Open access peer-reviewed chapter

Recent Computer-Aided Design Techniques for Rectangular Microstrip Antenna

By Sudipta Chattopadhyay and Subhradeep Chakraborty

Submitted: April 6th 2016Reviewed: October 14th 2016Published: February 22nd 2017

DOI: 10.5772/66355

Downloaded: 1650

Abstract

In modern microwave systems, rectangular microstrip patch antennas (RMPAs) are probably the most investigated topics among the planar antennas. There are several methods available in literature, for designing and analyzing such antennas, but most of them are very complex and give only approximate results. In this chapter, we have discussed the most accurate and updated computer-aided design (CAD) formulations related to probe-fed RMPA for computing its fundamental input characteristics (resonant frequency and input impedance) and improving radiation characteristics, i.e. gain and polarization purity (the parameter that signifies how much an RMPA is free from spurious modes). These formulations have evolved in the last decades and have been validated against numerous simulations and measurements. The present CAD formulas for resonant frequency and input impedance can accurately address a wide range of RMPA with patch width to patch length ratio (W/L) from 0.5 to 2.0, a substrate having thickness up to 0.23 λg where λg is the guide wavelength and relative permittivity (εr) ranging over 2.2–10.8. The role of a finite air gap on resonant frequency and gain of an RMPA have also been presented. The chapter will be surely useful to antenna designers to achieve a concrete understanding of the RMPA theory.

Keywords

  • rectangular microstrip antenna
  • resonant frequency
  • input impedance
  • gain
  • polarization purity
  • grounded microstrip patch

1. Introduction

‘Microstrip antennas’, the class of antennas which has been capturing the attention of the antenna research community for the last 63 years, starting from the 3rd Symposium on the US Air Force Antenna Research and Development Program, was proposed firstly by Deschamp and Sichak [1] in 1953. In [1], they proposed a microstrip feeding network for a waveguide system which comprised of 300 waveguide horn antennas. But, the ‘microstrip patch’, to which all the researchers associated to the antenna theory are familiar with, was theoretically analyzed by Howell in [2] and applied into practical applications by Munson in [3] for the first time. Still, the credit of the authors of the work [1] was to foster a very much new discipline of antenna engineering, and in addition to this, they highlighted the related performance superiority of this new antenna over the other commercially available conventional antenna. From 1972 onwards, researchers started to understand a microstrip patch in two approaches: (i) treating the patch as a lossy and open resonator cavity [2] and (ii) as an extended section of a microstrip line [3].

In the last four decades, several books [411] and collection of research papers [12, 13] have been published unfolding rigorous analytical and numerical techniques dealing with microstrip antennas. The computational methods like FDTD, FEM and MOM are very much versatile in nature particularly in analyzing irregular-shaped patch geometries with huge various types of substrates, but any of them give neither any physical insights into the radiation mechanism of the antenna nor any closed-form design formulations which are utmost necessary to any practicing antenna engineer, researcher, academician or scientist. In this context, cavity resonator model appears to be more effective than the other available methods to estimate the fundamental input characteristics (i.e. resonant frequency and input impedance) and to improve the crucial radiation characteristics (i.e. gain and polarization purity) for commonly available microstrip antennas of regular geometries with thin substrate. This method not only improvises the design steps of antenna design but also aids in achieving better performance.

In this chapter, the authors have presented comprehensive electromagnetic analyses on the fundamental input characteristics (i.e. resonant frequency and input impedance) and radiation characteristics (i.e. gain and polarization purity) of rectangular microstrip antennas with conventional and suspended geometries in light of the versatile cavity model method and discussed some improved and closed-form computer-aided design (CAD) formulas. Unlike other theories and work, the present CAD formulas can accurately address a wide range of aspect ratio or patch width to patch length ratio (W/L) from 0.5 to 2.0, a substrate having thickness up to 0.23 λg where λg is the guide wavelength and relative permittivity (εr) ranging over 2.2–10.8. (Discuss Novelty) A coaxially fed RMPA with length Land width Won a substrate (εr) above a variable air-gap over the ground plane is shown in Figure 1.

Air gap over the ground plane is shown in Figure 1. The variable air-gap height h1can be decreased to zero to achieve the conventional form. The fringing of the electric fields at the radiating and non-radiating edges of the rectangular patch is taken into account in terms of ΔLand ΔW, respectively. The present CAD formulas were introduced firstly in [14] by Chattopadhyay et al.

Figure 1.

Schematic diagram of a coax-fed rectangular microstrip patch antenna (RMPA).

