NOS VAMOS A SACAR CERO JAJAJAJAJAJAJAJAJAJA

JONATHAN STIVEN SUAREZ

solucionariosdelibros.blogspot.com

Abstract

En este trabajo se describe el anlisis y sntesis de antenas microstrip(microcinta O microtira) rejilla de matriz en las frecuencias de ondas milimtricas. El principio bsico de funcionamiento se vuelve a visitar a travs de un examen cuidadoso de las distribuciones de corriente, impedancia, y las caractersticas de radiacin de una antena tpica de rejilla de matriz de microcinta. Se lleva a cabo un extenso anlisis de microcinta rejilla-matriz de discos NAS antena de diferentes mallas sobre una variedad de sustratos, que muestra que la eleccin del sustrato tiene una fuerte influencia en el rendimiento de la antena de rejilla de matriz de microcinta. Se obtiene un conjunto de frmulas de forma cerrada para una sntesis inicial de una antena de rejilla-array microstrip. Se da un ejemplo de diseo particular. Una comparacin de los resultados simulados y medidos mostr buen acuerdo, que confirm la validez del anlisis y la sntesis.

Keywords: Millimeter wave; high-gain antenna; planar array antenna; microstrip patch array antenna; microstrip grid array antenna; antenna arrays; microstrip

1 . I ntrod uction

La antena grid array fue propuesto por Kraus en 1964 como una onda que viaja como una antena de polarizacin lineal (no resonante), con el lbulo principal de radiacin en una direccin de fuego-atrasado [1]. La antena GRID-ARRAY fue puesta en prctica en la tecnologa de microtira por Conti. En 1981 como una onda permanente la antena (resonante ) directamente polarizada, con la viga maestra de radiacin en la direccin de costado [2]. Mientras algn xito fue obtenido en el diseo de antenas de serie- rejilla de microtira, el trabajo publicado era de una naturaleza experimental [1], o basado en modelos de red aproximados [2]. Hildebrand y McNamara por lo tanto examinaron el funcionamiento de una antena de serie de rejilla de microtira con una tcnica de momento de equacin integral en 1993, y validaron el razonamiento ms temprano intuitivo usado en la ideacin de este tipo de antena [3]. Palmer y Cloete sugirieron con el diseo de la antena de microcinta rejilla-matriz como elementos de dipolo de microcinta alimentadas por lneas de microcinta en 1997 [4].

La antena grid array ha recibido considerable atencin por Nakano y sus asociados. Desde mediados de la dcada de 1990, se han reportado el diseo y anlisis de varias antenas de rejilla-array [5-16]. Por ejemplo, en 1994 [5], Nakano et al. llev a cabo un anlisis de onda completa de una antena de rejilla de matriz de microcinta con el mtodo de momentos, y revelaron que la radiacin del haz principal disminuye la frecuencia respecto a el avin de la antena. Propusieron una antena de rejilla-matriz de un solo Iayer y una antena de rejilla de matriz de doble Iayer en 1995.

A m b a s a n t e n a s d e r e j i l l a d e m a t r i z f u e r o n e x p u l s a d a s d e s u s t e r m i n a l e s c e n t r a l e s . L a a n t e n a d e r e j i l l a d e m a t r i z d e d o b l e I a y e r p u e d e i r r a d i a r s i m u l t n e a m e n t e v i g a s p o l a r i z a c i n h o r i z o n t a l y v e r t i c a l [ 6 ] . E n 1 9 9 7 , N a k a n o y K a w a n o m i n i a t u r i z a r o n u n a a n t e n a d e r e j i l l a d e m a t r i z d e m e a n d r o s p o r l o s l a d o s l a r g o s d e l a s m a l l a s . U n 6 2 % s e r e d u j o l a a n t e n a g r i d a r r a y l a c u a l m o s t r e l m i s m o a n c h o d e b a n d a d e f r e c u e n c i a p a r a l a g a n a n c i a c o m o l a a n t e n a d e r e j i l l a d e m a t r i z u n - m i n i a t u r i z a d a d e r e f e r e n c i a [ 7 ] . E n 1 9 9 8 , K a w a n o y N a k a n o p r o p o n e n l a a d i c i n d e u n a c a p a d e e l e m e n t o s d e C - c a l c u l a d a s e n u n a a n t e n a d e r e j i l l a - m a t r i z , p a r a c a m b i a r u n a o n d a p o l a r i z a d a l i n e a l m e n t e e n u n a o n d a p o l a r i z a d a c i r c u l a r m e n t e [ 8 ] . E n 1 9 9 9 , s e c o m b i n a r o n d o s a n t e n a s d e r e j i l l a d e m a t r i z e n u n a a n t e n a c r u z a d a m e s h a r r a y , y e n 2 0 0 0 , s e r e f i n a r o n l a a n t e n a d e m a l l a c r u z a d a m a t r i z p a r a i r r a d i a r o n d a s d e d o b l e p o l a r i z a c i n l i n e a l [ 1 0 ] . T a m b i n d e m o s t r a r o n q u e l a a n t e n a d e m a l l a c r u z a d a m a t r i z y u n a c a p a d e e l e m e n t o s d e C - c a l c u l a d a s p u e d e n i r r a d i a r o n d a s p o l a r i z a d a s c i r c u l a r m e n t e d u a l e s . E n 2 0 0 1 , N a k a n o e t a l . e s t u d i a m s a f o n d o l a a n t e n a c r u z a d a d e m a l l a - m a t r i z c o n c u a t r o t e r m i n a l e s d e a l i m e n t a c i n [ l I ] . E l l o s d e m o s t r a r o n q u e l a a n t e n a d e m a l l a c r u z a d a m a t r i z p u e d e i r r a d i a r o n d a s l i n e a l o c i r c u l a r m e n t e p o l a r i z a d a s c o n p l a n e s d e a l i m e n t a c i n a d e c u a d o s . M s r e c i e n t e m e n t e , N a k a n o e t a l . h a n c a m b i a d o s u i n t e r s e n l a m o d i f i c a c i n d e l a f o r m a d e l o s l a d o s c o r t o s d e l a s m a l l a s p a r a l a p o l a r i z a c i n c i r c u l a r o b a r r i d o d e h a z [ 1 5 , 1 6 ] .

Zhang y Sun revivieron microcinta antenas de rejilla de matriz en el desarrollo de la tecnologa de antenas-en-paquete [17]. Ellos demostraron que una antena de rejilla de matriz de microcinta es la antena de eleccin para la radio de 60 GHz, debido a sus ventajas de alta ganancia, amplio ancho de banda, de alimentacin simple,

y fcil de la construccin [1 08 al 20]. Chen y col. desarrollado un algoritmo gentico paralelo para optimizar el diseo de antenas de microcinta gridarray [2 1, 22].

