Chapter 1 Dimensional Analysis, Vector Differential Operators, and Electrostatic

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Problem 1 Gradient of Scalar Function
Problem 2 Divergence of Vector Function
Problem 3 Curl of Vector Function
Problem 4 Electric Potential of Conservative and Non – Conservative E-Fields                            Problem 5 Static Electric Fields
Problem 6 E-near-fields of the Electrically Short Non-Conducting Rod
Problem 7 E-near-fields of the Electrically Short Dipole
Problem 8 E-fields of Electrically Short Two-wire Line
Problem 9 E-field around Two Parallel Conductive Wires of Circular Cross-sections                      Problem 10 Uniformly Charged Sheet
Problem 11 Uniformly Charged Disk
Problem 12 Capacitor with Circular Plates
Problem 13 2D Parallel Strip Model of Capacitor

Chapter 3 POYNTING THEOREM. TWISTED BEAMS. FOSTER's REACTANCE and LORENTZ's RECIPROCITY THEOREMS

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Problem 1 Twisted LG (Laguerre-Gaussian) Circularly Polarized Beam
Problem 2 Bouncing back and forth Electric and Magnetic Energy in LC Resonance
Problem 3 Circuit Cavity Resonator of Rectangular Shape
Problem 4 The Field at Sharp Edges of Metal Cube
Problem 5 The Field at Sharp Edges of Metal Cone
Problem 6 Influence Conductive Surface Curvature on Electric Charge and Current
Problem 7 Distribution Smith Chart from Scratch
Problem 8 Foster’s Reactance Theorem. Ladder-Type Network
Problem 9 Lorentz’s Reciprocity Theorem

Chapter 2 Interaction E- and H-fields with Material Media. Metamaterials. Boundary Conditions. Eddy Current

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Problem 1 Rotation of Ball-and-Stick Model of Electric Dipole in Uniform E-field.
Problem 2 Rotation the Loop Carrying Steady Current in Uniform B-field (there are 2 readers comments)
Problem 3 Polarized Conductive Sphere in Uniform Electric Field.
Problem 4 PolarizedDielectric Sphere in Uniform Electric Field.
Problem 5 Electric Potential and Field due to Charge Placed above Plane Dielectric Boundary(Dielectric-Dielectric Interface with no free charge).
Problem 6 Electric Potential and Field due to Charge Placed above Perfect Conductive Plane (Dielectric-PECInterface).
Problem 7 Magnetic Potential and Field due to Line Current Placed above Plane Permeable Half-Space
Problem 8 Line Charge outside Dielectric Cylinder
Problem 9 Passive Magnetic Shielding. Cylindrical Shell with Permeable Core in Uniform External Magnetic Field.
Problem 10 Superconducting Disk in External Uniform Magnetic Field
Problem 11 Superconducting Sphere in External Uniform Magnetic Field.
Problem 12 Electrically Anisotropic Crystal
Problem 13 Hysteresis (B-H) Loop
Problem 14 Drude-Lorentz’s Model of Metal Dielectric Constant.
Problem 15 Illustration of Atom Electric Polarization
Problem 16 Force Precession in Fully Magnetized Ferrite
Problem 17 Eddy-Current Brakes Model
Problem 18 Bar Magnet Traveling through a Conducting Pipe
Problem 19 Eddy Current on Copper Disk in Uniform Magnetic Field of 50 Hz
Problem 20 Effect ofElectromagnetic Cloaking/Hiding Copper Cylinder (shown in yellow) by the Layer of Anisotropic
Problem 21 Inhomogeneous Metamaterial (yellow)

Chapter 5 POLARIZATION. ANTENNA PARAMETERS.

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Problem 1 EM Wave Polarization
Problem 2 Near-field Zone vs. Far-field Zone

Chapter 1 Magnetostatic

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Problem 1 H-fields due to a steady electric current carried by the infinitely long conductive wire in the z-direction
Problem 2 H-fields due to a steady electric current carried by two infinitely long non-magnetic perfectly conducting wires in the z-direction
Problem 3 H-fields due to a steady electric current carried by the infinitely long conductive rectangular wire in the z-direction
Problem 4 E- and H-fields produced by a finite wire with the steady filamentary current          Problem 5 H-fields due to a steady electric current carried by the circular loop/coil of conductive wire
Problem 6 H-fields due to a steady electric current carried by the rectangular loop of conductive wire
Problem 7 H-fields due to a single layer solenoid carrying a steady electric current    Problem 8 Wireless power transmission (WPT) through inductive coupling
Problem 9 Faraday’s Law of Electromagnetic Induction and Lenz’ Law. Magnet moving through a coil

Chapter 4 VECTOR POTENTIAL. RADIATION OF ELECTROMAGNETIC WAVES. SKIN EFFECT

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Problem 1 Top-hat Dipole Radiation
Problem 2 Electrically Small Current Loop Radiation
Problem 4 Huygens’ Radiator Radiation
Problem 5 Skin Effect

MXene Layer as Metamaterial with Complex Permeability and Permittivity in X-Band

1. Multilayer MXene stab should behave as a Metamaterial with complex permittivity and permeability

2. Since the energy stored in the near-field electrical fields much exceeds magnetic fields, i.e.  𝑾𝒆≫𝑾𝒎, we can expect that the relative dielectric and magnetic constants are 𝜺r ≫ 𝝁r
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5G Broadband Back-fed Stacked Radiator on Rohacell Substrate, and 5x16 Array Thereof

The phased antenna array is one of the lead front-end components of current and coming 5G communication systems that defines their massive MIMO performance. The trend outlined in recent years is to provide “… a robust and complete platform/wizard for RF/microwave engineers … “ to “… develop … more capable antenna and other RF front-end components in less time as before.” “Benefits of systems operating at mmWave frequencies include the small sizes of antennas and the larger available bandwidth.” Regrettably, a wide variety of application-driven requirements (city or rural environment, a realized gain, scan and polarization performance, impedance matching, etc.) cannot be met by single and forever designed element.

