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=1.68e08, tand=0, rough=1.5e07, f_low=1000.0, f_high=1000000000000.0, f_epr_tand=1000000000.0, compatibility_mode=None, *args, **kwargs)[source]¶
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 quasistatic models of chercteristic impedance and effective permittivity give the value at zero frequency. The dispersion models compute a frequencydependant values of these variables.
Quasistatic 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 quasistatic models add a certain amount to W to accound for nonzero thickness of the strip. Computation with zero thickness is possible.
 Parameters
frequency (
Frequency
object) – frequency band of the mediaz0 (number, arraylike, 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 arraylike) – width of conductor, in m
h (number, or arraylike) – height of substrate between ground plane and conductor, in m
t (number, or arraylike or None, optional) – conductor thickness, in m. Default is None (no width correction to account strip thickness).
ep_r (number, or arraylike) – relative permittivity of dielectric at frequency f_epr_tand, no unit
mu_r (number, arraylike) – relative permeability mof dielectric, no unit
model (str) –
microstripline quasistatic 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 arraylike, optional) – resistivity of conductor, ohm / m
tand (number, or arraylike) – dielectric loss factor at frequency f_epr_tand
rough (number, or arraylike) – RMS roughness of conductor in m
f_low (number, or arraylike) – lower frequency for wideband Debye Djordjevic/Svensson dielectric model, in Hz
f_high (number, or arraylike) – higher frequency for wideband Debye Djordjevic/Svensson dielectric model, in Hz
f_epr_tand (number, or arraylike) – 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)
Quasistatic relative permittivity and impedance will by used for loss computation instead of frequencydispersed values
Kobayashi and Yamashita models will disperse permittivity but keep quasistatic 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 overoptimistic 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
 2
https://github.com/Qucs/qucsator/blob/develop/src/components/microstrip/msline.cpp
 3
E. Hammerstad and Ø. Jensen, “Accurate Models for Microstrip ComputerAided Design”, Symposium on Microwave Theory and Techniques, pp. 407409, June 1980.
 4
M. Kirschning and R. H. Jansen, “Accurate Model for Effective Dielectric Constant of Microstrip with Validity up to MillimeterWave Frequencies”, Electronics Letters, vol. 8, no. 6, pp. 272273, Mar. 1982.
 5
R. H. Jansen and M. Kirschning, “Arguments and an accurate Model for the PowerCurrent Formulation of Microstrip Characteristic Impedance”, Archiv für Elektronik und Übertragungstechnik (AEÜ), vol. 37, pp. 108112, 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. 12461250, Aug. 1988.
 7
M. V. Schneider, “Microstrip Lines for Microwave Integrated Circuits”, The Bell System Technical Journal, vol. 48, pp. 14211444, May 1969.
 8
M. V. Schneider, “Microstrip Dispersion”, Proceedings of the IEEE, Letters, vol. 60, Jan. 1972, pp. 144146.
 9
H. A. Wheeler, “TransmissionLine Properties of a Strip on a Dielectric Sheet on a Plane, IEEE Trans. on Microwave Theory and Techniques, vol. 25, no. 8, pp. 631647, Aug. 1977.
 10
H. A. Wheeler, “Formulas for the Skin Effect,” Proceedings of the IRE, vol. 30, no. 9, pp. 412424, 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. 10361038, 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.191196.
 13
Djordjevic, R.M. Biljic, V.D. LikarSmiljanic, T.K. Sarkar, Wideband frequencydomain characterization of FR4 and timedomain causality, IEEE Trans. on EMC, vol. 43, N4, 2001, p. 662667.
Attributes
Characteristic Impedance. 

Alias fos Characteristic Impedance for backward compatibility. 

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). 

Characteristic Impedance. 
Methods
This function calculate the frequency dependent relative permittivity of dielectric and and tangeantial loss factor. 

This function compute the frequency dependent characteristic impedance and effective permittivity accounting for microstripline frequency dispersion. 

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

This function calculates the quasistatic 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. 

Ideal matched attenuator of a given length. 

Capacitor. 

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. 

Twoport network for an impedance mismatch. 

Inductor. 

Twoport 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. 

Resistor. 

Short (\(\Gamma_0 = 1\)) 

Shunts a 

Shunted capacitor. 

Shunted delayed load. 

Shunted delayed open. 

Shunted delayed short. 

Shunted inductor. 

Ideal, lossless nway splitter. 

Ideal, lossless tee. 

Convert electrical length to physical distance. 

Matched transmission line of length 0. 

Translate various units of distance into meters. 

Complex zeromean gaussian whitenoise network. 

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