1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
|
# -*- coding: utf-8 -*-
"""
Tutorials / CRLH_Extraction
Describtion at:
http://openems.de/index.php/Tutorial:_CRLH_Extraction
Tested with
- python 3.4
- openEMS v0.0.34+
(C) 2016 Thorsten Liebig <thorsten.liebig@gmx.de>
"""
### Import Libraries
import os, tempfile
from pylab import *
from CSXCAD import ContinuousStructure
from openEMS import openEMS
from openEMS.physical_constants import *
### Class to represent single CRLH unit cells
class CRLH_Cells:
def __init__(self, LL, LW, Top, Bot, GLT, GLB, SL, SW, VR):
self.LL = LL # Line length
self.LW = LW # Line width
self.Top = Top # top signal height
self.Bot = Bot # bottom signal height
self.GLT = GLT # gap length top
self.GLB = GLB # gap length bottom
self.SL = SL # stub length
self.SW = SW # stub width
self.VR = VR # via radius
self.props = dict() # property dictionary
self.edge_resolution = None
def createProperties(self, CSX):
for p in ['metal_top', 'metal_bot', 'via']:
self.props[p] = CSX.AddMetal(p)
def setEdgeResolution(self, res):
self.edge_resolution = res
def createCell(self, translate = [0,0,0]):
def append_mesh(mesh1, mesh2):
for n in range(3):
if mesh1[n] is None:
mesh1[n] = mesh2[n]
elif mesh2[n] is None:
continue
else:
mesh1[n] += mesh2[n]
return mesh1
translate = array(translate)
start = [-self.LL/2 , -self.LW/2, self.Top] + translate
stop = [-self.GLT/2, self.LW/2, self.Top] + translate
box = self.props['metal_top'].AddBox(start, stop, priority=10)
mesh = box.GetGridHint('x', metal_edge_res=self.edge_resolution, down_dir=False)
append_mesh(mesh, box.GetGridHint('y', metal_edge_res=self.edge_resolution) )
start = [+self.LL/2 , -self.LW/2, self.Top] + translate
stop = [+self.GLT/2, self.LW/2, self.Top] + translate
box = self.props['metal_top'].AddBox(start, stop, priority=10)
append_mesh(mesh, box.GetGridHint('x', metal_edge_res=self.edge_resolution, up_dir=False) )
start = [-(self.LL-self.GLB)/2, -self.LW/2, self.Bot] + translate
stop = [+(self.LL-self.GLB)/2, self.LW/2, self.Bot] + translate
box = self.props['metal_bot'].AddBox(start, stop, priority=10)
append_mesh(mesh, box.GetGridHint('x', metal_edge_res=self.edge_resolution) )
start = [-self.SW/2, -self.LW/2-self.SL, self.Bot] + translate
stop = [+self.SW/2, self.LW/2+self.SL, self.Bot] + translate
box = self.props['metal_bot'].AddBox(start, stop, priority=10)
append_mesh(mesh, box.GetGridHint('xy', metal_edge_res=self.edge_resolution) )
start = [0, -self.LW/2-self.SL+self.SW/2, 0 ] + translate
stop = [0, -self.LW/2-self.SL+self.SW/2, self.Bot] + translate
self.props['via'].AddCylinder(start, stop, radius=self.VR, priority=10)
start[1] *= -1
stop [1] *= -1
self.props['via'].AddCylinder(start, stop, radius=self.VR, priority=10)
return mesh
if __name__ == '__main__':
### Setup the simulation
Sim_Path = os.path.join(tempfile.gettempdir(), 'CRLH_Extraction')
post_proc_only = False
unit = 1e-6 # specify everything in um
feed_length = 30000
substrate_thickness = [1524, 101 , 254 ]
substrate_epsr = [3.48, 3.48, 3.48]
CRLH = CRLH_Cells(LL = 14e3, LW = 4e3, GLB = 1950, GLT = 4700, SL = 7800, SW = 1000, VR = 250 , \
Top = sum(substrate_thickness), \
Bot = sum(substrate_thickness[:-1]))
# frequency range of interest
f_start = 0.8e9
f_stop = 6e9
### Setup FDTD parameters & excitation function
CSX = ContinuousStructure()
FDTD = openEMS(EndCriteria=1e-5)
FDTD.SetCSX(CSX)
mesh = CSX.GetGrid()
mesh.SetDeltaUnit(unit)
CRLH.createProperties(CSX)
FDTD.SetGaussExcite((f_start+f_stop)/2, (f_stop-f_start)/2 )
BC = {'PML_8' 'PML_8' 'MUR' 'MUR' 'PEC' 'PML_8'}
FDTD.SetBoundaryCond( ['PML_8', 'PML_8', 'MUR', 'MUR', 'PEC', 'PML_8'] )
