docs: 归档 variation 上报量分析报告(V1.05 3B有符号) + 配套换算工具 variation_calc.py

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+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+variation_calc.py — vd960Loop variation ↔ ΔL / ΔL-L 换算工具
+
+物理关系（推导见 docs/variation-analysis.md §9）:
+ CAPVD ∝ T = 2π·√(LC) （周期域, 归一化到 MEASUREMENT_BASE≈131072）
+ variation = Origin − CAPVD （V1.05 起 3B 有符号补码, 正=金属进入方向）
+ variation/Origin = 1 − √(1 + ΔL/L0) （精确）
+ ΔL/L0 ≈ −2 × variation/Origin （一阶, |ΔL/L| ≪ 1 时, 残差 <0.2%）
+ Δf/f ≈ variation/Origin （频域对应: CAPVD ∝ 1/f）
+ L0 = 1/(4π²·f0²·C) （绝对电感, f0=上报频率, C=档位电容）
+
+电容档位无关性: Origin 与 CAPVD 均 ∝ √C, variation/Origin 中 C 消掉,
+四档电容(33/43/66/76nF)共用同一套 ΔL/L 换算表。
+
+用法示例:
+ # 正向: 频率+电容+variation+origin → L0, ΔL, ΔL/L
+ python3 variation_calc.py --freq 100 --cap 43 --variation 216 --origin 131072
+ # 反推: 给定 ΔL/L 看需要多大 variation
+ python3 variation_calc.py --freq 100 --cap 43 --dl-rel 0.33
+ # 解析协议 3B LE 有符号补码 (V1.05 variation 字段)
+ python3 variation_calc.py --parse-var F6FFFF
+ # 灵敏度档位对照表
+ python3 variation_calc.py --sens-table
+ # 交互模式
+ python3 variation_calc.py --interactive
+"""
+
+import argparse
+import math
+import sys
+
+# ---------------------------------------------------------------- 常量
+CAP_OPTIONS = (33, 43, 66, 76)  # 线圈内部电容四档 (nF)
+ORIGIN_DEFAULT = 131072  # MEASUREMENT_BASE = 2^17
+SENS_TABLE = {0: (216, 108), 1: (108, 72), 2: (36, 18), 3: (10, 9)}
+SENS_NAMES = {0: "0(低)", 1: "1(中)", 2: "2(高)", 3: "3(最高)"}
+
+
+# ---------------------------------------------------------------- 核心计算
+def inductance(freq_hz, cap_nf):
+    """绝对电感 L0 = 1/(4π²·f²·C), 返回 μH"""
+    c = cap_nf * 1e-9
+    return 1.0 / (4.0 * math.pi * math.pi * freq_hz * freq_hz * c) * 1e6
+
+
+def variation_ratio(variation, origin):
+    """variation/Origin (有符号)"""
+    return variation / origin
+
+
+def delta_ll(vr):
+    """ΔL/L: (精确, 一阶), 返回相对值(负=电感减小)"""
+    exact = vr * vr - 2.0 * vr
+    approx = -2.0 * vr
+    return exact, approx
+
+
+def variation_from_dl_rel(dl_rel_pct, origin):
+    """反推: 给定 |ΔL/L|(%) → 需要的 variation (计数域)"""
+    r = dl_rel_pct / 100.0  # ΔL/L = −r
+    vr = 1.0 - math.sqrt(1.0 - r)  # 精确
+    return vr * origin, vr
+
+
+def sens_hit(vr):
+    """当前 variation/Origin 落在哪档进入阈值 (SensTable/65536)"""
+    for sens in (0, 1, 2, 3):
+        thr = SENS_TABLE[sens][0] / 65536.0
+        if abs(vr) >= thr:
+            return sens, thr
+    return None, None
+
+
+def parse_var_3byte(hex_str):
+    """V1.05 协议 variation 字段: 3B LE 有符号补码 → int32
+    F6FFFF → −10; 000001 → 65536
+    """
+    h = hex_str.strip()
+    if len(h) != 6:
+        raise ValueError("需要 6 位 hex (3 字节 LE), 如 F6FFFF")
+    b0 = int(h[0:2], 16)
+    b1 = int(h[2:4], 16)
+    b2 = int(h[4:6], 16)
+    v = b0 | (b1 << 8) | (b2 << 16)
+    if v & 0x800000:
+        v |= 0xFF000000
+    if v >= 0x80000000:
+        v -= 0x100000000
+    return v
+
+
+def fmt_sens_table():
+    lines = ["灵敏度档位 → ΔL/L 触发阈值 (vd960Loop SensTable, 一阶 ΔL/L≈−2×vr):"]
+    lines.append(f"{'SENS':<8}{'进入表':<8}{'离开表':<8}{'Δf/f进入':<12}{'ΔL/L进入':<12}{'ΔL/L离开'}")
+    for sens in (0, 1, 2, 3):
+        sin, sout = SENS_TABLE[sens]
+        vr_in = sin / 65536.0
+        vr_out = sout / 65536.0
+        lines.append(f"{SENS_NAMES[sens]:<8}{sin:<8}{sout:<8}"
+                     f"{vr_in * 100:>7.4f}%{'':<4}{-2 * vr_in * 100:>8.4f}%{'':<4}{-2 * vr_out * 100:>8.4f}%")
+    return "\n".join(lines)
+
+
+def forward(freq, cap, variation, origin):
+    """正向计算并打印"""
+    f_hz = freq * 1000.0 if freq < 1e6 else freq
+    l0 = inductance(f_hz, cap)
+    vr = variation_ratio(variation, origin)
+    exact, approx = delta_ll(vr)
+    dl = l0 * exact
+
+    sens, thr = sens_hit(vr)
+
+    out = []
+    out.append("=" * 62)
+    out.append("正向换算: 频率+电容+variation+Origin")
+    out.append("=" * 62)
+    out.append(f" 上报频率 f0 : {f_hz / 1000.0:>10.3f} kHz")
