**Dual Port Ultra Wideband Antennas for Cognitive Radio and Diversity Applications**

Gijo Augustin , Bybi P. Chacko and Tayeb A. Denidni

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/52209

#### **1. Introduction**

Ultra-wideband (UWB) technology has become one of the most promising technology for short- range high speed data communication due to its high data transmission rate and large bandwidth. These systems utilize the frequency band from 3.1GHz to 10.6 GHz, which is al‐ located to the UWB systems by the Federal Communications Commission (FCC) [1]. In this ultra-wide spectrum, several unlicensed short range communication bands are overlapping such as IEEE 802.11a WLAN and HIPERLAN/2. Therefore, one of the most effective techni‐ que to eliminate these intereferences is to integrate a narro band reject filter in the UWB an‐ tenna [2-4].

In this emerging technology, antenna plays the role of a key system element. The design of low profile, easy to construct antennas in a limited space with good radiation characteristics is a challenging task for antenna engineers. The planar antennas are very attractive mainly because of their interesting physical features such as simple structure, compactness and low manufac‐ turing cost [5, 6]. However, the requirements such as via-hole connection in probe-fed anten‐ nas, larger ground plane size in microstrip fed designs and precise alignment between layers in multilayer configurations result in increased system complexity. One of the most commonly used feeding technique for modern antennas is the Coplanar Waveguide(CPW) which facili‐ tates key advantages such as low dispersion, less radiation loss and ease of integration with monolithic microwave integrated circuits in uniplanar configuration [7].

In this chapter, we present a comprehensive study on the design, analysis, and characteriza‐ tion of two Uniplanar Ultra Wide-Band(UWB) antennas which have the potential to serve the requirements of future wireless communication systems. The studies were also extended to pulse based, time domain analysis to ensure that it will enable rich broadband services of data, voice, HD video along with high speed internet.

© 2013 Augustin et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Augustin et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

In the first section of the chapter, we present an integrated uniplanar UWB antenna for cate‐ gory A cognitive radio application. The Federal Communications Commission (FCC) de‐ fines a cognitive radio as "a radio that can change its transmitter parameters based on the interaction with the environment in which it operates" [8]. This concept has originated from the urgent need to effectively utilize the available spectrum with the explosive growth in high-data rate wireless services. In general, cognitive radio networks can utilize different spectrum sensing and allocation methods namely category A and category B, in which cate‐ gory A uses two antennas. In these systems one antenna is wideband, feeding a receiver for spectrum sensing task meanwhile, the second antenna feeds a front end that can be tuned to the selected transmission band. The motivation behind this work is to illustrate a new inte‐ grated antenna for category A cognitive-radio systems by utilizing the uniplanar properties of coplanar wave guide [7], time domain characteristics of vivaldi inspired antennas [9] and recent developments in antenna integration techniques [10]. Although cognitive radio may initially cover lower frequencies, the integration method is demonstrated through UWB and WLAN bands.

nitive radio application [10, 22, 23] this design has advantages of uniplanar configuration, group delay variation less than 1ns and good isolation between the ports. The major design

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205

**i.** A coplanar wave guide (CPW) to coplanar strip line (CPS) transition (Figure 1a)

In this design each of these antenna elements were effectively integrated to form a dual port antenna with ultra wideband characteristics in first port and narrow band performance in the second port. The side and top view of the developed antenna in uniplanar configuration

**Figure 1.** Geometry of the Proposed Antenna. (a) CPW to CPS transition (b) Tapered slot antenna (c) rectangular ring

**CPW to CPS Transition:** The design is initiated by designing a coplanar waveguide with characteristic impedance 50Ω on Rogers™ TMM6 thermoset microwave laminate with die‐ lectric permittivity (εr) 6, loss tangent 0.0037 and thickness (h) 0.762mm using conventional design procedure [7].The open end of the coplanar waveguide is extended with a smooth curvature to form a CPW to coplanar stripline (CPS) transition [24], which is specified by geometrical parameters lgt, wg1 and g as shown in Figure 1a. In order to maintain geometri‐ cal symmetry lgt and wg1 are maintained constant on both sides of the transmission line re‐ sulting two striplines terminated at port –Pa and port-Pb. The parameters were optimized

**Tapered Slot antenna:** An elliptically tapered slot antenna characterized by two identical el‐ lipses with X and Y radius of wg2 and lgt, respectively is shown in Figure 1b. The tapering is optimized for wideband operation specified by FCC [1], while maintaining the initial ta‐

for wide impedance bandwidth while maintaining the compact size.