### Setup a basic mesh and create the CRLH unit cell
resolution = C0/(f_stop*sqrt(max(substrate_epsr)))/unit /30 # resolution of lambda/30
CRLH.setEdgeResolution(resolution/4)
mesh.SetLines('x', [-feed_length-CRLH.LL/2, 0, feed_length+CRLH.LL/2])
mesh.SetLines('y', [-30000, 0, 30000])
substratelines = cumsum(substrate_thickness)
mesh.SetLines('z', [0, 20000])
mesh.AddLine('z', cumsum(substrate_thickness))
mesh.AddLine('z', linspace(substratelines[-2],substratelines[-1],4))
# create the CRLH unit cell (will define additional fixed mesh lines)
mesh_hint = CRLH.createCell()
mesh.AddLine('x', mesh_hint[0])
mesh.AddLine('y', mesh_hint[1])
# Smooth the given mesh
mesh.SmoothMeshLines('all', resolution, 1.2)
### Setup the substrate layer
substratelines = [0] + substratelines.tolist()
start, stop = mesh.GetSimArea()
for n in range(len(substrate_thickness)):
sub = CSX.AddMaterial( 'substrate_{}'.format(n), epsilon=substrate_epsr[n] )
start[2] = substratelines[n]
stop [2] = substratelines[n+1]
sub.AddBox( start, stop )
### Add the feeding MSL ports
pec = CSX.AddMetal( 'PEC' )
port = [None, None]
x_lines = mesh.GetLines('x')
portstart = [ x_lines[0], -CRLH.LW/2, substratelines[-1]]
portstop = [ -CRLH.LL/2, CRLH.LW/2, 0]
port[0] = FDTD.AddMSLPort( 1, pec, portstart, portstop, 'x', 'z', excite=-1, FeedShift=10*resolution, MeasPlaneShift=feed_length/2, priority=10)
portstart = [ x_lines[-1], -CRLH.LW/2, substratelines[-1]]
portstop = [ +CRLH.LL/2 , CRLH.LW/2, 0]
port[1] = FDTD.AddMSLPort( 2, pec, portstart, portstop, 'x', 'z', MeasPlaneShift=feed_length/2, priority=10)
### Run the simulation
if 1: # debugging only
CSX_file = os.path.join(Sim_Path, 'CRLH_Extraction.xml')
if not os.path.exists(Sim_Path):
os.mkdir(Sim_Path)
CSX.Write2XML(CSX_file)
os.system(r'AppCSXCAD "{}"'.format(CSX_file))
if not post_proc_only:
FDTD.Run(Sim_Path, verbose=3, cleanup=True)
### Post-Processing
f = linspace( f_start, f_stop, 1601 )
for p in port:
p.CalcPort( Sim_Path, f, ref_impedance = 50, ref_plane_shift = feed_length)
# calculate and plot scattering parameter
s11 = port[0].uf_ref / port[0].uf_inc
s21 = port[1].uf_ref / port[0].uf_inc
plot(f/1e9,20*log10(abs(s11)),'k-' , linewidth=2, label='$S_{11}$')
plot(f/1e9,20*log10(abs(s21)),'r--', linewidth=2, label='$S_{21}$')
grid()
legend(loc=3)
ylabel('S-Parameter (dB)')
xlabel('frequency (GHz)')
ylim([-40, 2])
### Extract CRLH parameter form ABCD matrix
A = ((1+s11)*(1-s11) + s21*s21)/(2*s21)
C = ((1-s11)*(1-s11) - s21*s21)/(2*s21) / port[1].Z_ref
Y = C
Z = 2*(A-1)/C
iZ = imag(Z)
iY = imag(Y)
fse = interp(0, iZ, f)
fsh = interp(0, iY, f)
df = f[1]-f[0]
fse_idx = np.where(f>fse)[0][0]
fsh_idx = np.where(f>fsh)[0][0]
LR = 0.5*(iZ[fse_idx]-iZ[fse_idx-1])/(2*pi*df)
CL = 1/(2*pi*fse)**2/LR
CR = 0.5*(iY[fsh_idx]-iY[fsh_idx-1])/(2*pi*df)
LL = 1/(2*pi*fsh)**2/CR
print(' Series tank: CL = {:.2f} pF, LR = {:.2f} nH -> f_se = {:.2f} GHz '.format(CL*1e12, LR*1e9, fse*1e-9))
print(' Shunt tank: CR = {:.2f} pF, LL = {:.2f} nH -> f_sh = {:.2f} GHz '.format(CR*1e12, LL*1e9, fsh*1e-9))
### Calculate analytical wave-number of an inf-array of cells
w = 2*pi*f
wse = 2*pi*fse
wsh = 2*pi*fsh
beta_calc = real(arccos(1-(w**2-wse**2)*(w**2-wsh**2)/(2*w**2/CR/LR)))
# plot
figure()
beta = -angle(s21)/CRLH.LL/unit
plot(abs(beta)*CRLH.LL*unit/pi,f*1e-9,'k-', linewidth=2, label=r'$\beta_{CRLH,\ 1\ cell}$' )
grid()
plot(beta_calc/pi,f*1e-9,'c--', linewidth=2, label=r'$\beta_{CRLH,\ \infty\ cells}$')
plot(real(port[1].beta)*CRLH.LL*unit/pi,f*1e-9,'g-', linewidth=2, label=r'$\beta_{MSL}$')
ylim([1, 6])
xlabel(r'$|\beta| p / \pi$')
ylabel('frequency (GHz)')
legend(loc=2)
show()
|
