Engineering Commons^™

A Tool For Beamforming And Real-Time Link Budget Analysis In Aeronautical Communications Using Kinematics, M. Cenk Erturk, Yasin Aksan

Electrical Engineering Faculty Publications

Aeronautical Communication (AC) systems are likely to be a part of future tiered communication network structures. Therefore maintaining a robust AC link with a minimum power burden on the host platform has a critical importance. In this paper, we analyze the AC systems from a link budget analysis point of view and define the requirements for the parameters of link budget with an emphasize on antenna gains. First, we study the link budget analysis in an AC system. Then, we present a mathematical framework to provide an end-to-end link budget analysis utilizing the platform kinematics. Finally, we present the numerical …

Visualization Of 4d Q2psk And Ce Q2psk In Ideal Bandlimited Channels, Milton I. Quinteros, Edit J. Kaminsky, Kenneth V. Cartwright

Electrical Engineering Faculty Publications

This paper presents new visualization techniques for 4D Quadrature-Quadrature Phase Shift Keying (Q2PSK), Saha’s Constant Envelope (CE) Q2PSK, and Cartwright’s CEQ2PSK in ideal bandlimited channels. The signal diagrams analyzed are: time-signal eye patterns for 4D passband signals, 2D complex trajectory diagrams of baseband signals, and time-signal eye patterns for the 1D outputs of the baseband matched filter. These methods may be applied to other multidimensional modulation systems to obtain insight into the effects of noise, interference, and channel filtering.

A Further Look At Capacitors In Complex Arrangements, Kenneth V. Cartwright, Patrick Russell, Edit J. Kaminsky

Electrical Engineering Faculty Publications

Recently, a previous contributor showed how the delta-wye conversion may be applied to find the equivalent capacitance of five capacitors arranged in a bridge configuration. In fact, that contributor gave an algorithm for this purpose which showed that the equivalent capacitance depends upon all five capacitors. However, in this paper, we point out that there is a special case where the equivalent capacitance does not depend upon one of the five capacitors.

Finding The Minimum Input Impedance Of A Second-Order Twofold-Gain Sallen-Key Low-Pass Filter Without Calculus, Kenneth V. Cartwright, Edit J. Kaminsky

Electrical Engineering Faculty Publications

We derive an expression for the input complex impedance of a Sallen-Key second-order low-pass filter of twofold gain as a function of the natural frequency ωo and the quality factor Q. From this expression, it is shown that the filter behaves like a Frequency Dependent Negative Resistance (FDNR) element for low frequencies and as a single resistor at high frequencies. Furthermore, the minimum input impedance magnitude is found without using calculus. We discovered that the minimum input impedance magnitude is inversely proportional to Q and can be substantially less than its high-frequency value. Approximations to the minimum input impedance and …

Finding The Maximum And Minimum Magnitude Responses (Gains) Of Third-Order Filters Without Calculus, Kenneth V. Cartwright, Patrick Russell, Edit J. Kaminsky

Electrical Engineering Faculty Publications

The maximum and minimum gains (with respect to frequency) of third-order low-pass and high-pass filters are derived without using calculus. Our method uses the little known fact that extrema of cubic functions can easily be found by purely algebraic means. PSpice simulations are provided that verify the theoretical results.

Finding The Minimum Input Impedance Of A Second-Order Unity-Gain Sallen-Key Low-Pass Filter Without Calculus, Kenneth V. Cartwright, Edit J. Kaminsky

Electrical Engineering Faculty Publications

We derive an expression for the input complex impedance of a Sallen-Key second-order low-pass filter of unity gain as a function of the natural frequency , o  quality factor Q and the ratio of the resistors of the filter. From this expression, it is shown that the filter behaves like a single capacitor for low frequencies and as a single resistor at high frequencies. Furthermore, the minimum input impedance magnitude is found without using calculus. We discovered that the minimum input impedance magnitude is inversely proportional to Q and can be substantially less than its highfrequency value. Approximations to …

Finding The Maximum Magnitude Response (Gain) Of Second-Order Filters Without Calculus, Kenneth V. Cartwright, Patrick Russell, Edit J. Kaminsky

Electrical Engineering Faculty Publications

The maximum gain (with respect to frequency) of second-order filters such as low-pass, high-pass, band-pass, low-pass notch and high-pass notch filters is derived without using calculus. Our method uses the fact that the square of the magnitude response (gain) for these filters can be written as a positive constant divided by a quadratic function of frequency. Hence, the gain is maximized when the denominator of the gain is minimized, which is easily achieved without calculus, as the denominator is parabolic.

