208 行
9.8 KiB
Python
208 行
9.8 KiB
Python
# -*- coding: utf-8 -*-
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u"""受控阻抗 + IPC-2221 载流线宽计算器（纯数学，不连桥接）。
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/c/Python314/python .claude/pcb_calc.py # 回验本项目的定稿几何
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/c/Python314/python .claude/pcb_calc.py --zdiff 90 # 求 90Ω 差分的线宽
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/c/Python314/python .claude/pcb_calc.py --current 4 # 求 4A 的最小线宽
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/c/Python314/python .claude/pcb_calc.py --sweep # 叠层/铜厚变了扫一遍
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移植自 hyl64/jlcmcp 的 `src/calculators.ts`（MIT），改成 **mm 为主单位**
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（原版是 mil），并补了本项目的默认叠层。公式与 `五路直供电源板设计.md` §15.3
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写的是同两条，所以这支脚本可以直接回验文档里的 Z0 / Zdiff。
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⚠️ §15.3 已经写了：**打样前用板厂的阻抗计算器复核，别信这里的近似公式。**
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这支脚本的用途是「叠层/铜厚/线宽一改，先看会不会跑出 ±10% 窗口」，不是定稿依据。
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"""
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from __future__ import print_function
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import argparse
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import math
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MIL = 0.0254 # 1 mil = 0.0254 mm
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# ---- 本项目定稿（五路直供电源板设计.md §10.1 / §15.3）------------------------
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ER_FR4 = 4.3 # 嘉立创四层板 FR4
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H_L1L2_MM = 0.2104 # L1-L2 介质厚度，1.6mm 标准叠层
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T_1OZ_MM = 1.37 * MIL # 1 oz = 1.37 mil（§10.1 用的就是这个数，不是 1.4）
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T_2OZ_MM = 2.74 * MIL
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T_HALFOZ_MM = 0.685 * MIL
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W_USB_MM = 0.28 # §15.3 定稿线宽
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S_USB_MM = 0.18 # §15.3 定稿间距
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ZDIFF_TARGET = 90.0 # USB 2.0 HS，±10%
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DT_DEFAULT = 20.0 # °C 允许温升 —— 设计文档 §10.1 表头与 §4694 全篇用 20，不是 10
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# ---------------------------------------------------------------------------
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# 阻抗
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# ---------------------------------------------------------------------------
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def z0_microstrip(w_mm, h_mm, t_mm, er=ER_FR4):
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u"""表层微带线特征阻抗。Z0 = 87/√(εr+1.41) · ln(5.98h / (0.8W + t))"""
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return (87.0 / math.sqrt(er + 1.41)) * math.log(5.98 * h_mm / (0.8 * w_mm + t_mm))
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def z0_stripline(w_mm, h_mm, t_mm, er=ER_FR4):
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u"""内层带状线。Z0 = 60/√εr · ln(4h / (π(W + t)))"""
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return (60.0 / math.sqrt(er)) * math.log((4.0 * h_mm) / (math.pi * (w_mm + t_mm)))
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def zdiff_microstrip(w_mm, s_mm, h_mm, t_mm, er=ER_FR4):
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u"""差分微带。Zdiff = 2·Z0 · (1 − 0.48·e^(−0.96·S/h))"""
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z0 = z0_microstrip(w_mm, h_mm, t_mm, er)
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return 2.0 * z0 * (1.0 - 0.48 * math.exp(-0.96 * s_mm / h_mm))
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def zdiff_stripline(w_mm, s_mm, h_mm, t_mm, er=ER_FR4):
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u"""差分带状线。Zdiff = 120/√εr · ln(2h / (π(W + t + S)))"""
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return (120.0 / math.sqrt(er)) * math.log((2.0 * h_mm) / (math.pi * (w_mm + t_mm + s_mm)))
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def width_for_z(target, fn, h_mm, t_mm, er=ER_FR4, s_mm=None,
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lo=0.02, hi=5.0, tol=1e-4):
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u"""二分反解线宽。阻抗对线宽单调递减，所以 z > target 时要加宽。
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lo/hi 单位 mm。返回 (w_mm, z_actual)。
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"""
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def z_of(w):
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return fn(w, s_mm, h_mm, t_mm, er) if s_mm is not None else fn(w, h_mm, t_mm, er)
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if z_of(lo) < target or z_of(hi) > target:
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return (float('nan'), float('nan')) # 目标落在可解区间外
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for _ in range(200):
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mid = (lo + hi) / 2.0
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z = z_of(mid)
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if abs(z - target) < tol:
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return (mid, z)
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if z > target:
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lo = mid