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2. Input characteristics

2.1. Resonant frequency

After the work of Howell [2], Hammerstad [15] proposed comprehensive CAD formulations on resonance characteristics of an RMPA using the cavity resonator model (CRM) method. Till now, several theoretical analyses employing CRM method [6, 1618], transmission-line method [19, 20], method of moments [21, 22] and integral equation technique [23] are available in literature. But the CAD formulas presented in [6, 15] are found to be the most popular for the design purpose.

Nevertheless, a close inspections into these works show that the formulas available in [6, 15] can provide a reasonably good approximation only when the patches have aspect ratio (W/L) near to 1.5 and the substrate thickness is lower than 0.02 λg, where λg is the guide wavelength at the resonant frequency fr. Also, the computed frvalues using formulas in [6, 15] show errors in comparison with the measurements which can be found in [24, 25]. Those works [24, 25] used around 0.04 λg to 0.23 λg substrate thickness. The use of an air gap in between the substrate and the ground plane has been found in [2634] which helps in achieving tunability of an RMPA and enhancing its impedance bandwidth. Earlier, a cavity model was also discussed in detail in [5, 11]. In this section, authors have emphasized on a better CAD formulation as found in an earlier work of one of the present authors in [14] using the well-known CRM method called quasi-static approach [11] to estimate more accurately the dominant and the higher-order resonances in an RMPA with and without air gap. Here, ΔLand ΔWhave been considered as a function of the aspect ratio. In [14] Chattopadhyay et al. considered an equivalent circular patch with radius a, effective radius aeffand same resonant frequency as that of the RMPA. This helps to establish a relationship among the fringing parameters ΔL, ΔWand aeffby equating the zero-order resonant frequencies of both patches as found in one of the earlier works of Chattopadhyay in [14, 35].

From [3538] we can write

f0,r=c2LεrE2.1

where cis the velocity of light in free space. Following the earlier work of Chattopadhyay in [14, 35], we can assume that both antennas of same resonant frequencies have same circumference. Therefore, we can write

W+L=πaE2.2
L+2L+W+2W=πaeffE2.3

In Eq. (2.3) αis the first zero of the derivative of the Bessel function of order n= 1. Now, aeffis the effective radius of a circular patch due to fringing electric fields as found in [27]:

aeff=a1+qE2.4

where qis the fringing factor calculated from [27] as

q=u+v+uvE2.5

and

u=1+εre-14πa/hE2.6
v=23t×lnp8+πah)+1t-14+2.6ah+2.9haE2.7
t=0.37+0.63εreE2.8
p=1+0.8ah2+0.31ah41+0.9ahE2.9

u, v, tand pall are dummy variables.

εre=εr1+h1h21+εrh1/h2E2.10

where εreis the equivalent permittivity of the two-layer dielectric medium (Figure 1) having a total thickness h= (h1+h2).

Solving (2.1)–(2.4) and from one of the previous works of Chattopadhyay in [14, 35], one can write the following relations:

L=1.7aE2.11
W=1.44aE2.12
L+W=πa1+q-12E2.13

An empirical relation is used to determine ΔWin terms of ΔLfor a wide range of W/Lvalues, 2 >W/L> 0.5 as

W=L1.5-W2LE2.14

and ΔLcan be written as given in one of the previous works of Chattopadhyay in [14, 35]

L=πa1+q-122.5-0.5WLE2.15

Now, using the above Eqs. (2.1)–(2.15) discussed above and as in the previous work of Chattopadhyay in [14, 35], the resonant frequency of an RMPA with a variable air-gap h1is found as

fr,nm=c2εr,effnL+2L2+mW+2W21/2E2.16

where εr,effis the effective relative permittivity of the medium below the patch [14, 27, 35].

εr,eff=4εreεr,dynεre+εr,dyn2E2.17

From Eq. (2.16) we can found the dominant mode of an RMPA is TM10. εreis calculated using (2.10), and εr,dynis the dynamic dielectric constant as defined in [17, 28] and can be written as

εr,dyn=Cdynε=ε0εreCdynε=ε0E2.18
Cdyn=C0,dyn+Ce,dynE2.19

where Cdynis the total dynamic capacitance of the RMPA and suffixes 0and edenote the main and fringing components, respectively. C0,dynand Ce,dynare determined as discussed in one of the previous works of the present authors in [14, 35]:

C0,dyn=γnC0,statE2.20
Ce,dyn=1δCe,statE2.21

The values γnand δare as follows:

γn=1.0forn=0E2.22
=0.3525forn=1E2.23
=0.2865forn=2E2.23
=0.2450forn=3E2.25
δ=1.0forn=0E2.23
=2.0forn0E2.27

where C0,statand Ce,statare the static main and static fringing capacitances of the disc, and these are [35]

C0,stat=ε0εreπa2hE2.24
Ce,stat=C0,statqE2.25

Figure 2 shows the computed as obtained from the previous work of Chattopadhyay in [14, 35] and measured [24] resonant frequencies of an RMPA as a function of substrate thickness h2. The three measured values for thin and thick substrates show close agreement with proposed formulations.

