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Merge ec1d18217 into 950534a59

Pull Request Pull Request #1372: Lazy load most modules

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86.27

/skrf/media/rectangularWaveguide.py

"""
rectangularWaveguide (:mod:`skrf.media.rectangularWaveguide`)
================================================================

Represents a single mode of a homogeneously filled rectangular
waveguide of cross-section `a` x `b`. The mode is determined by
`mode-type` (`'te'` or `'tm'`) and mode indices ( `m` and `n` ).


====================================  =============  ===============
Quantity                              Symbol         Variable
====================================  =============  ===============
Characteristic Wave Number            :math:`k_0`    :attr:`k0`
Cut-off Wave Number                   :math:`k_c`    :attr:`kc`
Longitudinal Wave Number              :math:`k_z`    :attr:`gamma`
Transverse Wave Number (a)            :math:`k_x`    :attr:`kx`
Transverse Wave Number (b)            :math:`k_y`    :attr:`ky`
Characteristic Impedance              :math:`z_0`    :attr:`z0`
====================================  =============  ===============

.. autosummary::
   :toctree: generated/

   RectangularWaveguide

"""
from __future__ import annotations

from numbers import Number
from typing import TYPE_CHECKING

import numpy as np
from numpy import exp, pi, sqrt, where

from .. import constants as _const
from ..data import materials
from ..tlineFunctions import skin_depth
from .freespace import Freespace
from .media import Media

if TYPE_CHECKING:
    from ..constants import NumberLike
    from ..frequency import Frequency


class RectangularWaveguide(Media):
    r"""
    A single mode of a homogeneously filled rectangular waveguide.

    Parameters
    ----------
    frequency : :class:`~skrf.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
        resistivity (ohm-m) of the conductor walls. If array-like
        must be same length as frequency. if str, it must be a key in
        :data:`skrf.data.materials`.
    roughness : number, or array-like
        surface roughness of the conductor walls in units of RMS
        deviation from surface
    \*args, \*\*kwargs : arguments, keyword arguments
            passed to :class:`~skrf.media.media.Media`'s constructor
            (:func:`~skrf.media.media.Media.__init__`

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

    >>> freq = rf.Frequency(75,110,101,'ghz')
    >>> rf.RectangularWaveguide(freq,a= 100*mil)
    """

    def __init__(self, frequency: Frequency | None = None,
                 z0_port: NumberLike | None = None,
                 z0_override: NumberLike | None = None,
                 z0: NumberLike | None = None,
                 a: float = 1, b: float | None = None,
                 mode_type: str = 'te', m: int = 1, n: int = 0,
                 ep_r: None | NumberLike = 1, mu_r: None | NumberLike = 1,
                 rho: None | NumberLike = None,
                 roughness: None | NumberLike = None,
                 *args, **kwargs):
        Media.__init__(self, frequency = frequency,
                       z0_port = z0_port, z0_override = z0_override, z0 = z0)

        if b is None:
            b = a/2.
        if mode_type.lower() not in ['te','tm']:
            raise ValueError('mode_type must be either \'te\' or \'tm\'')



        self.a = a
        self.b = b
        self.mode_type = mode_type.lower()
        self.m = m
        self.n = n
        self.ep_r = ep_r
        self.mu_r = mu_r
        self.rho = rho
        self.roughness = roughness


    def __str__(self):
        f=self.frequency
        output = (
                f'Rectangular Waveguide Media.  {f.f_scaled[0]}-{f.f_scaled[-1]} {f.unit}.  {f.npoints} points'
                f'\n a= {self.a:.2e}m, b= {self.b:.2e}m')
        return output

    def __repr__(self):
        return self.__str__()


    @classmethod
    def from_z0(cls, frequency: Frequency, z0: NumberLike, f: Number,
                ep_r=1, mu_r=1, **kw) -> Media:
        """
        Initialize from specified impedance at a given frequency, assuming
        the fundamental TE10 mode.

