239 lines
8.2 KiB
Python
239 lines
8.2 KiB
Python
# -*- coding: utf-8 -*-
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"""
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Tutorials / CRLH_Extraction
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Description at:
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http://openems.de/index.php/Tutorial:_CRLH_Extraction
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Tested with
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- python 3.4
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- openEMS v0.0.34+
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(C) 2016 Thorsten Liebig <thorsten.liebig@gmx.de>
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"""
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### Import Libraries
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import os, tempfile
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from pylab import *
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from CSXCAD import ContinuousStructure
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from openEMS import openEMS
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from openEMS.physical_constants import *
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### Class to represent single CRLH unit cells
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class CRLH_Cells:
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def __init__(self, LL, LW, Top, Bot, GLT, GLB, SL, SW, VR):
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self.LL = LL # Line length
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self.LW = LW # Line width
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self.Top = Top # top signal height
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self.Bot = Bot # bottom signal height
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self.GLT = GLT # gap length top
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self.GLB = GLB # gap length bottom
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self.SL = SL # stub length
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self.SW = SW # stub width
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self.VR = VR # via radius
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self.props = dict() # property dictionary
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self.edge_resolution = None
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def createProperties(self, CSX):
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for p in ['metal_top', 'metal_bot', 'via']:
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self.props[p] = CSX.AddMetal(p)
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def setEdgeResolution(self, res):
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self.edge_resolution = res
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def createCell(self, translate = [0,0,0]):
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def append_mesh(mesh1, mesh2):
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for n in range(3):
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if mesh1[n] is None:
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mesh1[n] = mesh2[n]
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elif mesh2[n] is None:
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continue
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else:
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mesh1[n] += mesh2[n]
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return mesh1
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translate = array(translate)
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start = [-self.LL/2 , -self.LW/2, self.Top] + translate
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stop = [-self.GLT/2, self.LW/2, self.Top] + translate
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box = self.props['metal_top'].AddBox(start, stop, priority=10)
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mesh = box.GetGridHint('x', metal_edge_res=self.edge_resolution, down_dir=False)
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append_mesh(mesh, box.GetGridHint('y', metal_edge_res=self.edge_resolution) )
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start = [+self.LL/2 , -self.LW/2, self.Top] + translate
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stop = [+self.GLT/2, self.LW/2, self.Top] + translate
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box = self.props['metal_top'].AddBox(start, stop, priority=10)
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append_mesh(mesh, box.GetGridHint('x', metal_edge_res=self.edge_resolution, up_dir=False) )
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start = [-(self.LL-self.GLB)/2, -self.LW/2, self.Bot] + translate
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stop = [+(self.LL-self.GLB)/2, self.LW/2, self.Bot] + translate
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box = self.props['metal_bot'].AddBox(start, stop, priority=10)
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append_mesh(mesh, box.GetGridHint('x', metal_edge_res=self.edge_resolution) )
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start = [-self.SW/2, -self.LW/2-self.SL, self.Bot] + translate
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stop = [+self.SW/2, self.LW/2+self.SL, self.Bot] + translate
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box = self.props['metal_bot'].AddBox(start, stop, priority=10)
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append_mesh(mesh, box.GetGridHint('xy', metal_edge_res=self.edge_resolution) )
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start = [0, -self.LW/2-self.SL+self.SW/2, 0 ] + translate
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stop = [0, -self.LW/2-self.SL+self.SW/2, self.Bot] + translate
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self.props['via'].AddCylinder(start, stop, radius=self.VR, priority=10)
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start[1] *= -1
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stop [1] *= -1
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self.props['via'].AddCylinder(start, stop, radius=self.VR, priority=10)
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return mesh
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if __name__ == '__main__':
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### Setup the simulation
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Sim_Path = os.path.join(tempfile.gettempdir(), 'CRLH_Extraction')
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post_proc_only = False
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unit = 1e-6 # specify everything in um
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feed_length = 30000
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substrate_thickness = [1524, 101 , 254 ]
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substrate_epsr = [3.48, 3.48, 3.48]
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CRLH = CRLH_Cells(LL = 14e3, LW = 4e3, GLB = 1950, GLT = 4700, SL = 7800, SW = 1000, VR = 250 , \
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Top = sum(substrate_thickness), \
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Bot = sum(substrate_thickness[:-1]))
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# frequency range of interest
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f_start = 0.8e9
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f_stop = 6e9
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### Setup FDTD parameters & excitation function
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CSX = ContinuousStructure()
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FDTD = openEMS(EndCriteria=1e-5)
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FDTD.SetCSX(CSX)
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mesh = CSX.GetGrid()
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mesh.SetDeltaUnit(unit)
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CRLH.createProperties(CSX)
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FDTD.SetGaussExcite((f_start+f_stop)/2, (f_stop-f_start)/2 )
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BC = {'PML_8' 'PML_8' 'MUR' 'MUR' 'PEC' 'PML_8'}
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FDTD.SetBoundaryCond( ['PML_8', 'PML_8', 'MUR', 'MUR', 'PEC', 'PML_8'] )