AIthough la antena grid array microstrip tiene las ventajas que se seal anteriormente (con ms dada en [23]) amplias aplicaciones, no ha encontrado o recibido suficiente atencin. Un estudio de la literatura muestra que slo se han producido alrededor de 20 artculos publicados en los ltimos 45 aos. La mayora de ellos se han ocupado de microcinta antenas de rejilla de matriz en sustratos de baja permitividad en frecuencias ms bajas [1-16, 21, 22]. Sin embargo, ninguno de ellos proporciona detalles sobre los efectos de la permitividad o el espesor del sustrato sobre el rendimiento de la antena de rejilla de matriz de microcinta, ni frmulas de diseo para diseos apriori.

E n e s t e a r t c u l o s e p r e s e n t a u n e s t u d i o e x h a u s t i v o d e m i c r o c i n t a a n t e n a s d e r e j i l l a d e m a t r i z e n u n a v a r i e d a d d e s u s t r a t o s e n o n d a s m i l i m t r i c a s ( o n d a s m i l i m t r i c a s ) f r e c u e n c i a s e n t o r n o a 6 0 G H z . E n a l t a s f r e c u e n c i a s , u n a p e q u e a v a r i a c i n e n u n a d i m e n s i n d e m a l l a s e c o n v i e r t e e n u n f a c t o r d e s t r u c t i v o p a r a l a s i n c r o n i z a c i n d e f a s e . E l r e n d i m i e n t o s a t i s f a c t o r i o d e a n t e n a s m i c r o c i n t a d e r e j i l l a d e m a t r i z d e p e n d e e n g r a n m e d i d a d e c o r r i e n t e s u p e r f i c i a l s i n c r o n i z a d o : e l d i s e o d e a n t e n a s m i c r o s t r i p g r i d - a r r a y e s m u c h o m s i n v o l u c r a d o s e n l a s f r e c u e n c i a s m i l l i m e t e r w a v e . E l r e s t o d e l d o c u m e n t o e s t o r g a n i z a d o e n l o s s i g u i e n t e s p u n t o s . E l p r i n c i p i o b s i c o d e f u n c i o n a m i e n t o d e l a a n t e n a d e r e j i l l a d e m a t r i z m i c r o s t r i p s e r e v i s a e n l a S e c c i n 2 . U n e x t e n s o a n l i s i s d e m i c r o c i n t a a n t e n a s d e r e j i l l a d e m a t r i z d e d i f e r e n t e s m a l l a s s o b r e u n a v a r i e d a d d e s u s t r a t o s s e l l e v a a c a b o e n l a S e c c i n 3 . U n a s n t e s i s d e u n a a n t e n a d e r e j i l l a d e m a t r i z d e m i c r o c i n t a , y u n a c o m p a r a c i n d e l o s r e s u l t a d o s s i m u l a d o s y m e d i d o s , s e p r e s e n t a n e n l a s e c c i n 4 . P o r l t i m o , s e c o n c l u y e e l d o c u m e n t o e n l a S e c c i n 5 .

2. Revis iti ng the Pri nciple of Operation Una novela de microcinta rejilla de matriz de antena NA se

muestra en la Figura I. El radiador de rejilla - matriz est en la superficie superior de un sustrato con relativa tangente permitividad cI" perdida 8 , longitud a, ancho b, y espesor h. Se alimenta a un nico punto por un pasador de diametro p

h

z

) x J'

"---0 P

0 d

Figure 1 . The configuration of a novel microstrip grid-array antenna proposed by Nakano, who added two more short sides to make an equal number of short sides (radiating elements) in both the x and y directions.

a travs de una abertura de dimetro d en el plano de t ierra sobre la superficie inferior del sustrato. El radiador de rej i l la-matriz se compone de mallas rectangulares los lados largos de las cuales con una longitud I y una anchura w / 'con los lados cortos de la longitud y anchura s ws ' Como seala Kraus, en el funcionamiento de la antena, la adecuada eleccin de la frecuencia, longitudes de t ierra s , y el punto de al imentacin permite que la estructura de rej i l la-array para operar ya sea como un no resonante o una antena resonante. Este documento se concentra en este lt imo tipo, que requiere que aproximadamente I = Ag and s = Ag /2 , donde Ag es la longitud de onda guiada en la frecuencia central de la operacin [8]. La radiacin es esencialmente de corto lados, con los lados largos actuando principalmente como gua o de l neas de transmisin. Esto es debido a la corriente en cada lado corto es, bsicamente, en fase, mientras que cada lado largo soporta una corriente de longitud de onda completa. Con tal distribucin de corriente, la radiacin mxima sera de costado a la matriz. Assurne que la antena de rej i l la de matriz de la novela de microcinta se hace sobre un sustrato con un IC '= 4,5, bronceado 8 = 0.002, a = 25 mm, b = 25 mm, y h = 0.254 mm, con dimensiones de malla de 1 mm = 2,84, W / = 0. 1 mm, s = 1,42 mm, y Ws = 0. 1 mm. Deje que el dimetro de la al imentacin-pin sea p = 0. 125 mm y el dimetro de la abertura ser d = 0,25 mm. Hemos simulado el rendimiento con la tridimensional de elementos f initos de onda completa solucionador HFSS de Ansoft . La Figura 2a muestra la impedancia de entrada simulada de la antena como una funcin de la frecuencia. Se observ que la antena exhibi una resonancia en serie a 57 GHz, y una resonancia en paralelo a 60 GHz. La Figura 2b muestra la ISIII s imulada de la antena como una funcin de la frecuencia. Era evidente que la antena estaba mal igual a los 57 GHz, pero que Weil emparejados a 60 GHz con una fuente de 50 n. A 52 GHz, la magnitud de ISl l l era -8 dB, lo que indica una coincidencia aceptable. Fue elegido para examinar el comportamiento de la antena en la condicin no resonante. La f igura 2c muestra la ganancia de cresta real izado Ofthe antena na como una funcin de la frecuencia. Se podra observar que la ganancia mxima de 14 dBi apareci en la resonancia en paralelo de 60 GHz, con un ancho de banda de ganancia de 3 dB de 5 GHz.

