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Microstrip_SW.py
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Microstrip_SW.py
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#------------------ 50 Ohm Microstrip transmission line with an open termination (ZL = inf) ----------------------
#------------------ To plot standing waves (SW) on the line ------------------------------------------------------
#------------------ ABC at extreme boundaries ---------------------------------------------------------------
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
#----- Substrate and line dimensions for 50 Ohm----------
sub_l = 35e-3
sub_h = 0.794e-3
sub_w = 22e-3
strip_l = 2*sub_l/3
strip_w = 2.46e-3
#----- Substrate material and surrounding air ----------
eps0 = 8.854e-12
meu0 = 4*np.pi*1e-7
epsr = 2.2 # RT/Duroid material
meur = 1
epss = eps0*epsr # substrate
meus = meu0*meur
epsa = eps0 # air
meua = meu0
epse = (epsa + epss)/2 # Average eps
#---- EM wave -----------
c = 3e8
vmin = c/np.sqrt(epsr*meur)
vmax = c
fmax = 15e9
lamda = vmin/fmax
#------ FDTD cell length and time step---------
#------- Substrate thickness is in Y-direction
dx = lamda/35
dy = dx/2
dz = dx
dt = 1/(vmax*np.sqrt(1/np.power(dx,2) + 1/np.power(dy,2) + 1/np.power(dz,2)))
xoff = 4
yoff = 20
zoff = 10
Nx = int(round(sub_w/dx)) + xoff
Ny = int(round(sub_h/dy)) + yoff # upward
Nz = int(round(sub_l/dz)) + zoff
#----------- Start and end coordinates of the subsrate
sub_x1 = int(round(xoff/2))
sub_x2 = int(round(Nx-sub_x1))
sub_y1 = 1 # thickness starts from index 1
sub_y2 = int(round(sub_h/dy)) + sub_y1
sub_z1 = int(round(zoff/2))
sub_z2 = int(round(Nz-sub_z1))
#----------- Start and end coordinates of the strip
strip_x1 = int(round(0.5*(Nx-strip_w/dx)))
Nw = int(round(strip_w/dx))
strip_x2 = strip_x1 + Nw
strip_y = sub_y2 + 1 # strip is on the top surface of the substrate
strip_z1 = sub_z1 + 5 # strip is starting 5 cells into the substrate
strip_z2 = strip_z1 + int(round(strip_l/dz))
#-------- Feed point of the strip
feed_x = strip_x1 + int(round(0.5*strip_w/dx)) # center of strip
feed_y = sub_y1
feed_z1 = strip_z1 # feed starts at the strip edge
feed_z2 = strip_z2
#------- Initialise E,H,multipliers and ABC arrays ------------
ex = np.zeros((Nx,Ny,Nz))
ey = np.zeros((Nx,Ny,Nz))
ez = np.zeros((Nx,Ny,Nz))
hx = np.zeros((Nx,Ny,Nz))
hy = np.zeros((Nx,Ny,Nz))
hz = np.zeros((Nx,Ny,Nz))
const_ex = np.zeros((Nx,Ny,Nz))
const_ey = np.zeros((Nx,Ny,Nz))
const_ez = np.zeros((Nx,Ny,Nz))
const_hx = np.zeros((Nx,Ny,Nz))
const_hy = np.zeros((Nx,Ny,Nz))
const_hz = np.zeros((Nx,Ny,Nz))
#------- Default constants in update eqn
const_ex[0:Nx,0:Ny,0:Nz] = dt/(epsa*dx)
const_ey[0:Nx,0:Ny,0:Nz] = dt/(epsa*dy)
