skrf.media.coaxial.Coaxial

class skrf.media.coaxial.Coaxial(frequency=None, z0_port=None, z0_override=None, z0=None, Dint=0.00081, Dout=0.005, epsilon_r=1, tan_delta=0, sigma=58000000.0, tout=None, model='schelkunoff', dielectric=None, inner_conductor=None, outer_conductor=None, *args, **kwargs)

A coaxial transmission line defined in terms of its inner/outer diameters and permittivity.

Parameters:

• frequency (Frequency object) – Frequency band.

• 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)

• z0_override (number, array-like, or None) – z0_override override the characteristic impedance for the media. If z0_override is not None, the networks generated by the media have their characteristic impedance z0 overridden by z0_override. (Default is None)

• z0 (number, array-like, or None) – deprecated parameter, alias to z0_override if z0_override is None. Emit a deprecation warning.

• Dint (number, or array-like) – inner conductor diameter, in m

• Dout (number, or array-like) – outer conductor diameter, in m

• epsilon_r (number, or array-like, optional) – relative permittivity of the dielectric medium. Default is 1.

• tan_delta (number, or array-like, optional) – loss tangent of the dielectric medium. Default is 0.

• sigma (number, or array-like, optional.) – conductors electrical conductivity, in S/m. Default is 58e6, the conductivity of annealed copper at 20 °C (100% IACS).

• tout (number, array-like, or None, optional) – wall thickness of the outer conductor, in m. If None (default), the shield is infinitely thick.

• model (str, optional) – Model of the conductors. ‘schelkunoff’ (default) is the Bessel function solution of [1], ‘tesche’ the equivalent circuit approximation of [2].

• dielectric (dict or None, optional) – Material of the dielectric filling, as a dict taking the keys 'ep_r' (complex relative permittivity \(\epsilon_r (1 - j\tan\delta)\)) and 'mu_r' (complex relative permeability), both defaulting to 1. If None (default), the filling is described by epsilon_r and tan_delta.

• inner_conductor (dict, list of dict, or None, optional) – Material of the inner conductor. A single dict describes a bulk conductor, a list of dict a stack of coatings ordered from the dielectric inwards, of which the deepest layer is the bulk that carries the dc current. Each dict takes the keys 'sigma', 'mu_r' and 'ep_r' of the layer itself, and 'rms_roughness', 'boundary_loc' and 'distribution' of the boundary on top of it, which are handed to surface_impedance(). If None (default), the conductor is smooth and made of bulk sigma.

• outer_conductor (dict, list of dict, or None, optional) – Material of the outer conductor, described as inner_conductor.

Note

Dint, Dout, tout, epsilon_r, tan_delta, sigma can all be vectors as long as they are the same length

References

[1]

S. A. Schelkunoff, “The electromagnetic theory of coaxial transmission lines and cylindrical shields,” Bell Syst. Tech. J., vol. 13, no. 4, pp. 532-579, Oct. 1934. https://doi.org/10.1002/j.1538-7305.1934.tb00679.x

[2]

F. M. Tesche, “A Simple Model for the Line Parameters of a Lossy Coaxial Cable Filled With a Nondispersive Dielectric,” IEEE Trans. Electromagn. Compat., vol. 49, no. 1, pp. 12-17, Feb. 2007. https://doi.org/10.1109/TEMC.2006.888185

Examples

An RG58C/U flexible cable with copper conductors and a lossy polyethylene filling. Its characteristic impedance and the insertion loss of a 100 mm length of it at 5 GHz:

>>> import skrf as rf
>>> from skrf.media import Coaxial
>>> freq = rf.Frequency(1, 5, 101, unit='GHz')
>>> rg58 = Coaxial(freq, Dint=0.91e-3, Dout=2.95e-3, epsilon_r=2.3,
...                tan_delta=2e-4, sigma=58e6, z0_port=50)
>>> print(f"{rg58.z0[0]:.2f} ohm, {rg58.line(100, 'mm').s_db[-1, 1, 0]:.3f} dB")
46.56-0.05j ohm, -0.094 dB

The same cable roughened by 0.6 um rms at the inner conductor and by 1 um rms at the braided shield, which is described by giving each conductor a material of its own instead of the bulk sigma:

>>> rg58 = Coaxial(freq, Dint=0.91e-3, Dout=2.95e-3, epsilon_r=2.3,
...                tan_delta=2e-4, z0_port=50,
...                inner_conductor={'sigma': 58e6, 'rms_roughness': 0.6e-6},
...                outer_conductor={'sigma': 58e6, 'rms_roughness': 1e-6})
>>> print(f"{rg58.line(100, 'mm').s_db[-1, 1, 0]:.3f} dB")
-0.140 dB

An APC-7 air line whose two conductors carry an ENIG finish, 0.05 um of gold over 4 um of nickel over copper, roughened by 50 nm rms at the outside and by 0.2 um rms at the copper underneath:

>>> enig = [{'sigma': 41.1e6, 'rms_roughness': 50e-9, 'boundary_loc': 0},
...         {'sigma': 14.5e6, 'mu_r': 20, 'rms_roughness': 50e-9, 'boundary_loc': 0.05e-6},
...         {'sigma': 58e6, 'rms_roughness': 0.2e-6, 'boundary_loc': 4.05e-6}]
>>> freq = rf.Frequency(1, 18, 171, unit='GHz')
>>> apc7 = Coaxial(freq, Dint=3.04e-3, Dout=7.00e-3,
...                inner_conductor=enig, outer_conductor=enig)
>>> print(f"{apc7.z0[0]:.2f} ohm, {apc7.line(100, 'mm').s_db[-1, 1, 0]:.3f} dB")
50.22-0.25j ohm, -0.301 dB

Attributes

C	Distributed capacitance C, in F/m
G	Distributed conductance G, in S/m
L	Distributed inductance L, in H/m
R	Distributed resistance R, in Ohm/m.
Rs	Surface resistivity in Ohm/area.
Y	Distributed Admittance, \(Y^{'}\).
Z	Distributed Impedance, \(Z^{'}\).
Z0	Characteristic Impedance
a	Inner radius of the coaxial line
alpha	Real (attenuation) component of gamma.
b	Outer radius of the coaxial line
beta	Imaginary (propagating) component of gamma.
gamma	Propagation Constant, \(\gamma\).
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	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.
from_Z0_Dout	Init from characteristic impedance and outer diameter.
from_attenuation_VF	Init from electrical properties of the line: attenuation and velocity factor.
from_csv	Create a DistributedCircuit from numerical values stored in a csv file.
from_media	Initializes a DistributedCircuit from an existing Media instance.
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.
line_floating	Floating 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.