Wideband Probe-Fed Microstrip Patch Antennas and Modelling Techniques

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CHAPTER 2 Wideband Probe-Fed Microstrip Patch Antennas and Modelling Techniques

INTRODUCTORY REMARKS

 During recent years, much effort has gone into bandwidth enhancement techniques for microstrip antennas in general. As such, there is a great amount of information in the open literature and it covers a very broad range of solutions that have been proposed thus far [1]. The entire spectrum of approaches that have been suggested is too comprehensive to discuss here and therefore the discussion in this chapter will be restricted to techniques that have been applied to enhance the bandwidth of probe-fed microstrip patch antennas in particular. In this chapter, a broad overview will be given in terms of the various techniques that are currently available to enhance the band- width of probe-fed microstrip patch antennas. The performance, advantages and disadvantages of the most practical approaches will also be discussed. With these in mind, the new antenna element that forms the basis of this study, will be presented.
Another field in which there has been a tremendous amount of activity during recent years, is that of computational electromagnetics [15, 16]. These tools are essential for an accurate analysis and design of complex antenna elements and arrays. Although probe-fed microstrip patch antennas are structurally quite simple, an accurate analysis of their various characteristics proves to be rather intricate. This is partly due to the singular and rapidly-varying nature of the current in the vicinity of the probe-to-patch junction and also due to the presence of a multilayered substrate. This chapter will give a brief overview of the methods that are currently available, together with their associated strengths and shortcomings. Once again, with these in mind, an overview of the formulation that was implemented for the purposes of this study, will also be presented.
In this chapter, Section 2.2 gives an overview of wideband probe-fed microstrip antennas, while Section 2.3 presents the new wideband microstrip antenna elements, employing capacitive feed probes. Section 2.4 gives an overview of the modelling techniques that are currently available, while Section 2.5 presents the basic aspects of the theoretical formulation that was implemented for the purposes of this study.

OVERVIEW OF WIDEBAND PROBE-FED MICROSTRIP PATCH ANTENNAS

The impedance bandwidth of microstrip patch antennas is usually much smaller than the pattern bandwidth [17]. This discussion on bandwidth-enhancement techniques will therefore focus on in- put impedance rather than radiation patterns. There are a number of ways in which the impedance bandwidth of probe-fed microstrip patch antennas can be enhanced. According to Pozar [18], the various bandwidth-enhancement techniques can be categorised into three broad approaches: impedance matching; the use of multiple resonances; and the use of lossy materials. For the pur- pose of this overview, it has been decided to rather categorise the different approaches in terms of the antenna structures that are normally used. These include: wideband impedance-matching networks; edge-coupled patches; stacked elements; shaped probes; and finally capacitive cou- pling and slotted patches. In terms of Pozar’s categories, all these approaches can be identified as making use of either impedance matching or multiple resonances. In practice, lossy materials are not frequently used as it limits the radiation efficiency of the antenna. It will therefore not be considered here.

Wideband Impedance-Matching Networks

One of the most direct ways to improve the impedance bandwidth of probe-fed microstrip an- tennas, without altering the antenna element itself, is to use a reactive matching network that compensates for the rapid frequency variations of the input impedance. As shown in Figure 2.1, this can typically be implemented in microstrip form below the ground plane of the antenna ele- ment. The method is not restricted to antenna elements on either thin or a thick substrates, but the thick substrate will of course add some extra bandwidth.
Pues and Van de Capelle [19] implemented the method by modelling the antenna as a simple  resonant circuit. A procedure, similar to the design of a bandpass filter, is then used to synthesise the matching network. With this approach, they have managed to increase the bandwidth from 4.2% to 12% for a voltage standing-wave ratio (VSWR) of 2:1.  Subsequently to that,  An et   al. [20] used the simplified real frequency technique in order to design the matching network for a probe-fed microstrip patch antenna. They have managed to increase the bandwidth of one antenna element from 5.7% to 11.1% for a VSWR of 1.5:1, and that of another from 9.4% to 16.8% for  a VSWR of 2:1. Recently, De Haaij et al. [21] have shown how a parallel resonant circuit can increase the bandwidth from 3.2% to 6.9% for a VSWR of 1.5:1.
The advantages of using impedance-matching networks are that the antenna elements do not get al- tered and that the matching network can be placed behind the antenna’s ground plane. As such, the radiation characteristics of the antenna element stay unchanged, while radiation from the match- ing network is also minimised. The drawback of this method is that the matching network can potentially take up space that is very limited when microstrip feed networks are used to excite the individual elements in an antenna array. Another drawback is that, for single-element antennas, more than one substrate layer is required to support the antenna element and the matching network.

