Source code for

.. module::
rectangularWaveguide (:mod:``)

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`
====================================  =============  ===============

from scipy.constants import  epsilon_0, mu_0,pi,c
from numpy import sqrt, exp, sinc,where
import numpy as npy
from .media import Media
from import materials
from ..tlineFunctions import skin_depth

from .freespace import Freespace

[docs]class RectangularWaveguide(Media): ''' A single mode of a homogeneously filled rectangular waveguide Parameters ---------- frequency : :class:`~skrf.frequency.Frequency` object frequency band of this transmission line medium z0 : number, array-like, or None the port impedance for media. Only needed if its different from the characterisitc impedance of the transmission line. if z0 is None then will default to Z0 a : number width of waveguide, in meters. b : number height of waveguide, in meters. If `None` defaults to a/2 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 ``. roughness : number, or array-like surface roughness of the conductor walls in units of RMS deviation from surface *args,**kwargs : arguments, keywrod arguments passed to :class:``'s constructor (:func:`` 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) '''
[docs] def __init__(self, frequency=None, z0=None, a=1, b=None, mode_type = 'te', m=1, n=0, ep_r=1, mu_r=1, rho=None, roughness=None, *args, **kwargs): Media.__init__(self, frequency=frequency,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 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 = \ 'Rectangular Waveguide Media. %i-%i %s. %i points'%\ (f.f_scaled[0],f.f_scaled[-1],f.unit, f.npoints) + \ '\n a= %.2em, b= %.2em'% \ (self.a,self.b) return output def __repr__(self): return self.__str__()
[docs] @classmethod def from_Z0(cls,frequency, Z0,f, m=1,n=0,ep_r=1, mu_r=1, **kw): ''' Initialize from specfied impedance at a given frequency. Parameters ------------- frequency : Frequency Object Z0 : number /array scharacteristic impedance to create at `f` f : number frequency (in Hz) that the resultant waveguide has Z0=Z0 ''' if n !=0: raise NotImplemented() mu = mu_0*mu_r ep = 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=m, n=n, ep_r=ep_r, mu_r=mu_r))
return cls(**kw) @property def ep(self): ''' The permativity of the filling material Returns ------- ep : number filling material's relative permittivity ''' return self.ep_r * epsilon_0 @property def mu(self): ''' The permeability of the filling material Returns ------- mu : number filling material's relative permeability ''' return self.mu_r * mu_0 @property def k0(self): ''' Characteristic wave number Returns ------- k0 : number characteristic wave number ''' return 2*pi*self.frequency.f*sqrt(self.ep * @property def ky(self): ''' Eigen-value in the `b` direction. Defined as .. math:: k_y = n \\frac{\pi}{b} Returns ------- ky : number eigen-value in `b` direction ''' return self.n*pi/self.b @property def kx(self): ''' Eigen value in the 'a' direction Defined as .. math:: k_x = m \\frac{\pi}{a} Returns ------- kx : number eigen-value in `a` direction ''' return self.m*pi/self.a @property def kc(self): ''' 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 +**2) @property def f_cutoff(self): ''' cutoff frequency for this mode .. math:: max ( \frac{m \cdot v}{2a} , \frac{n \cdot v}{2b}) where v= sqrt(ep*mu) ''' v = 1/sqrt(self.ep* if not ( self.m==1 and self.n==0): print('f_cutoff not verified as correct for this mode ') if self.m/self.a > self.n/self.b: return self.m*v/(2*self.a) else: return self.n*v/(2*self.b) @property def f_norm(self): ''' frequency vector normalized to cutoff ''' return self.frequency.f/self.f_cutoff @property def rho(self): ''' conductivty 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 ``. Examples --------- >>> wg.rho = 2.8e-8 >>> wg.rho = 2.8e-8 * ones(len(wg.frequency)) >>> wg.rho = 'al' >>> wg.rho = 'aluminum' ''' if self.roughness != 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): if isinstance(val, str): self._rho = materials[val.lower()]['resistivity(ohm*m)'] else: self._rho=val @property def lambda_guide(self): ''' guide wavelength the distance in which the phase of the field increases by 2 pi ''' return 2*pi/self.beta @property def lambda_cutoff(self): ''' cuttoff wavelength .. math:: f_c * v where v= sqrt(ep*mu) ''' v = 1/sqrt(self.ep* return self.f_cutoff*v @property def gamma(self): ''' The propagation constant (aka Longitudinal wave number) Defined as .. math:: k_z = j \\pm \\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): ''' 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 ''' 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(self): ''' The characteristic impedance ''' omega = self.frequency.w impedance_dict = {'te': 1j*omega*, 'tm': -1j*self.gamma/(omega*self.ep),\ }
return impedance_dict[self.mode_type]