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Electrical Engineering Qualifying Exam
Written Requirement
James C. Stephenson
April 7th, 2004
1. Abstract
I have reviewed three technical papers for the
purpose of establishing relevance to my own
research area. The particular areas of research
defined by these different efforts have nothing in
common with each other than their applicability to
my own work. White et al. have demonstrated that
paramagnetic molecules can be contained within
small spatial regions by the magnetic gradient
force
that
exists
near
ferromagnetic
microelectrodes immersed in a homogeneous
magnetic field. Furse et al. reports their Plasma
Fluid Finite Difference Time Domain formulation
as a valid alternative to analytical methods when
complex antenna shapes, or plasma dynamics need
to be modeled. The third paper I reviewed was
related to an investigation of the dielectric
properties of laminate materials.
2. Introduction
My own research interest is in the electromagnetic
fingerprinting of molecules or particles in solution. I
propose the development of a micro Nuclear Magnetic
Resonance imaging cell that does not require an
expensive cryogenically cooled electromagnet.
Through simulation I have demonstrated that field
strengths of 1 – 3 Tesla are possible with rare earth
magnets combined with high permeability flux
guiding features. Coils will be used to alter the
magnetic field within this range.
After a brief description of each of the three papers
I will present the results obtained and establish
relevance within the context of my own research
interest.
White et al. in “Microscale Confinement of
Paramagnetic Molecules in Magnetic Field Gradients
Surrounding
Ferromagnetic
Microelectrodes”
demonstrated
that
paramagnetic
molecules
(electrogenerated in this case) could be confined to
regions in close proximity to a ferromagnetic
microelectrode for tens of seconds. Additionally, this
work demonstrated that the magnetic gradient forces
on a charged paramagnetic molecule are larger than
the Lorentz or gravity driven convective forces within
an electrochemical cell at or near the surface of the
ferromagnetic microelectrode.
Furse et al. in “The Response of a Short Dipole
Antenna in a Plasma Via a Finite Difference Time
Domain Model” demonstrated the validity of the
approach as an alternative to the analytical model.
The use of this approach would be indicated when
complex antenna shapes need to be analyzed or when
ion kinetics cannot be ignored. The results showed a
qualitative agreement with the analytical model for
various orderings of the gyration and plasma
frequencies. Simulations were performed for plasma
magnetization parallel and normal to the length of the
antenna.
Sharma et al. in “Laminate Materials with Low
Dielectric Properties” discusses the resin structure and
its effect on electrical properties of thermo set
polymeric resins. The motivation behind the effort
was based on the need for low loss substrates in highspeed digital, RF and microwave applications. While
the efforts presented in this paper have no direct
connection with my own efforts, the electromagnetic
characterization of materials or media is of great
interest.
3. Molecular Confinement
White et al. constructed an electrochemical cell
using a typical two-chamber configuration.
Ag (reference)
Fe or Pt (-q)
Auxiliary
B
Electrolyte
figure 2. Electrochemical cell schematic showing working
(Fe/Pt), the Ag reference, and the platinum auxiliary electrodes.
The working electrode materials (Fe, Pt) were chosen
based on their nearly identical electrical properties and
because iron is ferromagnetic, while platinum is
weakly paramagnetic (~10-5).
The magnetic field represented by horizontal
arrows in figure (2) will spatially orient to
accommodate a highly susceptible material, while no
reorientation will occur for low susceptibility
materials.
magnetic gradient forces.
It is clear that the I/V characteristics for the iron
and platinum electrodes are very different. The results
are presented relative to the no-field (B=0)
voltammetric response of each electrode separately.
There is a decrease in the current at the iron electrode
when the electrode surface normal is parallel to the
direction of the magnetic field, while an increase in
the current at the platinum electrode is observed under
the same conditions. The decrease in the cathode
current at the iron electrode is due to the retention of
NB- molecules after reduction, thus creating a barrier
for the incoming NB molecules. This was visually
explained via the use of video microscopy, as can be
seen below1.
