Antenna Arrays and Array Factor Analysis
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Questions and Answers

What is the ideal phase shift required for broadside radiation when the main beam is at θ=90°?

  • 𝜑 = 0 (correct)
  • 𝜑 = 2π
  • 𝜑 = π/2
  • 𝜑 = π

What happens to the main beam direction when the amplitude and phase of the array elements are uniform?

  • A broadside radiation pattern is achieved. (correct)
  • The main beam shifts to several angles.
  • No directivity is observed.
  • The array becomes ineffective.

What is the relationship between the separation distance (d) and the occurrence of grating lobes?

  • Grating lobes are independent of the separation distance.
  • Grating lobes can only occur at d = 0.
  • Smaller separation distances increase grating lobes.
  • Larger separation distances increase grating lobes. (correct)

If the elements of a broadside array are configured in the xy plane, at what angle is the broadside beam achieved?

<p>θ = 0° (B)</p> Signup and view all the answers

How is the directivity (D) of a broadside array with N elements calculated?

<p>$D = 2N imes (d / λ)$ (D)</p> Signup and view all the answers

What does the equation for the array factor change to when dipole centres are located along the y-axis?

<p>AF = 2cos(($eta d ext{sin} heta ext{sin} ext{φ} + ext{φ}$)) (C)</p> Signup and view all the answers

Which equation represents the normalized radiation pattern of two z-directed dipoles?

<p>F(θ, φ) = |sinθcos(($eta d ext{cos} heta$))| (C)</p> Signup and view all the answers

What change occurs to the radiation pattern when dipoles are replaced by point source elements?

<p>The radiation pattern becomes wider. (D)</p> Signup and view all the answers

What is indicated by the result that a narrower beam is achieved when using dipole elements?

<p>Dipoles provide a more focused direction for emitted energy. (C)</p> Signup and view all the answers

In the generalized equation for array factor provided, what factors determine the pattern shape?

<p>The number of elements and phase of the current. (B)</p> Signup and view all the answers

What is the primary consequence of mutual coupling in array antennas?

<p>Altered excitation amplitude and/or phase of array elements (D)</p> Signup and view all the answers

When discussing the array factor with 'N' elements, what does 'd' represent?

<p>The separation distance between adjacent elements. (A)</p> Signup and view all the answers

What effect do surface waves have in microstrip arrays?

<p>They enhance the mutual coupling across array elements (C)</p> Signup and view all the answers

What is the value of the array factor equation assuming φ=0 and the dipoles are along the z-direction?

<p>AF = 2cos(($eta d ext{cos} heta)$) (A)</p> Signup and view all the answers

In phased arrays, what alternative to phase shifters can be used to achieve required phase shifts?

<p>Transmission line sections with optimized lengths (A)</p> Signup and view all the answers

Which of the following influences the shape of the normalized far field patterns most significantly?

<p>The phase difference between dipoles. (A)</p> Signup and view all the answers

What can cause the measured radiation pattern of an array to differ from calculated values?

<p>Significant mutual coupling between array elements (C)</p> Signup and view all the answers

What assumption is made during array factor analysis regarding mutual coupling?

<p>It assumes isotropic radiators without mutual coupling (C)</p> Signup and view all the answers

How does mutual coupling impact the far field pattern of an antenna array?

<p>It deteriorates the far field pattern (D)</p> Signup and view all the answers

Why is it necessary to account for mutual coupling when designing array antennas?

<p>To maintain the designed excitation values for each antenna element (B)</p> Signup and view all the answers

What challenge does mutual coupling present in the design of array antennas?

<p>It complicates the phase shift requirements (A)</p> Signup and view all the answers

What type of antenna is created when the phase shift φ between elements is zero?

<p>Uniform broadside array (C)</p> Signup and view all the answers

What does the variable γ represent in the equation for the array factor?

<p>Propagation constant related to the antenna configuration (C)</p> Signup and view all the answers

What is the maximum value of the normalized array factor (AF)n that can be achieved?