+    out.append(f" 电容档 C     : {cap:>10d} nF")
+    out.append(f" 绝对电感 L0  : {l0:>10.3f} μH (L=1/(4π²f²C))")
+    out.append(f" Origin       : {origin:>10d} (CAPVD 基线)")
+    out.append(f" variation    : {variation:>10d} (3B 有符号)")
+    out.append(f" variation/Origin : {vr * 100:>9.4f} % (≈ Δf/f)")
+    out.append("-" * 62)
+    out.append(f" ΔL/L 一阶    : {-2 * vr * 100:>9.4f} % (≈ −2×vr)")
+    out.append(f" ΔL/L 精确    : {exact * 100:>9.4f} % (vr²−2vr)")
+    out.append(f" ΔL (绝对)    : {dl:>9.4f} μH")
+    out.append("-" * 62)
+    if sens is not None:
+        out.append(f" ≥ SENS={SENS_NAMES[sens]} 进入阈值 (vr_thr={thr * 100:.4f}%)")
+    else:
+        out.append(f" 低于全部进入阈值 (最小档 SENS=3: {10 / 65536 * 100:.4f}%)")
+    out.append("=" * 62)
+    return "\n".join(out)
+
+
+def reverse(freq, cap, dl_rel_pct, origin):
+    """反推: 给定 |ΔL/L|% → variation"""
+    f_hz = freq * 1000.0 if freq < 1e6 else freq
+    l0 = inductance(f_hz, cap)
+    variation, vr = variation_from_dl_rel(dl_rel_pct, origin)
+
+    out = []
+    out.append("=" * 62)
+    out.append(f"反推: ΔL/L = −{dl_rel_pct}% 需要的 variation")
+    out.append("=" * 62)
+    out.append(f" L0 = {l0:.3f} μH (f0={f_hz / 1000:.3f}kHz, C={cap}nF)")
+    out.append(f" ΔL = {l0 * (-dl_rel_pct / 100.0):.4f} μH")
+    out.append(f" variation/Origin = {vr * 100:.4f} %")
+    out.append(f" variation = {variation:.0f} (Origin={origin})")
+    out.append(f" 一阶估算 = {origin * dl_rel_pct / 200.0:.0f} (vr≈r/2)")
+    out.append("=" * 62)
+    return "\n".join(out)
+
+
+def interactive():
+    print("vd960Loop variation 换算工具 — 交互模式 (Ctrl+C 退出)")
+    cap = int(input("电容档 (33/43/66/76 nF): "))
+    if cap not in CAP_OPTIONS:
+        print(f"警告: {cap}nF 不在标准档位 {CAP_OPTIONS} 中")
+    freq = float(input("上报频率 (kHz, 如 100): "))
+    origin = int(input(f"Origin (默认 {ORIGIN_DEFAULT}): ") or ORIGIN_DEFAULT)
+    while True:
+        try:
+            variation = int(input("variation (有符号, q 退出): "))
+        except ValueError:
+            break
+        print()
+        print(forward(freq, cap, variation, origin))
+
+
+def main():
+    p = argparse.ArgumentParser(
+        description="vd960Loop variation ↔ ΔL/ΔL-L 换算工具",
+        formatter_class=argparse.RawDescriptionHelpFormatter,
+        epilog=__doc__)
+    p.add_argument("--freq", type=float, help="上报频率 (默认 kHz, <1e6 视为 kHz)")
+    p.add_argument("--cap", type=int, choices=CAP_OPTIONS,
+                   help="电容档位 nF: 33/43/66/76")
+    p.add_argument("--variation", type=int, help="variation (3B 有符号, 计数域)")
+    p.add_argument("--origin", type=int, default=ORIGIN_DEFAULT,
+                   help=f"Origin 基线 (默认 {ORIGIN_DEFAULT})")
+    p.add_argument("--dl-rel", type=float,
+                   help="反推模式: 给定 |ΔL/L|%% → 所需 variation")
+    p.add_argument("--parse-var", metavar="HEX6",
+                   help="解析 V1.05 协议 3B LE 有符号补码 (如 F6FFFF = −10)")
+    p.add_argument("--sens-table", action="store_true", help="打印灵敏度档位对照表")
+    p.add_argument("--interactive", action="store_true", help="交互模式")
+    args = p.parse_args()
+
+    if args.sens_table:
+        print(fmt_sens_table())
+        return
+
+    if args.parse_var:
+        v = parse_var_3byte(args.parse_var)
+        print(f"3B LE 补码 {args.parse_var.upper()} → {v}")
+        return
+
+    if args.interactive:
+        interactive()
+        return
+
+    if args.dl_rel is not None:
+        if not args.freq or not args.cap:
+            p.error("反推模式需要 --freq 和 --cap")
+        print(reverse(args.freq, args.cap, args.dl_rel, args.origin))
+        return
+
+    if None in (args.freq, args.cap, args.variation):
+        p.error("需要 --freq --cap --variation (或 --dl-rel / --sens-table / --interactive)")
+    print(forward(args.freq, args.cap, args.variation, args.origin))
+
+
+if __name__ == "__main__":
+    sys.exit(main())