skrf.media.rectangularWaveguide.RectangularWaveguide

class skrf.media.rectangularWaveguide.RectangularWaveguide(frequency=None, z0_port=None, z0_override=None, z0=None, a=1, b=None, mode_type='te', m=1, n=0, ep_r=1, mu_r=1, rho=1.724137931034483e-08, roughness=None, model='lomakin', dielectric=None, wall_a=None, wall_b=None, *args, **kwargs)

A single mode of a homogeneously filled rectangular waveguide.

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)

• 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.

• a (number, optional) – width of waveguide, in meters. Default is 1.

• b (number or None, optional) – height of waveguide, in meters. If None defaults to a/2. Default is None

• mode_type (['te','tm']) – mode type, transverse electric (te) or transverse magnetic (tm) to-z. where z is direction of propagation

• m (int) – mode index in ‘a’-direction

• n (int) – mode index in ‘b’-direction

• ep_r (number, array-like,) – filling material’s relative permittivity

• mu_r (number, array-like) – filling material’s relative permeability

• rho (number, array-like, string, or None) – resistivity (ohm-m) of the conductor walls. If array-like must be same length as frequency. if str, it must be a key in skrf.data.materials. Default is 1/58e6, the resistivity of annealed copper at 20 °C (100% IACS). Use 0, or None, for perfectly conducting walls.

• roughness (number, or array-like) – rms roughness of the conductor walls, in meter. It is handed to surface_impedance(), and it applies to any wall whose material does not carry an 'rms_roughness' of its own.

• model (str, optional) – Model of the loss. ‘lomakin’ (default) is the two-wire model of [1], where the loss of the walls shapes the phase constant as well as the attenuation (agrees better with EM simulations). ‘marcuvitz’ is the power loss method of [2], which is also given by the IEC 60153-2 and IEEE 1785.1 standards and discussed in [3]; it leaves the phase constant at its lossless value. A TM mode, or a mode with both indices nonzero, is not covered by ‘lomakin’ and follows ‘marcuvitz’ instead, which is warned about.

• dielectric (dict or None, optional) – Material filling the waveguide, as a dict taking the keys 'ep_r' (complex relative permittivity) and 'mu_r' (complex relative permeability), both defaulting to 1. If None (default), the filling is described by parameters ep_r and mu_r.

• wall_a (dict, list of dict, or None, optional) – Material of the pair of walls of width a. It describes both walls of the pair. A single dict describes a bulk conductor, a list of dict a stack of coatings ordered from the filling inwards, of which the deepest layer is the bulk. 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 pair is described by rho and roughness.

• wall_b (dict, list of dict, or None, optional) – Material of the pair of walls of width b, described in similar way as wall_a. The two pairs are usually of the same material, but would have different effective conductivities, e.g., different roughness due to machining or 3D printed waveguides [4], [5].

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

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

Note

The two-wire model is derived for the TE10 mode. It carries over to any TE_m0 and TE_0n mode. It does not carry over to a mode with both indices nonzero.

References

[1]

K. Lomakin, G. Gold and K. Helmreich, “Analytical Waveguide Model Precisely Predicting Loss and Delay Including Surface Roughness,” IEEE Trans. Microw. Theory Techn., vol. 66, no. 6, pp. 2649-2662, June 2018. https://doi.org/10.1109/TMTT.2018.2827383

[2]

N. Marcuvitz, “Transmission-line modes,” in Waveguide Handbook, 2nd ed. New York: McGraw-Hill, 1951, Chapter 2.

[3]

J. Skinner, D. Koller, H.-U. Nickel, N. M. Ridler and S. Lucyszyn, “Derivation of Rectangular Metallic Waveguide Attenuation Constant for IEC 60153-2 and IEEE 1785.1 International Standards,” IEEE Trans. THz Sci. Technol., vol. 15, no. 4, pp. 734-737, July 2025. https://doi.org/10.1109/TTHZ.2025.3573847

[4]

L. Zhu et al., “3-D Printed THz Waveguide Components,” IEEE Access, vol. 11, pp. 79073-79086, 2023. https://doi.org/10.1109/ACCESS.2023.3297271

[5]

K. Lomakin et al., “SLA-Printed 3-D Waveguide Paths for E-Band Using Electroless Silver Plating,” IEEE Trans. Compon. Packag. Manuf. Technol., vol. 9, no. 12, pp. 2476-2481, Dec. 2019. https://doi.org/10.1109/TCPMT.2019.2927671

Examples

Most common usage is standard aspect ratio (2:1) dominant mode, TE10 mode of wr10 waveguide can be constructed by

>>> import numpy as np
>>> import skrf as rf
>>> from skrf.constants import mil
>>> from skrf.media import RectangularWaveguide
>>> freq = rf.Frequency(75, 110, 101, unit='ghz')
>>> RectangularWaveguide(freq, a=100*mil)
Rectangular Waveguide Media.  75.0-110.0 GHz.  101 points
 a= 2.54e-03m, b= 1.27e-03m

A WR-12 guide of brass, with the a walls rougher than the b ones, and the attenuation of a 100 mm length of it at 90 GHz:

>>> freq = rf.Frequency(60, 90, 61, unit='GHz')
>>> wr12 = RectangularWaveguide(freq, a=3.0988e-3, b=1.5494e-3,
...     wall_a={'sigma': 0.28*58e6, 'rms_roughness': 1e-6},
...     wall_b={'sigma': 0.28*58e6, 'rms_roughness': 0.4e-6})
>>> print(f"{wr12.line(100, 'mm').s_db[-1, 1, 0]:.3f} dB")
-1.002 dB

A WR-6.5 waveguide (D-band) whose walls 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(110, 170, 61, unit='GHz')
>>> wr65 = RectangularWaveguide(freq, a=1.6510e-3, b=0.8255e-3,
...                             wall_a=enig, wall_b=enig)
>>> smooth_copper = RectangularWaveguide(freq, a=1.6510e-3, b=0.8255e-3, rho=1/58e6)
>>> np2db = 20*np.log10(np.e)
>>> print(f"{np2db*wr65.gamma[-1].real:.1f} dB/m, against "
...       f"{np2db*smooth_copper.gamma[-1].real:.1f} dB/m for smooth copper")
20.3 dB/m, against 4.6 dB/m for smooth copper

Attributes

Z0	Characteristic Impedance
alpha	Real (attenuation) component of gamma.
alpha_c	Loss of the walls by the power loss method, in Np/m.
beta	Imaginary (propagating) component of gamma.
ep	The permittivity of the filling material.
f_cutoff	cutoff frequency for this mode.
f_norm	Frequency vector normalized to cutoff.
gamma	The propagation constant (aka Longitudinal wave number).
k0	Characteristic wave number.
kc	Cut-off wave number.
kx	Eigenvalue in the 'a' direction.
ky	Eigenvalue in the b direction.
lambda_cutoff	Cutoff wavelength.
lambda_guide	Guide wavelength.
mu	The permeability of the filling material.
npoints	Number of points of the frequency axis.
rho	Resistivity of all four walls in ohm*m.
v_g	Complex group velocity (in m/s).
v_p	Complex phase velocity (in m/s).
z0	Return Characteristic Impedance z0_characteristic.
z0_characteristic	The 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	Initialize from specified impedance at a given frequency, assuming the fundamental TE10 mode.
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.