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Related Concept Videos

Vector Representation of Complex Numbers01:16

Vector Representation of Complex Numbers

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Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the...
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Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

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Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance.
At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
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Lossless Lines01:23

Lossless Lines

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In electrical engineering, a lossless transmission line is characterized by a purely imaginary propagation constant and a resistive characteristic impedance. The ABCD parameters, which describe the relationship between the input and output voltages and currents, indicate an equivalent π circuit with an imaginary series impedance and a shunt admittance. This results in a transmission line that, when the product of the phase constant (beta) and the length of the line is less than pi, exhibits...
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Lossy Lines and Overvoltages01:22

Lossy Lines and Overvoltages

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Transmission-line series resistance and shunt conductance cause three primary effects: attenuation, distortion, and power losses.
Attenuation
When constant series resistance and shunt conductance are present, voltage and current equations are modified. The propagation constant indicates that voltage and current waves consist of both forward and backward traveling components. These waves attenuate as they propagate, with the attenuation factor related to the resistance and conductance. In a...
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Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

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The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx  and a shunt capacitance CΔx.
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Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

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It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
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Updated: Feb 20, 2026

Demonstration of Equal-Intensity Beam Generation by Dielectric Metasurfaces
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Gain loss in metasurfaces caused by reflection-coefficient quantization: an error vector magnitude approach.

Ke Peng, Kai Da Xu, Qiang Chen

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    A new error vector magnitude (EVM)-based metric quantifies metasurface precision and predicts gain loss. This tool aids in designing efficient 5G and satellite communication systems.

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    Area of Science:

    • Electromagnetics and Metamaterials
    • Antenna Theory and Design

    Background:

    • Metasurfaces with discrete reflection states experience gain loss compared to continuous-phase designs.
    • Accurate prediction of this gain loss is crucial for practical applications.

    Purpose of the Study:

    • To introduce a novel metric, error vector magnitude (EVM)-based metric (ΓEVM), for evaluating metasurface unit precision.
    • To enable quantitative assessment of quantization precision and prediction of array gain loss.

    Main Methods:

    • Defined ΓEVM as the root-mean-square difference between ideal and realizable reflection coefficients.
    • Derived closed-form expressions for ΓEVM and its relation to gain loss under uniform phase PDF.
    • Developed a statistical method for nonuniform phase statistics using empirical phase PDFs.

    Main Results:

    • Established an empirical relation between ΓEVM and gain loss for direct radiation efficiency estimation.
    • Provided closed-form expressions for the expectation and variance of gain-loss statistics.
    • Validated the metric through simulations and experiments on 20x20 prototypes (1-bit to multi-bit resolution) with <0.34 dB deviation.

    Conclusions:

    • The proposed ΓEVM metric offers a generalizable and user-friendly approach for estimating metasurface gain loss.
    • This facilitates efficient design of metasurfaces for 5G and satellite communication systems.