<p>1 (D)</p> Signup and view all the answers

Which equation would be used to calculate the array factor for elements arranged along the x-axis?

<p>γ = (βdsin θcos φ + φ) (C)</p> Signup and view all the answers

Which of the following best describes what affects the main beam direction in an array antenna?

<p>The excitation, element separation, and single element radiation pattern (D)</p> Signup and view all the answers

What type of array factor is represented by the summation equation A_F = ∑ e^(j(n-1)γ)?

<p>Generalized form of the array factor (D)</p> Signup and view all the answers

In the context of antenna arrays, what does the term 'isotropic elements' refer to?

<p>Elements that radiate equally in all directions (C)</p> Signup and view all the answers

If an array has equal current amplitudes but a linear phase shift between elements, what type of array is it categorized as?

<p>Phased array (B)</p> Signup and view all the answers

What is the primary purpose of forming an antenna array with multiple dipole antennas?

<p>To achieve a higher gain in radiation or reception. (C)</p> Signup and view all the answers

In the equation for the radiated field from two z-directed dipoles, what does the term $I_1 + I_2$ denote?

<p>The complex currents of the individual antennas. (B)</p> Signup and view all the answers

What role does the array factor play in the radiation pattern of an antenna array?

<p>It describes the effects of individual dipole orientations and separations. (C)</p> Signup and view all the answers

In the expression for $E_θ$, what does the term $e^{-jβr}$ represent?

<p>The phase of the radiation pattern. (A)</p> Signup and view all the answers

What is the effect of changing the distance $d$ between the dipoles in an array?

<p>It modifies the array factor and hence the radiation pattern. (A)</p> Signup and view all the answers

What does the term $ ext{sin} θ$ in the equation for $E_θ$ represent in the context of the antenna array?

<p>The directivity of the radiated field. (D)</p> Signup and view all the answers

When the antennas are excited by complex currents of $I_0 e^{j2φ}$ and $I_0 e^{-j2}$, what does the phase difference represent?

<p>The contribution of each dipole to the overall field. (B)</p> Signup and view all the answers

Which component of the combined radiated field from the antennas does not depend on their spacing or orientation?

<p>The distance from the dipoles to the point of measurement. (B)</p> Signup and view all the answers

What is the main purpose of array factor calculations in antenna design?

<p>To provide physical insight into array radiation. (B)</p> Signup and view all the answers

What occurs when a second parasitic dipole is placed near a driven dipole?

<p>It causes an induced current due to the radiated field. (D)</p> Signup and view all the answers

How is the input impedance of the first antenna expressed mathematically?

<p>$Z_{in,1} = Z_{11} + \frac{Z_{21}}{I_2 I_1}$ (D)</p> Signup and view all the answers

What effect does increasing the separation distance between two antennas have?

<p>Leads to larger array size and potential grating lobes. (D)</p> Signup and view all the answers

Which of the following techniques can reduce mutual coupling between antennas?

<p>Incorporating a deformed ground plane or EBG surfaces. (D)</p> Signup and view all the answers

What is the typical acceptable level of the scattering parameter S21 for negligible mutual coupling?

<p>S21 ≤ -20 dB (B)</p> Signup and view all the answers

What is the primary function of the mutual impedance Z21 in relation to antenna design?

<p>It quantifies the coupling effects between the two antennas. (D)</p> Signup and view all the answers

Which of the following statements about mutual coupling is incorrect?

<p>Mutual coupling only affects driven dipoles. (B)</p> Signup and view all the answers

Flashcards

Antenna Array

A collection of individual antennas used to enhance radiation or reception in a specific direction.

Array Factor

Component of a radiation pattern that describes how antenna spacing, excitation phasing, and number affect the overall radiation pattern.

Radiation Pattern

Graphical representation of the radiation intensity from an antenna in different directions.

Element Pattern

Radiation pattern of a single antenna element in an array.

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Excitation Phase (φ)

The phase difference in the excitation of antennas in an array.

