# skrf.media.cpw.CPW¶

class skrf.media.cpw.CPW(frequency=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].

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

• z0 (number, array-like, or None (default None)) – the port impedance for media. Only needed if different from the characteristic impedance Z0 of the transmission line. In ohm

• 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__()

Note

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.

References

QUCSa

http://qucs.sourceforge.net/docs/technical.pdf

QUCSb

http://www.qucs.sourceforge.net/

DBLS01

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.

SvDe01

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

GhNa84

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.

GhNa83

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.

Cohn60

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.

GGBB96

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

FGVM91

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.

GMDK97

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.

Whee42

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

OwWu58

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.

Ghio93

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.

Attributes

 Z0 Characteristic impedance alpha Real (attenuation) component of gamma. beta Imaginary (propagating) component of gamma. gamma Propagation constant. npoints Number of points of the frequency axis. v_g Complex group velocity (in m/s). v_p Complex phase velocity (in m/s). z0 Characteristic Impedance.

Methods

 __init__ analyse_dielectric This function calculate the frequency-dependent relative permittivity of dielectric and tangential loss factor. analyse_dispersion This function computes the frequency-dependent characteristic impedance and effective permittivity accounting for coplanar waveguide frequency dispersion. analyse_loss The function calculates the conductor and dielectric losses of a complanar waveguide line using wheeler's incremental inductance rule. analyse_quasi_static 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. attenuator Ideal matched attenuator of a given length. capacitor Capacitor. copy Copy of this Media object. delay_load Delayed load. delay_open Delayed open transmission line. delay_short Delayed Short. electrical_length Calculate the complex electrical length for a given distance. extract_distance Determines physical distance from a transmission or reflection Network. get_array_of impedance_mismatch Two-port network for an impedance mismatch. inductor Inductor. isolator Two-port isolator. line Transmission line of a given length and impedance. load Load of given reflection coefficient. lossless_mismatch Lossless, symmetric mismatch defined by its return loss. match Perfect matched load ($$\Gamma_0 = 0$$). mode Create another mode in this medium. open Open ($$\Gamma_0 = 1$$). plot random Complex random network. resistor Resistor. short Short ($$\Gamma_0 = -1$$) shunt Shunts a Network. shunt_capacitor Shunted capacitor. shunt_delay_load Shunted delayed load. shunt_delay_open Shunted delayed open. shunt_delay_short Shunted delayed short. shunt_inductor Shunted inductor. splitter Ideal, lossless n-way splitter. tee Ideal, lossless tee. theta_2_d Convert electrical length to physical distance. thru Matched transmission line of length 0. to_meters Translate various units of distance into meters. white_gaussian_polar Complex zero-mean gaussian white-noise network. write_csv write this media's frequency, gamma, Z0, and z0 to a csv file.