parser.add_argument('dt', type=float, help='time step to view waveform')
args = parser.parse_args()
w = Waveform()
w.type = args.type
w.amp = args.amp
w.freq = args.freq
timewindow = args.timewindow
dt = args.dt
time = np.arange(0, timewindow, dt)
waveform = np.zeros(len(time))
timeiter = np.nditer(time, flags=['c_index'])
while not timeiter.finished:
waveform[timeiter.index] = w.calculate_value(timeiter[0], dt)
timeiter.iternext()
# Calculate frequency spectra of waveform
power = 20 * np.log10(np.abs(np.fft.fft(waveform))**2)
f = np.fft.fftfreq(power.size, d=dt)
# Shift powers so any spectra with negative DC component will start at zero
power -= np.amax(power)
# Set plotting range to 4 * centre frequency
pltrange = np.where(f > (4 * w.freq))[0][0]
# Plot waveform
fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, num=w.type, figsize=(20, 10), facecolor='w', edgecolor='w')
ax1.plot(time, waveform, 'r', lw=2)
def hertzian_dipole_fs(iterations, dt, dxdydz, rx):
"""Analytical solution of a z-directed Hertzian dipole in free space with a Gaussian current waveform (http://dx.doi.org/10.1016/0021-9991(83)90103-1).
Args:
iterations (int): Number of time steps.
dt (float): Time step (seconds).
dxdydz (float): Tuple of spatial resolution (metres).
rx (float): Tuple of coordinates of receiver position relative to transmitter position (metres).
Returns:
fields (float): Array contain electric and magnetic field components.
"""
# Waveform
w = Waveform()
w.type = 'gaussiandot'
w.amp = 1
w.freq = 1e9
# Waveform integral
wint = Waveform()
wint.type = 'gaussian'
wint.amp = w.amp
wint.freq = w.freq
# Waveform first derivative
wdot = Waveform()
wdot.type = 'gaussiandotdot'
wdot.amp = w.amp
wdot.freq = w.freq
# Time
time = np.linspace(0, 1, iterations)
time *= (iterations * dt)
# Spatial resolution
dx = dxdydz[0]
dy = dxdydz[1]
dz = dxdydz[2]
# Coordinates of Rx relative to Tx
x = rx[0]
y = rx[1]
z = rx[2]
if z == 0:
sign_z = 1
else:
sign_z = np.sign(z)
# Coordinates of Rx for Ex FDTD component
Ex_x = x + 0.5 * dx
Ex_y = y
Ex_z = z - 0.5 * dz
Er_x = np.sqrt((Ex_x**2 + Ex_y**2 + Ex_z**2))
tau_Ex = Er_x / c
# Coordinates of Rx for Ey FDTD component
Ey_x = x
Ey_y = y + 0.5 * dy
Ey_z = z - 0.5 * dz
Er_y = np.sqrt((Ey_x**2 + Ey_y**2 + Ey_z**2))
tau_Ey = Er_y / c
# Coordinates of Rx for Ez FDTD component
Ez_x = x
Ez_y = y
Ez_z = z
Er_z = np.sqrt((Ez_x**2 + Ez_y**2 + Ez_z**2))
tau_Ez = Er_z / c
# Coordinates of Rx for Hx FDTD component
Hx_x = x
Hx_y = y + 0.5 * dy
Hx_z = z
Hr_x = np.sqrt((Hx_x**2 + Hx_y**2 + Hx_z**2))
tau_Hx = Hr_x / c
# Coordinates of Rx for Hy FDTD component
Hy_x = x + 0.5 * dx
Hy_y = y
Hy_z = z
Hr_y = np.sqrt((Hy_x**2 + Hy_y**2 + Hy_z**2))
tau_Hy = Hr_y / c
# Coordinates of Rx for Hz FDTD component
Hz_x = x + 0.5 * dx
Hz_y = y + 0.5 * dy
Hz_z = z - 0.5 * dz
Hr_z = np.sqrt((Hz_x**2 + Hz_y**2 + Hz_z**2))
tau_Hz = Hr_z / c
# Initialise fields
fields = np.zeros((iterations, 6))
# Calculate fields
for timestep in range(iterations):
# Calculate values for waveform
fint_Ex = wint.calculate_value((timestep * dt) - tau_Ex, dt) * dx
f_Ex = w.calculate_value((timestep * dt) - tau_Ex, dt) * dx
fdot_Ex = wdot.calculate_value((timestep * dt) - tau_Ex, dt) * dx
fint_Ey = wint.calculate_value((timestep * dt) - tau_Ey, dt) * dy
f_Ey = w.calculate_value((timestep * dt) - tau_Ey, dt) * dy
fdot_Ey = wdot.calculate_value((timestep * dt) - tau_Ey, dt) * dy
