Microwire transmission line

round wire on dielectric with ground

2022-12-20 Revised 2026-02-12

Takayuki HOSODA

Microwire transmission line calculator

Frequency MHz

Electrical length deg

Dielectric relative permittivity (ε_r )

Dielectric thickness (h ) μm

Conductor diameter (d) μm

Impedance (Z₀) ≈ Ω

Effective permittivity (Ε_eff) ≈

Capacitance ≈    pF/m

Inductance ≈    nH/m

Velocity of propagation ≈

Phisical length ≈    mm

zmicrowire - Analyze microwire transmission line. Rev.0.3 (Feb. 12, 2026) (c) 2022 Takayuki HOSODA

This calculator uses an approximate model that applies microstrip-based formulas to a round conductor. As a result, the effective relative permittivity may be slightly overestimated. The error may increase when the conductor diameter is large relative to the substrate thickness (e.g., d/h ≥ 0.4). If the wire has an insulating coating, the electric field distribution changes significantly and the model may no longer be valid. For accurate impedance or effective permittivity values, measurement data or full electromagnetic simulation is recommended.

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(\displaystyle\frac{2h}{d}\right)$

where
η₀: characteristic impedance of vacuum of free space 376.730313668(57) Ω (CODATA 2022)

APPENDIX

Example of electric field solver results

microwireline electric field visualizathin

REFERENCE

Cohn, Seymour B., Characteristic Impedance of the Shielded Strip Transmission Line, IRE Transactions on Microwave Theory and Techniques, Vol. MTT-2, No.3, July 1954, pp 52-57
Hiberg, Wolfgang, Electrical Characteristics of Transmission Lines, Artech House, Norwood, MA, 1979
Caverly, Robert H., Characteristic Impedance of Integrated Bond Wires, IEEE Transactions on Microwve Theory and Techniques, Vol. MTT-34, No. 9, September 1986, pp. 982-984
Brian C. Wadell, Transmission Line Design Handbook, Artech House, 1991, ISBN 0-89006-436-9.
Wheeler, Harold A., Transmission-Line Properties of a Round Wire in a Polygon Shield, IEEE transactions on Microwave Theory and Techniques, Vol. MTT-27, No.8, August 1979, pp. 717-721
IPC, IPC-2141A: Design Guide for High-Speed Controlled Impedance Circuit Boards, IPC-2141A, March 2004.
NIST, Fundamental Physical Constants .

Frequency	MHz
Electrical length	deg
*Dielectric relative permittivity (ε_r* )**
Dielectric thickness (h )	μm
Conductor diameter (d)	μm
Impedance (Z₀) ≈	Ω
Effective permittivity (Ε_eff) ≈
Capacitance ≈	pF/m
Inductance ≈	nH/m
Velocity of propagation ≈
Phisical length ≈	mm