(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 5 Issue:1, 2011

Accurate CAD Formulation for Feed Reactance of Rectangular Microstrip Antenna with Varying Feed Location and Aspect Ratio A. Bhowmik1 , K. De2 , C. Chandan 3 , S. Roy4 , S. Chattopadhyay5 1

Department of Physics, University of Burdwan,Burdwan-713104, West Bengal, India. 1 [email protected] 2 Cognizant Technology Solutions India Private Ltd , Plot- 27,Kolkata IT Park, SEZ, Bantala, West Bengal, India 2 [email protected] 3 Tata Consultancy Services, Empire Plaza Building, Gandhinagar, Vikhroli, Mumbai, India. 3 [email protected] 4 Department: Design and Development (D&D),Hella India Electronics Pvt. Ltd., Gurgaon, India 4 [email protected] 5 Department of ECE, Siliguri Institute of Technology, P.O: Sukna, Siliguri-734009, Dist: Darjeeling, West Bengal, India 5 [email protected]

Abstract— A simple and efficient CAD formulation is presented to estimate the feed reactance of probe-fed rectangular microstrip patches accurately and efficiently. The formulation is based on Harrington’s formula which can address almost all sorts of variations of aspect ratio of microstrip antenna resulting in a more versatile form. The feed reactance for optimum location is an important issue for designer and it is found to be the function of the width of the patch. Computed results are verified with some simulated data and representative measured data show close agreement amongst them.

insight. Unlike previous theories the present investigation efficiently

W Keywords— Aspect Ratio, Feed Reactance, Microstrip Patch Antenna

 L

I. INTRODUCTION Microstrip patch of rectangular geometry is the well known genere of printed antenna. Feeding of a single microstrip element or arrays through coaxial probe is very popular and common in practice [1]. The reactance at the optimum feed position of the rectangular microstrip patch antenna is a critical issue from the point of view of design of the said antenna for optimum performance. But very few investigation were reported earlier which deals with the feed reactance of the microstrip patch from different aspects. The feed reactance significantly affects the input impedance matching and is sensitive to its position under the patch. Some researchers had developed some CAD formula [2] based on well known Harrington’s Formula [3] which could predict the feed reactance of a microstrip patch at its feed position. Some very recently reported investigation [4] predicts the input impedance behavior of rectangular microstrip patch but in [4] the feed reactance part is omitted. Moreover, the feed reactance of the probe fed microstrip patch severely depends on the width of the patch and is not addressed yet which is presented in this paper. An electromagnetic simulator [5] has been used to study the characteristics theoretically and also to explore the physical

(a) L

r

d

h

(b) Figure 1: Schematic diagram of probe fed rectangular Microstrip patch (a) Top view, (b) Side view

II. THEORETICAL FORMULATION The probe fed rectangular microstrip patch geometry is shown in Fig. 1. The formula for probe inductance derived in [3] ignores the patch boundary since this actually calculates the probe reactance associated with a parallel plate waveguide fed by a co-axial probe and is given by

©IJEECS

(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 5 Issue:1, 2011

Lf 

 kh   4  ln   0.577  2   kd  

(1)

Where is the intrinsic impedance of the medium, k is the wave number, and d is the diameter of the probe. The accurate feed reactance (Xf) of the patch as a function of feed location (ρ) and the aspect ratio (a=W/L) is derived as follows: A probe fed patch is commonly represented by an equivalent circuit like that of a parallel RLC circuit as in fig 2a and at resonance ideally it reduces to a resistance which is called as resonant resistance as in fig 2b. To show the dependence of the feed reactance on aspect ratio (W/L) we have assumed two such equivalent circuits for two different antenna system having different aspect ratio (a = W/L ), a1 and a2 , where a2 > a1.