Ag is the guided wavelength at the center fre quency of

La Figura 3a muestra la distribucin actual de la antena na en la resonancia en paralelo a los 60 GHz. Fue interesante observar que la corriente en cada lado corto era de hecho en fase, mientras que la corriente en cada lado largo cambiado la fase en su centro para formar una corriente de longitud de onda completa. En consecuencia, era la corriente en el lado corto que contribuy a la radiacin en campo lejano ms dominante que en el lado largo. Los patrones de radiacin en campo lejano en tanto el planos E y H, de la antena NA en la resonancia en paralelo a 60 GHz se muestran en las Figuras 3b y 3c, respectivamente. Como era de esperar, el haz de radiacin principal fue sin duda en la direccin andanada. El nivel de lbulo lateral era bastante bajo. La radiacin fue linealmente polarizada. El componente ms fuerte co-polarizado se debe a la existencia de la misma fase de las corrientes en todo el corto SI des, mientras que el componente de polarizacin cruzada ms dbil era debido a la presencia de antifase pareados actuales sobre todos los lados largos. La transicin de fase de las corrientes en los lados largos representaron los valores nulos en los patrones de polarizacin cruzada. La figura 4a muestra la distribucin actual de la antena en la resonancia en serie a 57 GHz. Tenga en cuenta que la fase de la corriente en corto no fue de la misma logitud en cada lado.

IEEE Antennas and Propagation Magazine. Vol . 53 , No. 6, December 20 1 1 43

a ) 8 0---------------------

. 6 0 o -; 4 0 u 2 0

"'0 0E . - - 2 0...... ::l Q. e 5 0 52 54 56 5 8 6 0 6 2 64 66 6 8 7 0

F req uency (G Hz)

b ) o------------------

-4

CO - 8 "'0 """-"

;: - 1 2 Cl)

- 1 6

'(V\ I \ I

50 52 54 56 5 8 60 62 64 66 68 7 0

Frequency (G Hz)

c) 1 6,--------------------------,

1 2

CO 8 "'0 """-"

e CO

l? 4

o

5 0 5 2 54 56 5 8 6 0 6 2 64 6 6 6 8 7 0

F req uency (G Hz)

x

y Figure 3a. The eurrent distribution at the parallel resonanee, 60 GHz.

2 7 0

24 0

2 1 0

o

-4 0

-6 0 :.

-

-- co cross

1 8 0

3 0

1 5 0

Figure 3b. The E-plane patterns at the parallel resonanee, 60 GHz.

2 7 0

2 1 0

o

-- co cross

30

1 2 0

1 5 0 Figure 2. (a) The input impedanee, (b) the magnitude of 1 8 0 Sl l , and (e) the peak realized gain as funetions of fre- Figure 3e. The H-plane patterns at the parallel resonanee, queney. 60 GHz.

44 IEEE Antennas and Propagation Magazine, Vol . 53 , No. 6, December 20 1 1

lo que indica que no todos los lados cortos podran trabajar simultneamente elementos radiantes como eficaces, lo que resulta en una menor ganancia en la Figura 2c. Adems, una corriente de oposicin de fase slida se poda detectar cerca del punto de alimentacin, que era otra razn para la menor ganancia en la resonancia en serie. La corriente tambin tendi a apuntar hacia afuera de la antena, que conduce a los patrones de radiacin de campo lejano que se muestran en las figuras 4b y 4c. El haz principal de radiacin en el plano H se desplaz ligeramente de la direccin de costado, y la radiacin polarizada cruzada no deseada se ha mejorado en gran medida por la corriente en fase en el lado largo. La figura 5a muestra la distribucin actual de la antena na en la frecuencia no resonante de 52 GHz. Se observ que una gran parte de las rejillas no proporcionan radiacin efectiva para t \ 1e escasez de corrientes superficiales en ellos. Los patrones de la radiacin IR. tanto el planos E y H de la antena, como se muestra en las figuras 5b y 5c, se escudri 52 GHz. La pureza de polarizacin se degrad.

Esta nueva visita confirm el principio bsico de funcionamiento de la antena de rejilla de matriz microstrip. La radiacin se controla por la geometra de rejilla. La frecuencia de resonancia depende de las dimensiones de malla. Las caractersticas de resonancia de la estructura de toda la matriz de determinar la respuesta de frecuencia general. Ms importante an, la revisita ha revelado que la microcinta rejilla-matriz se comporta mejor en la resonancia en paralelo que en la resonancia en serie, que es un hallazgo til para el modelado de circuito de la antena en la antena de circuito de co-diseo de una radio.

3. AnalysisLa teora de arreglos simples [1], la lnea de transmisin y

el mtodo de parmetros S [2], el mtodo de los momentos [3, 5, 13], como Weil como diferencias finitas dominio del tiempo Mtodo [10, 11] tiene sido empleado para analizar microcinta antenas de rejilla de matriz en sustratos de baja permitividad en frecuencias ms bajas. En esta seccin, se presenta un amplio anlisis de antenas microstrip gridarray sobre una variedad de sustratos en las frecuencias de ondas milimtricas, en torno a 60 GHz, utilizando HFSS. Se analizaron Microcinta antenas de rejilla de matriz con cuatro, nueve y 16 mallas. La antena de rejilla de matriz de microcinta con nueve mallas, que se muestra en la Figura I, tiene 16 lados cortos (o 16 elementos radiantes). Las antenas microstrip rejilla de matriz con cuatro y 16 mallas tienen nueve y 25 elementos radiantes, respectivamente. Los sustratos fueron 0,254 mm (0,0508: io), 0,381 mm (0,0762: Io), y 0,508 mm (0.10 16: io) de espesor, respectivamente, y tena las mismas dimensiones planas: a = b = 25 mm (5: io x 5: io). Las mallas y los planos de tierra eran 0,0 1 de 7 mm de cobre de espesor. Debido permitividades relativos, er 'y tangentes de prdida, o, para la mayora de los sustratos comercializados eran desconocidos a 60 GHz, que asumieron er = 2.2 y fuego = 0,0009 para Rogers 5880, er = 3,66 y fuego = 0,004 para 4350 y Rogers slice fundida, er = 4.5 y fuego = 0,002 para Rogers TMM4, er = 6 y fuego = 0,0023 para Rogers TMM6 y Ferro LTCC A6, er = 9.2 y fuego = 0,0022 para Rogers TMM IO y Kyocera LTCC GL950, y er = 10,2 y fuego = 0,003 para Rogers 32 10, en nuestro anlisis. Tambin hemos arreglado la colocacin de alimentacin como Weil

/x

y Figure 4a. The current distribution at the se ries resonance, 57 GHz.