Edge-Coupled Patches

The basic idea behind edge-coupled patches, is to increase the impedance bandwidth of a mi- crostrip patch through the introduction of additional resonant patches. By doing so, a few closely- spaced resonances can be created. Only one of the elements is driven directly. The other patches are coupled through proximity effects. An example of such an arrangement is shown in Figure 2.2.
This approach has been investigated by Wood [22] as well as Kumar and Gupta [23–25]. The parasitic patches can be coupled to either the radiating edges, the non-radiating edges or to both pairs of edges. The approach in [25] uses short transmission lines to couple the parasitic patches directly to the driven patch. With the edge-coupled approach, impedance bandwidths of up to 25.8% have been obtained for a VSWR of 2:1. This was achieved with four parasitic patches coupled to the driven patch.
The advantages of the edge-coupled approach include the fact that the structure is coplanar in nature and that it can be fabricated on a single-layer substrate. However, this approach also has a few drawbacks. Due to the fact that the different patches radiate with different amplitudes and phases at different frequencies, the radiation patterns change significantly over the operating fre- quencies. The enlarged size of the structure can also be a potential handicap in many applications. For example, in phased-array applications, the large separation distances between elements can introduce grating lobes.

Stacked Patches

A very popular technique, which is often used to increase the impedance bandwidth of microstrip patch antennas, is to stack two or more resonant patches on top of each other [2]. As with the edge- coupled resonators, this technique also relies on closely-spaced multiple resonances. However, in this case, the elements take up less surface area due to the fact that they are not arranged in a coplanar configuration. Figure 2.3 shows the geometry of such an antenna element where the bottom patch is driven by a probe and the top patch, which is located on a different substrate layer, is proximity-coupled to the bottom one.
In practice, the patches are usually very close in size so that the generation of two distinct res- onances can be avoided. Different shapes of patches can be used. These commonly include rectangular patches [26, 27], circular patches [26, 28, 29] and annular-ring patches [26, 30]. It has also been shown how a combination of shapes can be used [31, 32]. As far as impedance bandwidth goes, Waterhouse [26] reported a 26% 10 dB return-loss bandwidth for rectangular patches, Mitchell et al. [29] reported a 33% 10 dB return-loss bandwidth for circular patches, while Kokotoff et al. [30] reported a 22% 10 dB return-loss bandwidth for annular-ring patches. These bandwidths were all obtained for two patches stacked on top of each other. It is possible to stack more patches, but the performance may not be much better than with only two patches [2,18]. Instead of aligning the patches vertically, some researchers have also used a horizontal offset be- tween the patches [33]. However, due to the structural asymmetry, these configurations exhibit beam dispersion.
The stacked-patch configuration has a number of advantages over the edge-coupled configuration. Since it does not increase the surface area of the element, it can be used in array configurations without the danger of creating grating lobes. Its radiation patterns and phase centre also remains relatively constant over the operating frequency band. It has a large number of parameters that can be used for optimisation. However, due to this, the design and optimisation process can also be very complex. Another drawback of stacked patches, is that it requires more than one substrate layer to support the patches.

Shaped Probes

As was shown in Chapter 1, a thick substrate can be used to enhance the impedance bandwidth of microstrip patch antennas. However, the input impedance of probe-fed microstrip patch antennas become more inductive as the substrate thickness is increased. In order to offset this inductance, some capacitance is needed in the antenna’s feeding structure. One way to implement such a capacitive feed is to alter the shape of the probe. There are basically two approaches. In one approach, the probe is connected directly to the patch [34, 35], while in the other approach, the probe is not connected to the patch at all [36–39].
The direct feed can be implemented as shown in Figure 2.4(a), where the feeding structure consists of a stepped probe. The horizontal part of the probe couples capacitively to the patch. Chen and Chia [34] reported an impedance bandwidth of 19.5% for a VSWR of 2:1. Another option is to add a stub to one of the radiating edges of the patch and to feed the stub directly with a probe. For such an approach, Chen and Chia [35] reported an impedance bandwidth of 25%, once again for a VSWR of 2:1.
The proximity-coupled probe is implemented as shown in Figure 2.4(b), where the probe is bent into a L-shape. The horizontal part of the probe runs underneath the patch and also couples ca- pacitively to it. This solution has been implemented for a variety of patch shapes. Mak et al. reported an impedance bandwidth of 36% for a rectangular patch in [36] and 42% for a triangular patch in [39], while Guo et al. reported an impedance bandwidth of 27% for an annular-ring patch in [38]. These bandwidth figures were all quoted for a VSWR of 2:1. Instead of a L-shaped probe, Mak et al. [40] also used a T-shaped probe and managed to achieve an impedance bandwidth of 40% for a VSWR of 2:1.
A microstrip patch antenna with a shaped probe, be it directly driven or not, can usually be sup- ported on a single substrate layer. This makes it extremely suitable for antenna arrays where  cost has to be minimised. Most of these elements have radiation patterns with a slight squint in the E-plane and slightly high cross-polarisation levels in the H-plane. These are characteristics of probe-fed microstrip patch antennas on thick substrates. The stepped probe, though, exhibits somewhat lower cross-polarisation levels. The patches that are directly driven should be more robust that those with the proximity coupled probes. For the latter ones, care has to be taken with respect to the proper alignment of the pathes and probes. Another advantage of both approaches is that, since they do not increase the surface area of the element, they can be used in array configurations without the danger of creating grating lobes.