fint_Ez = wint.calculate_value((timestep * dt) - tau_Ez, dt) * dz
f_Ez = w.calculate_value((timestep * dt) - tau_Ez, dt) * dz
fdot_Ez = wdot.calculate_value((timestep * dt) - tau_Ez, dt) * dz
fint_Hx = wint.calculate_value((timestep * dt) - tau_Hx, dt) * dx
f_Hx = w.calculate_value((timestep * dt) - tau_Hx, dt) * dx
fdot_Hx = wdot.calculate_value((timestep * dt) - tau_Hx, dt) * dx
fint_Hy = wint.calculate_value((timestep * dt) - tau_Hy, dt) * dy
f_Hy = w.calculate_value((timestep * dt) - tau_Hy, dt) * dy
fdot_Hy = wdot.calculate_value((timestep * dt) - tau_Hy, dt) * dy
fint_Hz = wint.calculate_value((timestep * dt) - tau_Hz, dt) * dz
f_Hz = w.calculate_value((timestep * dt) - tau_Hz, dt) * dz
fdot_Hz = wdot.calculate_value((timestep * dt) - tau_Hz, dt) * dz
# Ex
fields[timestep,
0] = ((Ex_x * Ex_z) /
(4 * np.pi * e0 * Er_x**5)) * (3 * (fint_Ex +
(tau_Ex * f_Ex)) +
(tau_Ex**2 * fdot_Ex))
# Ey
try:
tmp = Ey_y / Ey_x
except ZeroDivisionError:
tmp = 0
fields[timestep, 1] = tmp * (
(Ey_x * Ey_z) /
(4 * np.pi * e0 * Er_y**5)) * (3 * (fint_Ey + (tau_Ey * f_Ey)) +
(tau_Ey**2 * fdot_Ey))
# Ez
fields[timestep, 2] = (1 / (4 * np.pi * e0 * Er_z**5)) * (
(2 * Ez_z**2 - (Ez_x**2 + Ez_y**2)) * (fint_Ez + (tau_Ez * f_Ez)) -
(Ez_x**2 + Ez_y**2) * tau_Ez**2 * fdot_Ez)
# Hx
fields[timestep,
3] = -(Hx_y / (4 * np.pi * Hr_x**3)) * (f_Hx +
(tau_Hx * fdot_Hx))
# Hy
try:
tmp = Hy_x / Hy_y
except ZeroDivisionError:
tmp = 0
fields[timestep, 4] = -tmp * (-(Hy_y / (4 * np.pi * Hr_y**3)) *
(f_Hy + (tau_Hy * fdot_Hy)))
# Hz
fields[timestep, 5] = 0
return fields
def hertzian_dipole_fs(iterations, dt, dxdydz, rx):
"""Analytical solution of a z-directed Hertzian dipole in free space with a Gaussian current waveform (http://dx.doi.org/10.1016/0021-9991(83)90103-1).
Args:
iterations (int): Number of time steps.
dt (float): Time step (seconds).
dxdydz (float): Tuple of spatial resolution (metres).
rx (float): Tuple of coordinates of receiver position relative to transmitter position (metres).
Returns:
fields (float): Array contain electric and magnetic field components.
"""
# Waveform
w = Waveform()
w.type = 'gaussiandot'
w.amp = 1
w.freq = 1e9
# Waveform integral
wint = Waveform()
wint.type = 'gaussian'
wint.amp = w.amp
wint.freq = w.freq
# Waveform first derivative
wdot = Waveform()
wdot.type = 'gaussiandotdot'
wdot.amp = w.amp
wdot.freq = w.freq
# Time
time = np.linspace(0, 1, iterations)
time *= (iterations * dt)
# Spatial resolution
dx = dxdydz[0]
dy = dxdydz[1]
dz = dxdydz[2]
# Length of Hertzian dipole
dl = dz
# Coordinates of Rx relative to Tx
x = rx[0]
y = rx[1]
z = rx[2]
if z == 0:
sign_z = 1
else:
sign_z = np.sign(z)
# Coordinates of Rx for Ex FDTD component
Ex_x = x + 0.5 * dx
Ex_y = y
Ex_z = z - 0.5 * dz
Er_x = np.sqrt((Ex_x**2 + Ex_y**2 + Ex_z**2))
tau_Ex = Er_x / c
# Coordinates of Rx for Ey FDTD component
Ey_x = x
Ey_y = y + 0.5 * dy
Ey_z = z - 0.5 * dz
Er_y = np.sqrt((Ey_x**2 + Ey_y**2 + Ey_z**2))
tau_Ey = Er_y / c
# Coordinates of Rx for Ez FDTD component
Ez_x = x
Ez_y = y
Ez_z = z
Er_z = np.sqrt((Ez_x**2 + Ez_y**2 + Ez_z**2))
tau_Ez = Er_z / c
# Coordinates of Rx for Hx FDTD component
Hx_x = x
Hx_y = y + 0.5 * dy
Hx_z = z
Hr_x = np.sqrt((Hx_x**2 + Hx_y**2 + Hx_z**2))
tau_Hx = Hr_x / c
# Coordinates of Rx for Hy FDTD component
Hy_x = x + 0.5 * dx
Hy_y = y
Hy_z = z
Hr_y = np.sqrt((Hy_x**2 + Hy_y**2 + Hy_z**2))