Figure 2.

Resonant frequency of the dominant mode as function of substrate thickness of the RMPA,εr= 2.33,L =11 mm,W= 17 mm,W/L= 1.54 [35].

In [14], Chattopadhyay et al. have also shown the close agreement between the values obtained using MOM and their theory.

Figures 3 and 4 show the computed (from the previous work of Chattopadhyay in [14, 35]), simulated and measured resonant frequencies of an RMPA with W/L= 1.5 having variable air-gap heights.

Figure 3.

Resonant frequency of RMPA versus air-gap height.εr= 2.2, L = 30 mm, W = 45 mm, W/L = 1.5, substrate thickness h2 = 1.575 mm [35].

Figure 4.

Dominant mode resonant frequency of RMPA versus air-gap height.εr= 2.33, L = 30 mm, W = 45 mm, h2 = 1.575 mm [35].

The simulated and measured values ranging from no air gap to an air gap of 4 mm show good agreement with the present formulations. The tunability of the RMPA as a function of the air gap height has also been studied. Table 1 compares the resonant frequencies as computed using the presented formulations (as given in the previous work of Chattopadhyay in [14, 35]) with that of Hammerstad [15], James et al. [6] and Chew and Liu [23] for different sets of RMPAs with W/L≈ 1.5 and for electrical thickness ranging from 0.037 to 0.166 λg. The presented formulations show very close agreement with measured data [24] with an average percentage error of (1.39%) for the present formulations.

Length, L(mm)W/LNormalized thickness (h2d)Measured fr(GHz) [24]Computed fr(GHz) [15]Computed fr(GHz) [6]Computed fr(GHz) [23]Computed fr(GHz) (from the earlier work of one of the present authors in [14, 35])
381.50.0372.312.38 (3.03%)2.30 (0.4%)2.37 (2.6%)2.32 (0.4%)
30.51.490.0472.892.90 (0.3%)2.79 (3.4%)2.90 (0.3%)2.83 (2%)
19.51.510.0684.244.34 (2.35%)4.11 (3.06%)4.32 (1.88%)4.18 (1.4%)
131.50.0945.846.12 (4.79%)5.70 (2.39%)6.07 (3.93%)5.86 (0.3%)
111.540.1106.807.01 (3.08%)6.47 (4.85%)6.90 (1.5%)6.65 (2.2%)
91.550.1257.708.19 (6.36%)7.46 (3.11%)7.87 (2.2%)7.73 (0.38%)
81.500.1418.279.01 (8.94%)8.13 (1.7%)8.39 (1.45%)8.50 (2.7%)
71.500.1489.149.97 (9.01%)8.89 (2.73%)8.69 (4.92%)9.3 (1.75%)
61.500.16610.2511.18 (9.07%)9.82 (4.19%)10.4 (1.46%)
Average error w.r.t measurement [24]5.21%2.87%2.34%1.39%

Table 1.

Comparison of the measured [24] and computed dominant mode resonant frequency of an RMPA.

Parameters: εr= 2.33, h2 = 3.175 mm, for W/L =1.5. Note: here, λd= λg= λ0/√εrand λ0are wavelengths corresponding to measured frequency.


Moreover, in [14] Chattopadhyay et al. showed the versatility of these formulations in accurately predicting the higher-order modes of an RMPA for W/L = 1. In [35], Chattopadhyay has predicted the higher-order modes of an RMPA for W/L = 0.7, 1.2, 1.5, 1.7 extending the work in [14]. One can refer to Table 1 of one of the previous works of Chattopadhyay et al. in [14] for a closer look into the topic. It is seen that the significant higher-order modes of an RMPA are TM01, TM02, TM12, TM20, TM30, TM03, etc. When W/L = 1, TM10 and TM01 become degenerate modes. The separation between resonant frequency of dominant TM10 mode and that of net higher-order mode TM02 is from 2 to 1.25fr,10 for 0.7 < W/L < 2 as discussed in [35] by Chattopadhyay. The effect of TM02 mode on the radiation characteristics of an RMPA is very detrimental [11, 14, 35], and the two newest techniques for mitigating this issue are discussed later in this chapter (see Section 4.2).

