janik
06c62e04f8
DC/AC resistance, power dissipation, and via/injection-area currents of copper zone fills. KiCad 10 IPC-API plugin (kicad-python/kipy): multi-layer via-coupled FDM solver, multi-part terminals via User.1/User.2 marker layers, pads as contacts, uniform-injection and equipotential contact models, per-foil skin effect, optional solder/copper buildup on mask openings. 54-case test suite incl. exact analytic references. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
79 lines
2.7 KiB
Python
79 lines
2.7 KiB
Python
"""Skin-effect corrections: frequency-dependent effective sheet
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resistance of a copper foil and via-barrel wall.
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1D diffusion through the foil thickness (exact): with tau = (1+j)/delta,
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the internal impedance per square of a foil of thickness t is
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one-sided field (plane over a return plane): Zs = tau*rho * coth(tau*t)
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two-sided field (isolated foil): Zs = tau*rho/2 * coth(tau*t/2)
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Both reduce to rho/t at DC and to rho/delta (resp. rho/(2*delta)) at
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high frequency. R_AC = Re(Zs) is used as the effective sheet resistance.
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HONESTY NOTE (also in the README): only the through-thickness current
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crowding is modeled. Lateral redistribution (proximity effect - AC
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current following the minimum-inductance path) needs a magneto-
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quasistatic solve and is NOT captured; since the resistance-driven
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distribution is the minimum-dissipation one, the reported AC resistance
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is a rigorous LOWER BOUND at the given frequency.
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"""
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from __future__ import annotations
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import cmath
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import math
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MU0 = 4e-7 * math.pi
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def skin_depth_m(freq_hz: float, rho_ohm_m: float) -> float:
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return math.sqrt(2.0 * rho_ohm_m / (2.0 * math.pi * freq_hz * MU0))
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def _coth(x: complex) -> complex:
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return 1.0 / cmath.tanh(x)
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def sheet_resistance_ac(thickness_m: float, freq_hz: float,
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rho_ohm_m: float, sides: int = 1) -> float:
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"""Effective sheet resistance [ohm/sq] of a foil at freq_hz.
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sides=1: field on one side (plane facing a return plane, conservative);
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sides=2: symmetric field on both sides (isolated foil)."""
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if freq_hz <= 0.0:
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return rho_ohm_m / thickness_m
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delta = skin_depth_m(freq_hz, rho_ohm_m)
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tau = (1.0 + 1.0j) / delta
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if sides == 2:
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zs = tau * rho_ohm_m / 2.0 * _coth(tau * thickness_m / 2.0)
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else:
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zs = tau * rho_ohm_m * _coth(tau * thickness_m)
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return zs.real
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def resistance_factor(thickness_m: float, freq_hz: float,
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rho_ohm_m: float, sides: int = 1) -> float:
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"""R_AC / R_DC of a foil (or barrel wall) of the given thickness."""
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if freq_hz <= 0.0:
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return 1.0
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return (sheet_resistance_ac(thickness_m, freq_hz, rho_ohm_m, sides)
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/ (rho_ohm_m / thickness_m))
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def parse_frequency(text: str) -> float:
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"""'0', '100k', '1.5M', '142500' -> Hz. Empty/invalid -> 0 (DC)."""
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t = text.strip().lower().replace(",", ".").removesuffix("hz").strip()
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if not t:
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return 0.0
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mult = 1.0
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if t.endswith("meg"):
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mult, t = 1e6, t[:-3]
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elif t.endswith("m"):
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mult, t = 1e6, t[:-1]
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elif t.endswith("k"):
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mult, t = 1e3, t[:-1]
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elif t.endswith("g"):
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mult, t = 1e9, t[:-1]
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try:
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return max(0.0, float(t) * mult)
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except ValueError:
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return 0.0
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