Possible exam problems of ECOET (Summer 2021)

1. Maxwell equations and physical interpretation of each of them in differential and integral forms.

Ampere law: Capacitor does not allow for conduction current (Jc) flow. However, connected to alternate current (AC)
source, current flow through the capacitor can be observed.
Gauss law (electric): The net electric flux through any hypothetical closed surface is equal to 1/ε times the net electric
charge within that closed surface.
Gauss law (magnetic): no magnetic charges exist
Faraday law: The induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the
magnetic flux enclosed by the circuit.
Charge conservation law: consider charges in a "container" and extend currents in conductors to the concept of current
density

2. Boundary conditions and their physical interpretations. The notions of perfect electric conductor (PEC) and perfect
magnetic conductor (PMC). How do the fields behave close to PEC and PMC?
3. What are Absorbing Boundary Conditions? Provide an example of use case.

Boundary procedures that are applied at the artificial numerical boundaries of a computational domain to miminize or
eliminate the spurious reflections at these boundaries which occur in the simulations of wave propagation phenomena.
ABC should interact only with radiation fields. When it interacts with induction fields it can cause errors or even instability
of simulation.
An example is FDTD simulation setup
4. Three main electromagnetic properties of materials and their relations with Maxwell equations. Provide examples
of three different materials and values of those properties for them.
Permittivity (ε), permeability(µ) and conductivity(σ),.

 vacuum:
 water:  ε = 88 at 0ºC (32ºF) ,  σ (Distilled water) = in the range of 0.5 to 3 µmhos/cm, µ  For a material to
be permeable it must possess porosity characteristics
 Air: ε = 1.0006, σ = 0.025 W/(m·K), µ is defined as the rate of airflow passing perpendicularly through a known area
under a prescribed air pressure differential between the two surfaces of a material.
5. Properties of TEM transmission lines. Provide at least three examples of such lines and their practical applications.

Characteristic impedance, Cut-off frequency, capacitance, inductance, phase velocity

Three examples are 1. microstrip line (as SMA or MMCX): used for example in filters or couplers; 2. coax cable: It has
applications as feedlines connecting radio transmitters and receivers to their antennas, computer network (e.g., Ethernet)
connections,… ; or 3. twin-lead cable: used as an antenna feedline at shortwave and VHF frequencies, to connect radio
receivers and transmitters to their antennas.
6. Describe basic properties of fields generated by a Hertzian dipole. What is the difference between near fields and
far fields?

The key difference between near field and far field is that near field is a region that is close to an antenna or a
scattering object, whereas far-field is the region that occurs at a distance from the antenna or the scattering
object.
7. Explain basic differences between the cases of normal and oblique incidence of a plane wave on a boundary
between two materials.
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8. Explain the effect of full reflection from a boundary of two dielectrics. How is that effect used in practical devices?
What is the advantage of reflection from the boundary of a dielectric when compared to the reflection from a
boundary of a metal?
In the case of having full reflection, no energy is transmitted (So, transmitted wave is nule). It is used in phenomena such
as mirages.
Tangential component of electric field is always continuous and thus must vanish at a boundary of a perfect conductor.
However, in the case of magnetic field and the boundary of a perfect conductor, it can be matched by a surface current
flowing along the boundary perpendicularly to the magnetic field.

9. Explain how investigation of oblique incidence is used for understanding of guided waves.
In the incidence with oblique wave the directions of the waves change and the transverse plane of polarization moves the
electric field since the electric field can be polarized elliptically or circularly. This study has helped with the decomposition
of any type of polarization into two linear and orthogonal polarizations in space: parallel and perpendicular.
 10. What are the basic properties of TEM lines and why are they sometimes considered as a bridge between the circuit
theory and the field theory? What are the basic parameters of TEM lines?
EJ5 + EJ 42 + Circuit theory assumes physical dimensions of the network smaller than electrical wavelength, while
transmission lines may be considerable fraction of wavelength.
11. Explain the equations for impedance transformation along a transmission line.

Being and , we know:

If we have a lossless line, we’ll have .

Also,
12. Explain the Smith chart and basic operations we can perform with it. Explain what kind of movement on that chart
is imposed by connecting elements like resistances, capacitances, inductances, and segments of transmission lines.
Smith's chart contains circles of constant resistance, circles of constant reactance, circles of constant standing wave ratio, and
radial curves representing the geometric places of lag on a constant value line; it is used in the resolution and calculation of
waveguides, adaptation of impedances of transmission lines.
When analyzing an electrical circuit, one of the parameters to be evaluated is the impedance Z(w)=R+jX(w) (or the admittance
Y(w)=1/Z(w) = G+jB(w) measured on one of its ports or between two terminals.
In RF circuit design it is possible to represent an impedance Z(ω) in terms of its reflection coefficient Γ=(Z-Z0)/(Z+Z0) with
respect to a reference impedance Z0: Z=Z0(1+Γ)/(1-Γ), due to Smith Chart is nomogram.
In addition, the Smith Chart can be used to calculate a line's VSWR, scattering
parameters, and design impedance adaptation networks between a generator
and a complex load impedance.
The outer circle represents the geometric place of the impedances whose
modulus of the reflection coefficient is unitary. Capacitive impedances
(negative reactance) are at the bottom of the diagram and inductive
impedances (positive reactance) at the top. The two halves are separated by a
line representing the purely resistive impedances.
Constant resistance circles identify impedances with the same real part and
constant reactance curves with the same imaginary part.
Connecting a serial inductor to Z causes clockwise displacement; to a series
capacitor in an anti-clockwise direction (resistance curve). If the resistance
increases the impedance shifts to the right; if it decreases, to the left (reactance
curve).
The behavior of the admittances is exactly the dual of the impedances, therefore to move along the admittance curves you have
to place admittances in parallel.
The Smith Charter can be used to synthesize impedance adaptation networks with the aim of maximizing the power delivered
to the load. To design the appropriate network you have to follow the Maximum Power Transfer Theorem and perform a
conjugate adaptation

13. Explain application of finite differences (central, forward, backward) and the obtained accuracy.

14. Explain application of the finite-difference time domain (FDTD) scheme to a TEM transmission line.

15. Explain the Yee cell and the application of the 3D FDTD method.
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16. Explain the Yee algorithm for the FDTD. What is the “leap-frog” notion related to?