2.2. Input impedance

An RMPA can be represented as an equivalent R-L-C parallel resonant circuit in order to find out its input impedance [11]. Near resonance of the dominant mode and its input impedance can be expressed as [39, 40]

Zinfx0=Rr1+QT2f¯-f¯-12+jXf-RrQTf¯-f¯-11+QT2f¯-f¯-12E2.26

where f¯=f/fr, fris the dominant mode resonant frequency and Rris the input resistance at resonance as [8].

Rrcan be expressed as

Rr=4hπλ0μη0QTL+2LW+2Wcos2π0.5L-x0L+2LE2.27

where η0is the intrinsic impedance of free space where η0= 377 Ω, x0is the distance from the centre of the patch and QTis the total quality factor.

QTcan be expressed in terms of the losses due to radiation (Qr), dielectric (Qd) and conductor (Qc) present in the radiating structure as given in an earlier work of one of the present authors in [40]:

QT=1Qr+1Qd+1Qc-1E2.28

In this context, another parameter εr,nis required to calculate Qrand Qdas found in [39]:

εr,n=εreff+12E2.29

Now, Qr, Qdand Qccan be expressed as given in [36, 39], and an earlier work of one of the present authors in [40]:

Qr=π4GrZrE2.30
Qd=πεr-1εr,n27.3εr,n-12εr,n-11tanδE2.31
Qc=hπfμ0σE2.32

where

Gr=W290λ02forW0.35λ0E2.33
=W120λ0-160π2for0.35λ0W2λ0E38
=W120λ0for2λ0<WE39

and

Zr=120πWh+1.393+0.667lnWh+1.444-1εr,nE2.34

The same approach is also valid for circular patches, and a detailed discussion on the resonant frequency and input impedance of a circular patch can be found in [11]. From [11], one can find that the dominant mode of a circular patch is TM11. The immediate higher-order modes are TM21, TM01, TM31, etc. The formulas are found to be very accurate in case of substrate with thin and moderate height.

Cavity model analysis of the resonant frequency and input impedance for a 60°–60°–60° equilateral triangular patch is found in [5]. The dominant mode of a triangular patch is TM10 [5]. The immediate higher-order modes are TM11, TM20, TM21, etc.

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3. Examples

(a)Find out the resonant frequency of an RMPA with length (L) 18.2 mm and width (W) 28 mm, etched on a PTFE substrate of height 1.575 mm with dielectric constant 2.33.

(b)Repeat the problem when 1 mm air gap is introduced between substrate and ground plane.

Solution:

(a) The resonant frequency of the patch can be obtained from Eq. (3.1) as

fr,nm=c2εr,effnL+2L2+mW+2W21/2E3.1

As the dominant mode is TM10, n= 1 and m= 0, and therefore the Eq. (3.1) reduces to

fr,10=c2εr,eff1L+2LE3.2

The expression for effective relative permittivity of the medium below the patch is

εr,eff=4εreεr,dynεre+εr,dyn2E3.3

and

εre=εr1+h1h21+εrh1/h2E3.4

As air gap height h2= 0

εre=εr=2.33E3.5

Fringing factor qis

q=u+v+uvE3.6

where

u=1+εre-14πah=0.147E3.7
t=0.37+0.63εre=1.83E3.8

and

p=1+0.8ah2+0.31ah41+0.9ah=27.86E3.9

Hence,

v=23t×lnp8+πah+1t-14+2.6ah+2.9haE3.10

Therefore,

q=u+v+uv=0.162E51

εr.dyncan be calculated using Eqs. (2.18)–(2.25) and (3.6)–(3.10) as

εr.dyn=1.94

and

εr,eff=2.12.

The fringing length ΔLmay be computed as

L=πa1+q-122.5-0.5WLE3.11

=1.365.

Therefore, the resonant frequency fr,10becomes

fr,10=c2εr,eff1L+2L=4.916GHzE53

(b) Now, if h2= 1 mm,

εre=εr1+h1h21+εrh1/h2=1.56E54

εr.dyn= 1.35

and

εr.eff= 1.43

and

u=1+εre-14πah=0.278E55
t=0.37+0.63εre=1.337E56
p=1+0.8ah2+0.31ah41+0.9ah=9.83E57

Hence,

v=23t×lnp8+πah)+1t-14+2.6ah+2.9ha=0.0253E58

Therefore,

q=u+v+uv=0.310E59

and hence

L=πa1+q-122.5-0.5WL=2.52E60

Therefore, the resonant frequency fr.10becomes

fr,10=c2εr,eff1L+2L=5.37GHzE61

(a) Find out the input resonant resistance at the edge of a square patch with length 30 mm and width 30 mm, etched on a PTFE substrate of height 1.575 mm with dielectric constant 2.33.