Figure 1. Ferromagnetic (left) and weakly paramagnetic (right)
objects immersed in a uniform magnetic field.
This spatial gradient in the magnetic field will result
in forces when a magnetic dipole is present.
F

 (m  B)
(1)
Where m is the magnetic moment vector and B is the
magnetic flux density vector. In this paper the
paramagnetic
molecule was electrogenerated through

the reduction of Nitro Benzene at the platinum or iron
electrodes (negative potential) during voltammetric
measurements.
Voltammetric measurements are
basically
an
I/V
characterization
of
the
electrochemical cell (sweep the voltage and measure
the current).
White et al. analyzed the voltammetric responses
of both the platinum and iron electrodes with respect
to the angle between the electrode surface normal and
the background magnetic field vector. The goal of
this approach was to separate the effects of the
Lorentz, the gravity driven convection, and the
Figure 3. Voltammetric measurement results for both the iron
(A) and platinum (B) electrodes for zero-field, 0 degrees, and 90
degree electrode surface normal rotation with respect to the
background magnetic field1.
Figure 3. Video microscopic images taken during the
voltammetric measurements for both the iron and platinum
microelectrodes. Top panels (no-magnetic field), middle
panels (electrode surface normal parallel to magnetic
field), bottom panels (electrode normal at 90 degrees with
respect to magnetic field)1.
When Nitro Benzene is reduced in to the
paramagnetic radical NB- its color is bright red as can
be seen in figure (3). According to White et al. there
is a slight decrease in mass density for the newly
reduced NB molecule, such that gravity will cause an
upward migration of the NB- molecule being replaced
by the slightly denser NB molecule. The top panels in
figure (3) indicate this upward flow. The middle
panels illustrate the magnetic forces involved, i.e. the
Lorentz and magnetic gradient forces. As the charge
molecules leave the electrode they will experience the
Lorentz force causing a vortex flow (see the right
middle panel). It can be seen that this Lorentz force
driven flow is inhibited by the large spatial gradient in
the magnetic field near the iron electrode (left middle
panel). This explains graphically the decrease in the
voltammetric current for the iron electrode oriented
parallel to the magnetic field presented in figure (3).
The edge-on view given in the bottom panels of figure
(3) explain qualitatively the increase of voltammetric
current for both the iron and platinum
microelectrodes.
The results of these experiments can be
summarized graphically with the inclusion of the
normalized current versus orientation angle data
obtained by White et al.
channel, possibly altering the particle or molecular
path as these molecules traverse the microsystem.
t=0
t=36 sec
Figure 5. Video images showing the behavior of
paramagnetic NB- in regions close to the ferromagnetic
microelectrode after the electrode current is shut off. Top
panels show the retention of molecules after 36 seconds
(magnetic field on). The bottom panels show the dispersive
nature of the molecules when the magnetic field is turned
off with the electrode current.
Figure 4. Plots of the normalized currents for both the
platinum (solid) and iron (dashed) electrodes as a function of
electrode rotation angle with respect to the magnetic field1.
This graph demonstrates some interesting dynamics
related to the electrochemical cell. The Lorentz force
direction will be upward for the 90 electrode
orientation and downward for the 270 orientation. At
270 the Lorentz force is in direct competition with
the mass density change driven flow discussed above.
The fact that the magnitudes of the currents are
essentially the same for both angles demonstrates that
the Lorentz force is larger than the gravity driven
force1. Further, This work has demonstrated the
ability to confine paramagnetic particles for tens of
seconds, see figure (5).
The implications resulting from this investigation
demonstrate phenomena that I will need to consider.
Lorentz forces will be present in any permutation of
my system (NMR, magnetic separation, etc.). I have
also indicated the use of high permeability materials
as a means to guide flux. These materials will be in
close proximity to the NMR microchannel. Large
gradients will exist near the inner surfaces of this
3.1 Additional Research Needs
Of particular interest to me would be the
relationship between retention times as a function of
field strength. Pure iron saturates at much higher flux
densities than were used in these experiments, leaving
room for further investigation.
