class, z0_port=None, z0_override=None, z0=None, w=0.003, s=0.0003, h=1.55, ep_r=4.5, t=None, diel='djordjevicsvensson', rho=1.68e-08, tand=0, f_low=1000.0, f_high=1000000000000.0, f_epr_tand=1000000000.0, has_metal_backside=False, compatibility_mode=None, *args, **kwargs)[source]

Coplanar waveguide.

A coplanar waveguide transmission line is defined in terms of width, spacing, and thickness on a given relative permittivity substrate of a certain height. The line has a conductor resistivity and a tangential loss factor. The backside of the strip can be made of air or metal (grounded coplanar waveguide).

This class is highly inspired by the technical documentation [QUCSa] and sources provided by the qucs project [QUCSb] .

In addition, Djordjevic [DBLS01] /Svensson [SvDe01] wideband debye dielectric model is considered to provide a more realistic modelling of broadband microstrip with causal time domain response.

A compatibility mode is provided to mimic the behaviour of QUCS or of Keysight ADS. There is known differences in the output of these simulators.

The quasi-static models of characteristic impedance and effective permittivity give the value at zero frequency. The dispersion models compute frequency-dependant values of these variables.

  • Quasi-static characteristic impedance and effective permittivity model use [GhNa84] and [GhNa83]. The models are corrected to account for strip thickness using a first-order approach described in [GGBB96]. A comparison shows that ADS simulator uses another thickness correction method that is according to ADS doc based on [Cohn60]. This second method is not implemented in skrf.

  • Frequency dispersion of impedance and effective permittivity model use [FGVM91] and [GMDK97].

  • Loss model is computed using Wheeler’s incremental inductance rule [Whee42] applied to coplanar waveguide by [OwWu58] and [Ghio93].

  • frequency (Frequency object, optional) – frequency band of the media. The default is None.

  • z0_port (number, array-like, or None) – z0_port is the port impedance for networks generated by the media. If z0_port is not None, the networks generated by the media are renormalized (or in other words embedded) from the characteristic impedance z0 of the media to z0_port. Else if z0_port is None, the networks port impedances will be the raw characteristic impedance z0 of the media. (Default is None)

  • z0_override (number, array-like, or None) – z0_override override the characteristic impedance for the media. If z0_override is not None, the networks generated by the media have their characteristic impedance z0 overrided by z0_override. (Default is None)

  • z0 (number, array-like, or None) – deprecated parameter, alias to z0_override if z0_override is None. Emmit a deprecation warning.

  • w (number, or array-like) – width of the center conductor, in m. Default is 3e-3 m.

  • s (number, or array-like) – spacing (width of the gap), in m. Default is 0.3e-3 m.

  • h (number, or array-like) – height of the substrate between backside and conductor, in m. Default is 1.55 m (equivalent to infinite height for default w and s).

  • t (number, or array-like, optional) – conductor thickness, in m. Default is None (no width correction to account for strip thickness).

  • has_metal_backside (bool, default False) – If the backside is air (False) or metal (True)

  • ep_r (number, or array-like, optional) – relative permittivity of the substrate at frequency f_epr_tand, no unit. Default is 4.5.

  • diel (str) –

    dielectric frequency dispersion model in:

    • ’djordjevicsvensson’ (default)

    • ’frequencyinvariant’

  • rho (number, or array-like, or None) – resistivity of conductor, ohm / m. Default is 1.68e-8 ohm /m (copper).

  • tand (number, or array-like) – dielectric loss factor at frequency f_epr_tand. Default is 0.

  • f_low (number, or array-like) – lower frequency for wideband Debye Djordjevic/Svensson dielectric model, in Hz. Default is 1 kHz.

  • f_high (number, or array-like) – higher frequency for wideband Debye Djordjevic/Svensson dielectric model, in Hz. Default is 1 THz.

  • f_epr_tand (number, or array-like) – measurement frequency for ep_r and tand of dielectric, in Hz. Default is 1 GHz.

  • compatibility_mode (str or None (default)) –

    If set to ‘qucs’, following behaviour happens :

    • Characteristic impedance will be real (no imaginary part due to tand)

  • *args (arguments, keyword arguments) – passed to Media’s constructor (__init__()

  • **kwargs (arguments, keyword arguments) – passed to Media’s constructor (__init__()


When the thickness of the strip is smaller than 3 skin depth, the losses model gives over-optimistic results and the media will issue a warning. At DC, the losses of the line could be smaller than its conductor resistance, which is not physical.