(b)Find out the optimum feed position.

Solution:

(a) The input impedance of a patch can be expressed as

Zinfx0=Rr1+QT2f¯-f¯-12+jXf-RrQTf¯-f¯-11+QT2f¯-f¯-12E3.12

where f¯=f/fr, frbeing the dominant mode resonant frequency and Rris the input resistance at resonance at the edge of the patch.

Now, frcan be obtained as done in the earlier example, and it is found to be fr= 3.13 GHz.

Rrcan be expressed as

Rr=4hπλ0μη0QTL+2LW+2Wcos2π0.5L-x0L+2LE3.13

where η0= 377 Ω and x0is the distance from the centre of the patch and QTis the total quality factor, expressed in terms of the losses due to radiation (Qr), dielectric (Qd) and conductor (Qc) present in the radiating structure as

QT=1Qr+1Qd+1Qc-1E3.14

Now,

λ0=cfr=95.84mmE3.15

ΔLcan be obtained as done in the earlier example, and it is ΔL= 1.381 mm.

Now,

W=L1.5-W2L=1.381mmE3.16

Now,

Gr=W290λ02E3.17

=0.001 as W = 30 mm which is smaller than 0.35 λ0.

εr,n=εreff+12=1.165E3.18

and

Zr=120πWh+1.393+0.667lnWh+1.444-1εr,nE3.19

=13.41 Ω.

Qr, Qd, Qcand QTcan be calculated as

Qr=π4GrZr=53.76E3.20
Qd=πεr-1εr,n27.3εr,n-12εr,n-11tanδ=232.19E3.21
Qc=hπfμ0σ=1333.31E3.22
QT=42.27E3.23

Therefore, the resonant resistance at edge (x0= 0.5 L)

Rr=4hπλ0μη0QTL+2LW+2Wcos2π0.5L-x0L+2L=333.43Ω.E74

(b) To obtain the optimum feed point, we need to find the point where input impedance of the patch becomes 50 Ω. From part (a), we get

L+ 2ΔL= 32.762 mm

W+ 2ΔW = 32.762 mm

QT= 42.27

Rr= 33.43 Ω

λg = 95.84 mm

Putting these in Eq. (3.3), we may write

4hπλ0μη0QTL+2LW+2Wcos2π0.5L-x0L+2L=50E3.24

or, (0.5L − x0) = 12.23

or, x0 = 2.77 mm.

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4. Radiation characteristics

4.1. Gain enhancement

Any RMPA has a strong influence of substrate permittivity (εr) on its gain. In general, an RMPA experiences a decrease in gain with the increase of εr. Normally, an RMPA’s gain is around 6 dBi when PTFE (εr= 2.33) is used as substrate. Here, we have discussed the role of air substrate on the gain enhancement issue of a simple RMPA. It is also found in an earlier work of one of the present authors in [41] that the use of air substrate leads to a symmetrical radiation pattern of an RMPA in its two principal planes.

The gain of an RMPA loaded with air substrate is directly related to its effective radiating area Aeff.Therefore, we can simply compare the change of the gain of an RMPA loaded with air substrate to a conventional (reference) RMPA loaded with PTFE (Figure 5) as discussed in an earlier work of one of the present authors in [41]:

ΔGindB=10log10Aeff/λ02airAeff/λ02refE4.1

Figure 5.

Schematic diagram of a rectangular patch using conventional PTFE (εr= 2.33) or air substrate (εr= 1): top and cross-sectional views.

where λ0is the operating wavelength. For a rectangular patch, as shown in Figure 5, its effective radiating area (Aeff) may be calculated as given in an earlier work of one of the present authors in [41]:

Aeff=L+2ΔLW+2ΔWE4.2

where Land Ware the physical length and width of the corresponding patch, respectively. The quantities ΔLand ΔWrepresent the effective increments in respective dimensions caused by the fringing electric fields (discussed in Section 2.1).

Now, the standard formula of gain (G) of any rectangular aperture is (as given in one of the earlier works of the authors in [42])

G=4πAeffλ2=εap4πApλ2E4.3

where Apis the physical aperture, respectively, and εapis the aperture efficiency. Following Eq. (4.3) we can write the expression for gain of an RMPA from our earlier work in [42]

G=4πL+2ΔLW+2ΔWλ2E4.4

It is seen that when air substrate is used in lieu of PTFE substrate, the electric field lines along the patch edges becomes more relaxed or loosely bound resulting in an increase in ΔLand ΔW, and hence Aeffincreases. Therefore, gain increases.

