行为模型中的记忆作为慢不变流形上的运动
Memory in Behavioral Models as Motion on a Slow Invariant Manifold
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中文总结 AI 辅助
本文证明非线性器件行为模型中的长期记忆可视为慢不变流形上的运动，并基于Floquet理论和参数化方法构造精确约化模型，验证了GaN HEMT中的热与俘获记忆特性。
中文摘要 AI 辅助
非线性二端口网络的单音大信号工作点是一个周期受迫电路的周期轨道。当器件具有记忆（自热、俘获）时，该轨道的Floquet指数分为快（电学）和慢（热与俘获）模态，长期记忆是附着于慢模态的不变流形上的运动。该流形的存在唯一性定理由Cabré、Fontich和de la Llave的参数化方法应用于轨道处的频闪映射得出；该流形是Haller和Ponsioen的谱子流形，无需小强迫参数。该流形是驱动相位圆上的一个丛，其纤维维数等于慢Floquet指数的个数，Verspecht等人的动态X参数核通过驱动幅度阶跃变化识别其约化动力学。因此，精确约化模型具有与慢指数个数相同的记忆状态，无记忆X参数面是约化动力学的固定点族，包络域模型是由包络驱动的约化动力学。对于具有三极点热网络和漏极滞后俘获的GaN HEMT紧凑模型，假设得到验证并构造了流形：俘获贡献了一个由线性化设定的$14\\,\mu$s时间常数，而非其$6$ ms发射时间；热子流形近似平坦，具有线性约化动力学；在俘获方向上的展开仅在几个热电压（$nV_T\approx26$ mV）内有效，因此俘获记忆需要流形的全局表示。
英文摘要
A single-tone large-signal operating point of a nonlinear two-port is a periodic orbit of a periodically forced circuit. When the device has memory, the Floquet exponents of that orbit separate into fast (electrical) and slow (thermal and trapping) modes, and long-term memory is motion on the invariant manifold attached to the slow modes. Existence and uniqueness of that manifold follow from the parameterization method of Cabré, Fontich and de la Llave, applied to the stroboscopic map at the orbit; the manifold is the spectral submanifold of Haller and Ponsioen, without a small-forcing parameter. The manifold is a bundle over the circle of drive phase, its fiber dimension the number of slow exponents, and the dynamic X-parameter kernel of Verspecht et al. identifies its reduced dynamics from the transient after a step in drive amplitude. An exact reduced model has one memory state per slow exponent, the memoryless X-parameter surface is the fixed-point family of the reduced dynamics, and the envelope-domain model is the reduced dynamics driven by the envelope. The hypotheses are verified and the manifold constructed for a GaN HEMT compact model with thermal and trap memory: the trap's time constant at the operating point, $14 μ$s, is set by the linearization, not by its $6$ ms emission time, and the trap's nonlinearity confines a polynomial representation of the manifold to a few millivolts of drive, so trap memory must be represented over the operating range, by tables or a fitted network, not by an expansion about the operating point.