I am also prepared to research the magnetic
moment formulation described in this paper. In other
words, under what circumstances can the Bohr
magneton be used? A personal study of chemistry is
unavoidable because I intend to use molecular
magnetic properties for identification, and therefore
need an accurate representation of the magnitude of
the moment associated with the molecules of interest.
4. Numerical Modeling
Furse et al. demonstrated in their work that an
FDTD simulation could model an antenna immersed
in magnetized plasmas. It is understood that my own
work has nothing in common with space plasmas, but
the formulations are just as applicable. I will
therefore present these formulations in some detail
and show relevance along the way. Additionally, I
will indicate where the assumptions are not applicable
to my system and/or describe how the model must be
changed to capture the dynamics associated with a
microfluidic analysis cell.
From the outset, a numerical model is indicated in
my work because of the complexity of the antenna or
probe I intend to use (helix). One of the motivations
for this PF-FDTD model was that it could be used to
model arbitrarily shaped antennas.
4.1 The Equations
The following analysis assumes measurements
within several Debye lengths and ions are assumed
stationary. The simplest model then becomes the fivemoment Maxwellian plasma fluid system2 taken from
this article. The first equation used is the relationship
between time the derivative of charge to the
divergence of the current density.
n
   nU   0
t
(2)
U 
mn  nq(E  U  B)    P  nmv(U V ) (3)
 t 
The divergence of U is assumed to be zero here by
assuming subsonic incompressible flows.
The
variables m, n, v, q are respectively the mass, density,
electron-neutral collision frequency, and charge.
P  nkT
U
m
U
e
 m  B
(5)
 p  E
(6)

Where n and U are the density and electron velocity
respectively. The momentum equation basically
relates the
forces and mass transport of the system.

general be present in the system (equation 3 does not
account for these).
Equations 2-4 must be modified to accommodate
these system dynamics. The velocity term U in
equations (2) and (3) will have a background DC
component due to the fluid flow through the channel.
The momentum equation given in (3) will need the
addition of the dipole gradient forces, as well as an
alteration of the electric field term to account for the
polarization of the water in the channel. The energy
terms for both electric and magnetic dipoles can be
found in any electrodynamics text4. The negative
gradient of these potentials will define the force.
(4)
P is the simplified energy equation with k and T equal
to Boltzmann’s constant and the kinetic temperature
of electrons respectively.

The micro NMR system would require a
fundamentally different set of equations representing
the fluid dynamics for the following reasons. (1) The
system consists of a background solution (water) and
particles, which may or may not carry a net charge.
(2) If charge particles are present in the fluid, the
velocity of these particles will have two components,
the fluid velocity in the channel, and the RF velocity
due to EM wave interaction. (3) The polar nature of
water will require an accounting of the RF
polarization. (4) Electric and magnetic dipoles will in
White et al. presented an average dipole moment
formulation in their paper that would apply here.
Since force
densities are considered in (3), (5) and (6)
would need to be multiplied by the density n.
It should not be assumed that I understand
completely the dynamics of my own system, however
these arguments are correct in that these additional
dynamics must be accounted for, but there are perhaps
many others.
In addition to the equations describing the mass
flow of the plasma (2–4), Maxwell’s equations were
included to complete the set of equations needed to
solve for the ten unknowns, i.e. N, Ux, Uy, Uz, Ex, Ey,
Ez, Bx, By, and Bz, where N is the charge species
density, U, E, and B are the three spatial coordinate
vectors for the velocity, electric, and magnetic fields
respectively.
This set of equations was then
discretized in both space and time according to the
temporal rules indicated by each equation and the
standard Yee cell as can be found in any FDTD text.
I will not include the details of the discretization
here for the sake of brevity, but will move directly
into the results obtained from the simulation.