const_ez[0:Nx,0:Ny,0:Nz] = dt/(epsa*dz)
#--------------------------------------
const_hx[0:Nx,0:Ny,0:Nz] = dt/(meua*dx)
const_hy[0:Nx,0:Ny,0:Nz] = dt/(meua*dy)
const_hz[0:Nx,0:Ny,0:Nz] = dt/(meua*dz)
#----------- Substrate---------
const_ex[sub_x1-1:sub_x2, sub_y1-1:sub_y2, sub_z1-1:sub_z2] = dt/(epss*dx)
const_ey[sub_x1-1:sub_x2, sub_y1-1:sub_y2, sub_z1-1:sub_z2] = dt/(epss*dy)
const_ez[sub_x1-1:sub_x2, sub_y1-1:sub_y2, sub_z1-1:sub_z2] = dt/(epss*dz)
#----------- Top substrate-air interface has eps_avg
const_ex[sub_x1-1:sub_x2, strip_y-1, sub_z1-1:sub_z2] = dt/(epse*dx)
const_ez[sub_x1-1:sub_x2, strip_y-1, sub_z1-1:sub_z2] = dt/(epse*dz)
#----------- Side substrate-air interface has eps_avg
const_ex[sub_x1-1:sub_x2, sub_y1-1:sub_y2, sub_z1-1] = dt/(epse*dx)
const_ey[sub_x1-1:sub_x2, sub_y1-1:sub_y2, sub_z1-1] = dt/(epse*dy)
const_ex[sub_x1-1:sub_x2, sub_y1-1:sub_y2, sub_z2-1] = dt/(epse*dx)
const_ey[sub_x1-1:sub_x2, sub_y1-1:sub_y2, sub_z2-1] = dt/(epse*dy)
const_ey[sub_x1-1, sub_y1-1:sub_y2, sub_z1-1:sub_z2] = dt/(epse*dy)
const_ez[sub_x1-1, sub_y1-1:sub_y2, sub_z1-1:sub_z2] = dt/(epse*dz)
const_ey[sub_x2-1, sub_y1-1:sub_y2, sub_z1-1:sub_z2] = dt/(epse*dy)
const_ez[sub_x2-1, sub_y1-1:sub_y2, sub_z1-1:sub_z2] = dt/(epse*dz)
#----------- Metal boundaries have Etan=0 ---------
#------- Constants in E-update eqn
gx = np.ones((Nx,Ny,Nz))
gy = np.ones((Nx,Ny,Nz))
gz = np.ones((Nx,Ny,Nz))
fx = np.ones((Nx,Ny,Nz))
fy = np.ones((Nx,Ny,Nz))
#---- GND plane
gx[sub_x1-1:sub_x2, sub_y1-1, sub_z1-1:sub_z2] = 0
gz[sub_x1-1:sub_x2, sub_y1-1, sub_z1-1:sub_z2] = 0
#---- Stripline
gx[strip_x1-1:strip_x2, strip_y-1, strip_z1-1:strip_z2] = 0
gz[strip_x1-1:strip_x2, strip_y-1, strip_z1-1:strip_z2] = 0
#------ ABC constants
ex_abc = np.zeros((Nx,Ny,Nz))
ey_abc = np.zeros((Nx,Ny,Nz))
ez_abc = np.zeros((Nx,Ny,Nz))
constz_abc = (vmax*dt-dz)/(vmax*dt+dz)
consty_abc = (vmax*dt-dy)/(vmax*dt+dy)
constx_abc = (vmax*dt-dx)/(vmax*dt+dx)
#------ Plot gx at the surface of the substrate to verify the model
arr = np.copy(gx[:,strip_y-1,:])
xdata = np.linspace(0,Nz-1,Nz, dtype=int)
ydata = np.linspace(0,Nx-1,Nx, dtype=int)
zdata = arr[0:Nx, 0:Nz]
XDAT, YDAT = np.meshgrid(xdata, ydata)
fig = plt.figure()
ax = plt.axes(projection="3d")
ax.plot_wireframe(XDAT, YDAT, zdata)
plt.xlim(0,Nz)
plt.ylim(0,Nx)
plt.show()
#------ Gaussian pulse ------------
Ts = 10*dt # pulse width
t0 = 3*Ts # delay
N_steps = 1 # default iteration steps
count = 0
voltage_in = np.zeros((1000000,1))
current_in = np.copy(voltage_in)
voltage_out = np.copy(voltage_in)
current_out = np.copy(voltage_in)
#current_in_corr = current_in
#************** Iteration loop ****************
while(int(round(N_steps))>0) :
N_steps = int(input('\nTime steps(0 to quit): '))
