Online calculator
Microwire transmission line



Microwire transmission line calculator

Frequency    MHz
Electrical length    deg
Dielectric relative permittivity (εr )   
Dielectric thickness (h )   μm
Conductor diameter (d)    μm
Impedance (Z0) ≈    Ω
Effective permittivity (Εeff) ≈    
Capacitance ≈     pF/m
Inductance ≈     nH/m
Velocity of propagation ≈     
Phisical length ≈     mm
zmicrowire - Analyze microwire transmission line. Rev.0.1 (Dec. 19, 2022) (c) 2022 Takayuki HOSODA

Formulas used [1]

\varepsilon_{eff} &=& \frac{\varepsilon_{r} + 1}{2} + \frac{\varepsilon_{r} - 1}{2}\left(\sqrt{\frac{d}{d + 12 h}} + \Delta \right) \\ \Delta &=& \left\{ \begin{array}{ll} 0.04 \left(1 - \displaystyle\frac{d}{h}\right)^2 \qquad &\text { if $d < h$,}\\ 0 & \text{ if $d \geq h$} \end{array} \right.\\ Z_0 &=& \frac{ \mu_0 c} {2 \pi \sqrt {\varepsilon_{eff}} }\ \cosh^{-1} \left(1 + \displaystyle\frac{2h}{d}\right)

where
η0 : Impedance of free space 376.730313668(57) Ω

APPENDIX

Example of field solver results (simulation box width W = 12 h + 4 t + 2 s + w, box height H = 8 h) Length unit in [ grid ].

w = 115, h = 200, ϵr=4.6, W = 1775, H = 915 : Z0 ≃ 80.883 Ω, ϵr_eff = 2.47

microwireline
Pseudo color visualization of absolute value of the electric field.
REFERENCE
  1. IPC-2141A "Design Guide for High-Speed Controlled Impedance Circuit Boards"

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