Indian Journal of Radio & Space Physics Vol. 34, December 2005, pp. 424-430

Analysis of slot-loaded rectangular microstrip patch antenna

Shivnarayan, Shashank Sharma & Babau R Vishvakarma

Department of Electronics Engineering, Institute of Technology, Banaras Hindu University, Varanasi 221 005, India

E-mail: brvish @bhu.ac.in

Received 23 November 2004; revised 17 February 2005: accepted 21 Apri/2005

In the present paper, the analysis of a slot-loaded rectangular microstrip patch antenna using equivalent circuit concept is presented. The slot is taken as a capacitive reactance on the patch. It is found that the resonance frequency decreases with increasing slot width for a given slot length. The decrease in the resonance frequency is in the higher side for longer slot length, whereas it is on the minimum side for the lower slot length. It is found that VSWR remains almost invariant with slot width and slot length. The impedance increases almost linearly with the slot width, but inversely with the slot length.

Keywords: Slot-loaded patch, Rectangular microstrip antenna, Microstrip antenna

PACS No.: 84.40 Ba

IPC Code: HOIQ9/00; HOIQ2!/00; HO!Q23/00

1 Introduction Narrow bandwidth is the major disadvantage of

microstrip antenna in practical applications. For present day wireless communication systems, the required operating bandwidth for antennas 1 is about 7.6% for a global system for mobile communication, 9.5% for a digital communication system and 12.2% for universal mobile telecommunication system. Several bandwidth enhancement or broadbanding techniques are recently employed, such as coplanar directly gap-coupled patches2

, use of a thick air or foam substrate3

, etc. It may be mentioned that bandwidth can also be improved by loadin? of suitable slots along the radiating edges of patch4

' . By embedding suitable slots in the radiating patch6

,

compact and dual band rnicrostrip antennas 7'8 can be

realized. Multiple slots are also used to control the impedance9 of the rnicrostrip antennas. These days, many methods such as FDTD method 10 and Hybrid multi port theor/ 1, etc. are used for the analysis of slot-loaded rnicrostrip antenna.

This paper presents the analysis of a slot-loaded rectangular microstrip antenna (Fig. 1) using equi­valent circuit concept in which patch and slot on the patch are represented in terms of equivalent circuit parameters. In this circuit the slot is taken as a capacitive reactance on the patch to counteract the

inductive reactance of the probe 12• It may be added

that the analysis of slot on the patch has been done by usin~ duality relationship between the dipole and sld . The aim of the work is to study the effect of narrow slot on the performance of the rectangular rnicrostrip antenna such as input impedance, VSWR and return loss.

2 Theoretical considerations Slot on the patch can be analyzed by using the

duality relationship between the dipole and the slot. In

y

patch

X

Coaxial cable

z

Fig. !--Geometry of slot-loaded rectangular microstrip patch antenna

SHIVNARA YAN et al.: SLOT- LOADED RECTANGULAR MICROSTRIP PATCH ANTENNA 425

the present work, the patch is fed by co-axial cable (50 ohm). Since the slot is thin, the voltage can be sinusoidal with zero voltage across the ends of slot. In this case, the voltage across the slot is given as 13

lzl~l ... (1)

where

L = Length of the slot

k 2n p . . f =- = ropagatwn constant m ree space 'A

V,n= Maximum input voltage

I z I= Distance along the length of the slot

The current distribution of long dipole is given by

z<O . .. (2)

where /m is the maximum input current in the dipole

antenna. The total electric field at the far-field point from

h . . b 13 t e antenna 1s g1ven y

Performing integration yields

E = JTJJ me-Jkr r cos[ *cos 8)- cos[* Jj ... (3) 0

2nr sin8

l where

llo = Characteristic impedance of free space

= 120r.: Q

r = Distance of far-field from centre of the dipole

The Poynting vector can be written as

P =_!_IE I·JH J = IER 1

2

since H = Ee r 2 8 <P 2 ' <P

11 o llo

... (4)

Therefore, the total power radiated from the dipole antenna is given by

Wr = J pds

n

= f P, 2rr r 2 sin 8 .d 8

0

= T] 0 / 111 J 2 2 de 2 nrcos(kLcose)-cos(kL)j

4rr 0 sine ... (5)

If the radiation resistance is defined in terms of maximum current, then it may be given as

n rcos( kL cos8)- cos( kL ]12

R = 2WT = ~f 2 2 d8 r 2

/ m 2n 0 sin8

On solving the above equation one gets

R, = 60{C + l" (kL )- Ci (kL)

+~sinkL.[Si (2kL)-2Si (kL)]

+~cos(kL l[ C +I, ( k~} C; (2kL)- 2C; (kL) ])

. .. (6)

where

C = Euler's constant = 0.5772 . . ...

