# skrf.media.definedAEpTandZ0.DefinedAEpTandZ0¶

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

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 (number, array-like, or None) – The port impedance for this medium. Only needed if different from the characteristic impedance of the transmission line. If z0 is None then will default to Z0

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

Attenuation due to conductor loss in dB/m/sqrt(Hz) The attenuation $$A(f)$$ 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.

• 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 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 Characteristic Impedance.

Methods

 __init__ 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.