        Parameters
        ----------
        frequency : Frequency Object
        z0 : number /array
            characteristic impedance to create at `f`
        f : number
            frequency (in Hz) at which the resultant waveguide has the
            characteristic impedance z0
        ep_r : number, array-like,
            filling material's relative permittivity
        mu_r : number, array-like
            filling material's relative permeability
        """

        mu = _const.mu_0*mu_r
        ep = _const.epsilon_0*ep_r
        w = 2*pi*f
        a =pi/(w*mu) * 1./sqrt(1/(z0*1j)**2+ep/mu)

        kw.update(dict(frequency=frequency,a=a, m=1, n=0, ep_r=ep_r, mu_r=mu_r))

        return cls(**kw)

    @property
    def ep(self) -> NumberLike:
        r"""
        The permittivity of the filling material.

        .. math:

            \varepsilon = \varepsilon_r \varepsilon_0

        Returns
        -------
        ep : number
            filling material's permittivity in F/m.
        """
        return self.ep_r * _const.epsilon_0

    @property
    def mu(self) -> NumberLike:
        r"""
        The permeability of the filling material.

        .. math::

            \mu = \mu_r \mu_0

        Returns
        -------
        mu : number
            filling material's permeability in H/m.

        """
        return self.mu_r * _const.mu_0

    @property
    def k0(self) -> NumberLike:
        r"""
        Characteristic wave number.

        .. math::

            k_0 = \frac{\omega}{v} = \omega \sqrt{\varepsilon_r \mu_r}

        Returns
        -------
        k0 : number
            characteristic wave number
        """
        return 2*pi*self.frequency.f*sqrt(self.ep * self.mu)

    @property
    def ky(self) -> NumberLike:
        r"""
        Eigenvalue in the `b` direction.

        Defined as

        .. math::

            k_y = n \frac{\pi}{b}

        Returns
        -------
        ky : number
                eigenvalue in `b` direction
        """
        return self.n*pi/self.b

    @property
    def kx(self) -> NumberLike:
        r"""
        Eigenvalue in the 'a' direction.

        Defined as

        .. math::

            k_x = m \frac{\pi}{a}

        Returns
        -------
        kx : number
                eigenvalue in `a` direction
        """
        return self.m*pi/self.a

    @property
    def kc(self) -> NumberLike:
        r"""
        Cut-off wave number.

        Defined as

        .. math::

            k_c = \sqrt {k_x^2 + k_y^2} = \sqrt {
                {m \frac{\pi}{a}}^2 + {n \frac{\pi}{b}}^2}

        Returns
        -------
        kc : number
                cut-off wavenumber
        """
        return sqrt( self.kx**2 + self.ky**2)


    @property
    def f_cutoff(self) -> NumberLike:
        r"""
        cutoff frequency for this mode.

        .. math::

            f_c = \frac{v}{2 \pi} \sqrt {
                {m \frac{\pi}{a}}^2 + {n \frac{\pi}{b}}^2}

        where :math:`v= 1/\sqrt{\varepsilon \mu}`.

        """
        v = 1/sqrt(self.ep*self.mu)
        return v* self.kc/(2*np.pi)

    @property
    def f_norm(self) -> NumberLike:
        """
        Frequency vector normalized to cutoff.
        """
        return self.frequency.f/self.f_cutoff

    @property
    def rho(self) -> NumberLike:
        """
        Conductivity of sidewalls in ohm*m.

        Parameters
        ----------
        val : float, array-like or str
            the conductivity in ohm*m. If array-like must be same length
            as self.frequency. if str, it must be a key in
            :data:`skrf.data.materials`.

