiltonian 微分代数方程 (pHDAE) 表示，介绍了特别适合设计问题的方法。然后开发了一种综合方法，从而解决了中等复杂性的优化问题。对于特定情况，这种复杂性恰好非常低。基于这一观察，第二种方法揭示了如何使用 pHDAE 和 LFT 表示之间的原始组合为更一般的情况获得这种复杂性。最后，一个数值例子显示了有效性并说明了这项工作的好处。使用 pHDAE 和 LFT 表示之间的原始组合。最后，一个数值例子显示了有效性并说明了这项工作的好处。使用 pHDAE 和 LFT 表示之间的原始组合。最后，一个数值例子显示了有效性并说明了这项工作的好处。