The formulations presented in this section are well validated against simulations and measurements [36, 41]. These formulations are found to be very much accurate for L-Ku band and for wide range of aspect ratios. Figure 6 shows increase in gain when PTFE substrate is replaced by air substrate for W/Lratio 1.5.

Figure 6.

Variation of the gain enhancement between the microstrip patches with air and PTFE substrate for different sets of patches having the most common aspect ratio (W/L= 1.5) forεr= 2.33.

Theoretically computed, simulated and measurement results show very close agreement among themselves.

4.2. Polarization purity

In general, a conventional RMPA radiates in the fundamental TM10 mode along the broadside of the element, and the field is primarily linearly polarized, called co-polarized (CO) radiation. However, some orthogonally polarized, called cross polarized (XP), radiations take place due to weak oscillations of higher-order modes inside an RMPA. The XP radiation becomes considerably prominent for probe-fed designs particularly when the thicknesses as well as the dielectric constant of the substrate increase. Thus, the XP radiation becomes an important issue for investigation for microstrip antenna research. The (XP) fields are more significant in H plane than in E plane as obtained in our earlier work in [45]. Therefore, the polarization purity (CO-XP isolation) deteriorates in H plane (only 9 dB), and the suppression of XP radiation performance of an RMPA to improve its polarization purity is the challenging issue for antenna research community. Lower polarization purity also limits the use of RMPA in different array applications There are several techniques to improve polarization purity of an RMPA such as the use of defected ground structure (DGS) [11], grounding the non-radiating edges of a patch [43, 45] and defected patch surface [46]. A thorough discussion on DGS-integrated RMPAs can be found in [11, 42]. However, DGS-integrated RMPAs always possess high back radiation, and only 15–20 dB of CO-XP isolation in H plane can be obtained from those [11, 42]. The two later techniques can address the limitations of DGS and minimum 25 dB of CO-XP isolation from those, and these are discussed clearly in this section. The two techniques are very simple to understand and very effective to implement over a wide microwave frequency range (L-Ku band).

An RMPA with three pairs of shorting plates placed at the non-radiating edges is shown in Figure 7. If the non-radiating edges are grounded using pairs of thin strips, the EM boundary conditions get altered and result in a significant change in field structure with in the cavity. Hence, the restructuring of field structure within the patch inevitably modifies the radiation properties of the RMPA. Some recent work in [43, 44] show the XP radiations are typically from the non-radiating edges of the RMPA. In fact, the oscillations of electric field beneath the patch in a direction, orthogonal to E plane, produce higher-order orthogonal resonance (higher-order orthogonal modes). The XP radiations are typically due to those higher-order orthogonal modes and the fields of those modes, located near the non-radiating edges of the patch. The electric field vectors for a grounded patch in TMnpmode may be obtained from our earlier work in [45] as

ExcosnπLysinpπWzE4.5a
HycosnπLycospπWzE4.5b
HzcosnπLysinpπWzE4.5c

Figure 7.

Schematic diagram of an RMPA with shorting strips. (a) Top view and (b) side view (LandWare the length and width of the patch,l1andd1are length and width of the shorting plates,εris the dielectric constant of the substrate andpcis the feed position).

where Ex, Hyand Hzare the electric and magnetic field components of the dominant mode. The number of half-wave variations along the length and width of the patch is denoted by nand p, respectively.

The electric surface current over the patch surface can be obtained from our earlier work in [45] as

Js=n̂×HE4.6

The co-sinusoidal variation in Eq. (4.5) shows the variation of Exalong the length (L) of the patch, while the sinusoidal variation shows the variation of Exalong the orthogonal direction. Therefore, any higher-order orthogonal resonance (i.e. for any non-zero value of p) leads to minimum electric field intensity when zapproaches W.In fact, the intensity of the electric fields near the non-radiating edges due to all higher-order orthogonal modes (primarily responsible for XP radiation) is forced to be minimum in order to mitigate the possibility of XP radiation from non-radiating edges due to higher-order orthogonal modes [45]. It is also seen that when the non-radiating edges are grounded with thin metallic strips, the electric fields near the non-radiating edges have least intensity when compared with the electric field intensity at the central region, but the dominant mode radiation characteristics remain unaltered. From the literature it is seen that the XP radiation from RMPA is typically from the non-radiating edges, and those are due to asymmetric field distribution along the length of the patch [43, 45]. This asymmetry in the field distribution is mainly due to the placement of feeding probe and is unavoidable for probe-fed patch. This asymmetry in the field causes asymmetry in the electric surface current (Js) along the patch length (as discussed in our previous work in [45]). For a conventional RMPA, the ycomponent of Jsdoes not become maximum at the centre [45]. This ycomponent of Jsattributes for high XP radiation from RMPA. However, in our earlier work in [45], the use of grounded strips in case of an RMPA shows a change of the field structure beneath the patch as a result of which the electric surface current at non-radiating edge does not follow the conventional profile. Therefore, XP radiations are mitigated keeping CO radiation unaltered.