**ii.** Tapered slot antenna with elliptical tapering (Figure 1b) and

**iii.** A rectangular loop slot antenna (Figure 1c).

elements of this antenna are,

is shown in Figure 1d

slot antenna (d) integrated antenna.

**Design:**

A uniplanar antenna for diversity application is presented in the second section of this chap‐ ter. Diversity techniques are highly desirable in modern wireless communication systems to increase the channel capacity and to combat the multipath fading problem in the environ‐ ment, which usually causes larger degradation in the system performance [11, 12]. There are different types of diversities and they are categorized in a broad perspective as spatial diver‐ sity, pattern diversity and polarization diversity [13-15]. Depending on the environment, footprint specificatons and the expected interference, designers can employ one or more of these methods to achieve diversity gain. In this era of compact wireless communication sys‐ tems, the pattern or polarization diversity is more suitable for portable devices than spatial diversity. In present wireless communication systems, particularly in a dense environment, a UWB system with diversity technique is a promising solution to enhance the system per‐ formance with high data rate and improved resolution [13, 16]. Such a system has potential applications in advanced instruments for microwave imaging, weapon detection radar which uses short impulses and require high speed data transfer. There have been significant efforts in recent years in various designs of dual polarized UWB antennas for future wireless communication systems [14, 17-21]. However most of them offers a large size [17] multilayer structure [14, 18], complex feeding network [20] and not equipped with band notch func‐ tionality [19].To full fill this gap, a compact, uniplanar, CPW fed, dual polarized UWB an‐ tenna with embeded notch filter is presented in this chapter.

#### **2. Integrated wide-narrowband antenna for cognitive radio applications**

#### **2.1. Antenna geometry and design**

*Geometry:* The evolution of integrated wide-narrowband antenna configuration along with associated parameters is shown in Figure1. The antenna lies in the XZ-plane with its normal direction being parallel to the Y-axis. Compared to the existing integrated antennas for cog‐ nitive radio application [10, 22, 23] this design has advantages of uniplanar configuration, group delay variation less than 1ns and good isolation between the ports. The major design elements of this antenna are,


In this design each of these antenna elements were effectively integrated to form a dual port antenna with ultra wideband characteristics in first port and narrow band performance in the second port. The side and top view of the developed antenna in uniplanar configuration is shown in Figure 1d

**Figure 1.** Geometry of the Proposed Antenna. (a) CPW to CPS transition (b) Tapered slot antenna (c) rectangular ring slot antenna (d) integrated antenna.

#### **Design:**

In the first section of the chapter, we present an integrated uniplanar UWB antenna for cate‐ gory A cognitive radio application. The Federal Communications Commission (FCC) de‐ fines a cognitive radio as "a radio that can change its transmitter parameters based on the interaction with the environment in which it operates" [8]. This concept has originated from the urgent need to effectively utilize the available spectrum with the explosive growth in high-data rate wireless services. In general, cognitive radio networks can utilize different spectrum sensing and allocation methods namely category A and category B, in which cate‐ gory A uses two antennas. In these systems one antenna is wideband, feeding a receiver for spectrum sensing task meanwhile, the second antenna feeds a front end that can be tuned to the selected transmission band. The motivation behind this work is to illustrate a new inte‐ grated antenna for category A cognitive-radio systems by utilizing the uniplanar properties of coplanar wave guide [7], time domain characteristics of vivaldi inspired antennas [9] and recent developments in antenna integration techniques [10]. Although cognitive radio may initially cover lower frequencies, the integration method is demonstrated through UWB and

