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# Antennas

## •Functions and parameters contained in this package:

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### •Package functions and their basic documentation along with simple examples

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#### •BaylissLinearArray

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Here is the array pattern for a Bayliss linear phased array:

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Here is the array pattern for the corresponding Bayliss continuoous line source:

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#### •BaylissLineB

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Usage message for BaylissLineB

#### •BaylissLineA

Usage message for BaylissLineA

#### •BaylissLineSource

This is the general analytic expression:

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Numerical results are generated automatically when called for:

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#### •BaylissLineZ

Usage message for BaylissLineZ

#### •BinomialLinearArray

There is a general expression for the array factor of the binomial array:

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For particular values of n this expands:

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Here is a normalized version:

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This is an example of a paremetric plot as a functoin of angle of the array pattern (power in dB) normalized to 0 dB at maximum:

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Here is the same but with a different interelement spacing:

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#### •BinomialLinearArray

Usage message for BinomialLinearArray

#### •DolphChebyshevLinearArray

Usage message for DolphChebyshevLinearArray

#### •DolphChebyshevLinearArray

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An 8 element Dolph-Chenyshev array with sidelobes 10 dB below main beam power level:

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Similar to the above but steered -30° off of boresight:

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#### •DolphTschebyscheffLinearArray

Usage message for DolphTschebyscheffLinearArray

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#### •GeneralLinearArray

With the choice of function as simply unity ( expressed as a pure function by we get the uniform array that is examined below under UniformLinearArray:

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Bringing this into a (perhaps) more familiar form:

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The first argument of GeneralLinearArray can also be a list of array weights.  This corresponds to an array with 5 equally weighted elements:

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Here is the array factor for weights that vary according to the form (give as a pure function) :

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Here is its normalized form for n=6 with an inter element spacing d=λ/2 steered to an angle of 45 degrees:

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As another example we consider an asymmetric distribution of array weights (this will lead to a monopulse type beam pattern):

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Here is an example for a 6-element array:

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Since this array will have a two-lobed (monopulse) main beam, we need to determine the location of a maximum to normalize.  To do this we use a function from the Mathematica standard add-on package NumericalMath`NMinimize`,  NMaximize.

First load the package:

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Now find the position of a maximum for a 10 element array:

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This also shows us that the angle between the two monopulse beams is (in degrees):

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The slope of the pattern on boresight is also easily determined via similar methods.

Finally plot the normalized result:

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The monopulse pattern in this broadside configuration is clear.

#### •NormalizationPoint

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#### •Normalized

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#### •Overhang

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#### •TaylorLinearArray

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To avoid generating very large exact expressions we use floating point values for the calculation:

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#### •TaylorLineA

Usage message for TaylorLineA

#### •TaylorLineExcitationCoeff

Usage message for TaylorLineExcitationCoeff

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#### •TaylorLineZ

Usage message for TaylorLineZ

#### •TryZTransform

Usage message for TryZTransform

#### •UniformLinearArray

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In terms of the frequency f:

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For steering angles α, β=0 and an elment spacing of :

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Steered to a phase :

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Compare broadside with endfire:

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