Numerical calculations are made to determine the

Wideband Complex Dipole Antenna

optimum antenna dimensions required in creating the

Design for Reference Measurements in the Human

equal-ripple reflection coefficient response as shown in

Body from Radio-Frequencies in the

figure.1.

5-6GHz Band

Equal-Ripple Reflection Coefficient

Daniel R. Brooks, Stuart Nicol, Jacek Wojcik,

APREL Laboratories

ABSTRACT ­ Finite Difference Time Domain (FDTD)

techniques were employed to design a complex half-

wavelength dipole antenna model with a characteristic

equal-ripple reflection coefficient across a frequency

band. We will show how the Chebychev polynomial

matching method discussed by Collin [1] Saad [2] and

Oltman [3] has been implemented to increase the

operational bandwidth of a dipole antenna design. This

design method created an optimum wideband antenna

used in the near-field of a phantom shell filled with a

biological tissue simulation fluid figure 7. This setup

can be used to determine the effects of peak and

average Specific Absorption Rate (SAR) for system

validation  or  for  reference  measurements  and

calculations. Numerical evaluations have been validated

figure.1

using experimental techniques, which involve electrical

measurements, and SAR assessments using the ALSAS-

10U, while the dipole is coupled to a dielectric which

The number of sections in the design determines the

simulates the human body (simulation fluid) figure 7

number of times the reflection coefficient ρm reaches the

(Universal Phantom Model with dipole) at the

maximum value, within the passband. The tolerance of

frequencies under consideration. Numerically and

ρm is fixed, and the angle θm gives rise to the fractional

experimentally derived peak and average SAR values

bandwidth obtained from the relation described in (3).

have not been included in this paper.

Chebychev Polynomial Matching Method

∆θ

4θ

∆f

(3)

=

=2-    m

π 2

π

f0

The phase and amplitude of the antenna feedpoint

reflection coefficient and impedance characteristics may

be compared under different operating configurations to

verify the response of our dipole model. The equal-

A wide fractional bandwidth, Faraone [4], can be

ripple characteristic is obtained by making the reflection

realized with rigorous control of the dipole antenna

coefficient  behave  according  to  a  Chebychev

geometry. Numerical optimization is used to locate and

polynomial as shown in (1).

then by adjusting the geometry, correctly position the

upper and lower reactive zero θz resonant points. The

optimum match is achieved when the reactive zeros θz

Z  A - Z0 TN (secθm cosθ )

(1)

Γ = e- jNθ

align with points of minimum return loss or reflection

Z  A + Z0   TN (secθm )

coefficient figure 10. With the electrical characteristics

attributed to the feed point of the antenna located close

In the passband the maximum value of ΤΝ ( secθm cosθ)

to the presence of the phantom that is filled with

is unity ΤΝ ( secθm cosθ)⎥ θ =θ m = 1, when θ = θm the

biological tissue simulation fluid.

maximum allowable coefficient ρm occurs at the edges

of the passband as shown in (2).

Z  A - Z0

1

(2)

ρm =

Z  A + Z0 TN (secθm )