tau_Hy = Hr_y / c
# Coordinates of Rx for Hz FDTD component
Hz_x = x + 0.5 * dx
Hz_y = y + 0.5 * dy
Hz_z = z - 0.5 * dz
Hr_z = np.sqrt((Hz_x**2 + Hz_y**2 + Hz_z**2))
tau_Hz = Hr_z / c
# Initialise fields
fields = np.zeros((iterations, 6))
# Calculate fields
for timestep in range(iterations):
# Calculate values for waveform, I * dl (current multiplied by dipole length) to match gprMax behaviour
fint_Ex = wint.calculate_value((timestep * dt) - tau_Ex, dt) * dl
f_Ex = w.calculate_value((timestep * dt) - tau_Ex, dt) * dl
fdot_Ex = wdot.calculate_value((timestep * dt) - tau_Ex, dt) * dl
fint_Ey = wint.calculate_value((timestep * dt) - tau_Ey, dt) * dl
f_Ey= w.calculate_value((timestep * dt) - tau_Ey, dt) * dl
fdot_Ey = wdot.calculate_value((timestep * dt) - tau_Ey, dt) * dl
fint_Ez = wint.calculate_value((timestep * dt) - tau_Ez, dt) * dl
f_Ez = w.calculate_value((timestep * dt) - tau_Ez, dt) * dl
fdot_Ez = wdot.calculate_value((timestep * dt) - tau_Ez, dt) * dl
fint_Hx = wint.calculate_value((timestep * dt) - tau_Hx, dt) * dl
f_Hx = w.calculate_value((timestep * dt) - tau_Hx, dt) * dl
fdot_Hx = wdot.calculate_value((timestep * dt) - tau_Hx, dt) * dl
fint_Hy = wint.calculate_value((timestep * dt) - tau_Hy, dt) * dl
f_Hy= w.calculate_value((timestep * dt) - tau_Hy, dt) * dl
fdot_Hy = wdot.calculate_value((timestep * dt) - tau_Hy, dt) * dl
fint_Hz = wint.calculate_value((timestep * dt) - tau_Hz, dt) * dl
f_Hz = w.calculate_value((timestep * dt) - tau_Hz, dt) * dl
fdot_Hz = wdot.calculate_value((timestep * dt) - tau_Hz, dt) * dl
# Ex
fields[timestep, 0] = ((Ex_x * Ex_z) / (4 * np.pi * e0 * Er_x**5)) * (3 * (fint_Ex + (tau_Ex * f_Ex)) + (tau_Ex**2 * fdot_Ex))
# Ey
try:
tmp = Ey_y / Ey_x
except ZeroDivisionError:
tmp = 0
fields[timestep, 1] = tmp * ((Ey_x * Ey_z) / (4 * np.pi * e0 * Er_y**5)) * (3 * (fint_Ey + (tau_Ey * f_Ey)) + (tau_Ey**2 * fdot_Ey))
# Ez
fields[timestep, 2] = (1 / (4 * np.pi * e0 * Er_z**5)) * ((2 * Ez_z**2 - (Ez_x**2 + Ez_y**2)) * (fint_Ez + (tau_Ez * f_Ez)) - (Ez_x**2 + Ez_y**2) * tau_Ez**2 * fdot_Ez)
# Hx
fields[timestep, 3] = - (Hx_y / (4 * np.pi * Hr_x**3)) * (f_Hx + (tau_Hx * fdot_Hx))
# Hy
try:
tmp = Hy_x / Hy_y
except ZeroDivisionError:
tmp = 0
fields[timestep, 4] = - tmp * (- (Hy_y / (4 * np.pi * Hr_y**3)) * (f_Hy + (tau_Hy * fdot_Hy)))
# Hz
fields[timestep, 5] = 0
return fields
timewindow = float(args.timewindow)
iterations = round_value((float(args.timewindow) / dt)) + 1
else:
raise CmdInputError('Time window must have a value greater than zero')
# If number of iterations given
else:
timewindow = (int(args.timewindow) - 1) * dt
iterations = int(args.timewindow)
time = np.linspace(0, 1, iterations)
time *= (iterations * dt)
waveform = np.zeros(len(time))
timeiter = np.nditer(time, flags=['c_index'])
while not timeiter.finished:
waveform[timeiter.index] = w.calculate_value(timeiter[0], dt)
timeiter.iternext()
print('Waveform characteristics...')
print('Type: {}'.format(w.type))
print('Amplitude: {:g}'.format(w.amp))
print('Centre frequency: {:g} Hz'.format(w.freq))
print('Time to centre of pulse: {:g} s'.format(1 / w.freq))
# Calculate pulse width for gaussian
if w.type == 'gaussian':
powerdrop = -3 #dB
start = np.where(
(10 * np.log10(waveform / np.amax(waveform))) > powerdrop)[0][0]
stop = np.where((10 * np.log10(waveform[start:] / np.amax(waveform))
) < powerdrop)[0][0] + start
