Designing broad-band patch antennas using the sequential quadratic programming method

Abstract

The utility of numerical codes is greatly enhanced if they can be used in design, a situation that typically involves iterative optimization algorithms. An attractive way is to use gradient-based algorithms developed for solving nonlinear programming (NLP) problems. In this letter, we examine the performance of a general sequential quadratic programming (SQP) optimization algorithm for designing patch antennas in conjunction with a finite-element boundary-integral code. Index Terms-Microstrip antennas. I. INTRODUCTION A NTENNA design involves the selection of the physical antenna parameters to achieve optimal gain, pattern performance, VSWR, bandwidth, and so on, subject to specified constraints. Over the past ten years, sophisticated computer codes have been developed for antenna analysis [1]-[3] based on a variety of popular methods. By and large, these codes have not been extended to include design capabilities primarily because of their complexity and nonlinearity with respect to the physical properties of the antenna (material constants, dimensions, feed location, and type, etc.). Some design algorithms have been proposed but these are applicable to specialized antenna shapes and do not address the general antenna optimization problem [4]. Recently, genetic algorithms (GA's) have been examined for array design and absorber optimization [5]-[7]. However, GA's, although robust, require large number of function evaluations to complete the optimization study. Also, GA's are more suitable for discrete variable problems. In contrast, antenna simulations rely on complex computationally intensive codes, which generate continuous functions. It may, therefore, be impractical to generate a sufficiently large sample space for carrying out an optimization study using GA's. An alternative optimization algorithm is the sequential quadratic programming (SQP) method, suitable for continuous nonlinear objective functions such as the input impedance, gain, pattern shape, etc. with both equality and inequality constraints. Convergence is typically achieved in a few iterations and, therefore, their interface with rigorous (but expensive) numerical antenna analysis codes is much more practical. SQP and other similar algorithms are routinely used for large structural design problems involving finite-element Manuscript

Designing rectangular patch antenna using the neurospectral method

“…We can put a generalized equation for (3) as (5) Using spherical transformation, followed by a substitution of the form , and using and , a new function is found for the integrand which is given by the expression , and hence the (5) becomes (6) and are respectively the real and imaginary parts of the integrand . Similarly, real and imaginary parts of are and .…”

“…The integrand functions in (6) contain singularities in the path of numerical integration. Therefore, it will be advantageous to find an alternative to numerical integration.…”

“…Cavity model (CA) [1]- [6] based models, for patches of regular shapes on electrically thin substrates, use closed-form formulas, and hence are simple and less accurate. Commercial software [7]- [10] use computer intensive (for user and developer) numerical methods like FEM, full-wave MoM, and FDTD.…”