2 7 0

2 1 0

o

-20

-40\ -60

-- co cross

1 8 0

9 0

1 5 0

Figure 4b. The E-plane patterns at the series resonance, 57 GHz.

2 7 0

2 4 0

2 1 0

o

-20

-40

-60," ;; " ... :.. ... , . . .

-- co cross

1 8 0

3 0

1 2 0

1 50

Figure 4c. The H-plane patterns at the se ries resonance, 57 GHz.

IEEE Antennas and Propagation Magazine, Vol . 53, No. 6, December 20 1 1 45

x

) ' Figure 5a. The current distribution at non-resonance, 52 GHz.

3 0 0

2 7 0

-2 -0 6 0 '" -4 0

-6 0 , 9 0 4 0 . . .' ' . .' 0#

/ 1 2 0

2 1 0

--- c o c r o s s

1 80 5 0

Figure 5b. The E-plane patterns at non-resonance, 52 GHz.

2 7 0

o 33 0 3 0 .< 0 /O

2 1 0

-4 0

-6 0

--- co c r o ss

1 80 5 0

6 0

Figure 5c. The H-plane patterns at non-resonance, 52 GHz.

as the characteristic impedances to be 1 00 n for the long sides and 1 00 n for the short sides of the microstrip grid-array antennas throughout the analysis.

3 . 1 Resonant Freq uency

The resonant frequency is the frequency at wh ich the parallel resonance occurs for the microstrip grid-array antenna. Figure 6 shows the simulated resonant frequency for the three different thicknesses as a function of relative permittivity, with the number of radiating elements as a parameter. As the substrate thickness was taken into account in calculating the effective relative permittivity to design the microstrip grid-array antenna, it could be noted that the resonant frequency changed slightly with the substrate thickness or with the number of radiating elements. For instance, the resonant frequency changed within 5% for most cases with a fixed relative permittivity as the substrate thickness varied from 0.254 mm, 0.3 8 1 mm, and 0.508 mm, or the number of radiating elements, n, varied among nine, 1 6, and 25 . It was furthernoted that the resonant frequency generally decreased with an increase in relative permittivity.

3.2 I m pedance Bandwidth

The impedance bandwidth of a microstrip grid-array anten na is typically from 6% to 1 2% for I SI d - 1 0 dB [2] .Figure 7 shows the simulated impedance bandwidth for the three different thicknesses as a function of the relative permittivity, with the number of radiating elements as a parameter. As with all microstrip structures, the substrate thickness and relative permittivity have a strong inftuence on the impedance bandwidth . Generally, a thicker substrate with a lower relative permittivity offers a microstrip grid-array antenna with a wider impedance bandwidth . Taking the microstrip grid-array antenna with nine radiating elements on the substrate of cr = 2.2 and h = 0. 1 0 1 6-10 as an example, it achieved a 36% impedance bandwidth . Similarly to other resonant array antennas, the impedance bandwidth of the microstrip grid-array antenna depends on the number of radiating elements . S imply stated, for a given substrate size and controlled by the gain-bandwidth relationship, the more radiating elements there are, the narrower is the impedance bandwidth.

3.3 Half-Power Beamwidth

The half-power beamwidth of a microstrip grid-array antenna can be wider or narrower, depending mainly on the number of radiating elements. Figure 8 shows the simulated half-power beamwidth ac ross the main radiation lobe in the E plane for the three different thicknesses as a function of the relative permittivity, with the number of radiating elements as a parameter. The half-power beamwidth in the H plane was very similar. As expected, the half-power beamwidth decreased

46 IEEE Antennas and Propagation Magazine, Vol . 53 , No. 6, December 20 1 1

N 64 I

62 >-0 c Q) 60 :::J 0-Q) 58 --

+J c cu 56 c 0 Cf) Q)

0::::

---N

I 66 (.9 ---

>. 64 c Q) 62 :::J 0- 60

--+J c 58 cu c 0 56 CI) Q)

0::

- . - n=9 -.- n= 1 6 -A- n=25

t::::::::. .

. . --.

-. .\-.

2 4 6 8 1 0 R e l at i ve perm itt i v ity

. / ..............

Aj--

. -.

2 4 6

- .- n=9 -.- n= 1 6 -A- n=25

-A

8 1 0 Relati ve perm itt ivi ty

-. - n=9

.l._. -.- n = 1 6 -.- n =25

,. A--./

2 4 6 8 1 0 Rel at ive perm itt ivi ty

Figure 6. The resonant frequency as a function of the relative permittivity: (a) h = 0.254 mm, (b) h = 0.3 8 1 mm, and (c) h = 0.508 mm.

5 0 '--"

..c +J 4 "'0

"'0 c 3 cu

..c Q) 0 2 c cu

"'0 Q) 1 Q. E

---

'Cf2. 1 6 '--"

..c 1 4 +J "'0 1 2 1 0 8

..c 6 Q) 4 c

/ .------- ./. /

2 4 6 8

- . - n=9 -.- n = 1 6 -A- n=25

\

1 0 R e l at i ve perm itt i v i ty

. /\ / . cu 2 "'0 .. O +---- E 2 4 6 8 1 0

R e l at i ve permitt i vity

40 35 ..c 30 25 "'0 c 20 cu

..c 1 5 Q) 1 0 c cu 5 "'0 Q) 0 a... E 2 4 8 1 0 6

Rel at ive perm itt ivi ty Figure 7. The impedance bandwidth as a function of the relative permittivity: (a) h = 0.254 mm, (b) h = 0.3 8 1 mm, and (c) h = 0.508 mm.

IEEE Antennas and Propagation Magazine, Vol . 53, No. 6, December 20 1 1 47

---Q) 70 r--------------- 0> Q)

o 60 -..c 50 . 40 co 30 L- 20 o

a.. ..!. co

I ---Q)

2 4 6 8 1 0 Re lat ive perm itt i v ity

1 20 0> --------------------r=== Q) 8- 1 00

..c ..... 80 "'0 . E 60 co Q) .c 40 L-Q) 20 0

a.. ..!. co

I ...-Q) Q) L-0> 90 Q)

o 80 --- 70 60 E 50 m 40 .c Q) 30

2

4 6 8 1 0 R e l at ive perm itt iv ity

. -. 20 o -,---,---.---.---,,- a.. ..!. co

I

2 4 6 8 1 0 Re lat ive perm itt iv ity

Figure 8. The half-power bearnwidth as a function of the relative perrnittivity: (a) h = 0.254 rnrn, (b) h = 0.3 8 1 rnrn, and (c) h = 0.508 rnrn.

with the number of radiating elements. The half-power beamwidth is sensitive to the substrate 's relative permittivity, but is not sensitive to the substrate 's thickness. The higher is the substrate 's relative permittivity, the wider is the half-power beamwidth, due to the excitation of a stronger surface wave.

3.4 Gai n

A microstrip grid-array antenna is a high-gain anten na [2, 4, 23] . Figure 9 shows the simulated gain in the broadside direction for the three different thicknesses as a function of relative permittivity, with the number of radiating elements as a parameter. Note that the gain decreased with relative permittivity or thickness, but increased with the number of radiating elements. The gain increment with the number of radiating elements will be limited by the attenuation of the microstrip lines that form the array. The gain decrement due to a higher permittivity or a thicker substrate can mainly be attributed to the excitation of a stronger surface wave. The larger attenuation of the microstrip l ines due to a higher permittivity and more feeding loss for a thicker substrate also reduce the gain. Furthermore, control over the phase synchronization for more radiating elements on a thicker substrate of a higher permiuivity becomes more difficult for a higher gain .

3.5 Gain Bandwidth

In addition to the impedance bandwidth, a number of bandwidths can be defined under the radiation-pattern characteristics ( i .e . , pattern shape, sidelobe level, gain, cross polarization, etc . ) . It was found that the most stringent bandwidth criterion is seen to be the gain bandwidth [2] . Figure 10 shows the simulated gain bandwidth for the three different thicknesses as a function of relative permittivity, with the number of radiating elements as a parameter. Note that the gain bandwidth of the microstrip grid-array anten na decreased with the number of the radiating elements, which was simi lar to other resonant array antennas . The gain bandwidth is sensitive to the substrate 's thickness. The thicker the substrate is, the wider is the gain bandwidth .

4. Synthesis

The synthesis of microstrip grid-array antennas has been attempted [ I , 2 , 4] ; however, no direct synthesis method or design procedure has been developed. In this section, we describe the synthesis and outline the design steps required to implement a microstrip grid-array antenna.

In synthesizing the microstrip grid-array anten na to satisfy specific performance requirements, the choice of the substrate must first be made, to know the relative permittivity Er ' the loss tangent, 0 , and thickness, h. The mesh lengths, l and s, necessary for the microstrip grid-array antenna to operate at the required resonant frequency, 10 ' can then be calculated as

48 IEEE Antennas and Propagation Magazine, Vol . 53 , No. 6, December 20 1 1

20

1 8

_ 1 6 00 -c 1 4 --c co 1 2

C) 1 0

8

1 8 1 6

:-=- 1 4 00 "'0 1 2 --c 1 0 co

C) 8 6

1 6 1 4

1 2 00 1 0 C co 8

C) 6 4

2

2

2

. -. . ----. ----------.

--........... . .

-. . -.

4 6 8 Relat ive permitt ivity

.-------.

""-.

:: 4 6 8

Re lat ive pe rm itt i vity

.---.

.

4 6 8 Rel at ive perm itt ivi ty

1 0

1 0

1 0

Figure 9. The realized peak gain as a function of the relative permittivity: (a) h = 0.254 mm, (b) h = 0.3 8 1 mm, and (c) h = 0.508 mm.

20 ..-... 1 8 0 -- 1 6 ..c .... "'0 1 4 . "'0 1 2 c 1 0 rn ..Q c 8 .-.-. . rn 6 -. .-.

( 1 )

and

(2)

for phase synchronization, where c is the velocity of light in free space and ceff is the substrate 's effective permittivity.

The choices of the mesh widths, w/ and ws ' are more involved. These are govemed by the impedance, transmission, and radiation properties. As previously stated, the long sides act mainly as transmission lines. The currents on them generate the undesired cross-polarized radiation. Hence, the width, w/ ' should be narrower to reduce this. A narrower width, w/ ' implies a higher characteristic impedance, as the characteristic impedance is approximately inversely proportional to the width, Wt . A narrower width, w/ ' also causes higher transmission loss. Because the transmission loss increases rapidly when the characteristic impedance is above 250 n [24] , the width, w/ , can be chosen to satisfy

Zo/ ( w/ ) 250 n, (3 )

where Zo/ represents the characteristic impedance of the long sides.

The short sides act as both radiating elements and transmission lines. The currents on them produce the desired copolarized radiation. The currents can be uniformly distributed, or tapered by varying the width, ws ' To find the proper width, Ws ' the radiation resistance of a short side was evaluated. Figure 1 1 shows the simulated radiation resistance at the parallel resonance, 60 GHz, for the three different thicknesses and the same loss tangent, tan 8 = 0.002 , as a function of the width, Ws ' with the relative permittivity as a parameter. Generally, the radiation resistance noticeably decreased with the width for Ws < 0.3 mm, but varied slowly as a function of the width for Ws > 0.3 mm. The radiation resistance was higher for a lower relative permittivity, and was lower for a thicker substrate. The radiation resistance varied from 1 00 n to 850 n. The radiation resistance can be considered to be the loads to the transmission l ines of both the long and short sides. The application of matching condition at the input terminal to the source yields the required width, Ws

Based on the formula for the radiation resistance of a re sonant half-wavelength microstrip line fed at one end [25] and simulated data, we obtained a formula to calculate the radiation resistance of a short side by curve fitting. It is expressed as

(4)

where ZOs represents the characteristic impedance of the short side, and

I = ( hJ { 1 .3 - 4/(3Cr ) + 0.53/ c; -[ 0.08856 - 0.08856/cr + 0.03795/ c; J ( Ws J -[ 0.2487 1 4 - 0.37307 1/cr + 0. 1 59887/ C; J (ljCeff )}

(5)

with the empirical factor

= -0. 1 0283 + O. 76642h

+ 1 .96385ws - 5 .63524hws + 5 . 54382h2ws (6)

- 2.23237w; + 1 4.30744hw; - 1 7 .3777h2w;

for 0.0375 h/ 0.0625 ,

= [-0. 1 0283 + O. 76642h -[ 1 6397 1 - 1 4 .30744h + 1 7 .3 777 h2 - 6.09502e0.008 ) w, 1 ( 1 .06527 + 0.00644cr - 0 .0 1 467C; ) (7)

for 0.0625 h/ 0.0875 , and

= [-0. 1 0283 + 0.76642h

+ [ 0.59266 + 0.6338 1 w, + 6.05902eO.0-;:". -6 1 .28545w,eO.

o:.:04 )w, 1 (2 .5 1 875 - 0.5 1 72cr + 0.02859C; ) (8)

for 0.0875 h/ 0. 1 2 .

It must be stressed that Equation (5) was derived from asymptotic expansions that not only makes it simple to calculate the radiation power integral, but also lends insight into the dependence of the radiation resistance upon the line width and substrate permittivity [25] . Nevertheless, some loss in accuracy was encountered, and this was overcome by introducing the empirical factor.

Next, the substrate 's length, a, and width, b, can be determined from the number of meshes required by the gain. The gain in dBi for the microstrip grid array can be estimated as

where

50 IEEE Antennas and Propagation Magazine, Vol . 53 , No. 6, December 20 1 1

E 700 ..c 0 --Q) 600 c co ...... 500 Cf) Cf) Q)

c 400 0 ...... co "'0 co

0:::

-E

..c o 800 --Q) c 600 co ...... Cf) Cf) Q) 400 c 0 ...... co 200 "'0 co

0:::

-E o 800

--Q) 600 c co ...... Cf)

400 Cf) Q)

c 200 0 ...... co "'0 co

0:::

- . - " = 2 . 2 - e - " = 3 . 7 , , - A - ,, = 4 . 5 - .., ,, =6 . 0 , ,

0 . 1 0 . 2 0 . 3 0 .4 0 . 5 0 . 6 Width w (mm)

s

-/ -\, __ -_._-_",_=_2_. 2_-_e_-_",_=_3 ._7

-1 - . - " = 4 . 5 - .., - ,, = 6 . 0 , ,

-.............. --------. --------e __ __ e _____ .------- .

_____ . __ ... __ . -A

0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 Wi dth w ( mm)

s

-

-------

- . - " = 2 . 2 - e - " =3 . 7 , , - . - " =4 . 5 - y - " =6 . 0 , , --------. ---------------

--. --e _. --.-. --.-.-.-.

0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 Width w (mm) s

Figure 1 1 . The radiation resistance as a function of the width of the short side: (a) h = 0.254 mm, (b) h = 0.3 8 1 mm, and (c) h = 0.508 mm.

jg1 (n ) = 2 1 6 - 0.52n + 0. ln2 g2 ( n ) = - 1 43 .2 - 1 . l 3n - 0.058n2 g3 (n ) = 30.3 + 0. 74n

for 0.0375 ::;; hj ::;; 0.0625 , j g1 (n ) = -505 + n .62n - 2.3 1n2 g2 (n ) = 1 33 . 57 - 26.52n + 0.83n2 g3 (n ) = 1 7 .43 + l . 77n - 0.03 8n2

for 0.0625 ::;; hj ::;; 0.0875 , and j g1 (n ) = -362 + 22n - 0.59n2 g2 (n ) = 1 4 1 - I On + 0.24n2 g3 (n ) = 9 + 1 .46n - 0.024n2

for 0.0875 ::;; hj ::;; 0. 1 2 .

( 1 0)

( 1 1 )

( 1 2)

The gain of a microstrip grid-array antenna is increased by 3 dBi when the number of radiating elements is doubled. However, this does not imply that the gain can be increased arbitrarily with an increased number of radiating elements, in practice. According to our experiments, the upper limit for a probe-fed millimeter-wave microstrip grid-array anten na with only one layer of radiating elements on a substrate of size 3 x 3 , with a relative permittivity ranging from 2 .2 to 1 0 and a thickness ranging from 0. 1 mm to 0.6 mm, i s not higher than 25 dBi .

Finally, the feeding point must be located, typically at the joint of the long and short sides near the middle of the antenna. The diameter, p, of the feeding pin and the diameter, d, of the aperture on the ground plane should be consistent with the feeding cable or connector.

In the following, the actual design procedure is dem onstrated for an example of a microstrip grid-array antenna designed to operate at 60 GHz, with a maximum gain of :2: 1 3 .5 dBi , and an impedance bandwidth on GHz [26-32] . It is shown that the formulae apply weil at 60 GHz. In addition, we have also tested the formulae when designing microstrip grid-array antennas at 24 GHz, and they have proven to be effective.

The Ferro LTCC A6-S ceramic type was chosen to be the substrate, wh ich had a relative permittivity of 5 .9 and a loss tangent of O.002. The substrate was 0 .385 mm ( 0 .077 ) thick to avoid the excitation of the TE1 mode surface wave. For the sake of low cost and easy fabrication, the width and thickness of the meshes were kept uniform at 0. 1 5 mm and 0.0 1 mm, respectively. Though fine tuning of the widths of the short and long sides, one can design a microstrip grid-array antenna for better performance. This is usually undertaken with an optimization tool, and is quite time consuming. The meshes were made of gold. At 60 GHz, the substrate 's effective

IEEE Antennas and Propagation Magazine. Vol . 53 , No. 6, December 20 1 1 5 1

penmttlVlty was &ejJ = 4.3 , and the guided wavelength was Ag = 2 .42 mm. The mesh lengths were I = 2 .5 mm Ag and s = 1 .365 mm Ag /2 . The characteristic impedances for the long and short sides of the mesh were equal : Zo/ = ZOs = 1 02 Q; the widths were w, = Ws = 0. 1 5 mm. The radiation resistance of a short side was Rr = 250 Q.

Given the specified gain value of 1 3 .5 dBi, the required number of meshes was found to be at least 1 4, which led to an estimation of the length and width of the substrate as a = 1 1 .5 mm and b = 5 mm, respectively. Considering the requirement for singulation in LTCC, we enlarged the length to a = 1 3 . 5 mm and the width to b = 8 mm. The diameter of the feed pin was p = 0. 1 5 mm, and the diameter of the aperture on the ground plane was d = 0.3 mm. Figure 1 2 shows a photo ofthe fabricated microstrip grid-array antenna.

Figure 1 3 shows the simulated results with the measured values for the microstrip grid-array antenna. It was evident from the figure that the measured 1 0 dB impedance bandwidth was 8 .7 GHz, from 56.3 GHz to 65 GHz, wh ich covered the whole band of 57-64 GHz. F igure 1 4 compares the simulated with the measured radiation patterns of the microstrip grid-

Figure 12. A photo of the 60-GHz microstrip grid-array antenna in LTCC.

0 -5

- 1 0 --. - 1 5 fl) "0 --- -20 (f) -25

-30 -35 56 58 60

-- Measured S imu lated

62 64 Freq uency (G Hz)

Figure 13. The simulated and measured I SI I I as a function of frequency.

o 33

300 - 1 5 -30

270 -45 -30

240 -- M e a s u red S i m u l ated

2 1 0 1 50 1 80

Figure 14a. The co-polar E simulated and measured radiation patterns.

o 330

/ 300 - 1 5

I

270 240

"

-30 },.. -45 f -30 .;J

-- M e a s u red " S i m u l ated

2 1 0 ------------'----....---- 1 50 1 80

60

90

1 20

Figure 14b. The cross-polar E simulated and measured radiation patterns.

