发表机构
Aqualytics（水分析科技公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明卡迪夫模型等频域行为模型的函数形式源于时间不变性，通过经典不变量理论给出完备性定理，并赋予指数物理意义，实验验证了四阶项的存在。
AI 中文摘要
非线性微波器件频域行为模型（卡迪夫模型、X参数、高阶正弦描述函数）所共有的函数形式通常被视为一种建模选择；本文证明它源于时间不变性。在时间原点平移下，第k次谐波相量旋转k倍基波角度，因此时间不变器件的频谱映射在圆群的加权作用下是等变的，经典不变量理论给出了所有此类映射的一般形式；三个学术界的相位归一化因子是其携带权重的因子。结果是一个完备性定理：在单音周期稳态下，任何时间不变二端口响应都不超出卡迪夫形式，且指数关系m=|n|+2r是零负载波处的光滑性条件。将每个卡迪夫项写成负载波中的单项式A^a \bar{A}^b，可赋予指数物理意义——m是负载侧非线性的阶数，n由驱动侧谐波决定，r=min(a,b)是共轭对的数量——以及负载侧多项式次数K的界r_max=floor(K/2)，因此熟悉的限制r≤1对于三次负载侧非线性是精确的，并在四阶时失效。对于有负载的器件，该界成为r的可测量衰减。定制的A-pull测量直接展示了这种分解，两次模拟重现了其已发表的检测项模式，并将第一个四阶项置于约-58 dBc，介于该测量的-40 dBc杂散底和-60 dBc噪声底之间。
英文摘要
Frequency-domain behavioral models of nonlinear microwave devices (the Cardiff model, X-parameters, higher-order sinusoidal describing functions, and the baseband models of power-amplifier predistortion) share one functional form, and each modeling framework justifies the form by its own argument, time invariance among them. Here we give the mathematical argument by which time invariance alone determines the model form, and state the result as a theorem for two-port devices, with its extension to any number of ports. Under a shift of the time origin each harmonic phasor rotates by a multiple of the fundamental's angle, so the spectral map of a time-invariant device is equivariant under a weighted circle action, and classical invariant theory gives its general form. The result is a completeness theorem for the form already in use: every time-invariant two-port response in single-tone periodic steady state is a phase factor attached to the fundamental multiplying a function of the wave magnitudes and their relative phase. The Cardiff exponents become counters: $m$ is the order of the load-side nonlinearity, $n$ is set by the drive-side harmonic, and $r$ is the number of conjugate pairs. The bound $r_{\max}=\lfloor K/2\rfloor$ for a load-side nonlinearity of degree $K$ makes the familiar restriction $r\le1$ a hypothesis about the device, exact for a cubic nonlinearity; for a loaded device the bound becomes a measurable decay in $r$. The results are illustrated with a published measurement and two simulations.
Comments10 pages, 4 figures, 5 tables. v3: one sentence in Sec. VIII corrected (the multi-harmonic extension uses the single circle, not a torus); running head corrected. v2: prior work attributed; Remark 1 (N ports) added; results unchanged. Companion papers: arXiv:2609.38771, arXiv:2610.01031. Toolkit: doi:10.5281/zenodo.22816760