X .

S; (x) = f sm x d.x 0 X

f cosx and C; (x) =- --d.x

X X

The input impedance of the dipole (slot) is given by'3

z, =~=--1 f Ezsink(h - izi)dz /m / Ill -h

... (7)

426 INDIAN I RADIO & SPACE PHYS, DECEMBER 2005

The electric field along the z-direction is given by

Ez =-'-------'- --+---2coskh--( j - kim ) ( e-Jk'i e - Jkl; e - Jk,;, l

4nw£ ~ ~ ~ . . . (8)

where

= Distance of far-field point from the upper end of the slot (dipole)

[ 2 ( )? ]Yz r

2= y +h- z - -

= Distance of far-field point from lower end of the slot (dipole)

[ 2 2 ]Yz r0 = y +z

= Distance of far-field point from centre of the slot (dipole)

Now substituting the value of E, from Eq. (16) in

Eq. (15), one gets the expression for input impedance as

z, = }.30 J( e-Jk'i + e - Jk'i - 2coskh e-Jkl;, l ~ ~ ~ ~

xsin k ( h -l zl) dz ... (9)

The above expression for impedance consists of both real and imaginary parts and can be written as

Z, = R, +}X, ... (10)

where real part IS R, equivalent to the radiation

resistance of dipole (i.e. slot) and imaginary parts X ,

is input reactance of the slot which is given b/ 3

X, =30{2S; (kL)+coskL[2S; (kL)-S; (2kL)

-sin kL[ 2C, (kL)-C, (2kL)- C, (~a:]]]) ... (11)

where, a= Width of the slot On substituting the value of all the parameters in

Eq. (11 ), one gets the va lue of X , with negative sign.

This shows that the reactance of the slot on the patch is capacitive. In this study, the capacitive reactance is

taken parallel to the reactance of the patch for the analysis of the slot-loaded rectangular microstrip patch antenna.

3 Equivalent circuits The slot-loaded rectangular microstrip patch

antenna can be considered as parallel combination of capacitance C1, inductance L 1 and resistance R1 of patch and capacitive reactance of the slot, where R1,

L~. C1 of patch are given b/ 4

... (12)

where h = Thickness of substrate £ e = Effective dielectric constant

£ 0 = Permittivity of free space

z0 = Feed point location along z-axis

(13)

... (14)

The equivalent circuit of slot-loaded rectangular microstrip patch antenna is presented in Fig. 2.

It may be noted that input impedance (Z;11) of the circuit in Fig. 2(a) excluding slot can be expressed as

The above equation can be expressed as

Z;n = R- }X

... (15)

... (16)

where, R and X are the real and imaginary part of Zin

respectively. The input impedance of the slot-loaded patch can

be calculated from Fig. 2 (b) as

z. = _,__( R_-_JX--')'--'-( J_X.::...:..., )

ms R- }X+ }X,

SHIVNARAYAN et al .: SLOT- LOADED RECTANGULAR MICROSTRIP PATCH ANTENNA 427

z __ x_. x_,S:.._+_J_R_. x-'s'­ins - R - j (X - X s )

.. . (17)

Using this value, the reflection coefficient, VSWR and return loss can be computed 15 as

Reflection coefficient (1) = z o - zins

Zo +Zins ... (18)

Where

Z0 =Characteristic impedance of the co-axial feed

(50 ohm)

v swR = s = -1 +_,_I r__,.l t-lrl

(a)

jXs

R

jX

... (19)

(b)

jXs

Fig. 2-Equivalent circuit of slot-loaded rectangular microstrip patch antenna

50

40

30

20

10 . ]

0 .. 2.99

0 ~ -20

w -30 u

t)_· · . • : ·· • .

' · ··o a. . • . ' :a .

• .•. :HJ3• • 3.07 . '· 3.11 3. 5

. :. ; i :i };;., ..... ,:.,,):; :j:: t 'l ''

~ 0 50 w ~ 40 - 30

20

10

0 ·.· .. . . ·. ·· .