        Examples
        ---------
        >>> wg.rho = 2.8e-8
        >>> wg.rho = 2.8e-8 * ones(len(wg.frequency))
        >>> wg.rho = 'al'
        >>> wg.rho = 'aluminum'
        """
        if self.roughness is not None:
            delta = skin_depth(self.frequency.f, self._rho, self.mu_r)
            k_w = 1. +exp(-(delta/(2*self.roughness))**1.6)
            return self._rho*k_w**2

        return self._rho

    @rho.setter
    def rho(self, val: NumberLike | str):
        if isinstance(val, str):
            self._rho = materials[val.lower()]['resistivity(ohm*m)']
        else:
            self._rho=val

    @property
    def lambda_guide(self) -> NumberLike:
        r"""
        Guide wavelength.

        .. math::

            \lambda_g = \frac{2\pi}{\beta}

        The distance in which the phase of the field increases by 2 pi.

        See Also
        --------
        k0
        """
        return 2*pi/self.beta

    @property
    def lambda_cutoff(self) -> NumberLike:
        r"""
        Cutoff wavelength.

        .. math::

            \lambda_c = v/f_c

        where :math:`v= 1/\sqrt{\varepsilon \mu}` and :math:`f_c` the cut-off frequency.

        See Also
        --------
        f_cutoff
        """
        v = 1/sqrt(self.ep*self.mu)
        return v/self.f_cutoff

    @property
    def gamma(self) -> NumberLike:
        r"""
        The propagation constant (aka Longitudinal wave number).

        Defined as

        .. math::

            k_z = \pm j \sqrt {k_0^2 - k_c^2}

        This is:

        * IMAGINARY for propagating modes
        * REAL for non-propagating modes,

        Returns
        -------
        gamma :  number
            The propagation constant
        """
        ## haringtons form
        if False:  #self.m==1 and self.n==0:
            fs = Freespace(frequency=self.frequency,
                           ep_r=self.ep_r,
                           mu_r=self.mu_r)


            g = where(self.f_norm>1.,
                     sqrt(1-self.f_norm**(-2))*fs.gamma,  # cutton
                 -1j*sqrt(1-self.f_norm**(2))*fs.gamma)  # cutoff

        else:
            # TODO:  fix this for lossy ep/mu (remove abs?)
            k0, kc = self.k0, self.kc
            g =  1j*sqrt(abs(k0**2 - kc**2)) * (k0>kc) +\
                    sqrt(abs(kc**2- k0**2))*(k0<kc) + \
                    0*(kc==k0)

        g = g + self.alpha_c *(self.rho is not None)

        return g


    @property
    def alpha_c(self) -> NumberLike:
        r"""
        Loss due to finite conductivity and roughness of sidewalls.

        In units of np/m
        See property `rho` for setting conductivity.

        Effects of finite conductivity are taken from [#]_. If
        :attr:`roughness` is not None, then its effects the conductivity
        by


        .. math::

            \sigma_c = \frac{\sigma}{k_w^2}


        where

        .. math::

            k_w = 1 + e^{(-\delta/2h)^{1.6}}

            \delta = \mbox{skin depth}

            h = \mbox{surface roughness }


        This is taken from Ansoft HFSS help documents.

        References
        ----------

        .. [#] Chapter 9, (eq 9.8.1) of Electromagnetic Waves and Antennas by Sophocles J. Orfanidis
            http://eceweb1.rutgers.edu/~orfanidi/ewa/
        """

        if self.rho is None:
            return 0

        a,b,w,ep,rho,f_n = self.a, self.b, self.frequency.w, self.ep, \
            self.rho, self.f_norm

        return 1./b * sqrt( (w*ep)/(2./rho) ) * (1+2.*b/a*(1/f_n)**2)/\
            sqrt(1-(1/f_n)**2)

    @property
    def z0_characteristic(self) -> NumberLike:
        """
        The characteristic impedance, :math:`z_0`.

        The characteristic impedance depends of the mode ('te' or 'tm').