Determining The Maximum Or Minimum Impedance Of A Special Parallel Rlc Circuit Without Calculus, Kenneth V. Cartwright, Edit J. Kaminsky

Electrical Engineering Faculty Publications

We show that the maximum or minimum impedance of a special parallel RLC studied in a previous paper can be found analytically, without using calculus. In fact, we show that the maximum or minimum value occurs when the driving frequency  is equal to o 1/ LC , a fact that was determined graphically in that previous paper. Furthermore, we show that either the maximum or minimum value is given by     2 2 R  1  3 ,where   L/C / R. Also, for the minimum impedance   2 min Z  R …

Circular And Near-Circular Polarization States Of Evanescent Monochromatic Light Fields In Total Internal Reflection, R. M. A Azzam

Electrical Engineering Faculty Publications

Conditions for the production of near-circular polarization states of the evanescent field present in the rarer medium in total internal reflection of incident monochromatic p-polarized light at a dielectric-dielectric planar interface are determined. Such conditions are satisfied if high-index (>3.2) transparent prism materials (e.g., GaP and Ge) are used at angles of incidence well above the critical angle but sufficiently below grazing incidence. Furthermore, elliptical polarization of incident light with nonzero p and s components can be tailored to cause circular polarization of the resultant tangential electric field in the plane of the interface or circular polarization of the …

Poincaré Sphere Representation Of The Fixed-Polarizer Rotating-Retarder Optical System, R. M.A. Azzam

Electrical Engineering Faculty Publications

The trajectory of the polarization state of a monochromatic light beam after it passes through a fixed linear polarizer and a rotating linear retarder of arbitrary retardance Δ is determined on the Poincaré sphere. The three-dimensional figure-8 contour is shown to be the line of intersection of a right-circular cylinder with the sphere. The cylinder is parallel to the polar (s₃) axis, touches the sphere at the equator (at the point that represents the linear polarization transmitted by the fixed polarizer), and has a radius r=sin²(Δ/2). Projections of the trajectory in the coordinate planes of the …

Three-Dimensional Polarization States Of Monochromatic Light Fields, R. M.A. Azzam

Electrical Engineering Faculty Publications

The 3×1 generalized Jones vectors (GJVs) [ExEyEz]t (t indicates the transpose) that describe the linear, circular, and elliptical polarization states of an arbitrary three-dimensional (3-D) monochromatic light field are determined in terms of the geometrical parameters of the 3-D vibration of the time-harmonic electric field. In three dimensions, there are as many distinct linear polarization states as there are points on the surface of a hemisphere, and the number of distinct 3-D circular polarization states equals that of all two-dimensional (2-D) polarization states on the Poincaré sphere, of which only two are circular states. The subset of 3-D polarization …

A Further Look At The 'Reactance Of A Parallel Rlc Circuit', Kenneth V. Cartwright, Edit J. Kaminsky

Electrical Engineering Faculty Publications

We show that the maximum impedance of the parallel combination of a resistor R, an inductor L and capacitor C, studied in a previous paper can be found analytically, without using calculus. In fact, we show that the maximum impedance of this parallel combination is just the value of the resistor R and occurs when the driving frequency  is equal to 1/ . o   LC These results were only demonstrated graphically in the aforementioned paper. We also provide PSpice simulations which verify the theoretical predictions.

Simplified Design Of Thin-Film Polarizing Beam Splitter Using Embedded Symmetric Trilayer Stack, R. M.A. Azzam

Electrical Engineering Faculty Publications

An analytically tractable design procedure is presented for a polarizing beam splitter (PBS) that uses frustrated total internal reflection and optical tunneling by a symmetric LHL trilayer thin-film stack embedded in a high-index prism. Considerable simplification arises when the refractive index of the high-index center layer H matches the refractive index of the prism and its thickness is quarter-wave. This leads to a cube design in which zero reflection for the p polarization is achieved at a 45 degrees angle of incidence independent of the thicknesses of the identical symmetric low-index tunnel layers L and L. Arbitrarily high reflectance for …

