Microwaves & RF
  • Resources
  • Directory
  • Webinars
  • White Papers
  • Video
  • Blogs
  • CAD Models
  • Advertise
    • Search
  • Top Stories
  • Products of the Week
  • Defense
  • Test
  • Components
  • Semiconductors
  • Embedded
  • Data Sheets
  • Topics
    - TechXchange Topics -- Markets -DefenseAutomotive- Technologies -Test & MeasurementComponentsCellular / 5G / 6G EDA
    Resources
    Top Stories of the WeekMWRF ResourcesDigital issuesEngineering AcademyWISESearch Data SheetsCompany DirectoryLibraryContributeSubscribe
    Advertise
    https://www.facebook.com/microwavesrf/
    https://www.linkedin.com/groups/3848060/profile
    https://twitter.com/MicrowavesRF
    https://www.youtube.com/channel/UCXKEiQ9dob20rIqTA7ONfJg
    Mwrf 9807 1118mw 30q Promo
    1. Technologies
    2. Components

    A Brief Tutorial on Microstrip Antennas (Part 3)

    Jan. 3, 2019
    The third installment of this series focuses in on microstrip antenna arrays, with analysis of both four-element and two-×-two arrays.
    Kenneth V. Puglia

    Download this article in PDF format.

    Continuing the series on microstrip antennas, this article examines antenna arrays. Parts 1 and 2 focused on the single-element, rectangular microstrip antenna.

    Microstrip Antenna Array

    Although a significant number of applications exist for the single-element microstrip antenna, in many cases, the performance enhancements and features available with multiple microstrip-element arrays add to an expanding list of new opportunities. A microstrip antenna array is formed by the arrangement, or grouping, of multiple, single-element microstrip antennas. The respective geometric positioning of the individual elements, as well as the element amplitude and phase excitation, determines the characteristics of the antenna array.

    Microstrip antenna arrays are typically designed to enhance antenna performance beyond that available from a single element. For example, arrays of single-element microstrip antennas offer increased gain and narrower beamwidth at the cost of larger aperture area. In addition, array antennas offer the ability to steer the principal radiation intensity beam via differential phase excitation and reduced sidelobe levels by variable power excitation to the individual elements of the array—properties that compel emphasis in many applications.

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Table1

    The individual dimensional elements of a microstrip antenna array may vary and may be spatially configured in a linear, planar, or volumetric arrangement. The radiation pattern of an array is determined by the dimensions, spatial distribution, and electrical excitation, i.e., amplitude and phase, of the individual elements. Given the number of variables, a general approach to the synthesis and design of antenna arrays is clearly required. To that end, antenna specialists have been successful in formulating a general methodology using the definitions in Table 1.

    The product of the array factor and the element factor is referred to as the pattern multiplication theorem. An example will illustrate the convenience and efficiency of the theorem.

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Fig1

    1. The linear array of isotropic radiating elements is depicted.

    Consider the linear distribution of equally spaced, isotropic radiating elements along the z-axis (Fig. 1). The E-field radiation pattern of the ith element may be written as:1

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Eq1

    The following definitions are applicable to this equation:

    F(θ,ɸ) represents the radiation pattern of the element, and k0 = 2π/λ0, Ii, and βi are the amplitude and phase excitation.

    For n identical elements, the radiation pattern is written as:

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Eq2

    The radiation pattern is the product of the two terms:

    F(θ,ɸ) is the element factor (EF), and

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Eq3

    is the array factor (AF).

    The perceptive reviewer may recognize the similarity between the array factor and the discrete Fourier transform of the complex linear distribution of amplitude and phase of the radiating elements. For the specified equally spaced condition and progressive phase of each element, one may write:

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Eq4

    and

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Eq5

    If the indicated substitutions are implemented, the array factor may be written:

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Eq6

    Solution of the equation using constant amplitude distribution (Ii = 1.0), parametric phase progression (β0 = 0, β0 = −π/4, β0 = π/4), number of elements (n = 16), and element spacing (d = λ0/2) is graphically illustrated within Figure 2.

    The maximum amplitude of the array factor occurs at θ = 90 degrees for 0-degree phase excitation; at 105 degrees for 45-degree phase progression; and at 75 degrees for −45-degree phase progression. Clearly, the phase progression excitation enables the significant property of main beamsteering of antenna arrays. An additional observation is that the array of isotropic radiating elements has provided focus, i.e. gain, over the single element. In this instance, the numeric gain is equal to the number of array elements, n.

    Another observation from Figure 2 is the sin(x)/x amplitude function. This behavior might have been anticipated due to the constant amplitude-element excitation and the discrete Fourier transform relationship.

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Fig2

    2. This figure illustrates array factor for a linear array of isotropic elements.

    Constant, or uniform, amplitude distribution has been considered to this point of the exercise. However, in addition to phase progression excitation, amplitude variation of the array elements also offers some interesting properties. Consider the graphic of Figure 3, where the array factor for constant amplitude element excitation is indicated in the top plot, while raised cosine element amplitude excitation has been implemented in the bottom plot.

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Fig3a
    Www Mwrf Com Sites Mwrf com Files 0119 21 A Fig3b

    3. This array factor versus element amplitude variation (note logarithmic amplitude scale) comparison reveals constant amplitude excitation (top) and cosine amplitude excitation (bottom).