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else:
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hi = mid
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mid = (lo + hi) / 2.0
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return (mid, z_of(mid))
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# ---------------------------------------------------------------------------
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# IPC-2221 载流
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# ---------------------------------------------------------------------------
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def ipc_width_mm(current_a, t_mm=T_1OZ_MM, dt_c=DT_DEFAULT, external=True):
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u"""IPC-2221：I = k·ΔT^0.44·A^0.725，反解线宽。
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k = 0.048（外层）/ 0.024（内层）。A 的单位是 mil²，所以内部换算。
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返回 (线宽 mm, 截面积 mil²)。
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"""
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k = 0.048 if external else 0.024
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a_mil2 = (current_a / (k * dt_c ** 0.44)) ** (1.0 / 0.725)
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t_mil = t_mm / MIL
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return (a_mil2 / t_mil * MIL, a_mil2)
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# ---------------------------------------------------------------------------
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def verify():
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print(u'=' * 74)
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print(u'回验 §15.3 定稿几何（W=%.2f / S=%.2f mm, h=%.4f mm, εr=%.1f, 1oz）'
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% (W_USB_MM, S_USB_MM, H_L1L2_MM, ER_FR4))
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print(u'=' * 74)
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z0 = z0_microstrip(W_USB_MM, H_L1L2_MM, T_1OZ_MM)
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zd = zdiff_microstrip(W_USB_MM, S_USB_MM, H_L1L2_MM, T_1OZ_MM)
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print(u' Z0 = %.1f Ω （文档写 ≈57.5） %s'
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% (z0, u'✓ 对上' if abs(z0 - 57.5) < 1.0 else u'✗ 对不上'))
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print(u' Zdiff = %.1f Ω （文档写 ≈90.5） %s'
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% (zd, u'✓ 对上' if abs(zd - 90.5) < 1.0 else u'✗ 对不上'))
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lo, hi = ZDIFF_TARGET * 0.9, ZDIFF_TARGET * 1.1
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print(u' 90 Ω ±10%% 窗口 = %.1f ~ %.1f Ω → %s'
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% (lo, hi, u'在窗口内' if lo <= zd <= hi else u'**出窗口**'))
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print(u'\n 文档那句「回到 2 oz 同样几何只剩 83 Ω，W 要收到约 0.24 mm」：')
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zd2 = zdiff_microstrip(W_USB_MM, S_USB_MM, H_L1L2_MM, T_2OZ_MM)
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w2, z2 = width_for_z(ZDIFF_TARGET, zdiff_microstrip, H_L1L2_MM, T_2OZ_MM,
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s_mm=S_USB_MM)
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print(u' 2oz 同几何 Zdiff = %.1f Ω （文档写 83） %s'
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% (zd2, u'✓ 对上' if abs(zd2 - 83) < 1.5 else u'✗ 对不上'))
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print(u' 2oz 下解 90 Ω 的线宽 = %.3f mm （文档写 ≈0.24） %s'
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% (w2, u'✓ 对上' if abs(w2 - 0.24) < 0.015 else u'✗ 对不上'))
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print(u'\n 反解自检（1oz，固定 S=%.2f）：' % S_USB_MM)
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w1, z1 = width_for_z(ZDIFF_TARGET, zdiff_microstrip, H_L1L2_MM, T_1OZ_MM,
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s_mm=S_USB_MM)
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print(u' 要正好 90.0 Ω 需 W = %.3f mm（现用 %.2f，差 %+.0f µm）'
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% (w1, W_USB_MM, (W_USB_MM - w1) * 1000))
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print(u'\n' + u'=' * 74)
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print(u'IPC-2221 载流（回验 §10.1 的「4A 外层 1oz 要 1.34 mm」）')
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print(u'=' * 74)
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print(u' %-8s %-10s %-8s %-12s %s' % (u'电流', u'层', u'ΔT', u'截面积', u'最小线宽'))
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for i, ext, dt in ((4.0, True, 20), (4.0, True, 10), (4.0, False, 20),
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(8.0, False, 20), (1.0, True, 20)):
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t = T_1OZ_MM if ext else T_HALFOZ_MM
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w, a = ipc_width_mm(i, t, dt, ext)
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print(u' %-8s %-10s %-8s %-12s %.2f mm'
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% (u'%.0f A' % i, u'外层 1oz' if ext else u'内层 0.5oz',
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u'%d °C' % dt, u'%.0f mil²' % a, w))
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w4, _ = ipc_width_mm(4.0, T_1OZ_MM, 20, True)
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print(u'\n 4A / 外层 1oz / ΔT=20°C → %.2f mm （文档写 1.34） %s'
