Microstrip Notch Filter

A straight MSL line with a open-ended stub to create a simple microwave filter.

Introduction

This tutorial covers:

Setup a mircostrip line (MSL) and MSL port
Apply an inhomogeneous mesh used for improved accuracy and simulation speed
Calculate the S-Parameter of the filter

Python Script

Get the latest version from git.

Import Libraries

import os, tempfile
import numpy as np
import matplotlib.pyplot as plt  # pip install matplotlib

from CSXCAD  import ContinuousStructure
from openEMS import openEMS
from openEMS.physical_constants import *

Setup the simulation

Sim_Path = os.path.join(tempfile.gettempdir(), 'NotchFilter')
post_proc_only = False

unit = 1e-6 # specify everything in um
MSL_length = 50000
MSL_width = 600
substrate_thickness = 254
substrate_epr = 3.66
stub_length = 12e3
f_max = 7e9

Setup FDTD parameters & excitation function

FDTD = openEMS()
FDTD.SetGaussExcite( f_max/2, f_max/2 )
FDTD.SetBoundaryCond( ['PML_8', 'PML_8', 'MUR', 'MUR', 'PEC', 'MUR'] )

Setup Geometry & Mesh

CSX = ContinuousStructure()
FDTD.SetCSX(CSX)
mesh = CSX.GetGrid()
mesh.SetDeltaUnit(unit)

resolution = C0/(f_max*np.sqrt(substrate_epr))/unit/50 # resolution of lambda/50
third_mesh = np.array([2*resolution/3, -resolution/3])/4

Do manual meshing

mesh.AddLine('x', 0)
mesh.AddLine('x',  MSL_width/2+third_mesh)
mesh.AddLine('x', -MSL_width/2-third_mesh)
mesh.SmoothMeshLines('x', resolution/4)

mesh.AddLine('x', [-MSL_length, MSL_length])
mesh.SmoothMeshLines('x', resolution)

mesh.AddLine('y', 0)
mesh.AddLine('y',  MSL_width/2+third_mesh)
mesh.AddLine('y', -MSL_width/2-third_mesh)
mesh.SmoothMeshLines('y', resolution/4)

mesh.AddLine('y', [-15*MSL_width, 15*MSL_width+stub_length])
mesh.AddLine('y', (MSL_width/2+stub_length)+third_mesh)
mesh.SmoothMeshLines('y', resolution)

mesh.AddLine('z', np.linspace(0,substrate_thickness,5))
mesh.AddLine('z', 3000)
mesh.SmoothMeshLines('z', resolution)

Add the substrate

substrate = CSX.AddMaterial( 'RO4350B', epsilon=substrate_epr)
start = [-MSL_length, -15*MSL_width, 0]
stop  = [+MSL_length, +15*MSL_width+stub_length, substrate_thickness]
substrate.AddBox(start, stop )

MSL port setup

port = [None, None]
pec = CSX.AddMetal( 'PEC' )
portstart = [ -MSL_length, -MSL_width/2, substrate_thickness]
portstop  = [ 0,  MSL_width/2, 0]
port[0] = FDTD.AddMSLPort( 1,  pec, portstart, portstop, 'x', 'z', excite=-1, FeedShift=10*resolution, MeasPlaneShift=MSL_length/3, priority=10)

portstart = [MSL_length, -MSL_width/2, substrate_thickness]
portstop  = [0         ,  MSL_width/2, 0]
port[1] = FDTD.AddMSLPort( 2, pec, portstart, portstop, 'x', 'z', MeasPlaneShift=MSL_length/3, priority=10 )

Filter-Stub Definition

start = [-MSL_width/2,  MSL_width/2, substrate_thickness]
stop  = [ MSL_width/2,  MSL_width/2+stub_length, substrate_thickness]
pec.AddBox(start, stop, priority=10 )

Run the simulation

if 0:  # debugging only
    CSX_file = os.path.join(Sim_Path, 'notch.xml')
    if not os.path.exists(Sim_Path):
        os.mkdir(Sim_Path)
    CSX.Write2XML(CSX_file)
    from CSXCAD import AppCSXCAD_BIN
    os.system(AppCSXCAD_BIN + ' "{}"'.format(CSX_file))


if not post_proc_only:
    FDTD.Run(Sim_Path, cleanup=True)

Post-processing and plotting

f = np.linspace( 1e6, f_max, 1601 )
for p in port:
    p.CalcPort( Sim_Path, f, ref_impedance = 50)

s11 = port[0].uf_ref / port[0].uf_inc
s21 = port[1].uf_ref / port[0].uf_inc

Plot s-parameter

fig, axis = plt.subplots(num="S11", tight_layout=True)
axis.plot(f/1e9, 20*np.log10(abs(s11)), 'k-',  linewidth=2, label='$S_{11}$')
axis.plot(f/1e9, 20*np.log10(abs(s21)), 'r--',  linewidth=2, label='$S_{21}$')
axis.grid()
axis.set_xmargin(0)
axis.set_xlabel('Frequency (GHz)')
axis.set_ylabel('S-Parameter (dB)')
axis.legend()

# show all plots
plt.show()

Images