Principal Angles And Principal Azimuths Of Frustrated Total Internal Reflection And Optical Tunneling By An Embedded Low-Index Thin Film, R. M.A. Azzam, F. F. Sudradjat

Electrical Engineering Faculty Publications

The condition for obtaining a differential (or ellipsometric) quarter-wave retardation when p- and s-polarized light of wavelength λ experience frustrated total internal reflection (FTIR) and optical tunneling at angles of incidence ϕ≥ the critical angle by a transparent thin film (medium 1) of low refractive index n1 and uniform thickness d, which is embedded in a transparent bulk medium 0 of high refractive index n0 takes the simple form: −tanh2x=tanδptanδs , in whichx=2πn1(d/λ)(N2sin2ϕ−1)1/2 , N=n0/n1 , and δp , δs are 01 interface Fresnel reflection phase shifts for the pand s polarizations. From this condition, the …

Finding The Exact Maximum Impedance Resonant Frequency Of A Practical Parallel Resonant Circuit Without Calculus, Kenneth V. Cartwright, Elton Joseph, Edit J. Kaminsky

Electrical Engineering Faculty Publications

A practical parallel resonant circuit has a resistor in series

with an inductor, and that combination is in parallel with a

capacitor. For such a circuit, it is well known that there are

two possible definitions for the resonant frequency: (i) the

resonant frequency , p f which is the frequency at which the

phase of the total impedance is zero, and (ii) the resonant

frequency m f , which is the frequency that achieves maximum

magnitude of the total impedance. To find the latter

traditionally requires calculus. However, in this paper, the

authors show how m f

can be …

Return-Path, Multiple-Principal-Angle, Internal-Reflection Ellipsometer For Measuring Ir Optical Properties Of Aqueous Solutions, Rasheed M.A. Azzam

Electrical Engineering Faculty Publications

A retroreflection (return-path) spectroscopic ellipsometer without a wave plate is described that uses an IR-transparent high-refractive-index hemicylindrical semiconductor substrate to measure the optical properties of aqueous solutions from multiple principal angles and multiple principal azimuths of attenuated internal reflection (AIR) at the semiconductor–solution interface. The pseudo-Brewster angle of minimum reflectance for the p polarization is also readily measured using the same instrument. This wealth of data can also be used to characterize thin films at the solid–liquid interface. Simulated results of AIR at the Si–water interface over the 1.2–11 μm IR spectral range are presented in support of this concept. …

Transmission Of P- And S-Polarized Light Through A Prism And The Condition Of Minimum Deviation, R. M.A. Azzam, Ryan M. Adams

Electrical Engineering Faculty Publications

The condition of minimum deviation (MD) by a transparent optically isotropic prism is re-derived, and expressions for the intensity transmittances Tp(θ) and Ts(θ) of an uncoated prism of refractive index n and prism angle α for incident p- ands-polarized light and their derivatives with respect to the internal angle of refraction θ are obtained. When the MD condition(θ=α/2) is satisfied, Ts is maximum and Tp is maximum or minimum. The transmission ellipsometric parametersψt,Δt of a symmetrically coated prism are also shown to be locally stationary with respect to θ at θ=α/2 . The constraint on (n,α) for …

Broadband Ir Polarizing Beam Splitter Using A Subwavelength-Structured One-Dimensional Photonic-Crystal Layer Embedded In A High-Index Prism, R. M.A. Azzam, H. K. Khanfar

Electrical Engineering Faculty Publications

An iterative procedure for the design of a polarizing beam splitter (PBS) that uses a form-birefringent, subwavelength-structured, one-dimensional photonic-crystal layer (SWS 1-D PCL) embedded in a high-index cubical prism is presented. The PBS is based on index matching and total transmission for the p polarization and total internal reflection for the s polarization at the prism-PCL interface at 45 degrees angle of incidence. A high extinction ratio in reflection (>50 dB) over the 4-12 mu m IR spectral range is achieved using a SWS 1-D PCL of ZnTe embedded in a ZnS cube within an external field of view …

Tilted Parallel Dielectric Slab As A Multilevel Attenuator For Incident P- Or S-Polarized Light, R. M.A. Azzam