The use of grounded strip loading in a conventional RMPA not only modifies the radiation property but also regulates the input characteristics of the RMPA [45]. The length (l1) of each thin grounding strip is essentially same as substrate thickness h, and when it is in the order of λ/10, one can write as discussed in our previous work in [45]:

l1=λgr/10E4.7
λgr=λr/εrE4.8
λr=c/frE4.9

where fris dominant mode resonant frequency, λgris the resonant wavelength within dielectric and εris the dielectric constant of substrate material.

The width of the strips (d1) is considered to be very thin. Each grounded strip or short dipole (l1× d1) produces the reactive impedance [45, 47] as

Xs=302Sikl1+coskl12Sikl1-Si2kl1-sinkl12Cikl1-Ci(2kl1-Ci2kd12l1]E4.10

which comes parallel to patch input impedance (Zp). Here, d12is the equivalent circular radius of dipole of width d1. For the dipole of noncircular cross section, d12(as discussed in our previous work in [45])

d12=0.25d1E4.11

Therefore, from [45]

kl1=2πλgλgr10=0.628ffrE4.12

and

2kd12l1=7.85ffrd12εrc2E4.13

The expression for reactive impedance can be written as [45]

Xs=302Si0.628ffr+cos0.628ffr2Si0.628ffr-Si2×0.628ffr-sin0.628ffr2Ci0.628ffr-Ci2×0.628ffr-Ci7.85ffrd12εrc2E4.14

The input impedance of conventional probe-fed RMPA can be written as

Zp=11Rr+jωC+1jωLE4.15

where Rris the resonant resistance of the patch at particular feed position. Cand Lare capacitance and inductance, respectively, and can be obtained from [9]. When this conventional probe-fed RMPA is loaded with short dipoles, the dipole reactance (Xs) will come in parallel to patch, and the resultant input impedance of dipole loaded patch can be written as [45, 47]

Zdp=11Rr+jωC+1jωL+jXsE4.16

Putting the values of Cand Lfrom [9]

Zdp=11Rr+jfQTfrRr-frQTfRr+jXsE4.17

where QTis the total quality factor.

Hence,

ReZdp=1/Rr(1Rr)2+jfQTfrRr-frQTfRr+jXs2E4.18
ImZdp=Xf-fQTfrRr-frQTfRr+jXs(1Rr2+jfQTfrRr-frQTfRr+jXs2E4.19

where Xfis the feed reactance and can be obtained from [36].

From our earlier work in [45], it is observed that when grounded strips are placed along the non-radiating edges, the structure becomes thick dipole loaded (dipole length to diameter ratio ~ 4.2 around resonant frequency), and it prevents the usual sharp variation of input reactance over the operating bandwidth. It is found from our previous work in [45] that the reactance of thick dipole slowly varies with the frequency, and as it is in parallel to patch reactance, the resultant reactance of the proposed patch varies slowly with frequency (Figure 8).

Figure 8.

Variations of imaginary part of input impedance (input reactance) as a function of frequency for conventional and proposed RMPA. (Total quality factorQT= 0.22, resonant resistanceRr= 50 Ω andL= 8 mm,W= 12 mm,h= 1.575 mm,εr= 2.33, feed reactanceXf= 15 Ω). Reproduced with permission of © 2016 FREQUENZ [45].

The formulations presented in this section were validated in case of an RMPA with length L= 8 mm and W= 12 mm designed over Taconic’s TLY-3-0620 PTFE material (εr= 2.33) with thickness h= 1.575 mm [45]. The ground plane dimensions were taken as 80 × 80 mm2.

Three pairs of thin copper strips of thickness 0.1 mm with height of h= l1= 1.575 mm and width d1= 1.5 mm have been placed along the non-radiating edges (Figure 7). Around 25–40 dB of minimum CO-XP isolation in H plane along with input impedance of 1.32 GHz is found from the patch (see Figure 9) [45].

Figure 9.

Simulation and measured reflection coefficient profile for conventional and proposed RMPA and simulated and measured radiation patterns for conventional (f= 10.05 GHz) and proposed RMPA (f= 12.9 GHz) at fundamental resonant mode in H plane. Reproduced with permission of © 2016 FREQUENZ [45].

