Antennas: from Theory to Practice 6 Antennas: from Theory to Practice 6. Computer-Aided Antenna Design and Analysis Yi HUANG Department of Electrical Engineering & Electronics The University of Liverpool Liverpool L69 3GJ Email: Yi.Huang@liv.ac.uk This is a general rule, but it may need modification for certain situation.

Objectives of This Chapter To give a brief review of antenna software development To introduce the basic theory behind computer simulation tools and To demonstrate how to use industrial standard software to analyse and design antennas

Antenna design is a complex issue. 6.1 Introduction Antenna design is a complex issue. Analytical solutions can only be found for simple antennas Computer based methods have been introduced and many good computational tools are available, for example: NEC: numerical electromagnetic code HFSS: high frequency structure simulator CST Microwave Studio IE3D

6.2 Computational Electromagnetics Classification:

Method of Moment (MoM) z 2l y for receiving case Let’s take a dipole as an example. The source can either be an excitation at the feed from a transmission line or a plane wave The boundary conditions are: on the surface the total electric field must be zero except in the feed gap, i.e. 2l 2d y for receiving case

Because: On the surface of the antenna: b = 2p/l We therefore need to solve the following Pocklington integral equation

Using the Method of Moment, the 1st step is to approximate the unknown current by a series of known expansion/ basis functions Fn: Then choose a set of weighting/testing functions Wm(z) and integrate: For m= 1 to M, the equations can be written in matrix form as

If we choose pulse functions as the basis functions and the Derac d functions as the weighting functions, that is we enforce the integral equation at N points on the axis of the antenna, this process is called point-matching: z z I(z) IN In I1 N 1

Key issues: Selection of the basis and weighting functions Complexity, accuracy and convergence

Other characteristics of the antenna can be obtained using current distribution: Input impedance For a half-wavelength dipole, it is about 73 , which is linked to the diameter. Radiated field (hence the radiation pattern):

Examples: current distribution and radiation pattern

It may be implemented in four steps: FEM Finite Element Method (FEM) was originally developed for structural analysis. Particularly suitable for problems involving irregular boundaries and non-homogenous material properties. It may be implemented in four steps: Discretisation of the solution region into elements (usually triangular, called “nodes”) and each element has approximated with a constant value; Generation of equations for the fields or potentials at each element; Integration or assembly of all elements; Solution of the resulting system of equations.

An example: circular patch antenna

FDTD Finite Difference Time Domain (FDTD) method was introduced by Yee in 1966 It imposes a rectangular grid over the region of interest and solves a discretized version of field equations at the nodes of the grid. The solution points for the electric field offset from the magnetic–field solution points. Since the dynamic problems involve time-changing electric and magnetic fields, Maxwell’s equations are solved at each grid point in an iterative manner.

To ensure that abrupt field changes do not occur between spatial sample locations: the biggest of x, y and z no more than /20

An example: pulse propagation along a monopole Absorbing boundary conditions are important. Computational resource could be a problem for some cases

Another example: horn antenna pulse propagation Other parameters can also be calculated using the known calculated fields and currents.

Numerical Method Comparison

High-Frequency Methods Particularly suitable for electrically large structures which could be a problem for numerical methods (memory, runtime or convergence) Field based methods Geometrical optics (GO) or ray optics. Geometrical theory of diffraction (GTD) Uniform theory of diffraction (UTD) Current based methods Physical optics (PO) or wave optics, building on Huygens’s principle.

6.3 Examples of CAD Design and Analysis There are many EM simulation tools: some are simple and cheap whilst the others are complex and expensive. Here we are going to introduce two software packages: one simple and cheap, the other is complex and expensive. For wire type antennas, we are going to use EZNEC software (<$100), which is based on MoM. For more complicated antennas, we are going to use Ansoft’s HFSS (>$10000), which is based on the finite element method.

EZNEC A powerful but very easy-to-use programme for modelling and analyzing various (especially wire-type) antennas in their intended operating environment. It was developed by Roy Lewallen (W7EL). The major features are that The antenna is constructed by straight wire conductors, thus a surface structure is approximated with wire meshes. The input of the antenna is done via a spreadsheet-like entry, the start and end coordinates are required, so is the number of segments. The simulation set-up is very straightforward and many short-cuts are built in

The computation is very fast and efficient. 2D current distribution and 2D and 3D plots of radiation patterns are available; other information such as the gain, input impedance, VSWR, 3dB beamwidth, front-to-back ratio, takeoff angle, and sidelobe characteristics are also readily available. If required, transmission lines, a realistic ground, and loads to simulate loading coils, traps, or similar components can be selected and added to the simulation. Antenna descriptions and pattern plots are easily saved and recalled for future analysis.

Design example 14 MHz (20 m band) is one of the amateur radio (ham radio) bands widely used around the world. Assume that you are going to make a dipole as a transceiver antenna which will be placed in your garden. Use EZNEC to design the antenna and analyse the effects of the ground plane on the antenna input impedance, gain and radiation pattern. Horizontal polarisation is assumed.

Solution: 14 MHz has a wavelength of 21.4 m. To make a resonant and efficient dipole, the dipole length L should be close to l/2, which is affected by the ground. Now let’s use EZNEC Demo V.50 (it is free!) to aid the analysis and design. The simulation should follow these steps: define the antenna view the input antenna run the simulation check the results

User interface (Src: Source; FF: far field; NF: near field)

Wires input interface Source input interface

Antenna view showing controls and current distribution

VSWR and impedance of a dipole in free space

VSWR and impedance of a dipole 3 m above a perfect ground See changes?

Radiation pattern and gain of a dipole in free space

Radiation pattern and gain of the dipole above a ground

Radiation pattern for a dipole placed 9 m above a real ground

Another design example Two quarter-wave monopoles are separated by a quarter-wavelength. They are placed above a perfect ground plane and fed with the same amplitude and variable phase. Analyse how the phase difference in the feed affects the array performance and compare with theoretical results.

Solution: For convenience, we choose the frequency to be 300 MHz and assume the array is made of perfect conducting wire with a diameter of 2 mm. Each quarter-wave monopole is divided into 8 segments (< l/20). There are now two sources placed at the ends of the monopoles.

Phase difference 0 = 0

Phase difference 0 = 90 degrees

Array factor: Thus

EZNEC for more complicated structures

HFSS High frequency structure simulator (HFSS) utilizes a 3D full-wave FEM to compute the circuit and field behaviours of high-frequency and high-speed components. The major features include: Suitable for almost all structures and configurations (wire- or non-wire-types); All antenna results are given, and some animated results may also be shown; Easy to optimise the design (using its parametric function or Optimetrics software); Good accuracy.

Design example Planar Inverted F Antennas (PIFAs) are popular in mobile phones. The main reasons are that a). they are of low profile; b). their radiation patterns are near omni-directional; c). they are installed above the phone circuitry, “re-using” the space within the phone to some degree; d). they exhibit a low specific absorption rate (SAR). Design a dual-band PIFA for a GSM mobile handset. It should cover 880 – 960 MHz (E-GSM 900) and 1710 – 1880 MHz (DCS 1800 or GSM 1800). The dimensions should be small enough for a standard mobile handset.

Design idea: The two centre frequencies are 920 MHz and 1755 MHz. We should create two current paths which are about ¼ of the wavelengths.

Detailed dimensions of the design

HFSS simulation to validate and tune the design

Convergence plot

S11 in dB plot

3D radiation pattern

Meshes and current distribution

The antenna was made

and measured