LEAP FROG  because E and H separated in time by Helf iteration (Leap-frog).

SOL2:
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18. FDTD algorithm allows to use several types of excitation signals. Consider just two of them: “sinusoidal” and
“pulse-of-spectrum” - for each of them provide an example of an appropriate use case and the reason of your
choice. That results can be obtained in those cases?
19. What are the sources of errors in simulations using the FDTD method? What actions should be undertaken by FDTD
solver user to minimize values of those errors?

20. Explain the “Total-Field/Scattered Field Boundary” notion. Why is it commonly used in EM simulations?

21. Using an example of a simple microstrip band-reject filter (from the lecture) tuned for 6 GHz, provide constraints
on FDTD grid sizes? What are their reasons?
22. Compare “stair-case” and “conformal” mesh styles in terms of representation of the object geometry, EM modeling
accuracy, computational effort.

Staircase subsections are rectangular subsections, which can have a linear current gradient in the x and/or y direction.
Conformal subsections offer more degrees of freedom: their shape and orientation follow the underlying polygon,
and the current on a conformal subsection has more degrees of freedom compared to a staircase subsection

23. What results can be obtained from a 3D FDTD electromagnetic simulation (including post-processing algorithms)?
Provide 5 different practical examples.
24. What is a coupled thermal-electromagnetic simulation? Describe the algorithm (provide the iteration diagram).
What are typical problems related with implementation of this type of simulations?

25. Compare full 3D with vector 2D (V2D) FDTD electromagnetic simulation. Consider types of problems, which can be
solved, memory & CPU requirements, simulation time.
26. Describe factors which influence significantly calculation time of FDTD simulation. What can be done to obtain
results in a shorter time? Justify your answer in terms of different problem types.
27. What are absorbing boundary conditions? How they are implemented in FDTD? What is their purpose? Provide an
example.

An example of usecase, when modeling of a free space is necessary  (foto)

28. Describe constrains, which you need to take into account during mesh setup in FDTD simulation scenario.

29. What is NTF? What is the purpose of using this element? Describe and sketch an example scenario.
NTF boundary and plane wave excitation boundary should be placed as close to the antenna as possible.
30. Provide names of at least 5 commercial 3D electromagnetic solvers which can be useful for a microwave engineer.
What are the algorithms used by those tools?

31. Discuss software and hardware methods for speeding up electromagnetic simulations especially for FDTD method:
comment on the state-of-the-art and prospects for the future.

32. Discuss arithmetic intensity and machine balance in context of the FDTD leap - frog algorithm.

33. Estimate FDTD simulation speed (iterations per second) for a scenario which consists of 200 cells along X axis, 200
cells along Y axis, and 400 along Z axis. Assume typical PC Flops value 100 GFlops and typical PC memory bandwidth
20 GB/s.
 34. It is commonly assumed, that in FDTD method the cell size value should not be larger than approximately 1/12 of
the wavelength. Explain reasons for this condition.
1er parrafo de meshing:

35. An impedance matching circuit with a single shorted stub has been designed using microstrip technique. This
design requires verification using an FDTD solver. Provide description of the simulation scenario including: type and
location of wave source and waveform, type and location of boundary conditions (indicate them the on the
provided sketch). Provide reasonable meshing (calculate cell sizes) along X, Y and Z axis assuming frequency of
operation f=2 GHz, Ɛr=4.5, Ɛr_eff=3.36, strip width w=1.86mm, dielectric thickness h=1mm.

First, the
AFS is applied to the MoM method for producing
a rational function. Then, the rational function is
synthesized by using the Caeur technique to
First, the
AFS is applied to the MoM method for producing
a rational function. Then, the rational function is
synthesized by using the Caeur technique to
 Number of cells = (cells along X axis)* (cells along Y axis)* (cells along Z axis)
Stub length = Lstub(short) / sqrt(3.36)
Stub distance = dtub / sqrt(3.36)

36. Superposition of solutions of Maxwell equations. When and how can we add two different solutions in the same
environment?

37. what are the basic parameters of antennas? How can the solutions for a Hertzian dipole be used to calculate
properties of more complicated antennas?
38. Properties of a small loop working as an antenna (as compared to the properties of a Herzian dipole).

39. Explain the difference between parallel and perpendicular polarisation of a wave obliquely incident on a boundary
betwen two dielectrics. Extend the explanation to a practical case of a sunlight refelecting from a wet road surface.
What is the dominant polarisation in the reflected light?
40. What is the relation between wavelength inside a metal waveguide and wavelength of a free-space wave of the
same frequency?
41. Explain when a circuit can be called 0D, 1D, 2D, 2DV, 3D; and give examples of such circuits.

42. What are the basic properties of TEM lines and why are they sometimes considered as a bridge between the circuit
theory and the field theory? What are the basic parameters of TEM lines?

43. Telegraphists equations

44. Properties of plane wave

47. Why prediction of electromagnetic waves propagation for the purpose of broadcast TV transmissions cannot be
modeled with FDTD solver? What approach can be used in such a case? What are typical propagation effects which
need to be taken into account? What types of data are necessary to accurately solve this kind of problems?

DATA: