Microwave Ring Circuits and Related Structures phần 9 pdf

CHAPTER ELEVEN

Ring Antennas and Frequency￾Selective Surfaces

297

Microwave Ring Circuits and Related Structures, Second Edition,

by Kai Chang and Lung-Hwa Hsieh

ISBN 0-471-44474-X Copyright © 2004 John Wiley & Sons, Inc.

11.1 INTRODUCTION

The ring antenna has been used in many wireless systems. The ring resonator

is constructed as a resonant antenna by increasing the width of the microstrip

[1–4]. As shown in Figure 11.1, a coaxial feed with the center conductor

extended to the ring can be used to feed the antenna. The ring antenna has

been rigorously analyzed using Galerkin’s method [5, 6]. It was concluded that

the TM12 mode is the best mode for antenna applications, whereas TM11 mode

is best for resonator applications.Another rigorous analysis of probe-feed ring

antenna was introduced in [7]. In [7], a numerical model based on a full-wave

spectral-domain method of moment is used to model the connection between

the probe feed and ring antenna.

The slot ring antenna is a dual microstrip ring antenna. It has a wider imped￾ance bandwidth than the microstrip antenna. Therefore, the bandwidth of the

slot antenna is greater than that of the microstrip antenna [8–10]. By intro￾ducing some asymmetry to the slot antenna, a circular polarization (CP) radi￾ation can be obtained.The slot ring antenna in the ground plane of a microstrip

transmission line can be readily made into a corporate-fed array by imple￾menting microstrip dividers.

Active antennas have received great attention because they offer savings

in size, weight, and cost over conventional designs. These advantages make

them desirable for possible application in microwave systems such as wireless

communications, collision warning radars, vehicle identification transceiver,

self-mixing Doppler radar for speed measurement, and microwave identifica￾tion systems [11, 12].

Frequency-selective surfaces (FSSs) using circular or rectangular rings have

been used as the spatial bandpass or bandstop filters. This chapter will briefly

discuss these applications. Also, a reflectarray using ring resonators will be

described in this chapter.

11.2 RING ANTENNA CIRCUIT MODEL

The annular ring antenna shown in Figure 11.1 can be modeled by radial trans￾mission lines terminated by radiating apertures [13, 14]. The antenna is con￾structed on a substrate of thickness h and relative dielectric constant er. The

inside radius is a, the outside radius is b, and the feed point radius is c. This

model will allow the calculation of the impedance seen from an input at point

c. The first step in obtaining the model is to find the E and H fields supported

by the annular ring.

11.2.1 Approximations and Fields

The antenna is constructed on a substrate of thickness h, which is very small

compared to the wavelength (l). The feed is assumed to support only a z￾298 RING ANTENNAS AND FREQUENCY-SELECTIVE SURFACES

FIGURE 11.1 The annular ring antenna configuration.

directed current with no variation in the z direction (d/dz = 0). This current

excitation will produce transverse magnetic (TM) to z-fields that satisfy the

following equations in the (r, f, z) coordinate system [15]:

(11.1)

(11.2)

(11.3)

where

(11.4)

fn(f) is a linear combination of cos(nf) and sin(nf), An and Bn are arbitrary

constants, Jn is the nth-order Bessel function, and Yn is the nth-order Neumann

function.

The equations for Ez(r) and Hf(r), without the f dependence, are

(11.5)

(11.6)

where Jn

¢ (kr) is the derivative of the nth-order Bessel function and Yn

¢ (kr) is

the derivative of the nth-order Neumann function with respect to the entire

argument kr.

These fields are used to define modal voltages and currents. The modal

voltage is simply defined as Ez(r). The modal current is -rHf(r) or rHf(r) for

power propagating in the r or -r direction, respectively. This results in the fol￾lowing expressions for the admittance at any point r:

(11.7)

Y (11.8) H

E

c z

r r r

r r f ( ) = - ( )

( ) , >

Y

H

E

c z

r r r

r r f ( ) = ( )

( ) , <

H jk

f r AJ k BY k nn n n wm

( ) =- ¢ [ ] ( ) r r + ¢( ) 0

E AJ k BY k z nn n n ( ) r rr = ( ) + ( )

y

we r rf

w mee

w

m

e

= ( ) () ( ) + ( )

=

=

=

=

j

k A J k BY k f

k

j

nn n n n

r

2

0 0

frequency in radians per second

permeability of free space

permittivity of free space

= –1

0

0

Hf

d

dr = - Y

Hr r

d

df = 1 Y

E k

j z =

2

we

Y

RING ANTENNA CIRCUIT MODEL 299