Djordjevic, R.M. Biljic, V.D. Likar-Smiljanic, T.K. Sarkar, Wideband frequency-domain characterization of FR-4 and time-domain causality, IEEE Trans. on EMC, vol. 43, N4, 2001, p. 662-667.


C. Svensson, G.E. Dermer, Time domain modeling of lossy interconnects, IEEE Trans. on Advanced Packaging, May 2001, N2, Vol. 24, pp.191-196.


G. Ghione and C. Naldi. “Analytical Formulas for Coplanar Lines in Hybrid and Monolithic MICs”, Electronics Letters, Vol. 20, No. 4, February 16, 1984, pp. 179-181.


G. Ghione and C. Naldi. “Parameters of Coplanar Waveguides with Lower Common Planes”, Electronics Letters, Vol. 19, No. 18, September 1, 1983, pp. 734-735.


S. B. Cohn, “Thickness Corrections for Capacitive obstacles and Strip Conductors”, IRE Trans. on Microwave Theory and Techniques, Vol. MTT-8, November 1960, pp. 638-644.


K. C. Gupta, R. Garg, I. J. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, 2nd ed.Artech House, Inc., 1996.


M. Y. Frankel, S. Gupta, J. A. Valdmanis, and G. A. Mourou, “Terahertz Attenuation and Dispersion Characteristics of Coplanar Transmission Lines” IEEE Trans. on Microwave Theory and Techniques, vol. 39, no. 6, pp. 910-916, June 1991.


S. Gevorgian, T. Martinsson, A. Deleniv, E. Kollberg, and I. Vendik, “Simple and accurate dispersion expression for the effective dielectric constant of coplanar waveguides” in Proceedings of Microwaves, Antennas and Propagation, vol. 144, no. 2.IEE, Apr. 1997, pp. 145-148.


H. A. Wheeler, “Formulas for the Skin Effect,” Proceedings of the IRE, vol. 30, no. 9, pp. 412-424, Sept. 1942.


G. H. Owyang and T. T. Wu, “The Approximate Parameters of Slot Lines and Their Complement” IRE Transactions on Antennas and Propagation, pp. 49-55, Jan. 1958.


G. Ghione, “A CAD-Oriented Analytical Model for the Losses of General Asymmetric Coplanar Lines in Hybrid and Monolithic MICs” IEEE Trans. on Microwave Theory and Techniques, vol. 41, no. 9, pp. 1499-1510, Sept. 1993.



Characteristic Impedance


Real (attenuation) component of gamma.


Imaginary (propagating) component of gamma.


Propagation constant.


Number of points of the frequency axis.


Complex group velocity (in m/s).


Complex phase velocity (in m/s).


Return Characteristic Impedance z0_characteristic.


Characteristic Impedance, \(z_0\).


Port Impedance.


Port Impedance.




This function calculate the frequency-dependent relative permittivity of dielectric and tangential loss factor.


This function computes the frequency-dependent characteristic impedance and effective permittivity accounting for coplanar waveguide frequency dispersion.


The function calculates the conductor and dielectric losses of a complanar waveguide line using wheeler's incremental inductance rule.


This function calculates the quasi-static impedance of a coplanar waveguide line, the value of the effective permittivity as per filling factor, and the effective width due to the finite conductor thickness for the given coplanar waveguide line and substrate properties.


Ideal matched attenuator of a given length.




Capacitor with Q factor.


Copy of this Media object.


Delayed load.


Delayed open transmission line.


Delayed Short.


Calculate the complex electrical length for a given distance.


Determines physical distance from a transmission or reflection Network.



Two-port network for an impedance mismatch.




Inductor with Q factor.


Two-port isolator.


Transmission line of a given length and impedance.


Load of given reflection coefficient.


Lossless, symmetric mismatch defined by its return loss.


Perfect matched load (\(\Gamma_0 = 0\)).


Create another mode in this medium.


Open (\(\Gamma_0 = 1\)).



Complex random network.




Short (\(\Gamma_0 = -1\))


Shunts a Network.


Shunted capacitor.


Shunted delayed load.


Shunted delayed open.


Shunted delayed short.


Shunted inductor.


Shunted resistor.


Ideal, lossless n-way splitter.


Ideal, lossless tee.


Convert electrical length to physical distance.


Matched transmission line of length 0.


Translate various units of distance into meters.


Complex zero-mean gaussian white-noise network.


write this media's frequency, gamma, Z0, and z0 to a csv file.