In E plane, CO-XP isolation is more than 35 dB (Figure 10).

Figure 10.

Comparison of simulated and measured radiation patterns for conventional (f= 10.05 GHz) and proposed RMPA (f= 12.9 GHz) at fundamental resonant mode in E plane. Reproduced with permission of © 2016 FREQUENZ [45].

One can write the field components corresponding to TM02 mode beneath the patch as discussed in our previous work in] (see Figure 11 for coordinates) [46]:

Ex=Ccos2πWzE4.20
Hy=Csin2πWzE4.21

Figure 11.

Schematic diagram of an RMPA with arc-defected patch surface (top view).

Eqs. (4.20 and 4.21) show that at z = 0 and at z = W/2, Exis maximum and is equal to C.

Hence, the null occurs in between these limits, i.e. [46]

Ex=Ccos2πWz=0for0<z<W/2E4.22

From Eq. (4.22) one can write that

2πWz1=mπ2wherem=1,3,5,E4.23

Therefore,

z1=mW4=W4E4.24

Along the middle section of the patch, i.e. when W → 0; , 97% of the maximum field exists (as discussed in our earlier work in [46]) if

Ex=Ccos2πWz=0.97CE4.25

Hence, from our previous work in [46], we can write

2πWz2=cos-10.97=2π25E4.26

Therefore,

z2=W25E4.27

A defect can be incorporated within this region, i.e. from z1to z2. This in fact will perturb the fields corresponding to TM02 mode which is mainly responsible for XP radiation.

The electric surface current (Js) on the patch surface corresponding to TM02 mode can be written as given in our earlier work in [46]:

Js=n̂×H=ax̂×HyaŷE4.28

Therefore,

Js=Csin2πWzaẑE4.29

In case of an RMPA with length L= 8 mm and width W= 12 mm, the value of z1and z2is found to be 3 mm and 0.5 mm [46]. Based on the formulations described here, an arc-shaped defect has been cut on patch (L= 8 mm and W= 12 mm) symmetrically along the non-radiating edges as shown in Figure 11 in our earlier work in [46]. The centre of the arc defect (a) is chosen in such a way that the defect can be cut through the patch corners. Around 25–35 dB, CO-XP isolation is reported from such an RMPA in H plane with such arc-shaped defect over the patch surface in [46]. However, the bandwidth is comparable with that of a conventional RMPA. Therefore, it can be observed that the effect of TM02 mode can be mitigated to a large extent by opting either grounding the non-radiating edges of an RMPA or judicious incorporation of defects over the patch surface. Such types of new antenna structures are surely be utmost useful for scientific and research community for designing low-profile wireless communication devices where polarization purity is required to establish over the whole operating band.

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5. Conclusion

In this chapter, some recent developments in the CAD techniques have been presented lucidly but thoroughly for rectangular microstrip antennas. The presented formulations are very much accurate and are valid for wide range of aspect ratios and substrate thickness compared to other formulations. It is hoped that the work would be helpful for researchers and engineers working in the field of microstrip antennas and will help them to gain an insight into the physics of any RMPA.

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Acknowledgments

Authors would like to express their deep sense of gratitude to Prof. L. Lolit Kumar Singh of Mizoram University, Mizoram; Prof. Gautam Das of Siliguri Institute of Technology, West Bengal; Prof. Debatosh Guha and Dr. Jawad Y. Siddiqui of the Institute of Radio Physics and Electronics, Calcutta University and Prof. B. N. Basu of Sir. J. C. Bose School of Engineering, Mankundu, West Bengal, India, for fruitful discussions during the preparation of the manuscript.

Subhradeep Chakraborty thanks Prof. Santanu Chaudhury, Director, CSIR-CEERI, Pilani; Dr. S. N. Joshi, Ex-Emeritus Scientist; Chirag P. Mistry, Scientist, TWT Group; Dr. Amitavo Roy Choudhury, Senior Scientist, TWT Group; Dr. Sanjay Kumar Ghosh, Principal Scientist and Head of TWT Group and Dr. R. K. Sharma, Principal Scientist and Head of MWT Division, CSIR-CEERI, Pilani, for always encouraging research endeavours and their support.

© 2017 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Sudipta Chattopadhyay and Subhradeep Chakraborty (February 22nd 2017). Recent Computer-Aided Design Techniques for Rectangular Microstrip Antenna, Modern Antenna Systems, Mohammad A. Matin, IntechOpen, DOI: 10.5772/66355. Available from:

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