RF, Digital Radio and
Metamaterial Fundamentals
Project
Metamaterials
Overview
Work in assigned project groups.
The objective of this project is to do 3D simulation of metamaterials.
NOTE: Use the Project Report Template and keep answers to questions on consecutive sheets
of paper with all plots at the end.
IN NO CASE may code or files be exchanged between students, and
each student must answer the questions themselves and do their own
plots, NO COPYING of any sort! Nevertheless, students are
encouraged to collaborate in the lab session.
Part 1: 3D simulation of metamaterials
Fig 001
Fig 002
- Save a snapshot for
your report.
- Select the Boundaries::perfectH in the project manager pane
on the left side of the HFSS window, and note that these are the short walls of
the waveguide. The perfectH
boundary is similar to perfectE boundary.
PerfectE is a PEC (perfect electric conductor) that does not allow tangential
electric fields at the boundary. PerfectH is a PMC (perfect
magnetic conductor) that does not allow tangential magnetic
fields at the boundary.
- What is the radius of the ring?
- Zoom in to the gap in the ring by selecting
Sheet::LumpedRLC::Rectangle2 (blue arrow below) and zooming in
(red arrow below) to zoom into the sheet (yellow arrow below)
that is placed in the gap. This "RLC" sheet is
used as a capacitor in the gap.
New HFSS views above (older below)
Fig 003
- Use MenuBar::Modeler::Measure::Position to measure the gap
length by measuring the length of the sheet in the gap.
Click one end of the sheet, and observe the distance as you
move the mouse
- What is the length of the gap in the ring?
- Select the Boundaries::LumpRLC1 item in the project manager
(yellow arrow below) and observe the capacitance of the sheet
in the gap (red arrow below)
New HFSS views above (older below)
Fig 004
- What is the capacitance of the lumped RLC sheet in the gap?
- Run the simulation (blue circle above)
- When the simulation completes, select the first two results
plots as illustrated below.
- Plot the relative
permeability as shown (blue arrows below) by
double-clicking XYplot1
- Plot the S-parameters S11 and S21 as shown (red arrows
below) by double-clicking "Sparameter"
Fig 005
- Note the frequency range where the
relative permeability is negative (yellow arrow
above).
- This is the desired metamaterial
behavior.
- Save a snapshot of the S-parameter plot as above, but with
all scales/axes visible, and save it for your
report.
- Using the equation
for a circular loop here, what is the theoretical
inductance of the ring?
- Based on the capacitance of the lumped RLC sheet in the gap,
and the inductance from the previous question, what is your
computed value of the resonant frequency is f0=1/{ 2 pi
sqrt(LC) }? Save this for the table in your report.
- Click the ReMuEps plot (red arrow and red circles below) to
plot extracted permittivity and permeability as shown below
Fig 006
- Save a snapshot of the relative permeability and
permittivity as shown above, but with all scales/axes visible,
and paste it into your report. ( P6 )
- Note the region of negative permeability (yellow circle
above)
- From the capacitance value of the lumped RLC, and from the
frequency of the resonance in the S-parameters, compute the
inductance of the ring that resonates with the capacitance of
the lumped RLC.
- What are the real parts of relative permeability (mur) and
relative permittivity (epsr) at the lowest frequency (2.5 GHz)
in the plot? ( Q10 )
- What are the real parts of relative permeability (mur) and
relative permittivity (epsr) at the highest frequency (3.5
GHz) in the plot? ( Q11 )
- Note, by right clicking results (in upper left pane of above
figure near red arrow) and selecting output variables, you can
see the formulas used to extract the mu and epsilon (generally
these are approximations below), See http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1210783
for details on the formulas:
- dd = .01 (length in meters of the physical region
being characterized, typically the diameter of the ring)
- v1 = S(1,1)+S(2,1)
- v2 = S(2,1)-S(1,1)
- k0 = 6.28*Freq/3e8
- mur = 2/(cmplx(0,1)*k0*dd)*(1-v2)/(1+v2)
- epsr = mur+2*cmplx(0,1)/(k0*dd)
- epsr2 =
2/(cmplx(0,1)*k0*dd)*(1-v1)/(1+v1)
- Note: above formulas should be used when de-embedding is
up to within approx 1mm of edge of ring. To see
de-embedding, select Excitation in the upper left pane,
select the waveport, right-click properties, and click the
postprocessing tab. When the waveport is selected, you
should see an 3D arrow indicating how far the results are
deembedded from the waveport.
- De-embedding effectively moves the waveport closer to the
split ring, so the measurement primarily consists of the
effect of the split ring. Otherwise, the measurement
would include the effect of a long portion of empty waveguide
in addition to the effect of the split ring.
- Select Excitation in the upper left pane, select the
waveport, right-click properties, and click the postprocessing
tab. When the waveport is selected, you should see a 3D
arrow indicating how far the results are de-embedded from the
waveport. Save a snapshot showing, but with all
scales/axe the de-embedding arrow, and paste it into your
report.
Part 2: simulating an electric resonator
- In this part, you will simulate a simple electric resonator metamaterial
in a parallel-plate waveguide, a type of EDR (electric disk resonator)
- First, open the split-ring design in wageduide from above
- You will modify this copy to create a parallel-plate
waveguide
- To make a copy of your previous design:
- Run Mosaic::Engineering::Electrical::HFSS
- Open your previous design with the split ring in waveguide
MenuBar::File::Open
- Right-click the design icon (red arrow below) and select
copy (blue arrow below)
- Right-click the main project folder (yellow arrow below)
and "paste"
- Name the new design "ibeamParPlate"
Fig 007
- Open the new copy of the design
- Delete the ring (torus) and sheet (red arrows below) using
right-click delete
Fig 008
- Insert an i-beam structure
- Draw a first box: MenuBar::Draw::Box And at the
bottom of the screen enter x=50 y=11.5 z=3 mm,
and then type "enter "or "carriage return" then type
dx=0.1 dy=0.1 dz=5.2 mm, and then type "enter "or
"carriage return" Alterntively, click the DrawBox tool
icon , draw any box, click the "createBox" item, and edit
the properties .