A uniplanar antenna for diversity application is presented in the second section of this chap‐ ter. Diversity techniques are highly desirable in modern wireless communication systems to increase the channel capacity and to combat the multipath fading problem in the environ‐ ment, which usually causes larger degradation in the system performance [11, 12]. There are different types of diversities and they are categorized in a broad perspective as spatial diver‐ sity, pattern diversity and polarization diversity [13-15]. Depending on the environment, footprint specificatons and the expected interference, designers can employ one or more of these methods to achieve diversity gain. In this era of compact wireless communication sys‐ tems, the pattern or polarization diversity is more suitable for portable devices than spatial diversity. In present wireless communication systems, particularly in a dense environment, a UWB system with diversity technique is a promising solution to enhance the system per‐ formance with high data rate and improved resolution [13, 16]. Such a system has potential applications in advanced instruments for microwave imaging, weapon detection radar which uses short impulses and require high speed data transfer. There have been significant efforts in recent years in various designs of dual polarized UWB antennas for future wireless communication systems [14, 17-21]. However most of them offers a large size [17] multilayer structure [14, 18], complex feeding network [20] and not equipped with band notch func‐ tionality [19].To full fill this gap, a compact, uniplanar, CPW fed, dual polarized UWB an‐

**2. Integrated wide-narrowband antenna for cognitive radio applications**

*Geometry:* The evolution of integrated wide-narrowband antenna configuration along with associated parameters is shown in Figure1. The antenna lies in the XZ-plane with its normal direction being parallel to the Y-axis. Compared to the existing integrated antennas for cog‐

tenna with embeded notch filter is presented in this chapter.

**2.1. Antenna geometry and design**

WLAN bands.

204 Advancement in Microstrip Antennas with Recent Applications

**CPW to CPS Transition:** The design is initiated by designing a coplanar waveguide with characteristic impedance 50Ω on Rogers™ TMM6 thermoset microwave laminate with die‐ lectric permittivity (εr) 6, loss tangent 0.0037 and thickness (h) 0.762mm using conventional design procedure [7].The open end of the coplanar waveguide is extended with a smooth curvature to form a CPW to coplanar stripline (CPS) transition [24], which is specified by geometrical parameters lgt, wg1 and g as shown in Figure 1a. In order to maintain geometri‐ cal symmetry lgt and wg1 are maintained constant on both sides of the transmission line re‐ sulting two striplines terminated at port –Pa and port-Pb. The parameters were optimized for wide impedance bandwidth while maintaining the compact size.

**Tapered Slot antenna:** An elliptically tapered slot antenna characterized by two identical el‐ lipses with X and Y radius of wg2 and lgt, respectively is shown in Figure 1b. The tapering is optimized for wideband operation specified by FCC [1], while maintaining the initial ta‐ pered slot width as 'g'. The length of curvaure AB and AC are defined [25] as ¼thof the pe‐ rimeter formed by the ellipse (1),

$$AB = AC = \frac{\pi}{2} \sqrt{\frac{(\lg t^2 + wg2^2)}{2}} \tag{1}$$

(a) (b)

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Measurement of both frequency and time domain characteristics are essential to evaluate the performance of an UWB antenna. In frequency domain the S-parameters, gain, efficiency, ra‐ diation pattern and polarization are measured and analysed in section 2.2.1. In time domain, the antenna performance is evaluated using very short pulses. The group delay, antenna transfer function, impulse response and fidelity were analysed and discussed in section 2.2.2

The measured reflecton and transmission coefficients of the antenna along with the simula‐

It is found that the UWB antenna excited through port-P1 provides a 2:1 VSWR bandwidth from 2.6GHz to 11GHz, meanwhile, the narrowband (NB) antenna excited through port-P2 provides 2:1 VSWR bandwidth from 5 GHz to 5.5 GHz. Thus the integrated antenna meets

**Figure 2.** Photograph of the fabricated prototype (a) front view (b) perspective view

**Figure 3.** Simulated and measured S parameters of the Wide-Narrowband Antenna.

*2.2.1. Frequency domain characteristics*

tion results are plotted in Figure 3.

**Rectangular loop slot antenna:** The rectangular loop slot antenna inspired from [26], with geometrical parameters l2, w2, g1 and g2 is shown in Figure 1c. The antenna is fed with an inset open circuited single layer CPW stub for good impedance matching and radiation characteristics.

