skrf.media.mline.MLine

class skrf.media.mline.MLine(frequency=None, z0=None, w=3, h=1.6, t=None, ep_r=4.5, mu_r=1.0, model='hammerstadjensen', disp='kirschningjansen', diel='djordjevicsvensson', rho=1.68e-08, tand=0, rough=1.5e-07, f_low=1000.0, f_high=1000000000000.0, f_epr_tand=1000000000.0, compatibility_mode=None, *args, **kwargs)

A microstripline transmission line defined in terms of width, thickness and height on a given relative permittivity substrate. The line has a conductor resistivity and a tangential loss factor.

This class is highly inspired from the technical documentation 1 and sources provided by the qucs project 2 .

In addition, Djordjevic 3 /Svensson 4 wideband debye dielectric model is considered to provide more realistic modelling of broadband microstrip with as 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 chercteristic impedance and effective permittivity give the value at zero frequency. The dispersion models compute a frequency-dependant values of these variables.

• Quasi-static characteristic impedance and effective permittivity models:

  • Hammerstad and Jensen (default)

  • Schneider

  • Wheeler

• Frequency dispersion of impedance and effective permittivity models:

  • Hammerstad and Jensen

  • Kirschning and Jansen (default)

  • Kobayashi

  • Schneider

  • Yamashita

  • (No dispersion)

• Strip thickness correction model:

  • all quasi-static models add a certain amount to W to accound for non-zero thickness of the strip. Computation with zero thickness is possible.

Parameters

• frequency (Frequency object) – frequency band of the media

• z0 (number, array-like, or 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 conductor, in m

• h (number, or array-like) – height of substrate between ground plane and conductor, in m

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

• ep_r (number, or array-like) – relative permittivity of dielectric at frequency f_epr_tand, no unit

• mu_r (number, array-like) – relative permeability mof dielectric, no unit

• model (str) –

  microstripline quasi-static impedance and dielectric model in:

  • ’hammerstadjensen’ (default)

  • ’schneider’

  • ’wheeler’

• disp (str) –

  microstripline impedance and dielectric frequency dispersion model in:

  • ’hammerstadjensen’

  • ’kirschningjansen’ (default)

  • ’kobayashi’

  • ’schneider’

  • ’yamashita’

  • ’none’

• diel (str) –

  dielectric frequency dispersion model in:

  • ’djordjevicsvensson’ (default)

  • ’frequencyinvariant’

• rho (number, or array-like, optional) – resistivity of conductor, ohm / m

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

• rough (number, or array-like) – RMS roughness of conductor in m

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

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

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

• compatibility_mode (str or None (default)) –

  If set to ‘qucs’, following behavious happens :

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

  • Quasi-static relative permittivity and impedance will by used for loss computation instead of frequency-dispersed values

  • Kobayashi and Yamashita models will disperse permittivity but keep quasi-static impedance values

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

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

Note

In the case dispersion model only include effective permittivity, no dispersion is used for impedance in QUCS mode and Kirschning Jansen is used in ADS mode. QUCS mode is the default.

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

1

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

2

https://github.com/Qucs/qucsator/blob/develop/src/components/microstrip/msline.cpp

3

E. Hammerstad and Ø. Jensen, “Accurate Models for Microstrip Computer-Aided Design”, Symposium on Microwave Theory and Techniques, pp. 407-409, June 1980.

4

M. Kirschning and R. H. Jansen, “Accurate Model for Effective Dielectric Constant of Microstrip with Validity up to Millimeter-Wave Frequencies”, Electronics Letters, vol. 8, no. 6, pp. 272-273, Mar. 1982.

5

R. H. Jansen and M. Kirschning, “Arguments and an accurate Model for the Power-Current Formulation of Microstrip Characteristic Impedance”, Archiv für Elektronik und Übertragungstechnik (AEÜ), vol. 37, pp. 108-112, 1983.

6

M. Kobayashi, “A Dispersion Formula Satisfying Recent Requirements in Microstrip CAD”, IEEE Trans. on Microwave Theory and Techniques, vol. 36, no. 8, pp. 1246-1250, Aug. 1988.

7

M. V. Schneider, “Microstrip Lines for Microwave Integrated Circuits”, The Bell System Technical Journal, vol. 48, pp. 1421-1444, May 1969.

8

M. V. Schneider, “Microstrip Dispersion”, Proceedings of the IEEE, Letters, vol. 60, Jan. 1972, pp. 144-146.

9

H. A. Wheeler, “Transmission-Line Properties of a Strip on a Dielectric Sheet on a Plane, IEEE Trans. on Microwave Theory and Techniques, vol. 25, no. 8, pp. 631-647, Aug. 1977.

10

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

11

E. Yamashita, K. Atsuki, and T. Ueda, “An Approximate Dispersion Formula of Microstrip Lines for Computer Aided Design of Microwave Integrated Circuits”, IEEE Trans. on Microwave Theory and Techniques, vol. 27, pp. 1036-1038, Dec. 1979.

12

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

13

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.

Attributes

Z0	Characteristic Impedance.
Z0_f	Alias fos Characteristic Impedance for backward compatibility.
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 and tangeantial loss factor.
analyse_dispersion	This function compute the frequency dependent characteristic impedance and effective permittivity accounting for microstripline frequency dispersion.
analyse_loss	The function calculates the conductor and dielectric losses of a single microstrip line using wheeler's incremental inductance rule.
analyse_quasi_static	This function calculates the quasi-static impedance of a microstrip line, the value of the effective permittivity as per filling factor and the effective width due to the finite conductor thickness for the given microstrip 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.