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سجل التغييرات الكاملالمحرّك 1.26.4

Controlled Impedance & Delay

المسارات والنحاس

Characteristic impedance for six transmission-line types, propagation delay, and the critical length.

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المدخلات

ملف اللوحة

Fills Dielectric constant from your board profile.

FR-4 ≈ 4.2–4.6 · Rogers 4350 ≈ 3.48 · PTFE ≈ 2.2, at your signal frequency
Tolerances

النتائج

Characteristic impedance Z0
48.9Ω
أظهر خطوات الحساب
  1. Geometry ratiow / h = 0.2 mm / 0.11 mm = 1.818
  2. Effective permittivityε_eff at w/h = 1.82, ε_r = 4.2, t = 35 µm, microstrip (Hammerstad-Jensen) = 3.009
  3. Characteristic impedanceZ₀ = f(w/h, ε_eff), microstrip (Hammerstad-Jensen) = 48.9 Ω
Effective εr
3.009
كل النتائج (2)
Inductance
0.283nH/mm
Capacitance
0.118pF/mm
Z0 vs width

إلى أي حد نعرف هذا الرقم

من أين تأتي الطريقة
  • Hammerstad and Jensen
  • Cohn

Hammerstad and Jensen, Accurate Models for Microstrip Computer-Aided Design المعادلة

Cohn, Characteristic Impedance of the Shielded-Strip Transmission Line المعادلة

صادقة ضمن
  • Dielectric constant 1 to 20

Dielectric constant The closed-form fits were derived for ordinary laminate permittivities. Hammerstad and Jensen

مدى دقتها
Closed-form fits to the exact static solution.

Within their range, ε_r (quoted at one frequency, not yours) and etch tolerance move the answer more than model error does. Use the tolerance analysis to see the band.

عملياً يهيمن على عدم اليقين مدخل واحد: Dielectric constant. ضيّقه يضِق معه الجواب.

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المقطع العرضي

المبدأ

Every trace over a reference plane is a transmission line. Whether you must treat it as one depends on the rise time, not the clock: if the round trip along the trace is comparable with the edge, reflections distort the waveform.

Microstrip (Hammerstad-Jensen)
Z0=η02πεeff  ln⁡ ⁣(f(u)u+1+(2u)2),u=whZ_0 = \frac{\eta_0}{2\pi\sqrt{\varepsilon_{eff}}}\;\ln\!\left(\frac{f(u)}{u} + \sqrt{1 + \left(\frac{2}{u}\right)^{2}}\right), \qquad u = \frac{w}{h}
f(u) = 6 + (2π − 6)·exp(−(30.666/u)^0.7528), with the paper’s thickness correction folded into u. Outside 0.1 ≤ w/h ≤ 10 you get a warning: a conservative range set here, not one quoted from the paper.
Effective dielectric constant (microstrip)
εeff=εr+12+εr−12(1+10u)−a(u) b(εr)\varepsilon_{eff} = \frac{\varepsilon_r + 1}{2} + \frac{\varepsilon_r - 1}{2}\left(1 + \frac{10}{u}\right)^{-a(u)\,b(\varepsilon_r)}
a(u) and b(εr) are the paper’s fitted exponents. Embedded microstrip moves this toward εr with burial depth: εeff,em = εeff·e^(−2h₂/h) + εr·(1 − e^(−2h₂/h)).
Stripline (Cohn, exact at t = 0)
Z0=30πεr  K(k)K(k′),k=sech ⁣(πw2b)Z_0 = \frac{30\pi}{\sqrt{\varepsilon_r}}\;\frac{K(k)}{K(k')}, \qquad k = \t{sech}\!\left(\frac{\pi w}{2 b}\right)
K is the complete elliptic integral. Copper thickness enters through Wheeler’s effective-width correction; b is the plane-to-plane spacing.
Grounded coplanar waveguide
Z0=60πεeff  1K(k1)K(k1′)+K(k3)K(k3′),k1=ww+2sZ_0 = \frac{60\pi}{\sqrt{\varepsilon_{eff}}}\;\frac{1}{\tfrac{K(k_1)}{K(k_1')} + \tfrac{K(k_3)}{K(k_3')}}, \qquad k_1 = \frac{w}{w + 2s}
k₃ = tanh(πw/4h)/tanh(π(w+2s)/4h). Conformal mapping per Ghione-Naldi; the model assumes zero copper thickness.
Differential (edge-coupled, IPC-2141)
Zdiff≈2Z0(1−0.48 e−0.96 s/h)  microstripZ_{diff} \approx 2 Z_0\left(1 - 0.48\,e^{-0.96\,s/h}\right)\;\t{microstrip}
2Z₀(1 − 0.347·e^(−2.9 s/b)) for stripline. These empirical factors are the weakest step, about ±10 %.
Propagation delay
tpd=εeffc0≈3.34 εeff  ps/mm=84.7 εeff  ps/incht_{pd} = \frac{\sqrt{\varepsilon_{eff}}}{c_0} \approx 3.34\,\sqrt{\varepsilon_{eff}}\;\t{ps/mm} = 84.7\,\sqrt{\varepsilon_{eff}}\;\t{ps/inch}
Line parameters
Z0=LCtpd=LCZ_0 = \sqrt{\frac{L}{C}} \qquad t_{pd} = \sqrt{LC}
Critical length
lcrit=tr2 tpd(electrically long)ldesign=tr6 tpd(safe)l_{crit} = \frac{t_r}{2\,t_{pd}} \quad(\t{electrically long}) \qquad l_{design} = \frac{t_r}{6\,t_{pd}} \quad(\t{safe})
Signal bandwidth from rise time
fknee≈0.35trf_{knee} \approx \frac{0.35}{t_r}
  • wwtrace width
  • hhdielectric height to the reference plane (b for stripline)
  • h2h_2dielectric above an embedded trace
  • ttcopper thickness
  • sspair spacing, or the CPW gap to the coplanar ground
  • trt_r10–90 % rise time of the driver
  • η0\eta_0impedance of free space, 376.73 Ω
تفاصيل إضافية

Layout rules

  • Never route across a plane split. The return current cannot follow, and the loop area grows. It is a common cause of EMC failures.
  • Add a return via next to any signal via that changes reference plane, or a decoupling capacitor if the planes are at different potentials.
  • Match delay, not length. Microstrip and stripline on FR-4 differ, about 5.8 against 6.9 ps/mm.
Sanity check on FR-4 (εr = 4.2). About 0.19 mm for 50 Ω microstrip over a 0.11 mm prepreg. Solder mask, trapezoidal etch and the frequency dependence of εr move the real value, so take the fabricator's stack-up as the final answer.
References: E. Hammerstad and Ø. Jensen, Accurate Models for Microstrip Computer-Aided Design; S. B. Cohn, Characteristic Impedance of the Shielded-Strip Transmission Line; G. Ghione and C. Naldi, Electronics Letters; B. C. Wadell, Transmission Line Design Handbook; IPC-2141; IPC-2251. For anything above ~2 GHz use a 2-D field solver and your fabricator's measured stack-up.

إصدار المحرك ⁨1.26.4⁩