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Separation Distance (d)

Distance between antenna elements in an array.

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Combined radiated field

Calculated radiated field from multiple antennas working together determined by individual antenna patterns and the combined array factor.

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Array Gain

The gain of an antenna array compared to the gain of a single antenna element used in the array.

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Array Factor (AF)

A factor that modifies the radiation pattern of a single element antenna when multiple elements are arranged in an array.

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Equation (85)

A general equation for calculating the radiation of an array of elements.

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Equation (86a)

Array factor for dipoles located along the y-axis.

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Equation (86b)

Array factor for dipoles located along the x-axis.

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Array Element Separation (d)

Distance between adjacent elements in an antenna array.

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Normalised Radiation Pattern (F(θ,φ))

A normalized representation of the radiation intensity of an antenna array over different angles (θ and φ).

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Infinitesimal Dipoles

Very small antennas used for calculating radiation patterns of arrays.

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Point Source Elements

Antenna elements that radiate as point sources, often used as a simplified model to antennas.

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Broadside Array

An antenna array designed to radiate a main beam perpendicular to the array axis, achieving maximum signal strength in a specific direction.

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Uniform Amplitude Excitation

All antenna elements in a broadside array are given the same strength of signal.

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Progressive Phase Shift

The phase of the signal fed to each element in a broadside array is adjusted to create a specific direction for the main beam.

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Directivity of a Large Broadside Array

The ability of a broadside array to focus power in a specific direction, calculated based on the number of elements and spacing.

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Array Factor Pattern

A graphical representation of the radiation pattern created by an antenna array, showing where the signal is strongest and weakest.

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Phased Array

An antenna array where individual antennas are fed with equal current amplitudes but with a linear phase shift (φ) between elements, resulting in a directed beam.

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Uniform Broadside Array

A special case of a phased array where the phase shift (φ) between elements is zero, resulting in a beam perpendicular to the array.

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What is γ in the Array Factor equation?

γ = (βd cos θ + φ). It represents the phase difference between the signal from adjacent elements in the array, considering the spacing (d), direction (θ), and phase shift (φ).

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How is the array factor calculated?

The array factor for N elements is calculated by summing the contributions of each element with its phase shift, resulting in a sum of exponentials with increasing phase shifts.

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How is the AF normalized?

The Array Factor is normalized by dividing it by its maximum value (N) to represent its relative strength in different directions. This gives a maximum value of 1 at the main beam direction.

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How does the main beam direction depend on the elements?

The main beam direction is determined by both the single antenna element's radiation pattern and the array factor, which depends on the excitation (φ) and spacing (d) between elements.

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What is the effect of changing the array's orientation?

Depending on whether the array is aligned with the x, y, or z axis, the γ equation changes to incorporate different angles (θ, 𝜙) affecting the main beam direction.

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Mutual Coupling

Electromagnetic interaction between antenna elements in an array, affecting their excitation amplitude and phase. This can alter the array's far-field pattern and impedance matching.

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Surface Waves

Electromagnetic waves propagating along the surface of a substrate, contributing to mutual coupling in microstrip antenna arrays.

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Isotropic Radiator

A hypothetical antenna radiating equally in all directions, used as a simplified model in array analysis.

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Discrepancies in Array Radiation

Differences between the calculated array factor and the measured radiation pattern of a real array, due to factors like mutual coupling and element characteristics.

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Array Factor Analysis

Study of how the radiation pattern of an antenna array is affected by the arrangement, spacing, and phasing of elements.

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Practical Phased Array

A real-world antenna array consisting of actual antenna elements, unlike idealized models.

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Phase Shifter

Device used in a feed network to introduce a specific phase shift to each antenna element in a phased array.

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Transmission Line Section

A length of transmission line used to introduce a specific phase shift in a feed network, instead of a dedicated phase shifter.

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Parasitic Antenna

An antenna that receives energy from another antenna's radiation, passively amplifying the signal.

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Driven Antenna

The antenna that is directly connected to the power source and initiates the radiation.