        Returns
        -------
        z0_characteristic : np.ndarray
            Characteristic Impedance in units of ohms
        """
        omega = self.frequency.w
        impedance_dict = {'te':   1j*omega*self.mu/(self.gamma),
                          'tm':   -1j*self.gamma/(omega*self.ep),\
                         }

        return impedance_dict[self.mode_type]

1	"""
2	rectangularWaveguide (:mod:`skrf.media.rectangularWaveguide`)
3	================================================================
4
5	Represents a single mode of a homogeneously filled rectangular
6	waveguide of cross-section `a` x `b`. The mode is determined by
7	`mode-type` (`'te'` or `'tm'`) and mode indices ( `m` and `n` ).
8
9
10	==================================== ============= ===============
11	Quantity Symbol Variable
12	==================================== ============= ===============
13	Characteristic Wave Number :math:`k_0` :attr:`k0`
14	Cut-off Wave Number :math:`k_c` :attr:`kc`
15	Longitudinal Wave Number :math:`k_z` :attr:`gamma`
16	Transverse Wave Number (a) :math:`k_x` :attr:`kx`
17	Transverse Wave Number (b) :math:`k_y` :attr:`ky`
18	Characteristic Impedance :math:`z_0` :attr:`z0`
19	==================================== ============= ===============
20
21	.. autosummary::
22	:toctree: generated/
23
24	RectangularWaveguide
25
26	"""
27	from __future__ import annotations	5✔
28
29	from numbers import Number	5✔
30	from typing import TYPE_CHECKING	5✔
31
32	import numpy as np	5✔
33	from numpy import exp, pi, sqrt, where	5✔
34
35	from .. import constants as _const	5✔
36	from ..data import materials	5✔
37	from ..tlineFunctions import skin_depth	5✔
38	from .freespace import Freespace	5✔
39	from .media import Media	5✔
40
41	if TYPE_CHECKING:
42	from ..constants import NumberLike
43	from ..frequency import Frequency
44
45
46	class RectangularWaveguide(Media):	5✔
47	r"""
48	A single mode of a homogeneously filled rectangular waveguide.
49
50	Parameters
51	----------
52	frequency : :class:`~skrf.frequency.Frequency` object
53	frequency band of this transmission line medium
54	z0_port : number, array-like, or None
55	`z0_port` is the port impedance for networks generated by the media.
56	If `z0_port` is not None, the networks generated by the media are
57	renormalized (or in other words embedded) from the characteristic
58	impedance z0 of the media to `z0_port`.
59	Else if `z0_port` is None, the networks port impedances will be the raw
60	characteristic impedance z0 of the media.
61	(Default is None)
62	z0_override : number, array-like, or None
63	`z0_override` override the characteristic impedance for the media.
64	If `z0_override` is not None, the networks generated by the media have
65	their characteristic impedance `z0` overridden by `z0_override`.
66	(Default is None)
67	z0 : number, array-like, or None
68	deprecated parameter, alias to `z0_override` if `z0_override` is None.
69	Emit a deprecation warning.
70	a : number, optional
71	width of waveguide, in meters.
72	Default is 1.
73	b : number or None, optional
74	height of waveguide, in meters.
75	If `None` defaults to a/2.
76	Default is None
77	mode_type : ['te','tm']
78	mode type, transverse electric (te) or transverse magnetic