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### Setup a basic mesh and create the CRLH unit cell
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resolution = C0/(f_stop*sqrt(max(substrate_epsr)))/unit /30 # resolution of lambda/30
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CRLH.setEdgeResolution(resolution/4)
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mesh.SetLines('x', [-feed_length-CRLH.LL/2, 0, feed_length+CRLH.LL/2])
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mesh.SetLines('y', [-30000, 0, 30000])
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substratelines = cumsum(substrate_thickness)
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mesh.SetLines('z', [0, 20000])
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mesh.AddLine('z', cumsum(substrate_thickness))
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mesh.AddLine('z', linspace(substratelines[-2],substratelines[-1],4))
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# create the CRLH unit cell (will define additional fixed mesh lines)
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mesh_hint = CRLH.createCell()
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mesh.AddLine('x', mesh_hint[0])
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mesh.AddLine('y', mesh_hint[1])
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# Smooth the given mesh
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mesh.SmoothMeshLines('all', resolution, 1.2)
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### Setup the substrate layer
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substratelines = [0] + substratelines.tolist()
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start, stop = mesh.GetSimArea()
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for n in range(len(substrate_thickness)):
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sub = CSX.AddMaterial( 'substrate_{}'.format(n), epsilon=substrate_epsr[n] )
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start[2] = substratelines[n]
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stop [2] = substratelines[n+1]
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sub.AddBox( start, stop )
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### Add the feeding MSL ports
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pec = CSX.AddMetal( 'PEC' )
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port = [None, None]
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x_lines = mesh.GetLines('x')
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portstart = [ x_lines[0], -CRLH.LW/2, substratelines[-1]]
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portstop = [ -CRLH.LL/2, CRLH.LW/2, 0]
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port[0] = FDTD.AddMSLPort( 1, pec, portstart, portstop, 'x', 'z', excite=-1, FeedShift=10*resolution, MeasPlaneShift=feed_length/2, priority=10)
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portstart = [ x_lines[-1], -CRLH.LW/2, substratelines[-1]]
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portstop = [ +CRLH.LL/2 , CRLH.LW/2, 0]
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port[1] = FDTD.AddMSLPort( 2, pec, portstart, portstop, 'x', 'z', MeasPlaneShift=feed_length/2, priority=10)
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### Run the simulation
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if 1: # debugging only
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CSX_file = os.path.join(Sim_Path, 'CRLH_Extraction.xml')
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if not os.path.exists(Sim_Path):
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os.mkdir(Sim_Path)
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CSX.Write2XML(CSX_file)
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os.system(r'AppCSXCAD "{}"'.format(CSX_file))
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if not post_proc_only:
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FDTD.Run(Sim_Path, verbose=3, cleanup=True)
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### Post-Processing
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f = linspace( f_start, f_stop, 1601 )
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for p in port:
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p.CalcPort( Sim_Path, f, ref_impedance = 50, ref_plane_shift = feed_length)
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# calculate and plot scattering parameter
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s11 = port[0].uf_ref / port[0].uf_inc
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s21 = port[1].uf_ref / port[0].uf_inc
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plot(f/1e9,20*log10(abs(s11)),'k-' , linewidth=2, label='$S_{11}$')
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plot(f/1e9,20*log10(abs(s21)),'r--', linewidth=2, label='$S_{21}$')
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grid()
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legend(loc=3)
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ylabel('S-Parameter (dB)')
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xlabel('frequency (GHz)')
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ylim([-40, 2])
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### Extract CRLH parameter form ABCD matrix
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A = ((1+s11)*(1-s11) + s21*s21)/(2*s21)
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C = ((1-s11)*(1-s11) - s21*s21)/(2*s21) / port[1].Z_ref
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Y = C
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Z = 2*(A-1)/C
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iZ = imag(Z)
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iY = imag(Y)
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fse = interp(0, iZ, f)
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fsh = interp(0, iY, f)
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df = f[1]-f[0]
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fse_idx = np.where(f>fse)[0][0]
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fsh_idx = np.where(f>fsh)[0][0]
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LR = 0.5*(iZ[fse_idx]-iZ[fse_idx-1])/(2*pi*df)
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CL = 1/(2*pi*fse)**2/LR
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CR = 0.5*(iY[fsh_idx]-iY[fsh_idx-1])/(2*pi*df)
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LL = 1/(2*pi*fsh)**2/CR
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print(' Series tank: CL = {:.2f} pF, LR = {:.2f} nH -> f_se = {:.2f} GHz '.format(CL*1e12, LR*1e9, fse*1e-9))
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print(' Shunt tank: CR = {:.2f} pF, LL = {:.2f} nH -> f_sh = {:.2f} GHz '.format(CR*1e12, LL*1e9, fsh*1e-9))
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### Calculate analytical wave-number of an inf-array of cells
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w = 2*pi*f
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wse = 2*pi*fse
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wsh = 2*pi*fsh
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beta_calc = real(arccos(1-(w**2-wse**2)*(w**2-wsh**2)/(2*w**2/CR/LR)))
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# plot
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figure()
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beta = -angle(s21)/CRLH.LL/unit
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plot(abs(beta)*CRLH.LL*unit/pi,f*1e-9,'k-', linewidth=2, label=r'$\beta_{CRLH,\ 1\ cell}$' )
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grid()
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plot(beta_calc/pi,f*1e-9,'c--', linewidth=2, label=r'$\beta_{CRLH,\ \infty\ cells}$')
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plot(real(port[1].beta)*CRLH.LL*unit/pi,f*1e-9,'g-', linewidth=2, label=r'$\beta_{MSL}$')
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ylim([1, 6])
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xlabel(r'$|\beta| p / \pi$')
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ylabel('frequency (GHz)')
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legend(loc=2)
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show() |