- Draw a second box: MenuBar::Draw::Box And at the
bottom of the screen enter x=48 y=9.5 z=1 mm,
and then type "enter "or "carriage return" then type
dx=4 dy=4 dz=1 mm, and then type "enter "or "carriage
return" Alterntively, click the DrawBox tool icon ,
draw any box, click the "createBox" item, and edit the
properties .
- Draw a third box: MenuBar::Draw::Box And at the
bottom of the screen enter x=48 y=9.5 z=8.2 mm,
and then type "enter "or "carriage return" then type
dx=4 dy=4 dz=1 mm, and then type "enter "or "carriage
return" Alterntively, click the DrawBox tool icon ,
draw any box, click the "createBox" item, and edit the
properties .
- Select all three box items and right-click AssignMaterial
as copper
- Draw a rectangle: MenuBar::Draw::Rectangle (if the
non-Model prompt appears, select no you dont want a
non-model object) And at the bottom of the screen
enter x=50 y=11.5 z=2 mm, and then type "enter
"or "carriage return" then type dx=1 dy=0.1 dz=0 mm,
and then type "enter "or "carriage return"
Alterntively, click the DrawBox tool icon , draw any box,
click the "createBox" item, and edit the properties .
- Select the rectangle sheet, and change the orientation to
Y (in new HFSS, click createRexctangle and set axis to Y), and zoom in to inspect the sheet (red arrow below) looks
as follows
- Check that everything is OK (red circle below)
Fig 009
- Select all 3 boxes with control key held down, and zoom in
(blue circle below) so that your view looks like above
- Select the rectangle sheet (red arrow above), right-click it
AssignBoundary::LumpedRLC
- Save a snapshot of the i-Beam structure as shown above, for your report.
- Set inductance to 5 nH (red arrows below)
- Zoom to the sheet (blue circle below) and assign a current
flow line (blue arrows below)
Fig 010
- Select the Boundaries::LumpedRLC1 item (yellow circle above)
and zoom in as shown above to check your RLC sheet
- Save a snapshot of the RLC sheet structure as shown above,
and paste it into your report.
- Run the simulation
- Display the S-parameters as follows
Fig 011
- Save a snapshot of the i-beam S-parameters as shown above, for your report.
- Click the ReMuEps plot (yellow arrow below) to plot
extracted permittivity and permeability as shown below
Fig 012
- Save a snapshot of the i-beam relative permeability and
permittivity as shown above, but with all scales/axes visible,
for your report.
- In the project manager pane on the left, select
Boundaries::PerfectH and delete the two perfectH boundaries
associated with the short walls of the waveguide
- Select the face of the short waveguide wall on the right
using MenuBar::Edit::Select::Faces
- Right-click the selected face and AssignBoundary::PrefectH
to set a perfect-H boundary
(perfect magnetic conductor)
- The perfectH boundary is similar to perfectE boundary.
PerfectE is a perfect conductor that does not allow tangential
electric fields at the boundary. PerfectH is a perfect
magnetic conductor that does not allow tangential magnetic
fields at the boundary.
- Save your work before exiting
Report Data
- ============================
WARNING !! ====================================
- **** WARNING **** YOU MUST USE
THE PROJECT REPORT TEMPLATE Below:
- See the Project
Report Template at bottom of this page
- A well-written report/paper is
EXPECTED
- STRONGLY RECOMMEND that you read IEEE
authorship series: How to Write for Technical Periodicals
& Conferences
- Clearly describe everything, including:
- variables in block diagrams
- variables in formulas
- units of variables kHz, pF, nH, m, s,
- all traces on plots
- all curves on plots
- all results in any tables
- Minimum required data content for
your report and demos
- Required theory/formulas numbered as below:
- (1) formula for theoretical mu of SSRR (singe split ring resonator)
- (2) formula for theoretical epsilon of EDR (electric disk resonator)
- Required figures:
- Any illegible plots receive zero credit (must be able to read all numbers, axes, labels, curves, grids, titles, legends)
- All plots must of professional quality as in IEEE papers
- LEGIBLE snapshot of the SSRR split ring in waveguide as in Fig 002 above (make sure split is visible), with appropriate caption.
- LEGIBLE plot of S11 and S21 of SSRR as in bottom right of Fig 005
- LEGIBLE plot of Re{mur} and Re{epsr} of SRRR as in Fig 006
- LEGIBLE snapshot of the EDR in waveguide as in Fig 009 above (make sure split is visible)
- LEGIBLE plot of S11 and S21 of EDR as in Fig 011
- LEGIBLE plot of Re{mur} and Re{epsr} of EDR as in Fig 012
- Required tabular data content:
- Table with 2 columns: parameter, value
- Row 1: length of the gap in the ring in mm
- Row 2: capacitance of RLC sheet in ring gap, pF
- Row 3: computed theoretical value of the resonant frequency of SRRR, GHz
- Row 4: measured value of the resonant frequency of SRRR, GHz
- Row 5: measured value of the resonant frequency of EDR, GHz
- See report template below
NOTE ReportTemplate: Use the Project Report Template
YOU MUST ADD CAPTIONS AND FIGURE
NUMBERS TO ALL FIGURES!!
Copyright © 2010-2018 T. Weldon
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