79	(tm) to-z. where z is direction of propagation
80	m : int
81	mode index in 'a'-direction
82	n : int
83	mode index in 'b'-direction
84	ep_r : number, array-like,
85	filling material's relative permittivity
86	mu_r : number, array-like
87	filling material's relative permeability
88	rho : number, array-like, string
89	resistivity (ohm-m) of the conductor walls. If array-like
90	must be same length as frequency. if str, it must be a key in
91	:data:`skrf.data.materials`.
92	roughness : number, or array-like
93	surface roughness of the conductor walls in units of RMS
94	deviation from surface
95	\args, \\*kwargs : arguments, keyword arguments
96	passed to :class:`~skrf.media.media.Media`'s constructor
97	(:func:`~skrf.media.media.Media.__init__`
98
99	Examples
100	--------
101	Most common usage is standard aspect ratio (2:1) dominant
102	mode, TE10 mode of wr10 waveguide can be constructed by
103
104	>>> freq = rf.Frequency(75,110,101,'ghz')
105	>>> rf.RectangularWaveguide(freq,a= 100*mil)
106	"""
107
108	def __init__(self, frequency: Frequency \| None = None,	5✔
109	z0_port: NumberLike \| None = None,
110	z0_override: NumberLike \| None = None,
111	z0: NumberLike \| None = None,
112	a: float = 1, b: float \| None = None,
113	mode_type: str = 'te', m: int = 1, n: int = 0,
114	ep_r: None \| NumberLike = 1, mu_r: None \| NumberLike = 1,
115	rho: None \| NumberLike = None,
116	roughness: None \| NumberLike = None,
117	args, *kwargs):
118	Media.__init__(self, frequency = frequency,	5✔
119	z0_port = z0_port, z0_override = z0_override, z0 = z0)
120
121	if b is None:	5✔
122	b = a/2.	5✔
123	if mode_type.lower() not in ['te','tm']:	5✔
124	raise ValueError('mode_type must be either \'te\' or \'tm\'')	×
125
126
127
128	self.a = a	5✔
129	self.b = b	5✔
130	self.mode_type = mode_type.lower()	5✔
131	self.m = m	5✔
132	self.n = n	5✔
133	self.ep_r = ep_r	5✔
134	self.mu_r = mu_r	5✔
135	self.rho = rho	5✔
136	self.roughness = roughness	5✔
137
138
139	def __str__(self):	5✔
140	f=self.frequency	×
141	output = (	×
142	f'Rectangular Waveguide Media. {f.f_scaled[0]}-{f.f_scaled[-1]} {f.unit}. {f.npoints} points'
143	f'\n a= {self.a:.2e}m, b= {self.b:.2e}m')
144	return output	×
145
146	def __repr__(self):	5✔
147	return self.__str__()	×
148
149
150	@classmethod	5✔
151	def from_z0(cls, frequency: Frequency, z0: NumberLike, f: Number,	5✔
152	ep_r=1, mu_r=1, **kw) -> Media:
153	"""
154	Initialize from specified impedance at a given frequency, assuming
155	the fundamental TE10 mode.
156
157	Parameters
158	----------
159	frequency : Frequency Object
160	z0 : number /array
161	characteristic impedance to create at `f`
162	f : number
163	frequency (in Hz) at which the resultant waveguide has the
164	characteristic impedance z0
165	ep_r : number, array-like,
166	filling material's relative permittivity
167	mu_r : number, array-like
168	filling material's relative permeability
169	"""
170
NEW 171	mu = _const.mu_0*mu_r	×
NEW 172	ep = _const.epsilon_0*ep_r	×
173	w = 2pif	×
174	a =pi/(wmu) 1./sqrt(1/(z01j)*2+ep/mu)	×
175
176	kw.update(dict(frequency=frequency,a=a, m=1, n=0, ep_r=ep_r, mu_r=mu_r))	×
177
178	return cls(**kw)	×
179
180	@property	5✔
181	def ep(self) -> NumberLike:	5✔