Electrical Engineering Faculty Publications

Under the condition of first-order blooming, a parallel dielectric slab, which is inserted in the path of an obliquely incident p- or s-polarized light beam, introduces multiple discrete attenuation levels given by 1/3, 4/27, 4/243,...... in reflection and 4/9, 4/81, 4/729,...... in transmission. These attenuation levels are independent of the slab refractive index, incident p or s linear polarization, or the presence of identical transparent surface coatings at the front and back sides of the slab. Therefore, the tilted slab provides multidecade reflectance and attenuation reference values that can be used in calibrating spectrophotometers and filters, and also …

A Trellis-Coded Modulation Scheme With A Novel Expanded 16-Dimensional Constant Envelope Q2psk Constellation, Milton I. Quinteros, Edit J. Kaminsky, Kenneth V. Cartwright

Electrical Engineering Faculty Publications

This paper presents a TCM scheme that uses a new expanded 16-Dimensional Constant Envelope Q2PSK constellation along with a simple convolutional encoder of rate 2/3. An effective gain of 2.67 dB over uncoded CEQ2PSK is achievable with low complexity, and without suffering from constellation expansion penalty. Larger coding gains are easily achieved with encoders of higher rates. In addition, an optimal hardware implementation of the required decoders is described.

Plurality Of Principal Angles For A Given Pseudo-Brewster Angle When Polarized Light Is Reflected At A Dielectric-Conductor Interface, R. M.A. Azzam, A. Alsamman

Electrical Engineering Faculty Publications

The pseudo-Brewster angle ϕpB of minimum reflectance for p-polarized light and the principal angle ϕ¯ at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function ε of a dielectric–conductor interface over the entire complex ε plane. In particular, the spread of ϕ¯for a given ϕpB is determined, and the maximum difference (ϕ¯−ϕpB)max is obtained as a function of ϕpB . The maximum difference (ϕ¯−ϕpB)max approaches 45° and 0 in the limit as ϕpB→0 and 90°, respectively. ForϕpB<22.666° , multiple principal angles ϕ¯i , i=1,2,3 , appear for each ε in a subdomain of fractional optical constants. …

In-Line Broadband 270 Degrees (3 Lambda/4) Chevron Four-Reflection Wave Retarders, R. M.A. Azzam, H. K. Khanfar

Electrical Engineering Faculty Publications

The net differential phase shift Δ_t introduced between the orthogonal p and s linear polarizations after four successive total internal reflections inside an in-line chevron dual-Fresnel-rhomb retarder is a function of the first internal angle of incidence φ and prism refractive index n. Retardance of 3λ/4 (i.e., Δ_t=270°) is achieved with minimum angular sensitivity when φ=45° and n=1.900822. Several optical glasses with this refractive index are identified. For Schott glass SF66 the deviation of Δ_t from 270° is ≤4° over a wavelength range of 0.55≤λ≤1.1 μm in the visible and …

Quasi Index Matching For Minimum Reflectance At A Dielectric-Conductor Interface For Obliquely Incident P- And S-Polarized Light, R. M.A. Azzam, A. Alsamman

Electrical Engineering Faculty Publications

Conditions for reducing the reflectance of a dielectric-conductor interface for p- and s-polarized light to a minimum at any angle of incidence ϕ are determined. The refractive indices of a transparent immersion medium (liquid) that achieve minimum reflectance at normal incidence, ϕ=0, and at ϕ=45° are independent of polarization. These indices provide sufficient data to determine the real and imaginary parts of the complex refractive index of an absorbing substrate. Reflection at a dielectric-Au interface at 500 nm wavelength is considered as an example. It is shown that the lowest possible reflectance is attained for p …

Reflection Coefficients Of P- And S-Polarized Light By A Quarter-Wave Layer: Explicit Expressions And Application To Beam Splitters, R. M.A. Azzam, F. F. Sudradjat

Electrical Engineering Faculty Publications

The complex-amplitude reflection coefficients of p- and s-polarized light by a transparent freestanding, embedded, or deposited quarter-wave layer (QWL) are derived as explicit functions of the angle of incidence and layer refractive index. This provides the basis for the design of 50%-50% beam splitters for incident s-polarized or unpolarized light that use a high-index (e.g., TiO₂ or Ge) QWL embedded in a glass cube in the visible and near infrared spectral range. These simple devices have good angular and spectral response and are insensitive to small film thickness errors to the first order.