300 -30

270 -45 -30

240 -- M ea s u red 1 20 S i m u l ated

2 1 0 1 50 1 80

Figure 14c. The co-polar H simulated and measured radiation patterns.

52 IEEE Antennas and Propagation Magazine, Vol . 53 , No. 6, December 20 1 1

3 0 0

2 7 0

0 3 3 0 3 0

0

- 1 5

- 3 0

-30

-- M e a s u red S i m u l ated

1 50 1 80

9 0

Figure 14d. The cross-polar H simulated and measured radiation patterns.

array antenna. They revealed that both the E- and H-plane patterns had the main radiation beam in the broadside direction, with small cross-polarization radiation components . Note that the measured and simulated co-polar patterns at 60 GHz agreed very weil .

5. Conclusion

This paper described a most comprehensive study of the microstrip grid-array antenna for the first time. It was found in revisiting the basic principle of operation that the microstrip grid array performs better at the parallel resonance than at the series resonanee. This is a useful result for circuit modeIing of the antenna in the antenna-circuit co-design of a radio. An extensive analysis was presented, with an emphasis on the effeets of the substrate and the number of radiating elements . It was shown that the substrate has a strong inftuence on the performance of the microstrip grid-array antenna. A thin substrate at mil limeter-wave frequencies provides adequate gain, bandwidth, and cross-polarization quality. As the substrate becomes thieker, more surface-wave modes can propagate, and ean carry more power. They are diffracted from the substrate 's edges, possibly causing undesirable effects on sidelobe levels, polarization, or main-beam shape [33] . It was also shown that the microstrip grid-array antenna follows a gain-bandwidth relationship: the more radiating elements there are, the narrower is the impedanee bandwidth, and the higher is the gain. A set of c1osed-form formulas was obtained for the initial synthesis, and the design steps were developed. A design example was given, and the measured results demonstrated the validity ofthe analysis and synthesis.

6. Acknowledgment

The authors would like to acknowledge Dr. M. Sun for her contribution.

7. References I . 1. D. Kraus, "A Backward Angle-Fire Array Antenna," IEEE Transactions on Antennas and Propagation, AP-12, I , January 1 964, pp. 48-50.

2 . R. Conti, 1. Toth, T. Dowling, and 1. Weiss, "The Wire-Grid Microstrip Antenna," IEEE Transactions on Antennas and Propagation, AP-29, I , January 1 98 1 , pp. 1 57- 1 66 .

3 . L. T . Hildebrand and D. A. McNamara, "Experimental Verification of Integral Equation Analysis of Etched Wire-Grid Antenna Arrays," IEEE International Symposium on Antennas and Propagation, June 28-July 2, 1 993, pp. 1 494- 1 497.

4. K. D . Palmer and J . H . Cloete, "Synthesis of the Microstrip Wire Grid Array," 1 0th International Conference on Antennas and Propagation, April 1 4- 1 7 , 1 997, pp. 1 1 4- 1 1 8 .

5 . H . Nakano, I . Oshima, H . Mimaki, 1 . Yamuchi, and K . Hirose, "Numerical Analysis of a Grid Array Antenna," International Conferenee on Communieations Systems, November 1 4- 1 8 , 1 994, pp. 700-704.

6 . H. Nakano, I. Oshima, H. Mimaki, K. Hirose, and 1. Yamauchi "Center-Fed Grid Array Antennas," IEEE International Symposium on Antennas and Propagation, June 1 8-23 , 1 995, pp. 20 1 0-20 1 3 .

7 . H . Nakano and T. Kawano, "Grid Array Antennas," IEEE International Symposium on Antennas and Propagation, July 1 3 - 1 8 , 1 997, pp. 236-239.

8 . T. Kawano and H . Nakano, "Grid Array Antenna with C-Figured E lements," IEEE International Symposium on Antennas and Propagation, June 2 1 -26, 1 998, pp. 1 1 54- 1 1 57 .

9 . T . Kawano and H . Nakano, "Cross-Mesh Array Antennas for Dual LP and CP Waves," IEEE International Symposium on Antennas and Propagation, July 1 1 - 1 6, 1 999, pp. 2748-275 1 .

1 0. T. Kawano and H . Nakano, "Dual-Polarized Cross-Mesh Array Antennas," IEEE International Symposium on Antennas and Propagation, July 1 6-2 1 , 2000, pp. 522-525.

1 1 . H . Nakano, T. Kawano, and 1 . Yamauehi, "A Cross-Mesh Array Antenna," 1 1 th International Conference on Antennas and Propagation, April 1 7-20, 200 1 , pp. 327-330.

1 2 . H . Nakano, T. Kawano, H . Mimaki, and 1 . Yamauehi, "Analysis of a Printed Grid Array Antenna by a Fast MoM Calculation Technique," 1 1 th International Conference on Antennas and Propagation, April 1 7-20, 200 1 , pp. 302-305 .

1 3 . H . Nakano, T . Kawano, H . Mimaki, and 1 . Yamauchi, "A Fast MoM CaIculation Technique Using Sinusoidal Basis and Testing Funetions for a Wire on a Dielectric Substrate and Its Application to Meander Loop and Grid Array Antennas," IEEE Transactions on Antennas and Propagation, AP-53, 1 0, Oetober 2005 , pp. 3300-3307.

IEEE Antennas and Propagation Magazine, Vol . 53 , No. 6, Deeember 20 1 1 53

14 . H. Nakano, H. Osada, and J. Yamauchi, "Strip-Type Grid Array Antenna with a Two-Layer Rear-Space Structure," 7th International Symposium on Antennas, Propagation and EM Theory, October 26-29, 2006, pp. 327-330.

1 5 . H . Nakano, H, Osada, H . Mimaki, Y. Iitsaka, and J . Yamauchi, "A Modified Grid Array Antenna Radiating a Circularly Polarized Wave," International Symposium on Microwave, Antennas, Propagation and EMC Technologies for Wireless Communications, August 1 4- 1 7, 2007, pp. 4527-4530 .

1 6 . Y. Iitsuka, J. Yamauchi, and H. Nakano, "Grid Array Antenna Composed of V-Shaped and Rhombic Elements for Beam Scanning," IEEE International Symposium on Antennas and Propagation, June 1 -5 , 2009, pp. I -4.