:_ .u:· .. •. ....

-1d2r 2.99

-20

-30

30~g· . ~ : :307 . • 3.11 3. 5

· ~ Q Lh.l: .o: .. : :joul"'l'"

and

Return loss= 201ogl 1 I . .. (20)

4 Design parameters For designing the slot-loaded rectangular micro­

strip patch antenna, following parameters were used

Design frequency = 3.0 GHz

Free space wavelength (A) = lOOmm Dielectric constant (R-T Duroid) = 2.2 Loss tangent ( tan o) = 0.0033

The thickness of the substrate (h) . - 0.0159A.

Length of the patch (L) = 0.329A.

Width of the patch (W) = 0.395A.

5 Calculations The input impedance of the slot-loaded patch was

calculated using Eq. (17) for different values of slot width and slot length. The data thus obtain are shown in Fig. 3. The value of VSWR and return Joss were calculated using Eqs (19) and (20) for different slot widths and slot lengths. The resulting data are shown in Figs 4 and 5. The variations of resonance

frequency, VSWR, Re ( Z;11

) and bandwidth with slot

width for different slot lengths are shown in Figs 6, 7, 8 and Table 1, respectively.

50

40

30

20 ' ·

10 · ·~ : o.<:· -0 ~--~,_~· .~b~·· ~·~·~-~·~---.-----1 e.:- . · .. ·•. · . .., ·,.

-1d2. 2.99 3'.h3~ : : .307 . ' . 3.11 3. 5

-20 ° .... g:·: i;·;i; ~; l ;;,1 : . . :: : ·.:;; ;:;q • n;r ~' -30

50 ~----~~~~=:----

40

30

20 . ' · . . .. 10 ·,· •.

o: :•. . ill ' •.

0 ~--~----~~ .•. ~"~:-. -.~.-.---.-----4

3.o3s r ei~k: ... :~;1'1 •·· · · · •1' '' 2.99

-20 -30 L_ __________________________ ~

FREQUENCY , GHz

Fig. }--Variation of input impedance with frequency for different slot width (a= 1.0, 1.4, 1.8, 2 .2, 2.4 mm) for given slot length (L, = 16, 20, 24, 30 mm) [ - R. (2;11) ; ---- - /"' (2;11 ) ; * without slot; • 1.0 mm; e 1.4 mm; o 1.8 mm; o 2.2 mm; o 2.4 mm]

428 INDIAN J RADIO & SPACE PHYS, DECEMBER 2005

2 .95 2.99 3.03 3 0 7 3.11 3 15

~ 1.5 1 .5

{/)

> L~ =30 mm

1 ~--~----~~~----1---~

2.95 2.99 3.03 3 07 3.11 3.15 2.95 2.99 3.03 3.07 3 .11 3 .15

FREQUENCY , GHz

Fig. 4-Variation ofVSWR with frequency for different slot width (a= 1.0, 1.4, 1.8, 2.2, 2.4 mm) for given slot length (L, = 16, 20. 24,

30 mm) [- Re(Z;u); ---------/111(Z;n); * Without slot; • 1.0 mm; e 1.4 mm; o 1.8 mm; 0 2 .2 mm; 0 2.4 mm]

0 0

-1 0 -10

-20 -20

-30 -30

o:l Ls= 16 mm

-o -4 0 -40 {/) 2 95 3 .05 3.1 3.15 2.95 3 3 .05 3.1 3 .1 5 {/)

0 ,..J

~ 0 0

~ f- -10

~ -1 a

- 20

l -~ " -20

- 30 - 30

Ls~ 24 mm -40 -40

2.95 3 3 .05 3 .1 3 .15 2 .95 3 3 .05 3 1 3 15

FREQUENCY , GHz

Fig. 5--Variation ofretum loss with frequency for different slot width (a = 1.0, 1.4, 1.8, 2.2, 2.4 mm) for given slot length (L, = 16, 20. 24, 30 mm) [-- Rc (Z;,) ; --------i111 (Z;n); * Without slot ; • 1.0 mm ; • 1.4 mm ; o 1 .8 mm ; o 2.2 mm ; o 2.4 mm]

6 Results and discussion

The variation of input impedance with different slot widths and slot lengths is shown in Fig. 3. It is observed that the resonance frequency decreases with increasing slot width for a given slot length. A similar result has been also reported by Fan Yang 16

. The

range of frequency variation with slot width for a given slot length is found to be maximum (0.040 GHz) for the lowest slot length (L,=l6 mm), whereas it is minimum (0.016 GHz) for the largest slot length (L,=30 mm). It is important to note that there is a significant change in resonance frequency with the slot on the patch as compared to patch without slot.