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Functionalized Graphene Nanoribbon Films as a Radiofrequency and Optically Transparent Material

Radiofrequency (RF) transmissions are used in a wide range of communication applications such as antennas and radomes, mobile services, and global positioning systems. We recently reported RF-transparent, electrically conductive hexadecylated graphene nanoribbon (HD-GNR) films for targeted voltageinduced deicing of RF equipment such as radar domes (radomes) and phased array antennas.1 A large-scale HDGNR composite film fabrication was demonstrated by spraycoating HD-GNRs on a polymer substrate whereby the HDGNRs were embedded in polyurethane atop a polyimide flexible substrate rendering a black and optically opaque film. The HD-GNR films were transparent to RF, and they transmitted up to 20 W (7 × 103 W/m2) of average RF power without significant loss. However, at >7 × 103 W/m2 of average RF power density, there was some RF absorbance localized at thicker spots on the HD-GNR film that caused local increases in temperature. Subsequent thermal breakdown and carbonization of the polyurethane coating and polyimide substrate significantly reduced the RF transmittance. Thus, fabrication of highly uniform HD-GNR films would enhance RF transparency.

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5G Switched-Beam Base Station Antenna

Expected Frequency Bands: 24.25 to 27.5 GHz, 31.8 to 33.4 GHz, 37.0 to 43.5 GHz, 45.4 to 50.2 GHz, 50.4 to 52.6 GHz, 66 to 76 GHz, 81 to 86 GHz.
Wavelengths at Central Frequencies: 11.5mm, 9.2mm, 7.45mm, 6.28mm, 5.82mm, 4.22mm, 3.59mm
Total Passband: 33 GHz in all Frequency Bands
Relative Passband : 12.6%, 4.91%, 16.14%, 10%, 4.27%, 14%, 6%
Total Number of Simultaneous Independent Beams is up to several hundreds and depends on communication intensity. In dense urban high-rise scenarios with tall buildings and high number of subscriber, an antenna with beam steering in both Azimuthal and Elevation directions is the most beneficial option.
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Radio-Frequency-Transparent, Electrically Conductive Graphene Nanoribbon Thin Films as Deicing Heating Layers

Ice-elimination system are very common in large radio-frequency (RF) structures. They can be classified as either passive antiicing films (preventing the accumulation of ice) or active deicing devices (removing ice after accumulation). Typicallly,  an icing protection system is in radomes. Radomes are protecting shells or covers for radar instruments in aviation and marine environments. The radomes are subject to hostile environments, such as high winds containing sand, rain, hailstones, and saltwater, over wide temperature variations. Explosive pressure blasts can also take place nearby the radomes. Thus, radome deicing conductive films must be extremely tough with good adhesiveness to the heated surface. In addition, these deicing structures must not compromise the reliability of the original RF system, which, in the case of radome applications, means that the deicing film must be predominately transparent to RF radiation at any polarization with minimal impact on the antenna scan performance. It is desirable that this film be lightweight and low-cost, with physical characteristics that allow it to cover large curved surface areas.

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Reflect Patch Array for Radar

Overview. The proposed new antenna for AN/SPS-49 radar is expected to meet various requirements:
Incorporate electronic beam steering in elevation  providing more than two elevation beams, incorporate cosec2 coverage, handle peak power delivered through the rotary joint up to 300 kW at 4% duty cycle, sidelobe reductions and beamwidth, the gain not less than 28 dBi measured relative to the RF power supplied by the rotary joint
Incorporate the electronic steering and stabilization of beams in the elevation plane (“row-board”) to lower overall and maintenance cost, extend the radar operational life and improve its reliability
No radome is required to meet antenna assembly weight constraint.
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Udo-Yagi PCB Wide Band Linear Polarized MIMO Antenna for 5G Network Base Station

Basic Parameters:
Linear Polarized
Covers several 5G subband between 23.3-35.6GHz
5-8 dBi peak directivity
Total (Ohmic + Mismatch Loss) Efficiency >= -0.5 dB
Return Loss <= -10dB in ∆𝒇 ≤ 12.315GHz (Bandwidth = 41.8%)
Return Loss <= -12dB in ∆𝒇≤ 10.849GHz (Bandwidth = 36.8%)
Sizes: 13.33(L)*4.21(W)*1.24(H) mm size
Microstrip Input of 50 Ohms
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24 – 30 GHz Phased Array for 5G Network Base Station. Element Design and Comparative Array Analysis with all Mutual Copupling Included

This article discusses and compares different ways of 5G phased array platform/wizard development and provides some recommendations to obtain consistent results. The phased antenna array is one of the lead front-end components of current and coming 5G communication systems that defines their massive MIMO performance. Regrettably, a wide variety of application-driven requirements (city or rural environment, a realized gain, scan and polarization performance, impedance matching, etc.) cannot be met by single and forever designed element. It means that any practically convenient model platform must contain an extensive library of predesigned antenna elements. Misfortunately, 5G antennas belong to a class of relatively small and densely populated phased arrays where the total number of radiators typically does not exceed several hundred. If so, the consistency of results obtained through such system-level platform ultimately depends on the correctness of the phased array elements’ model that should include the relatively strong (-15dB or 0.18V relative to 1V element excitation and sometimes even higher) mutual coupling with other elements in the array.

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