1 7 . Y. P. Zhang and M. Sun, "Grid Array Antennas and an Integration Structure," PCT filed on 1 2 December 2008.

1 8 . M. Sun and Y. P. Zhang, "Design and Integration of60-GHz Grid Array Antenna in Chip Package," Asia-Pacific Microwave Conference, December 1 8-20, 2008, pp. 1 627- 1 630.

1 9 . Y. P. Zhang and M. Sun, "An Overview of Recent Antenna Array Designs for Highly-Integrated 60-GHz Radios," European Conference on Antennas and Propagation, March 23-27, 2009, pp. 3783-3786.

20. M. Sun, Y. P. Zhang, Y. X. Guo, K. M. Chua, and L. L. Wai, "Integration of Grid Array Antenna in Chip Package for Highly Integrated 60-GHz Radios," IEEE Antennas and Wireless Propagation Letters, 8, December 2009, pp. 1 364- 1 366.

2 1 . X. Chen, K. Chen, and K. Huang, "A Microstrip Grid Array Antenna Optimized by a Parallel Genetic Algorithm," Microwave and Optical Technology Letters, 50, 1 1 , November 2008, pp. 2976-2978.

22. X. Chen, G. S . Wang, and K. Huang, "A Novel Wideband and Compact Microstrip Grid Array Antenna," IEEE Transactions on Antennas and Propagation, AP-58, 2, February 20 1 0, pp. 596-599.

23 . J . D. Kraus, "Backward Angle Traveling Wave Wire Mesh Antenna Array," US Patent 3 209 688, 1 966.

24. R. E . Collin, "Transmission Lines and Waveguides," in Foundationsfor Microwave Engineering, Second Edition, New York, McGraw-Hil l , 1 992.

25. A . E . Gera, "The Radiation Resistance of a Microstrip Element," IEEE Transactions on Antennas and Propagation, AP-38, 4, April 1 990, pp. 568-570.

26. Y. P. Zhang, M. Sun, and L. H . Guo, "On-Chip Antennas for 60-GHz Radios in Si l icon Technology," IEEE Transactions on Electron Devices, 52, 7, July 2005, pp. 1 664- 1 668.

27 . Y. P. Zhang, "Antenna-in-Package (AiP) Technology for Modem Radio Systems," 2nd IEEE International Workshop on Antenna Technology, March 6-8, 2006, pp. 37-40.

28. Y. P. Zhang, M. Sun, K. M. Chua, L . L. Wai, D. Liu, and B. Gaucher, "Antenna-in-Package in LTCC for 60-GHz Radio," 3rd IEEE international Workshop on Antenna Technology, March 2 1 -23 , 2007, pp.279-282.

29. Y. P. Zhang, M. Sun, K. M. Chua, L . L . Wai, and D. Liu, "Integration of Slot Antenna in LTCC Package for 60-GHz Radios," Electronics Letters, 44, 5, March 2008, pp. 330-33 1 .

30 . M . Sun, Y. P. Zhang, K. M . Chua, L . L. Wai, D. Liu, and B . Gaucher, "Integration of Yagi Antenna in LTCC Package for Differential 60-GHz Radio," IEEE Transactions on Antennas Propagation, AP-56, 8, August 2008, pp. 2780-2783 .

3 1 . Y. P. Zhang and D. Liu , "Antenna-on-Chip and Antennain-Package Solutions to Mil l imeter-Wave Devices for Wireless Communication," IEEE Transactions on Antennas and Propagation, AP-57, 1 0, October 2009, pp. 2830-284 1 .

32 . Y. P. Zhang, M . Sun, K. M . Chua, L . L. Wai, and D . Liu, "Antenna-in-Package Design for Wirebond Interconnection to Highly-Integrated 60-GHz Radios," IEEE Transactions on Antennas and Propagation, AP-57, 1 0, October 2009, pp. 2842-2852.

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I ntrod ucing the Featu re Article Authors

Ring Zhang was born in 1 982 in Taiyuan, China. He received his BE from the Civil Aviation University of China, Tianj in, China, in 2004, and his ME from Shanxi University, Taiyuan, China in 2008, both in Electrical and Electronic Engineering. He is currently working toward the PhD in the School of Electrical and Electronic Engineering at Nanyang Technological University, Singapore. His research interests include design and optimization of RF oscillators and lownoise amplifiers, design and optimization of microstrip array antennas, and antenna-in-package for wireless communication.

54 IEEE Antennas and Propagation Magazine, Vol. 53, No. 6, December 20 I l

Yue Ping Zhang received a BE and ME from Taiyuan Polytechnic Institute and Shanxi Mining Institute of Taiyuan University of Technology, Shanxi, China, in 1 982 and 1 987, respectively. He received a PhD from the Chinese University of Hong Kong, Hong Kong, in 1 995, all in Electronic Engineering.

From 1 982 to 1 984, he worked at Shanxi Electronic Industry Bureau. From 1 990 to 1 992, he worked at the University of Liverpool, Liverpool, UK, and from 1 996 to 1 997, he worked at City University of Hong Kong. From 1 987 to 1 990, he taught at Shanxi Mining Institute, and from 1 997 to 1 998, he taught at the University of Hong Kong. He was promoted to a full Professor at Taiyuan University of Technology in 1 996. He is now an Associate Professor with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore . He has broad interests in radio science and technology. He has delivered scores of invited papers/ keynote addresses at international scientific conferences.

Prof. Zhang received the Sino-British Technical Collaboration Award in 1 990 for his contribution to the advancement of subsurface radio science and technology. He received the Best Paper Award from the Second IEEE International Symposium on Communication Systems, Networks and Digital Signal Processing, July 1 8-20, 2000, Bournemouth, UK, and the Best Paper Prize from the Third IEEE International Workshop on Antenna Technology, March 2 1 -23, 2007, Cambridge, UK. He was awarded a William Mong Visiting Fellowship from the University of Hong Kong in 2005 . He was a Guest Editor of the International Journal 0/ RF and Microwave Computer-A ided Engineering, and an Associate Editor of the International Journal 0/ Microwave Science and Technology. He serves as an Editor of the ETRI Journal, and an Associate Editor of the International Journal 0/ Electromagnetic Waves and Applications. He also serves on the editorial boards of a large number of journals, including IEEE Transactions on Microwave Theory and Techniques and IEEE Microwave and Wireless Components Letters . f,

IEEE Antennas and Propagation Magazine, Vol . 53 , No. 6, December 20 1 1 55