Efficiency Of Linear-To-Circular Polarization Conversion For Light Reflection At The Principal Angle By A Dielectric-Conductor Interface, R. M.A. Azzam, A. Alsamman

Electrical Engineering Faculty Publications

The efficiency ηLC of linear-to-circular polarization conversion when light is reflected at a dielectric–conductor interface is determined as a function of the principal angle ϕ¯ and principal azimuth ψ¯ . Constant- ηLC contours are presented in the ϕ¯ ,ψ¯ plane for values of ηLC from 0.5 to 1.0 in steps of 0.05, and the corresponding contours in the complex plane of the relative dielectric function ϵ are also determined. As specific examples, efficiencies ⩾88% are obtained for light reflection by a Ag mirror in the visible and near-IR (400–1200nm) spectral range, and ≥40% for the reflection of extreme ultraviolet (EUV) …

Polarization Properties Of Retroreflecting Right-Angle Prisms, R. M.A. Azzam, H. K. Khanfar

Electrical Engineering Faculty Publications

The cumulative retardance Δ_t introduced between the p and the s orthogonal linear polarizations after two successive total internal reflections (TIRs) inside a right-angle prism at complementary angles Φ and 90°−Φ is calculated as a function of Φ and prism refractive index n. Quarter-wave retardation (QWR) is obtained on retroreflection with minimum angular sensitivity when n=(√2+1)^1/2=1.55377 and Φ=45°. A QWR prism made of N-BAK4 Schott glass (n=1.55377 at λ=1303.5 nm) has good spectral response (<5° retardance error) over the 0.5-2 μm visible and near-IR spectral range. A ZnS-coated right-angle Si prism achieves QWR with an error of <±2.5° in the 9-11 μm (CO₂ laser) IR spectral range. This device functions as a linear-to-circular polarization transformer and can be tuned to exact QWR at any …

A Novel Expanded 16-Dimensional Constant Envelope Q2psk Constellation, Milton I. Quinteros, Kenneth V. Cartwright, Edit J. Kaminsky, Ricardo U. Gallegos

Electrical Engineering Faculty Publications

We introduce a 16-dimensional constant-amplitude constellation that is generated by concatenating either four constant envelope quadrature-quadrature phase shift keying (CEQ2PSK) symbols from Saha and Birdsall or four CEQ2PSK symbols recently discovered by Cartwright and also introduced here. Our new constellation doubles the number of points available for data transmission without decreasing the distance between points or increasing energy, and may therefore be used in a trellis coded modulation (TCM) system without constellation expansion penalty. Because the new constellation has constant envelope, the modulation scheme becomes very attractive for nonlinear channels such as the magnetic recording channel or the satellite channel …

Classification Of Cylindrical Targets Buried In Seafloor Sediments, Edit J. Kaminsky, Madalina Barbu

Electrical Engineering Faculty Publications

This paper presents the development and evaluation of a time-frequency processing technique for detection and classification of buried cylindrical targets from chirpbased parametric sonar data. The software is designed to discriminate between cylindrical targets —such as cables— of different diameters, which need to be identified as different from other strong reflectors or point targets. The method is evaluated on synthetic data generated with an acoustic scattering model for elastic cylinders for seven different diameters. The model generates characteristic responses of targets acquired by a parametric sonar system. The signal at the sonar receiver hydrophones is first windowed to reduce the …

Sub-Bottom Profiling Using Time-Frequency Analysis, William Sanders, Dale Bibee, Edit J. Kaminsky

Electrical Engineering Faculty Publications

No abstract provided.

Embedded Centrosymmetric Multilayer Stacks As Complete-Transmission Quarter-Wave And Half-Wave Retarders Under Conditions Of Frustrated Total Internal Reflection, S. R. Perla, R. M.A. Azzam

Electrical Engineering Faculty Publications

A centrosymmetric multilayer stack of two transparent materials, which is embedded in a high-index prism, can function as a complete-transmission quarter-wave or half-wave retarder (QWR or HWR) under conditions of frustrated total internal reflection. The multilayer consists of a high-index center layer sandwiched between two identical low-index films with high-index–low-index bilayers repeated on both sides of the central trilayer, maintaining the symmetry of the entire stack and constituting a QWR ( Δt=90° or 270°) or HWR (Δt=180°) in transmission. A QWR design at wavelengthλ=1.55 μm is presented that employs an 11-layer stack of Si and SiO2 thin films, which is …