182	r"""
183	The permittivity of the filling material.
184
185	.. math:
186
187	\varepsilon = \varepsilon_r \varepsilon_0
188
189	Returns
190	-------
191	ep : number
192	filling material's permittivity in F/m.
193	"""
194	return self.ep_r * _const.epsilon_0	5✔
195
196	@property	5✔
197	def mu(self) -> NumberLike:	5✔
198	r"""
199	The permeability of the filling material.
200
201	.. math::
202
203	\mu = \mu_r \mu_0
204
205	Returns
206	-------
207	mu : number
208	filling material's permeability in H/m.
209
210	"""
211	return self.mu_r * _const.mu_0	5✔
212
213	@property	5✔
214	def k0(self) -> NumberLike:	5✔
215	r"""
216	Characteristic wave number.
217
218	.. math::
219
220	k_0 = \frac{\omega}{v} = \omega \sqrt{\varepsilon_r \mu_r}
221
222	Returns
223	-------
224	k0 : number
225	characteristic wave number
226	"""
227	return 2piself.frequency.fsqrt(self.ep self.mu)	5✔
228
229	@property	5✔
230	def ky(self) -> NumberLike:	5✔
231	r"""
232	Eigenvalue in the `b` direction.
233
234	Defined as
235
236	.. math::
237
238	k_y = n \frac{\pi}{b}
239
240	Returns
241	-------
242	ky : number
243	eigenvalue in `b` direction
244	"""
245	return self.n*pi/self.b	5✔
246
247	@property	5✔
248	def kx(self) -> NumberLike:	5✔
249	r"""
250	Eigenvalue in the 'a' direction.
251
252	Defined as
253
254	.. math::
255
256	k_x = m \frac{\pi}{a}
257
258	Returns
259	-------
260	kx : number
261	eigenvalue in `a` direction
262	"""
263	return self.m*pi/self.a	5✔
264
265	@property	5✔
266	def kc(self) -> NumberLike:	5✔
267	r"""
268	Cut-off wave number.
269
270	Defined as
271
272	.. math::
273
274	k_c = \sqrt {k_x^2 + k_y^2} = \sqrt {
275	{m \frac{\pi}{a}}^2 + {n \frac{\pi}{b}}^2}
276
277	Returns
278	-------
279	kc : number
280	cut-off wavenumber
281	"""
282	return sqrt( self.kx2 + self.ky2)	5✔
283
284
285	@property	5✔
286	def f_cutoff(self) -> NumberLike:	5✔
287	r"""
288	cutoff frequency for this mode.
289
290	.. math::
291
292	f_c = \frac{v}{2 \pi} \sqrt {
293	{m \frac{\pi}{a}}^2 + {n \frac{\pi}{b}}^2}
294
295	where :math:`v= 1/\sqrt{\varepsilon \mu}`.
296
297	"""
298	v = 1/sqrt(self.ep*self.mu)	5✔
299	return v* self.kc/(2*np.pi)	5✔
300
301	@property	5✔
302	def f_norm(self) -> NumberLike:	5✔
303	"""
304	Frequency vector normalized to cutoff.
305	"""
306	return self.frequency.f/self.f_cutoff	5✔
307
308	@property	5✔
309	def rho(self) -> NumberLike:	5✔
310	"""
311	Conductivity of sidewalls in ohm*m.
312
313	Parameters
314	----------
315	val : float, array-like or str
316	the conductivity in ohm*m. If array-like must be same length
317	as self.frequency. if str, it must be a key in
318	:data:`skrf.data.materials`.
319
320	Examples
321	---------
322	>>> wg.rho = 2.8e-8
323	>>> wg.rho = 2.8e-8 * ones(len(wg.frequency))
324	>>> wg.rho = 'al'
325	>>> wg.rho = 'aluminum'
326	"""
327	if self.roughness is not None:	5✔
328	delta = skin_depth(self.frequency.f, self._rho, self.mu_r)	5✔
329	k_w = 1. +exp(-(delta/(2self.roughness))*1.6)	5✔
330	return self._rhok_w*2	5✔
331
332	return self._rho	5✔
333
334	@rho.setter	5✔
335	def rho(self, val: NumberLike \| str):	5✔
336	if isinstance(val, str):	5✔
337	self._rho = materials[val.lower()]['resistivity(ohm*m)']	5✔
338	else:
339	self._rho=val	5✔
340
341	@property	5✔