Where, p   and L

I 01 and I 02 is the current at   0 for

the first and the second system respectively. Hence, Equation (4) and (5) can be written as V B1  L f 1 cos 2 p

dI 01 dt

(8)

V B 2  L f 2 cos 2 p

dI 02 dt

(9)

Now, the resonant resistance also vary with the aspect ratio as obtained from [9] and is given by 2 1 (10) Rr (a )  90 r . 2  r 1 a The current will show a complementary nature with the resistance and hence the current equation can be written as 1  r 1 2 (11) I (a)  a 90  r2 Now, based on equations (8) and (9) we can write the circuit equation as dI (12) V B1  L f 1 cos 2 p 01 dt VB 2  L f 2 (cos 2 p  k1 )

Figure 2: Equivalent circuit of probe fed patch antenna (a) at off resonance, (b) at resonance

dI 02 dt

22

Simulated Computed [Present Theory]

20

VB 2  L f 2

dI 2 (  , a 2 )  V A2 dt

(3)

resistance is zero, we can write dI 1 (  , a1 ) dt

(4)

VB 2  L f 2

dI 2 (  , a 2 ) dt

(5)

Now, due to the complementary nature of current and resonant resistance as indicated in [2], current for a particular patch is proportional to the cosine function of feed location and can be written as (6) I 1 (  , a1 )  I 01 cos 2 p I 2 (  , a 2 )  I 02 cos 2 p

(7)

16 14 12 10 8

Unlike the earlier reported investigation [2], here both feed current and resonant resistance is considered to be the function of both feed location and aspect ratio and is given by I 1 (  , a1 ) and I 2 (  , a 2 ) . But, both current and resonant resistance is constant for a particular antenna. If, both the antennas are fed at centre where resonant

V B1  L f 1

18

Feed Reactance

Two different voltage equation can be written from the above two system dI (  , a1 ) (2) V B1  L f 1 1  V A1 dt

(13)

6 4 0.10

0.15

0.20

0.25

0.30

0.35

0.40

Normalised Feed Location Figure 3: Comparison of simulated and computed feed reactance as a function of feed location for a patch with aspect ratio 0.7 Parameters: L=30 mm, h=1.575 mm, εr=2.33

k1 is the increment in the current due to the increment in the aspect ratio, compared to the 1st antenna with aspect ratio a1. For a particular system k should be constant and the feed location and aspect ratio are independent of each other and hence, k should be an explicit function of aspect ratio only. Hence, introducing the effect of aspect ratio and using equation (11), the equation (13) can be written as 1  r  1 2 dI 02 (14) V  L (cos 2 p  g . a ) B2

f2

90  r2

dt

Where, the constant of proportionality g = 84.4. ©IJEECS

(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 5 Issue:1, 2011 Hence, we can write a generalized equation of the feed reactance as 1  r 1 2 (15) X ( f ,  , a )  X (cos 2 p  g . a )

Simulated Computed [Present Theory]

25

90  r2

f

Feed Reactance

20

15

10

5

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Normalised Feed Location Figure 4: Comparison of simulated and computed feed reactance as a function of feed location for a patch with aspect ratio 1.0 Parameters as in Fig. 3

III. RESULTS The proposed formula of the feed reactance is verified with calculated data for a wide range of aspect ratio (from 0.5 to 1.7), where the patch length is kept constant at 30mm. Some representtative results are shown in Fig. 3-6 individually for each value of aspect ratio. All the results shows very close agreement with the proposed theory for all values of aspect ratio. In order to validate the proposed theory, the results obtained with proposed theory has been compared with the measured results for two different aspect ratios with two different feed location.

100 =3.5 Rmeas Xmeas

28

80

Simulated Computed [Present Theory]

26 24

60

20

Rin & Xin

Feed Reactance

22

18 16

40 20 0

14 12

-20

10 8 0.10

0.15

0.20

0.25

0.30

0.35

-40 2.8

0.40

3.0

3.2

3.4

3.8

(a)

Figure 5: Comparison of simulated and computed feed reactance as a function of feed location for a patch with aspect ratio 1.2 Parameters as in Fig. 3

100

=6mm Rmeas Xmeas

80 32

60

28

Rin & Xin

Simulated Computed [Present Theory]

30

26

Feed Reactance

3.6

f(GHz)

Normalised Feed Location

40 20

24

0

22 20

-20

18

-40

16 14

2.6

2.8

3.0

3.2

3.4

f in GHz

12

(b) 0.10

0.15

0.20

0.25

0.30

0.35

0.40

Normalised Feed Location Figure 6: Comparison of simulated and computed feed reactance as a function of feed location for a patch with aspect ratio 1.5 Parameters as in Fig. 3