    The raised cosine amplitude excitation of the array elements significantly reduced the array sidelobes. Unfortunately, the array amplitude also was reduced while the beamwidth increased. These are the significant tradeoffs when considering application of antenna-array implementation.

    Microstrip antenna arrays will be further explored within the electromagnetic (EM) simulations in the upcoming sections. In many instances, the element spacing for most applications is approximately half-wavelength (λ0/2) in air. Although somewhat higher gain may be attained using element spacing beyond half-wavelength, increased sidelobe levels, particularly near ±90 degrees off-boresight (grating lobes), are a direct result. Therefore, in the simulations that will follow, element spacing in the plane of the antenna will be maintained at approximately half-wavelength.

    Linear Microstrip Array Antennas

    Figure 4 illustrates the configuration of a parallel-feed (alternately referred to as corporate feed) linear array composed of four in-line elements. Each element of the linear array is fed from the output of a power divider, which facilitates excitation of either equal or unequal power to each element. The power distribution to the elements of an array, as previously indicated, is commonly referred to as amplitude taper, and is utilized to reduce sidelobe levels. Amplitude taper is accompanied by increased beamwidth and reduced gain with respect to uniform, or equal, power distribution to each element.

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Fig4

    4. Here’s a four-element linear array.

    The excitation to each element of the array may also be varied in phase. Progressive differential phase excitation is employed to steer the main beam off-boresight and is a unique and attractive feature for large phased-array radar applications as an alternative to inertial (mechanical) platforms.

    A four-element linear array has been constructed using the single-element, 5.80-GHz microstrip antenna previously described and analyzed. The data from EM analysis of the four-element array is summarized in Table 2.

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Table2

    Table 3 documents the performance of a four-element linear array that has an amplitude taper applied to it. As mentioned previously, the amplitude taper is utilized to reduce sidelobe levels. The amplitude taper is implemented by changes to the impedance of the power divider’s lines in a manner that alters the impedance at the principal junction of the power divider. A simple equation governs the power-divider design under the specified conditions.3

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Table3

    Table 4 illustrates the configuration of a two-×-two array. The two-×-two array excitation is generally uniform; the most prominent feature is that the gain is typically 6 dB above the single-element configuration with the commensurate reduction in E-plane and H-plane beamwidth. In this case, the gain, 11.45 dB, is limited due to the inclusion of line and impedance-mismatch loss. The conductor current discloses that each element of the array is uniformly excited in amplitude and phase.

    Www Mwrf Com Sites Mwrf com Files 0119 21 A Table4

    The differential feed at the center of the conductor pattern may be implemented from a balun located below the plane of the array. Differential feed is required in this case due to the inverse polarity of the radiating edges. The input impedance is 100 Ω at the center frequency, which is commensurate with typical balun impedance.

    The individual excitation parameters of amplitude and phase determine the principal radiation intensity beamwidth, gain, direction, and sidelobe level. Clearly, antenna arrays are significant performance determinants to communication and radar systems.

    References

    1. Bahl, I. J. and Bhartia, P., Microstrip Antennas, Chapter 7, Artech House, Dedham, Mass., 1980.

    2. The current density annotation feature available within the AXIEM EM analysis software provides significant, physically insightful information. The graphic indicates that the amplitude and phase of the individual element excitation are equal. This feature is uniquely valuable in evaluation of proper amplitude and phase excitation of more complex array structures.

    3. The unequal power divider is documented at the website: http://www.microwaves101.com/encyclopedia/calpowerdivider.cfm.

    Continue Reading

    An Investigation into Wireless Signal Propagation

    11 Myths About Radar and Intelligent IoT

    Sponsored Recommendations

    Near and Far Field Measurement

    Oct. 31, 2023

    S-parameters for High-frequency Circuit Simulations

    Oct. 31, 2023

    Common Mode Filter Chokes for High Speed Data Interfaces

    Oct. 31, 2023

    Simulation Model Considerations: Part I

    Oct. 31, 2023

    New

    Performing eCall Testing in an EMC Test Environment

    Monopulse Comparators Offer Ultra-Broadband Beamforming from 0.5 to 40 GHz

    2024 Innovators Changing the Microwaves & RF Industry

    Most Read

    Empowering SOMs for IoT Devices with Matter Connectivity

    Quick Poll: What’s the #1 College for Electrical Engineering in the U.S.?

    Products of the Week: November 20, 2023

    Sponsored

    Key Parameters for Selecting RF Inductors

    Using Baluns and RF Components for Impedance Matching

    AnTune Antenna Impedance Matching and Antenna Efficiency Measurement Demonstration

    Microwaves & RF
    https://www.facebook.com/microwavesrf/
    https://www.linkedin.com/groups/3848060/profile
    https://twitter.com/MicrowavesRF
    https://www.youtube.com/channel/UCXKEiQ9dob20rIqTA7ONfJg
    • About Us
    • Contact Us
    • Advertise
    • Do Not Sell or Share
    • Privacy & Cookie Policy
    • Terms of Service
    © 2023 Endeavor Business Media, LLC. All rights reserved.
    Endeavor Business Media Logo