4.2 Results & Discussion
The simulations were setup to explore the behavior
of the antenna impedance with three different
orderings of the gyration frequency relative to the
plasma frequency, i.e. p > , p = , p < . The
antenna is expected to exhibit resonance properties at
these different frequencies. Each of these orderings
was simulated with a background magnetic field
oriented parallel and then normal to the length of the
antenna.
The simulations were compared with
Balmain’s analytical model.
Figure 6. Magnitude of the impedance plotted against the
normalized frequency. This plot represents the result for
the magnetic field parallel to antenna length and p > .
Balmain’s analytical data is plotted for comparison2.
The impedance plot in figure 6 shows a good
qualitative agreement with the analytical model.
Differences at low frequencies are explained as
originating from numerical errors and the lack of data
points2.
All of the simulations show similar qualitative
agreement with theory and will therefore be omitted in
this report. In the context of my work I would like to
comment on why these results directly apply.
In order to perform an NMR experiment, the
interrogating radio frequency must be efficiently
coupled to the medium under test. Therefore, the
ability to calculate the expected impedance based on
antenna geometry and liquid dynamics is essential.
The interrogating frequency in NMR is determined by
the DC magnetic field strength and the gyromagnetic
ratio for a particular element (gyromagnetic data can
be found in tables).
f  B

(7)
In Magnetic Resonance Imaging this frequency is
called the Larmor frequency. A nuclear magnetic
moment can occupy one of two states in the context of
NMR, corresponding to the moment parallel to the DC
magnetic field and the other to anti-parallel
orientation. The nuclear moment can either give up
energy (transition from anti-parallel to parallel), or
absorb energy (transition from parallel to antiparallel). The NMR signal is basically the difference
between the absorbed and emitted energy.
Given that my device will be characterized by very
small dimensions, the inductance and capacitance
values associated with the helix antenna will be quite
small making the antenna’s self resonance frequency
very high. The largest efficiency in the RF energy
transmission into the medium will occur at this
frequency. Larmor frequencies are typically within
the range of 15 and 80 MHz for hydrogen imaging,
well below the expected helix resonance frequency (~
GHz). Using a model such as that described by Furse
et al. will enable me to determine the energy
transmission characteristics of my helical antenna at
the Larmor frequency.
Another contribution made by the authors if this
paper relates to the FDTD simulation itself. The
solution region must be truncated in order to
accommodate the finite nature of computer memory,
and as such must contain boundaries.
These
boundaries must approximate infinity in order for the
solution to be at all accurate (conservation of energy).
The trick is to simulate the propagation of EM waves
(plasma waves) at the boundary as if the spatial
distance between the boundary and infinity is
represented at this boundary.
Absorbing boundary methods have been developed
for FDTD simulations such retarded time absorbing,
and perfectly matched layer boundary conditions.
These methods assume propagation at the speed of
light, which would suffice in simulations if plasma
waves were not considered. However, the underlying
goal of this work was to more accurately represent
dynamics associated with time varying plasma
conditions, which propagate at slower velocities.
Furse et al. argued that since plasma exhibits quasineutral behavior, the variations in density would not
be visible beyond a couple of Debye lengths from the
antenna. They further reasoned that since the antenna
was electrically short, the energy coupling into the far
field would be poor. With these two assumptions, the
inclusion of the time varying plasma density and
velocity near the solution boundaries was gradually
removed from the FDTD loop and considered
constant. The method is graphically demonstrated in
figure 7, which was taken from the article.
function of
relationship.
density
described
the
following
2
e
  n m
2
(9)
e
p
o
e
Where e, epsilon, and m are the electronic charge,
permittivity of free space, and electronic mass
respectively.
 Looking at the plot in figure 8, results in
the conclusion that altering the simulation size and
time iterations may not fully correct the instabilities in
the solution.
4.3 Additional Work
Figure 7. Representation of the simulation near the
boundary, illustrating the relationship between the fields
at different spatial locations. The density N was
assumed constant within a few cells from the boundary,
followed by the removal of the plasma velocity prior to
the simulation edge2.
