skrf.media.definedAEpTandZ0.DefinedAEpTandZ0

class skrf.media.definedAEpTandZ0.DefinedAEpTandZ0(frequency=None, A=0.0, f_A=1.0, ep_r=1.0, tanD=0.0, z0_port=None, z0=50.0, Z0=None, f_low=1000.0, f_high=1000000000000.0, f_ep=1000000000.0, model='frequencyinvariant', *args, **kwargs)

Transmission line medium defined by A, Ep, Tand and Z0.

This medium is defined by attenuation A, relative permittivity Ep_r, loss angle tand and characteristic impedance Z0.

Djirdjevic [2] / Svennson [1] dispersion model is provided for dielectric. Default behaviour is frequency invariant.

Parameters:

• frequency (Frequency object) – Frequency band of this transmission line medium

• 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)

• A (number, array-like, default 0.0) –

  Attenuation due to conductor loss in dB/m/sqrt(Hz) The attenuation \(A(f)`at frequency :math:`f\) is:

  \[A(f) = A\sqrt{\frac{f}{f_A}}\]

• f_A (number, default 1.0) – Frequency scaling in Hz for the attenuation. See A.

• ep_r (number, array-like, default 1.0) –

  Real part of the relative permittivity of the dielectric: \(\epsilon_r'=\Re[\epsilon]\).

  If model=’frequencyinvariant’, the complex relative permittivity is:

  \[\epsilon_r(f) = \epsilon'_r + j \cdot \epsilon'_r \cdot \tan\delta\]

  if model=’djordjevicsvensson’, the complex relative permittivity is:

  \[\epsilon_r(f) = \epsilon_\inf + m \cdot \ln{\frac{f_{high} + j f_\epsilon}{f_{low} + j f_\epsilon}}\]

  where \(\epsilon_\inf\) is the permittivity value when frequency approaches infinity. In this case, the value of \(\epsilon_r\) and \(\tan\delta\) (tanD) are given for frequency \(f_\epsilon\):

  \[\epsilon_r(f_\epsilon) = \epsilon'_r+ j \cdot \epsilon'_r \cdot \tan\delta\]

• tanD (number, array-like, default 0.0) – Dielectric relative permittivity loss tangent \(\tan\delta\). See ep_r.

• z0 (number, array-like, default 50.0) – Quasi-static characteristic impedance of the medium.

• Z0 (number, array-like, or None) – deprecated parameter, only emmit a deprecation warning.

• f_low (number, default 1e3, optional) – Low frequency in Hz for for Djirdjevic/Svennson dispersion model. See ep_r.

• f_high (number, default 1e12, optional) – High frequency in Hz for for Djirdjevic/Svennson dispersion model. See ep_r.

• f_ep (number, default 1e9, , optional) – Specification frequency in Hz for for Djirdjevic/Svennson dispersion model. ep_r and tanD parameters are specified for this frequency. See ep_r.

• model (string, 'frequencyinvariant' or 'djordjevicsvensson', optional) – Use Djirdjevic/Svennson wideband Debye dispersion model or not. Default is frequency invariant behaviour.

• *args (arguments and keyword arguments)

• **kwargs (arguments and keyword arguments)

Examples

>>> from skrf.media.definedAEpTandZ0 import DefinedAEpTandZ0
>>> from skrf.frequency import Frequency
>>> f = Frequency(75,110,101,'ghz')
>>> DefinedAEpTandZ0(frequency=f, A=1, f_A=1e9, ep_r=3, z0=50)
>>> DefinedAEpTandZ0(frequency=f, A=1, f_A=1e9, ep_r=3, tand=0.02, z0=50)
>>> DefinedAEpTandZ0(frequency=f, A=1, f_A=1e9, ep_r=3, tand=0.02, z0=50,
                    f_low=1e3, f_high=1e12, f_Ep=1e9,
                    model='djordjevicsvensson')

References

[1]

C. Svensson and G. E. Dermer, “Time Domain Modeling of Lossy Interconnects,” IEEE Trans. Advanced Packaging, Vol. 24, No. 2, May 2001. https://doi.org/10.1109/6040.928754

[2]

A. R. Djordjevic, R. M. Biljic, V. D. Likar-Smiljanic, and T. K. Sarkar, “Wideband Frequency-Domain Characterization of FR-4 and Time-Domain Causality,” IEEE Trans. Electromagnetic Compatibility, Vol. 43, No. 4, November 2001. https://doi.org/10.1109/15.974647

Attributes

Z0	Characteristic Impedance
alpha	Real (attenuation) component of gamma.
alpha_conductor	Losses due to conductor resistivity.
alpha_dielectric	Losses due to dielectric
beta	Imaginary (propagating) component of gamma.
beta_phase	Phase parameter
ep_r_f	Frequency dependent complex relative permittivity of dielectric.
gamma	Propagation constant.
npoints	Number of points of the frequency axis.
tand_f	Frequency dependent dielectric loss factor.
v_g	Complex group velocity (in m/s).
v_p	Complex phase velocity (in m/s).
z0	Return Characteristic Impedance z0_characteristic.
z0_characteristic	Characteristic Impedance, \(z_0\)
z0_override	Port Impedance.
z0_port	Port Impedance.

Methods

__init__
attenuator	Ideal matched attenuator of a given length.
capacitor	Capacitor.
capacitor_q	Capacitor with Q factor.
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.
inductor_q	Inductor with Q factor.
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.
shunt_resistor	Shunted resistor.
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.