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Input Impedance (Zin)

The resistance an antenna presents to the incoming signal, it's how easily the antenna accepts the signal.

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Self Impedance (Z11)

The impedance of an antenna when it's isolated from other antennas in an array.

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Mutual Impedance (Z21)

The impedance between two antennas in an array, describing their coupling.

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Scattering Parameter S21

A measure of the signal transmitted from one antenna to another, indicating the strength of their coupling.

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Acceptable Coupling Level

A level of mutual coupling between antennas that is considered low enough not to significantly degrade performance.

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Study Notes

Antenna Arrays

  • Antenna arrays use multiple single antenna elements (e.g., dipoles) to achieve higher gain.
  • Gain enhancement is directionally dependent, influenced by phasing and positioning of individual antennas.
  • Radiation pattern in a plane is the product of individual element pattern and array factor in that plane.

Array Factor

  • Combined radiated field from two z-directed dipoles is given by a specific equation (64).
  • The equation involves factors like distance (r₁ and r₂), separation (d), angle (θ), and wave number (β).
  • The array factor (AF) is the product of individual element radiation patterns, considering the phasing and locations.

Array Factor Variations

  • The equation for AF changes depending on dipole arrangement locations.
  • AF= 2cos(βdsinθsinφ+q) (x-axis)
  • AF= 2cos(βdsinsinφ+q) (y-axis)

Normalised Radiation Patterns

  • Plots show the radiation pattern of two z-directed dipoles with specific separation and array placement, with q=0.
  • The pattern shape changes when the dipole elements are considered as point sources instead.

Array Factor of N Elements

  • AF can be derived by considering an array of isotropic elements along the z-axis.
  • The general equation for AF is related to complex currents (Ie) and spacing distance (d).
  • A closed-form normalised AF is N[sin(Nγ/2)] /[Nsin(γ/2)] Where γ= βdcosθ+φ

Array Direction

  • Main beam direction depends on individual element radiation pattern and array factor.
  • Arrays with larger separations can cause grating lobes.
  • Smaller separations might lead to stronger mutual coupling
  • Proper element separation (d) and excitation (q) are important for desired radiation characteristics.

Broadside Arrays

  • Broadside arrays have main beam orthogonal to the array axis, typically at θ=90°.
  • The maximum array factor (AF) is achievable when γ = 0.
  • The directivity of large broadside arrays (with N elements) is given the equation (D) = 2N

End-Fire Arrays

  • End-fire arrays have main beam along array axis, typically at θ=0°, and for the maximum array factor (AF), γ = 0.
  • Directivity of large end-fire arrays (with N elements) is given the equation (D) = 4N

Yagi-Uda Arrays

  • Yagi-Uda arrays are end-fire array examples involving a fed resonant element, reflector, and directors.
  • The gain (performance) depends on the number of directors and separation distances between elements.

Phased Arrays

  • Phased arrays can be designed to achieve a main beam in any desired direction using specific excitation phases.
  • Phase shifts in the feed network are used to steer the main radiation beam to desired directions. Excitation phases for x, y, and z-directed arrays are expressed φ₂ = −ẞd cos em φx = −βd sin em cos φ φy = −βd sin em sin φ

Mutual Coupling

  • Mutual coupling occurs where antenna elements in proximity have an impact on each other (modifying impedance and radiation patterns).
  • Factors such as antenna size, separation distance, and shape affect mutual coupling.
  • Strong mutual coupling negatively impacts efficiency and impedance matching. Techniques like using a proper impedance matching, or using surfaces like EBGs, could reduce mutual coupling.
  • Measuring S21 can assess the mutual coupling of a design. S21 ≤ -20 dB is generally an acceptable level.

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Description

This quiz explores the concepts of antenna arrays and the significance of array factors in antenna design. It covers the principles of gain enhancement, radiation patterns, and the variations of array factors based on dipole arrangements. Test your knowledge on the mathematical formulations and practical implications in antenna technology.

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