EM theory assignment 3

em_helper.py

from math import *
from numpy import *

class Layer:

  def __init__(self, params = {}):
    self.eps = params["eps"]
    self.l_coef = params["l_coef"]
    self.n = sqrt( self.eps )

  def impedance(self, thita):
    return 377.0 * sqrt( 1.0 / self.eps )

    
  def beta_l(self, thita):
    return sqrt(self.eps) * 2.0 * pi * cos(thita) / self.l_coef

  def abcd_matrix_hor(self, thita):
    a = cos(self.beta_l(thita))
    b = 1j * (self.impedance(thita) / cos(thita)) * sin(self.beta_l(thita))
    c = 1j * sin(self.beta_l(thita)) / (self.impedance(thita) / cos(thita))
    d = cos(self.beta_l(thita))
    return matrix([ [a, b], [c, d] ])

  def abcd_matrix_ver(self, thita):
    a = cos(self.beta_l(thita))
    b = 1j * (self.impedance(thita) * cos(thita)) * sin(self.beta_l(thita))
    c = 1j * sin(self.beta_l(thita)) / (self.impedance(thita) * cos(thita))
    d = cos(self.beta_l(thita))
    return matrix([ [a, b], [c, d] ])

em_thoery_assignment3.py

import sys
sys.path.extend(["lib"])

from em_helper import Layer

import matplotlib as mpl
mpl.use("Agg")

import pylab
import numpy
import scipy
import math

t = numpy.arange(0,90,0.1)
tt = t * math.pi / 180

layer_list = []
layer_list.append(Layer({ "eps": 2, "l_coef": 4 }))
layer_list.append(Layer({ "eps": 4-1j, "l_coef": 3 }))
layer_list.append(Layer({ "eps": 2, "l_coef": 4 }))

gamma_h = []
tau_h   = []
gamma_v = []
tau_v   = []

for angle in tt:
  thita1 = math.asin(math.sin(angle) / layer_list[0].n)
  thita2 = math.asin(math.sin(angle) / layer_list[1].n)
  thita3 = math.asin(math.sin(angle) / layer_list[2].n)


  # prepare hor
  hor_matrix = layer_list[0].abcd_matrix_hor(thita1) * layer_list[1].abcd_matrix_hor(thita2) * layer_list[2].abcd_matrix_hor(thita3)

  [[a,b], [c,d]] = hor_matrix.tolist()

  ita1h = a + b / (377.0/math.cos(angle))
  ita2h = (c + d / (377.0/math.cos(angle))) * (377.0/math.cos(angle))

  gamma_h.append( abs(( ita1h - ita2h ) / ( ita1h + ita2h )) )
  tau_h.append( abs( 2 / ( ita1h + ita2h ) ) )



  ver_matrix = layer_list[0].abcd_matrix_ver(thita1) * layer_list[1].abcd_matrix_ver(thita2) * layer_list[2].abcd_matrix_ver(thita3)
  
  [[a, b], [c, d]] = ver_matrix.tolist()

  ita1v = c * (377.0 * math.cos(angle)) + d
  ita2v = ( a * (377.0 * math.cos(angle)) + b ) / (377.0 * math.cos(angle))

  gamma_v.append( abs( ( ita1v - ita2v ) / ( ita1v + ita2v ) ) )
  tau_v.append( abs( 2 / ( ita1v + ita2v ) ) )


p1 = pylab.plot(t, gamma_h)
p2 = pylab.plot(t, tau_h)

p3 = pylab.plot(t, gamma_v)
p4 = pylab.plot(t, tau_v)

pylab.xlabel("thita")
pylab.ylabel("ratio")

pylab.legend([p1, p2, p3, p4], ["Horizontal Reflection", "Horizontal Transmission", "Vertical Reflection", "Vertical Transmission"], loc = "upper left")

pylab.grid(True)
pylab.savefig("ratio.png")


pylab.gcf().clear()
p1 = pylab.plot(t, map((lambda x,y: x**2+y**2), gamma_v, tau_v))
p2 = pylab.plot(t, map((lambda x,y: x**2+y**2), gamma_h, tau_h))

pylab.title("Average Power Transmission")
pylab.legend([p1,p2], ["Vertical Polarization", "Horizontal Polarization"])
pylab.grid(True)
pylab.savefig("power.png")

power.png

power_dis.png

ratio.png

ratio_dis.png