for n in range (int(round(N_steps))):
time = count*dt
count = count + 1
print('\n\tTime step : ', count)
# ----- Sinusoidal signal of 10 GHz---------
pulse = np.sin(2*np.pi*10e9*time)
ey[strip_x1-1:strip_x2, sub_y1-1:sub_y2, feed_z1-1] = pulse/dy
#------------------------ compute H -------------------------
#j = (np.ones(Ny-1, dtype = int),np.linspace(0, Ny-2, Ny-1, dtype = int),np.ones(Ny-1, dtype = int))
#k = (np.ones(Nz-1, dtype = int), np.ones(Nz-1, dtype = int), np.linspace(0, Nz-2, Nz-1, dtype = int))
for j in range(Ny-1):
for k in range(Nz-1):
hx[:,j,k] = hx[:,j,k] + fx[:,j,k]*(const_hz[:,j,k]*(ey[:,j,k+1]-ey[:,j,k])-const_hy[:,j,k]*(ez[:,j+1,k]-ez[:,j,k]))
for i in range(Nx-1):
for k in range(Nz-1):
hy[i,:,k] = hy[i,:,k] + fy[i,:,k]*(const_hx[i,:,k]*(ez[i+1,:,k]-ez[i,:,k])-const_hz[i,:,k]*(ex[i,:,k+1]-ex[i,:,k]))
for i in range(Nx-1):
for j in range(Ny-1):
hz[i,j,:] = hz[i,j,:] + const_hy[i,j,:]*(ex[i,j+1,:]-ex[i,j,:]) - const_hx[i,j,:]*(ey[i+1,j,:]-ey[i,j,:])
#------------------------- compute E ------------------------
for j in range(1,Ny-1):
for k in range(1,Nz-1):
ex[:,j,k] = ex[:,j,k] + gx[:,j,k]*(const_ey[:,j,k]*(hz[:,j,k]-hz[:,j-1,k])-const_ez[:,j,k]*(hy[:,j,k]-hy[:,j,k-1]))
for i in range(1,Nx-1):
for k in range(1,Nz-1):
ey[i,:,k] = ey[i,:,k] + gy[i,:,k]*(const_ez[i,:,k]*(hx[i,:,k]-hx[i,:,k-1])-const_ex[i,:,k]*(hz[i,:,k]-hz[i-1,:,k]))
for i in range(1,Nx-1):
for j in range(1,Ny-1):
ez[i,j,:] = ez[i,j,:] + gz[i,j,:]*(const_ex[i,j,:]*(hy[i,j,:]-hy[i-1,j,:])-const_ey[i,j,:]*(hx[i,j,:]-hx[i,j-1,:]))
#----------------- ABC---------------------
#---------- XY plane
ex[:,:,0] = ex_abc[:,:,1] + constz_abc*(ex[:,:,1]-ex[:,:,0])
ey[:,:,0] = ey_abc[:,:,1] + constz_abc*(ey[:,:,1]-ey[:,:,0])
ex[:,:,Nz-1] = ex_abc[:,:,Nz-2] + constz_abc*(ex[:,:,Nz-2]-ex[:,:,Nz-1])
ey[:,:,Nz-1] = ey_abc[:,:,Nz-2] + constz_abc*(ey[:,:,Nz-2]-ey[:,:,Nz-1])
#---------- XZ plane
# bottom plane (index 1) is already defined GND
ex[:,Ny-1,:] = ex_abc[:,Ny-2,:] + consty_abc*(ex[:,Ny-2,:]-ex[:,Ny-1,:])
ez[:,Ny-1,:] = ez_abc[:,Ny-2,:] + consty_abc*(ez[:,Ny-2,:]-ez[:,Ny-1,:])
#---------- YZ plane
ey[0,:,:] = ey_abc[1,:,:] + constx_abc*(ey[1,:,:]-ey[0,:,:])
ez[0,:,:] = ez_abc[1,:,:] + constx_abc*(ez[1,:,:]-ez[0,:,:])
ey[Nx-1,:,:] = ey_abc[Nx-2,:,:] + constx_abc*(ey[Nx-2,:,:]-ey[Nx-1,:,:])
ez[Nx-1,:,:] = ez_abc[Nx-2,:,:] + constx_abc*(ez[Nx-2,:,:]-ez[Nx-1,:,:])
ex_abc = np.copy(ex)
ey_abc = np.copy(ey)
ez_abc = np.copy(ez)
#---------- Plot Ey on the strip-----------------
fig2 = plt.figure()
e = np.zeros(Nz)
e[:] = abs(ey[feed_x+2, strip_y-1, :])
k = np.linspace(strip_z1-1, strip_z2-1, strip_z2-strip_z1+1, dtype = int)
plt.plot(k,e[k])
plt.xlim(strip_z1-1, strip_z2)
plt.ylim(0)
plt.title('Ey on strip')
plt.show()