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Twisted wire transmission line



Twisted-pair calculator

Frequency    MHz
Electrical length    deg
Wire model 
Conductor diameter (d)    μm
Wire diameter (D)   μm
Dielectric relative permittivity (εr )   
Relative permeability (μr)  =     
Twist pitch(P)   mm
Impedance (Z0) ≈    Ω
Effective permittivity (εe) ≈    
Capacitance ≈     pF/m
Inductance ≈     nH/m
Velocity of propagation ≈     
Phisical length ≈     mm
ztwistedwire - Analyze twisted wire transmission line. Rev.0.24 (July 21, 2024) (c) 2022 Takayuki HOSODA

Note : The calculation is optimized for a twist angle ranging from 20° to 45° and,
its VSWR is expected to be within 1.1. The skin effect has been neglected.

Formulas used [1]

Z_0 &=& \frac{ \eta_0}{ \pi}{ \sqrt{ \frac{\mu_r}{\varepsilon_{e}}} }\cosh^{-1}\left(\frac{D}{d}\right)\\ \varepsilon_{e} &=& 0.25 + 0.0004 \ \theta^2\\ \theta &=& \tan^{-1}\left(\frac{\pi D}{p}\right)
η0   :   Impedance of free space   376.730313668   [Ω]

Note : Jefferson[1] found these equations sufficiently accurate to design transmission lines with VSWR ≤ 1.1 : 1.

REFERENCE

  1. Lefferson, Peter, "Twisted Magnet Wire Transmission Line" IEEE Transactions on Parts, Hybrids, and Packaging, Vol. PHP-7, No. 4, December 1971, pp. 148-154, and errata.
  2. Brian C. Wadell, "Transmission Line Design Handbook", Artech House, Inc., 1991, ISBN 0-89006-436-9, pp.68-69
  3. IPC-2141A "Design Guide for High-Speed Controlled Impedance Circuit Boards"

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