Capacitive Coupling and Slotted Patches

There are two alternative approaches that can also be used to overcome the inductive nature of the input impedance associated with a probe-fed patch on a thick substrate. These are capacitive coupling or the use of slots within the surface of the patch element. Examples of such approaches are shown in Figures 2.5(a) and (b) respectively. It can be argued that these two approaches are structurally quite similar. The approach in Figure 2.5(a) has a small probe-fed capacitor patch, which is situated below the resonant patch [41–43]. The gap between them acts as a series capaci- tor. Similarly, the annular slot in Figure 2.5(b) separates the patch into a small probe-fed capacitor patch and a resonant patch [44, 45]. In this case, the slot also acts as a series capacitor. In princi- ple, both of these approaches employ some sort of capacitive coupling and are functionally also, to some degree, equivalent to the L-probe and T-probe as described in Section 2.2.4.
Liu et al. [46] combined the capacitively-coupled feed probe with stacked patches and reported a impedance bandwidth of 25.7% for a VSWR of 2:1. To achieve this, they used two stacked patches with a small probe-fed patch below the bottom resonant patch.  In another approach, Gonza´lez et al. [47] placed a resonant patch, together with the small probe-fed capacitor patch just below it, into a metallic cavity. With this configuration, they managed to obtain a impedance bandwidth of 35.3% for a VSWR of 2:1.

Synopsis 
Samevatting 
Acknowledgements 
Preface
1 Introduction
1.1 Background and Motivation
1.2 Objectives and Scope
1.3 Original Contributions
1.4 Overview of the Thesis
2 Wideband Probe-Fed Microstrip Patch Antennas and Modelling Techniques
2.1 Introductory Remarks
2.2 Overview of Wideband Probe-Fed Microstrip Patch Antennas
2.2.1 Wideband Impedance-Matching Networks
2.2.2 Edge-Coupled Patches
2.2.3 Stacked Patches
2.2.4 Shaped Probes
2.2.5 Capacitive Coupling and Slotted Patches
2.3 New Wideband Microstrip Patch Antennas with Capacitive Feed Probes
2.4 Overview of Modelling Techniques
2.4.1 Approximate Methods
2.4.2 Full-Wave Methods
2.4.3 Spatial-Domain Moment Method
2.4.4 Spectral-Domain Moment Method
2.5 Proposed Formulation
2.6 Concluding Remarks
3 Implementation of the Spectral-Domain Moment-Method Formulation 
3.1 Introductory Remarks
3.2 General Formulation
3.3 Spectral-Domain Formulation
3.4 Green’s Function
3.4.1 Reflection Coefficients
3.4.2 Wave Amplitudes
3.4.3 Wave Functions
3.4.4 Components of the Green’s Function
3.5 Basis Functions
3.5.1 Piecewise-Sinusoidal Basis Functions on the Probes
3.5.2 Rooftop Basis Functions on the Rectangular Capacitor Patche
3.5.3 Sinusoidal Basis Functions on the Resonant Patches .
3.6 Attachment Modes
3.6.1 Rectangular Attachment Mode
3.6.2 Circular Attachment Mode
3.6.3 Higher-Order Circular Attachment Mode
3.7 System of Linear Equations
3.8 Evaluation of the Interaction-Matrix Entries
3.9 Integration Strategies
3.9.1 Integration Strategy for Overlapping Basis and Testing Functions
3.9.2 Integration Strategy for Separated Basis and Testing Functions
3.9.3 Integration Strategy for Separated Axisymmetric Basis and Testing Functions
3.10 Identification of Duplicate Entries in the Interaction Matrix .
3.10.1 Interaction between Axisymmetric Functions .
3.10.2 Interaction between Axisymmetric Functions and Functions with Rectangular Support
3.10.3 Interaction between Functions with Rectangular Support
3.11 Evaluation of the Excitation-Vector Elements
3.12 Solution of the Current-Density Coefficients
3.13 Evaluation of the Network Parameters
3.14 Evaluation of the Far Fields
3.15 Concluding Remarks. .
4 Numerical and Experimental Results 
4.1 Introductory Remarks
4.2 Validation of the Spectral-Domain Moment-Method Implementation
4.3 Characterisation of Antenna Elements with Capacitive Feed Probes
4.4 Applications
4.5 Alternatively-Shaped Patches
4.6 Concluding Remarks
5 Conclusions and Future Research
5.1 General Conclusions
5.2 Future Research
References
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