SHJVNARA Y AN eta!.: SLOT- LOADED RECTANGULAR MICROSTRIP PATCH ANTENNA 429

N 3.07

:t 0 ->-u 3.05 z r.l.l ;:J 0 r.l.l ~ .,.. 3.03 r.l.l u z -< z 0 3.01 </)

~

2.99

0 0.5 1.5

SLOT WIDTH , nun

2

--+-- 16 mm -tt-18 mm --.--20 mm -+--- 22 mm -<>-- 24 mm -e-- 26 mm

2.5

Fig. 6---Variation of resonance frequency with slot width for different slot length

~ </)

>

1.1 ,----------------------,

0 0.5 1.5

SLOT WIDTH , mm

---+---16 mm -------18 mm --.-20 mm ---.-.- 22 mm --+---24 mm -a- 26 mm ---c- 28 mm --<>-- 30 mm

2 2.5

Fig. ?-Variation of VSWR with slot width for different slot length

52 .2

52

51.8

E 51.6 .c 0

51 .4

£1 r:l. 51 2

-----1 8 mm --.- zo mm --+- 22 mm

51 ---+--- 24 mm -e-- 26 mm

50 8 ---tr-- 28 mm --e-- 30 mm

50.6

0 0.5 1.5 2.5

SLOT WIDTH , mm

Fig. 8-Variation of R" (Z;11 ) with slot width for different slot length

Table !-Variation of bandwidth with slot width having different slot lengths

Length % Bandwidth for slot width (a)

of slot 1.0 mm 1.4 mm 1.8mm 2.2 mm 2.4mm (L,) mm

16 2.96 2 .97 2 .98 2 .998 2.998

18 2.895 2 .97 2 .975 2.985 2.99

20 2.958 2.960 2 .970 2 .975 2 .980

22 2.95 2.96 2 .97 2.97 2 .978

24 2 .95 2.96 2.965 2.97 2.970

26 2 .95 2.96 2.97 2 .97 2.975

28 2 .95 2 .96 2.96 2.97 2 .97

30 2.95 2.96 :? .96 2.97 2.97

Note: In the case of without slot, the % bandwidth is 2.926 for all cases (slot widths)

The variation in the resonance frequency with slot width is attributed to the fact that increasing dimension of the slot modifies the effective values of capacitive reactance, which renders the change in the resonance frequency.

The variation of VSWR with frequency for different slot width and slot length is shown in Fig. 4. It is found that the resonance frequency decreases with increasing slot width for a given slot length. The decrement occurs in resonance frequency, i.e. 1.31 % for L, = 16 mm and 0.59% for L, = (26-30 mm) with the variation of slot width . This is also corroborated from Fig. 6.

It may be noted that the decrease in the resonance frequency is on the higher side for higher slot length, whereas it is on the lower side for the lower slot length. Further, it may be noted that the change in the resonance frequency is minimum (0.016 GHz) for the longest slot length (30 mm), whereas it is maximum (0.040 GHz) for the minimum slot length (16 mm). This is also corroborated from return loss data shown in Fig. 5.

The variation of VSWR with slot width for different slot length is shown in Fig. 7. It is observed that the value of VSWR remains around 1.03 for different slot widths and slot lengths which is slightly higher as compared to the value for patch without slot, i.e. 1.02.

The variation of real part of input impedance with slot width for a given slot length is shown in Fig. 8. It is found that the real part of the input impedance at resonance increases minutely with increasing slot width for all slot lengths considered. However, it may be noted that the values are slightly higher with

430 INDIAN J RADIO & SPACE PHYS, DECEMBER 2005

decreasing slot length. From Fig. 8, it is also observed that the real part of input impedance increases almost linearly with slot width but inversely with the slot length.

7 Conclusions It may be concluded that loading of patch with

narrow slot. affects significantly the resonance frequency, input impedance and bandwidth increase with slot width for a given slot length (Table 1 ).

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