#import scipy.special as sp

import numpy as np

import math

from mpmath import mp

# pip install mpmath

import matplotlib.pyplot as plt

import time as time

tim = time.time()

mu0 = 4*math.pi*10**-7; # Vs/Am

eps0 = 8.854*10**-12; # As/Vm

c0 = 299792457; # m/s

############

# Thomas numbers

############

# a = 0.25/2*10**-3; # mm

# b = 135/2*10**-3; # mm

# c = 139.7/2*10**-3; # mm

# sigma = 5.76*10**7; # 1/Ohm*m

# epsPE = 1.0;

############

# Tesche numbers

############

a = 2.5*10**-3; # mm

b = 9.345*10**-3; # mm

c = 9.945*10**-3; # mm

sigma = 5.76*10**7; # 1/Ohm*m

epsPE = 2.5;

############

# RG58 or Jans numbers

############

a = 0.4675*10**-3; # mm

b = 1.475*10**-3; # mm

c = 1.8 *10**-3; # mm

sigma = 5.8*10**7; # 1/Ohm*m

epsPE = 1.9;

f = np.logspace(5, 8, 100);

omega = 2*math.pi*f;

Lp = mu0/(2*math.pi)*mp.log(b/a); # ln(ra/ri)

Cp = 2*math.pi*eps0*epsPE/(mp.log(b/a)); # ln(ra/ri)

etac = np.sqrt(1j*omega*mu0/sigma);

gammac = np.sqrt(1j*omega*mu0*sigma);

# shortcuts

i0 = lambda x: mp.besseli(0,x)

i1 = lambda x: mp.besseli(1,x)

k0 = lambda x: mp.besselk(0,x)

k1 = lambda x: mp.besselk(1,x)

# Zap = etac/(2*math.pi*a)*(sp.iv(0,gammac*a) / sp.iv(1,gammac*a));

ZapA = etac/(2*math.pi*a)

#Zbp = etac/(2*math.pi*b)* (sp.iv(0,gammac*b) * sp.kv(1,gammac*c) + sp.kv(0,gammac*b) * sp.iv(1,gammac*c)) / (sp.iv(1,gammac*b)*sp.kv(1,gammac*b) - sp.iv(1,gammac*b)*sp.kv(1,gammac*b))

ZbpA = etac/(2*math.pi*b)

ZL = mp.matrix(f.size, 1)

YC = mp.matrix(f.size, 1)

Zap = mp.matrix(f.size, 1)

Zbp = mp.matrix(f.size, 1)

Zp = mp.matrix(f.size, 1)

Yp = mp.matrix(f.size, 1)

Zc = mp.matrix(f.size, 1)

A = np.ndarray(f.size)

R = np.ndarray(f.size)

I = np.ndarray(f.size)

Gr = np.ndarray(f.size)

Gi = np.ndarray(f.size)

for n in range(f.size):

Zap[n] = ZapA[n]*( i0(gammac[n]*a) / i1(gammac[n]*a) )

Zbp[n] = ZbpA[n] * ((i0(gammac[n]*b) * k1(gammac[n]*c) + k0(gammac[n]*b)*i1(gammac[n]*c)) / ( i1(gammac[n]*c)*k1(gammac[n]*b) - i1(gammac[n]*b)*k1(gammac[n]*c) ) )

ZL[n] = 1j*omega[n]*Lp

YC[n] = 1j*omega[n]*Cp

Zp[n] = Zap[n] + Zbp[n] + ZL[n]

Yp[n] = YC[n] # + G[n]

Zc[n] = mp.sqrt(Zp[n]/Yp[n])

A[n] = mp.fabs(Zc[n])

R[n] = mp.re(Zc[n])

I[n] = mp.im(Zc[n])

Gr[n] = mp.re(mp.sqrt(Zp[n]*Yp[n]))

Gi[n] = mp.im(mp.sqrt(Zp[n]*Yp[n]))

fig = plt.figure()

plt.plot(f/10**6, A, label='Magnitude', color='red')

plt.xlabel('Frequency [MHz]')

plt.ylabel('Magnitude of Z$_{c}$ [$\Omega$]')

plt.legend()

plt.xlim([-0.3,100])

#plt.show()

fig2 = plt.figure()

plt.plot(f/10**6, R, label='Real Part', color='red')

plt.xlabel('Frequency [MHz]')

plt.ylabel('Real Part of Z$_{c}$ [$\Omega$]')

plt.legend()

plt.xlim([-0.3,100])

#plt.show()

fig2 = plt.figure()

plt.plot(f/10**6, I, label='Imaginary Part', color='red')

plt.xlabel('Frequency [MHz]')

plt.ylabel('Imaginary Part of Z$_{c}$ [$\Omega$]')

plt.legend()

plt.xlim([-0.3,100])

print("Total duration: ", time.time() - tim, " s")

#plt.show()

fig4 = plt.figure()

plt.plot(f/10**6, A, label='Amplitude', color='red')

plt.plot(f/10**6, R, label='Real Part', color='blue')

plt.plot(f/10**6, I, label='Imaginary Part', color='green')

plt.xlabel('Frequency [MHz]')

plt.ylabel('Z$_c$ [$\Omega$]')

plt.legend()

plt.xlim([-0.3, 100])

#plt.show()

fig5 = plt.figure()

plt.semilogx(f/10**3, A, label='Magnitude', color='red')

plt.semilogx(f/10**3, R, label='Real Part', color='blue')

plt.semilogx(f/10**3, I, label='Imaginary Part', color='green')

plt.legend()

plt.xlabel('Frequency [kHz]')

plt.ylabel('Characteristic Impedance Z$_c$ [$\Omega$]')

plt.grid()

fig6 = plt.figure()

plt.loglog(f/10**6, Gr, label='Attenuation constant [1/m]', color='red')

plt.loglog(f/10**6, Gi, label='Propagation phase constant [1/m]', color='blue')

plt.xlabel('Frequency [MHz]')

plt.ylabel('Propagation constant')

plt.legend()

plt.show()

#print("Zc \n", Zc)