342	def lambda_guide(self) -> NumberLike:	5✔
343	r"""
344	Guide wavelength.
345
346	.. math::
347
348	\lambda_g = \frac{2\pi}{\beta}
349
350	The distance in which the phase of the field increases by 2 pi.
351
352	See Also
353	--------
354	k0
355	"""
356	return 2*pi/self.beta	×
357
358	@property	5✔
359	def lambda_cutoff(self) -> NumberLike:	5✔
360	r"""
361	Cutoff wavelength.
362
363	.. math::
364
365	\lambda_c = v/f_c
366
367	where :math:`v= 1/\sqrt{\varepsilon \mu}` and :math:`f_c` the cut-off frequency.
368
369	See Also
370	--------
371	f_cutoff
372	"""
373	v = 1/sqrt(self.ep*self.mu)	×
374	return v/self.f_cutoff	×
375
376	@property	5✔
377	def gamma(self) -> NumberLike:	5✔
378	r"""
379	The propagation constant (aka Longitudinal wave number).
380
381	Defined as
382
383	.. math::
384
385	k_z = \pm j \sqrt {k_0^2 - k_c^2}
386
387	This is:
388
389	* IMAGINARY for propagating modes
390	* REAL for non-propagating modes,
391
392	Returns
393	-------
394	gamma : number
395	The propagation constant
396	"""
397	## haringtons form
398	if False: #self.m==1 and self.n==0:	5✔
399	fs = Freespace(frequency=self.frequency,
400	ep_r=self.ep_r,
401	mu_r=self.mu_r)
402
403
404	g = where(self.f_norm>1.,
405	sqrt(1-self.f_norm*(-2))fs.gamma, # cutton
406	-1jsqrt(1-self.f_norm(2))fs.gamma) # cutoff
407
408	else:
409	# TODO: fix this for lossy ep/mu (remove abs?)
410	k0, kc = self.k0, self.kc	5✔
411	g = 1jsqrt(abs(k02 - kc2)) (k0>kc) +\	5✔
412	sqrt(abs(kc2- k02))*(k0<kc) + \
413	0*(kc==k0)
414
415	g = g + self.alpha_c *(self.rho is not None)	5✔
416
417	return g	5✔
418
419
420	@property	5✔
421	def alpha_c(self) -> NumberLike:	5✔
422	r"""
423	Loss due to finite conductivity and roughness of sidewalls.
424
425	In units of np/m
426	See property `rho` for setting conductivity.
427
428	Effects of finite conductivity are taken from [#]_. If
429	:attr:`roughness` is not None, then its effects the conductivity
430	by
431
432
433	.. math::
434
435	\sigma_c = \frac{\sigma}{k_w^2}
436
437
438	where
439
440	.. math::
441
442	k_w = 1 + e^{(-\delta/2h)^{1.6}}
443
444	\delta = \mbox{skin depth}
445
446	h = \mbox{surface roughness }
447
448
449	This is taken from Ansoft HFSS help documents.
450
451	References
452	----------
453
454	.. [#] Chapter 9, (eq 9.8.1) of Electromagnetic Waves and Antennas by Sophocles J. Orfanidis
455	http://eceweb1.rutgers.edu/~orfanidi/ewa/
456	"""
457
458	if self.rho is None:	5✔
459	return 0	5✔
460
461	a,b,w,ep,rho,f_n = self.a, self.b, self.frequency.w, self.ep, \	5✔
462	self.rho, self.f_norm
463
464	return 1./b * sqrt( (wep)/(2./rho) ) (1+2.b/a(1/f_n)**2)/\	5✔
465	sqrt(1-(1/f_n)**2)
466
467	@property	5✔
468	def z0_characteristic(self) -> NumberLike:	5✔
469	"""
470	The characteristic impedance, :math:`z_0`.
471
472	The characteristic impedance depends of the mode ('te' or 'tm').
473
474	Returns
475	-------
476	z0_characteristic : np.ndarray
477	Characteristic Impedance in units of ohms
478	"""
479	omega = self.frequency.w	5✔
480	impedance_dict = {'te': 1jomegaself.mu/(self.gamma),	5✔
481	'tm': -1jself.gamma/(omegaself.ep),\
482	}
483
484	return impedance_dict[self.mode_type]	5✔

scikit-rf / scikit-rf / 25805732079

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