Predicting the behaviour of a finite phased array from an infinite one Jacki van der Merwe MScEng University of Stellenbosch

Introduction Simulation of large antenna arrays Very time consuming Need lots of memory and computational power Very large arrays are impossible to simulate at the moment Need a method to make analysis of antenna arrays more efficient

Antenna Array Analysis Why infinite Arrays? Can use periodic boundary conditions What do we want to know? S-parameters (Y-, Z-parameters) Radiation Pattern

Calculating the S-parameters

Active Reflection coefficient: Incoming signal on the Nth element can be described in terms of excitation signals and coupling coefficients (S- parameters) To get an expression for the active reflection coefficient, we divide by the excitation signal of the Nth element:

Calculating the S-parameters Excitation signal in phased array: Dividing two excitation signals leaves only the difference in phase-shift Active Reflection coefficient can now be expressed in terms of a Fourier Series: S-parameters can thus be solved the FFT:

Calculating the S-parameters Example: 2D Dipole Array: Elements Y-directed Length = 0.4 λ Frequency = GHz a = b = 0.6 λ

Calculating S-parameters Results: S 0m along x-axis Edge Effects

Calculating S-parameters Results: S 0n along y-axis Edge Effects

Calculating S-parameters Results: S-parameters 3D

Calculating the Radiation Pattern Conventional Array Theory: Problem: Ignores effects of mutual coupling and scattering Rather use embedded element pattern: Def: “Pattern of infinite array, when only one element is excited and all others are match terminated” Radiation Pattern of infinite array:

Calculating the Radiation Pattern Array Factor: If m is limited to finite number: Approximated to finite array Infinite array with finite number of excited elements, other’s are:  Open circuited  Short circuited  Match Terminated

Calculating the Radiation Pattern Results: Radiation Pattern for 9x9 dipole array example

Conclusion and Way Forward Using these methods, analysis of very large antenna arrays will be possible Generic Code will be developed to enable analysis of any large array topology. Finally, these methods will be used to analyse FPA’s

Any Questions?