This approach worked well for the EM fields traveling
at the speed of light, but was not completely effective
in the representation of the slower moving plasma
waves. This problem was overcome under certain
conditions by altering the plasma parameters and
simulation size. This is illustrated in figure 8.
During my own analysis of the boundary condition
development presented in this article, the complexity
of my own system became more apparent. As was
mentioned in the article, the PF-FDTD boundary
conditions deal well with the radiation propagating at
the speed of light, but were unable to accurately
absorb the slower moving plasma waves. My analysis
will be conducted in the liquid phase, thus reducing
the speed of particle density propagation even further.
Additionally, the lateral boundaries of my system will
include a dU/dt = 0 relationship due to the constant
fluid flow through the channel. However, the NMR
analysis will occur in the brief moment of time when
the particles/molecules are positioned within the helix
(~ milliseconds). The quasi-stationary nature of the
carrier fluid within the time scale of the NMR
experiment would allow the removal of the
background constant velocity fluid velocity.
With respect to the article described in this section,
the need for further work related to the boundary
conditions seems necessary due to the properties of
the plot in figure 8. Instability in any FDTD
simulation refers to an increase in the magnitude of
the solution caused by the spatial grid as time
increases6. This paper reports that certain plasma
conditions result in instability at the simulation edge.
Consider the curve for a plasma frequency of 15 MHz
in figure 8.
Figure 8. Plot showing the relationship between three
different plasma parameters (plasma frequency) and the
number of plasma cycles needed versus simulation time2.
The plasma parameters are altered via the plasma
frequency. Remember that the plasma frequency is a
5. Dielectric Properties of Laminate
Materials
Sharma et al. used the Bereskin test method to
characterize the dielectric properties of various
materials including resins and laminates. This method
involves the use of stripline conductors in contact with
the material of interest. Microwave propagation along
stripline conductors is treated in detail in any
microwave engineering text6. The test setup would
look something like the following.
Dielectric material
Stripline conductor
Ground plane
Figure 9. Graphic illustration of a possible
Bereskin stripline test setup.
Two control materials were chosen based on their
respective dielectric loss coefficients being in the
region of interest, i.e. polytetrafluoroethylene (PTFE)
and polyethersulphone (PES). The loss coefficients
for these materials are reported as being 0.002 for
PTFE and 0.007 for PES.
The dielectric thicknesses given in the article for
the two materials were 0.060”  0.002” for PTFE and
0.080”  0.002” for PES. The conductor length for
each of the two experiments was 3.5” and 3”
respectively.
The remaining details of the
experimental setup are missing from the article.
At this point I need to bring up a number of
concerns I have about the quality of this report. (1)
The lack of theoretical background and/or information
related to the experimental method, (2) the uncertainty
in the dielectric control film thicknesses was on the
order of a few percent, (3) there is no description of
how the stripline foil was mounted on the control
films, and (4) an analysis of the experimental data
suggests only error and uncertainty in what the
dielectric properties actually are.
I am left with a number of questions related to
these concerns.
First, was the 2-mil thickness
variation seen across on film, or was this a sample-tosample variation? Second, what experimental
deficiency caused the large variations in the measured
dielectric properties?
Given that the information presented in this article
was at best inconclusive, I will give a brief description
of how this experiment might be carried out such that
useful information could be obtained.
There is nothing fundamentally wrong with the
Bereskin test method proposed by these authors so I
will continue assuming the test setup depicted in
figure 9.
5.1 Experimental Methods
In any experiment great care must be taken to
remove as many variables and process parameter
variations as possible. The process parameters for this
characterization effort will include, stripline
dimensions (length, width, thickness), dielectric film
thickness and processing conditions, and the wire
bonding required for electrical connection. Variables
in this experiment would include temperature and
humidity. Humidity was mentioned in this article as a
main contributor to dielectric property variation
(water absorption into the polymer matrix). The
experimental method is presented in bulleted form
below.
1. Spin or spray coating techniques can be
used to obtain repeatable film thicknesses
on top of a conducting substrate.
Thickness of the film can be determined
within 100 angstroms with a surface
profiler.