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% (w4, u'✓ 对上' if abs(w4 - 1.34) < 0.03 else u'✗ 对不上'))
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def sweep():
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print(u'\n' + u'=' * 74)
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print(u'叠层敏感度：Zdiff 随介质厚度 h 与铜厚变化（W=%.2f / S=%.2f 固定）'
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% (W_USB_MM, S_USB_MM))
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print(u'=' * 74)
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print(u' %-12s %-12s %-12s %s' % (u'h (mm)', u'1oz', u'2oz', u'判定(1oz)'))
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for h in (0.15, 0.18, 0.2104, 0.25, 0.30):
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a = zdiff_microstrip(W_USB_MM, S_USB_MM, h, T_1OZ_MM)
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b = zdiff_microstrip(W_USB_MM, S_USB_MM, h, T_2OZ_MM)
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ok = u'✓' if 81 <= a <= 99 else u'✗ 出窗口'
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mark = u' ← 定稿' if abs(h - H_L1L2_MM) < 1e-6 else u''
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print(u' %-12s %-12s %-12s %s%s'
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% (u'%.4f' % h, u'%.1f Ω' % a, u'%.1f Ω' % b, ok, mark))
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print(u'\n ⇒ h 从 0.2104 掉到 0.15（板厂换 prepreg）就掉出 ±10% 窗口。')
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print(u' §15.3 那句「叠层一变就得重算」是有量的：h 每变 0.01 mm，Zdiff 约变 %.1f Ω。'
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% abs(zdiff_microstrip(W_USB_MM, S_USB_MM, H_L1L2_MM + 0.01, T_1OZ_MM)
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- zdiff_microstrip(W_USB_MM, S_USB_MM, H_L1L2_MM, T_1OZ_MM)))
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def main():
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ap = argparse.ArgumentParser()
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ap.add_argument('--zdiff', type=float, help=u'目标差分阻抗 Ω，反解线宽')
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ap.add_argument('--z0', type=float, help=u'目标单端阻抗 Ω，反解线宽')
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ap.add_argument('--spacing', type=float, default=S_USB_MM, help=u'差分间距 mm')
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ap.add_argument('--height', type=float, default=H_L1L2_MM, help=u'介质厚度 mm')
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ap.add_argument('--er', type=float, default=ER_FR4)
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ap.add_argument('--copper', choices=('0.5oz', '1oz', '2oz'), default='1oz')
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ap.add_argument('--stripline', action='store_true', help=u'内层带状线（默认表层微带）')
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ap.add_argument('--current', type=float, help=u'载流 A，求最小线宽')
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ap.add_argument('--dt', type=float, default=DT_DEFAULT,
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help=u'允许温升 °C（默认 20，跟设计文档 §10.1 一致）')
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ap.add_argument('--internal', action='store_true', help=u'载流按内层算')
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ap.add_argument('--sweep', action='store_true')
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a = ap.parse_args()
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t = {'0.5oz': T_HALFOZ_MM, '1oz': T_1OZ_MM, '2oz': T_2OZ_MM}[a.copper]
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if a.zdiff:
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fn = zdiff_stripline if a.stripline else zdiff_microstrip
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w, z = width_for_z(a.zdiff, fn, a.height, t, a.er, s_mm=a.spacing)
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print(u'目标 %.1f Ω 差分%s，S=%.2f h=%.4f εr=%.1f %s'
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% (a.zdiff, u'带状线' if a.stripline else u'微带', a.spacing,
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a.height, a.er, a.copper))
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print(u' → W = %.3f mm （实得 %.2f Ω）' % (w, z))
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return
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if a.z0:
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fn = z0_stripline if a.stripline else z0_microstrip
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w, z = width_for_z(a.z0, fn, a.height, t, a.er)
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print(u'目标 %.1f Ω 单端 → W = %.3f mm （实得 %.2f Ω）' % (a.z0, w, z))
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return
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if a.current:
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w, area = ipc_width_mm(a.current, t, a.dt, not a.internal)
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print(u'%.2f A / %s / %s / ΔT=%.0f°C → 最小线宽 %.2f mm（截面 %.0f mil²）'
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% (a.current, u'内层' if a.internal else u'外层', a.copper, a.dt, w, area))
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return
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verify()
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if a.sweep:
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sweep()
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if __name__ == '__main__':
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main()
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