docs: 灵敏度等级与ΔL/L物理关系分析
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## 2026-07-21 — 灵敏度等级与 ΔL/L 的物理关系分析
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### 参数表
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```c
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// sens_in: 进入阈值, sens_out: 离开阈值 (0=低, 2=高)
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SensTable = { 108, 54, 28 }; // 进入
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SensTable1 = { 81, 32, 16 }; // 离开
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```
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### 计算链路
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**Step 1:阈值差值**
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```c
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loop1_dlt_ORG = (Origin * sens) >> 16; // = Origin × sens / 65536
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```
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**Step 2:进入判定**
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```c
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if (CAPVD < Origin - dlt_ORG) // ← ΔCAPVD / Origin > sens / 65536
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```
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**Step 3:CAPVD → 电感**
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线圈振荡频率 `f ∝ 1/√L`,周期 `T ∝ √L`。测量窗 CAPVD 正比于平均周期:
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```
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ΔCAPVD / Origin = ΔT / T₀ = (√L - √L₀) / √L₀
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```
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对微小变化泰勒展开:`dT/T ≈ dL/(2L)`,即:
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```
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ΔL / L ≈ 2 × ΔCAPVD / Origin
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```
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**Step 4:最终 ΔL/L 公式**
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```
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ΔL/L_entry = 2 × sens_in / 65536
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ΔL/L_exit = 2 × sens_out / 65536
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```
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### 灵敏度等级对应 ΔL/L
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| 等级 | sens_in | ΔL/L 进入 | sens_out | ΔL/L 离开 | 迟滞比 |
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|------|---------|----------|----------|----------|--------|
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| 低 (0) | 108 | **0.330%** | 81 | **0.247%** | 1.33 |
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| 中 (1) | 54 | **0.165%** | 32 | **0.098%** | 1.69 |
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| 高 (2) | 28 | **0.085%** | 16 | **0.049%** | 1.75 |
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### 物理验证
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典型 100μH 线圈:
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- 现代轿车经过:ΔL/L ≈ 5%–15%,任一灵敏度均能可靠触发
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- 高灵敏度 0.085%:足够敏感,需注意温漂(~20°C 引起约 0.1% 的感量偏移)和邻道串扰
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- 迟滞比 1.33–1.75:防止车辆边界状态反复跳变,低灵敏度迟滞最小
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### 快速换算
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`sens` 值直接对应 **千分之 2×sens 的感量变化百分比**——除以 1000 就是 ΔL/L(%)。
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---
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## 2026-07-21 (午后) — 修复灵敏度 bug + 有限存在时间 + 版本号
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### BLE 灵敏度无法修改
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