Figure 7: Measured resistance and reactance of two probe fed patches (a) with aspect ratio 1.0 (b) with aspect ratio Parameters as in Fig. 3

©IJEECS

1.5

(IJEECS) International Journal of Electrical, Electronics and Computer Systems. Vol: 5 Issue:1, 2011 Table 1 Present formula compared with measurements in [4] L = 30 mm, r = 2.33, Substrate thickness = 1.575 Feed Location W/L (mm)



1.0 1.5

(mm) 3.5 6.0

Feed Reactance Measured Computed (ohm) (ohm) 20.7 22.59

21.9 23

[5]

B. M. Alargani and J. S. Dahele, “Feed Reactance of Rectangular Microstrip Patch Antenna with Probe Feed,” Electron letters, Vol.36, pp.388-390, 2000.

[6]

A. K. Verma and Nasimuddin, “Input Impedance of Rectangular Microstrip Patch Antenna with Iso/Anisopropic SubstrateSuperstrate,” IEEE Microwave and Wireless Components Letters, Vol.11, No. 11, pp.456-458, 2001.

[7]

W. Chen, K. F. Lee and R. Q. Lee, “Input Impedance of Coaxially Fed Rectangular Microstrip Antenna on Electrically Thick Substrate.” Microstrip and Optical Technology letters, Vol.6, No.6, pp 387-390, 1993. R. Garg, P. Bhartia, I. Bhal and A. Ittipiboon, Microstrip Antenna Design Handbook, Boston, MA: Artech House, 2001.

[8]

Figure 7 shows the measured resistance and reactance profile for two individual patches with L= 30 mm. The diameter of the probe for both the cases are fixed at d = 1.3 mm. It is clear from the figure that the feed reactance at resonance for two individual patches are 22.59 Ohm and 20.7 Ohm. The results are summarized in tabular form in the Table-I. It shows excellent mutual agreement amongst proposed theory and measured data. The comparison of the present formulation has been made with earlier available Modified Wolf Model (MWM) [6] on a patch with aspect ratio 1.5 and substrate thickness of 1.59 mm. It is seen that, such patch with, εr = 2.64 and probe diameter d = 1.27 mm produces a feed reactance of 12 Ω at resonance [6] using MWM. Our present theory predicts the feed reactance of 12.224 Ω for the same case which show an excellent agreement of the present formulation with MWM.

[9]

IV. CONCLUSIONS A novel and versatile formulation for the estimation of feed reactance of the probe-fed rectangular microstrip patch antenna is proposed. The feed reactance for particular feed location is an important issue to design an antenna with optimum performance and it is found to be the function of the aspect ratio of the patch. The proposed formulation is verified with simulation results, measured data and earlier theory shows an excellent accuracy in determining feed reactance and can efficiently address all sorts of variation in feed locations and aspect ratios which will be helpful for scientific and research community.

[1]

REFERENCES R. F. Harrington, Time Harmonic Electromagnetic Fields, Newyork: McGraw-Hill, 1961.

[2]

D. Guha, M. Biswas and J. Y. Siddiqui, “Harrington’s Formula Extended to Determine Accurate Feed Reactance of Probe-Fed Microstrip Patches,” IEEE Trans. Antennas and Wireless Propagation, Vol.6, 2007.

[3]

S. Chattopadhyay, M. Biswas, J. Y. Siddiqui and D.Guha, “Rectangular Microstrip with Variable Air Gap and Varying Aspect ratio: Improved formulation and experiments,” Microwave and Optical Technology Letters, Vol.51, No.1, 2009. S. Chattopadhyay, M. Biswas, J. Y. Siddiqui and D. Guha, “Input Impedance of Probe-fed Rectangular Microstrip Antennas with Variable Air Gap and Varying Aspect Ratio,” IET Microwave, Antennas and Propagation, 2009.

[4]

©IJEECS

J. D. Kraus, R. J. Marhefka, A. S. Khan, Antennas for All Application, 3ed, Tata McGraw-Hill Publishing Book Company Limited, 2006.