2. Sputter deposit the stripline conductor on
top of the dielectric film and pattern the
desired feature with lift-off lithography to
avoid polymer damage with etching. Use
the surface profiler tool to obtain actual
dimensions.
3. In order to remove variation in
experiments, a custom test fixture can be
machined
from
aluminum
with
appropriate network analyzer couplers
mounted on the ends (typical two port
network analysis).
4. The ends of the stripline would then be
wire bonded to the couplers in the test
fixture.
The conducting substrate is
electrically coupled to the test fixture with
conductive epoxy.
Only after a procedure such as this is followed can
any conclusions about dielectric properties be made.
Once the experimental setup is proved with control
materials (PTFE or PES), process parameters related
to the polymer can be varied in order to correlate
polymer structure with dielectric properties.
I believe the significance of this article is in the
stated intent. It is clear that dielectric properties of
materials will be dictated by the internal structure of
these materials and the polar nature of polymeric
chains that make up the film. Additionally, water
uptake or absorption is of great concern because of its
polar nature. The lack of conclusive evidence or clear
definition of methods does not detract from the value
of the intent.
My own experiments will require the
characterization of the electronic double layer that is
present at any electrode/solution interface. This is
actually why I chose to review this paper in the first
place.
The composition of this double layer
capacitance will be a function of the ion and/or
molecular concentration within the NMR cell.
Understanding how these molecules affect the
polarization dynamics will be essential.
6. Conclusion
Several forces exist within an electrochemical cell
immersed in a background magnetic field. White et
al. was able to show through experiment that
electrochemical currents could be altered based on the
interaction of these forces. The most significant
finding was that paramagnetic molecules could be
retained for tens of seconds within a 1-millimeter
diameter of the ferromagnetic microelectrode. While
I am not immediately interested in the confinement of
molecules, this finding does provide an additional tool
for particle manipulation. I was able to establish a
connection with these results due to the similar nature
of my device with electrochemical cell.
The review of the PF-FDTD article has led me to
some conclusions about the complexity of my own
numerical modeling efforts. An understanding of the
antenna impedance immersed in an isotropic medium
as a function of frequency was the underlying theme
of this paper, which directly impacts my own work.
Furse et al. were able to show qualitative agreement
with the analytical method. The significance of this is
in the full-wave nature of the PF-FDTD solution and
in its ability to accommodate complex antenna
geometries. Further, this FDTD method has opened
the door for the addition of more plasma parameters
allowing the more accurate description of the
dynamics and associated impact on antenna
impedance.
The third paper was actually quite valuable in the
sense that critical thinking is essential in any
development work. I gained additional respect for the
difficulty in obtaining meaningful results.
7. References
[1] Micah D. Pullins, Kyle M. Grant, and Henry S.
White*, “Microscale confinement of Paramagnetic
Molecules in Magnetic Field Gradients Surrounding
Ferromagnetic Microelectrodes”, J. Phys. Chem. B 2001,
105, 8989-8994.
[2] Jeffrey Ward, Charles Swenson, and Cynthia Furse,
“The Response of a Short Dipole Antenna in a Plasma Via
a Finite Difference Time Domain Model”, January 15, 2004
[3] Jyoti Sharma, Marty Choate, and Steve Peters,
“Laminate Materials with Low Dielectric Properties”,
presented at IPC Printed Circuits Expo, 2002
[4] John David Jackson, “Classical Electrodynamics, third
edition”, pages 146-190 “review of the dynamics of electric
and magnetic dipoles and their energies within EM fields”,
John Wiley & Sons, Inc., 1999
[5] David M. Pozar, “Microwave Engineering, second
edition”, pages 153-166 “approximate representation of the
stripline impedance”, John Wiley & Sons, Inc., 1998
[6] Matthew N. O. Sadiku, “Numerical Techniques in
Electromagnetics”, pages 161-165, “Stability and accuracy,
and description of the techniques used to control these”,
CRC Press, Inc. 1992