**The Integrated Antenna:** At the first stage of integration, the elliptically tapered slot anten‐ na is integrated to the ports Pa and Pb of CPW to CPS transition, resulting uni-planar UWB antenna configuration. The antenna parameters wg2 and lgt were fine tuned to fix the lower cut-off frequency to facilitate wide impedance bandwidth covering the FCC specified spec‐ trum from 3.1GHz to 10.6GHz. In the second stage, the narrow band antenna with CPW feed is embedded at the space between two tapered slots, without affecting the performance of the UWB antenna. The geometrcial parameters of the antenna were optmized using com‐ mercial tool CST Microwave Studio® (CST MWS) based on finite integration technique (FIT). The optimum parameters are listed in Table 1 which are a trade off between wide im‐ pedance bandwidth, small foot print and improved isolation.


**Table 1.** Geometrical parameters of the integrated antenna shown in Figure 1

#### **2.2. Simulation with experimental validation**

After optimizing the integrated antenna, a prototype is fabricated using LPKF® circuit board plotter. The entire fabrication process is relatively simple and can also be performed using conventional low cost PCB processing technology such as photolithography. In addition, the single layer design eliminates the requirement of alignment holes. Therefore this design fa‐ cilitates accurate, efficient and cost effective fabrication. The fabricated prototype with a me‐ chanical calibration standard is shown in Figure 2a for comparison. A perspective view of the wide-narrowband antenna mounted for measurement in the anechoic chamber is pro‐ vides in Figure 2b.

**Figure 2.** Photograph of the fabricated prototype (a) front view (b) perspective view

Measurement of both frequency and time domain characteristics are essential to evaluate the performance of an UWB antenna. In frequency domain the S-parameters, gain, efficiency, ra‐ diation pattern and polarization are measured and analysed in section 2.2.1. In time domain, the antenna performance is evaluated using very short pulses. The group delay, antenna transfer function, impulse response and fidelity were analysed and discussed in section 2.2.2

#### *2.2.1. Frequency domain characteristics*

pered slot width as 'g'. The length of curvaure AB and AC are defined [25] as ¼thof the pe‐

2 2

**Rectangular loop slot antenna:** The rectangular loop slot antenna inspired from [26], with geometrical parameters l2, w2, g1 and g2 is shown in Figure 1c. The antenna is fed with an inset open circuited single layer CPW stub for good impedance matching and radiation

**The Integrated Antenna:** At the first stage of integration, the elliptically tapered slot anten‐ na is integrated to the ports Pa and Pb of CPW to CPS transition, resulting uni-planar UWB antenna configuration. The antenna parameters wg2 and lgt were fine tuned to fix the lower cut-off frequency to facilitate wide impedance bandwidth covering the FCC specified spec‐ trum from 3.1GHz to 10.6GHz. In the second stage, the narrow band antenna with CPW feed is embedded at the space between two tapered slots, without affecting the performance of the UWB antenna. The geometrcial parameters of the antenna were optmized using com‐ mercial tool CST Microwave Studio® (CST MWS) based on finite integration technique (FIT). The optimum parameters are listed in Table 1 which are a trade off between wide im‐

**Parameters Value, mm Parameters Value, mm Parameters Value, mm**

**wc** 3 **lgt** 10 **l2** 5

**wg1** 15 **lct** 12.9 **g2** 0.5

**wg2** 22 **g** 0.35 **g1** 0.25

**lgb** 25.8 **w2** 14 **h** 0.762

After optimizing the integrated antenna, a prototype is fabricated using LPKF® circuit board plotter. The entire fabrication process is relatively simple and can also be performed using conventional low cost PCB processing technology such as photolithography. In addition, the single layer design eliminates the requirement of alignment holes. Therefore this design fa‐ cilitates accurate, efficient and cost effective fabrication. The fabricated prototype with a me‐ chanical calibration standard is shown in Figure 2a for comparison. A perspective view of the wide-narrowband antenna mounted for measurement in the anechoic chamber is pro‐

*t wg AB AC* p

pedance bandwidth, small foot print and improved isolation.

**Table 1.** Geometrical parameters of the integrated antenna shown in Figure 1

**2.2. Simulation with experimental validation**

vides in Figure 2b.

2 2 (lg 2

<sup>+</sup> = = (1)

rimeter formed by the ellipse (1),

206 Advancement in Microstrip Antennas with Recent Applications

characteristics.

The measured reflecton and transmission coefficients of the antenna along with the simula‐ tion results are plotted in Figure 3.

**Figure 3.** Simulated and measured S parameters of the Wide-Narrowband Antenna.

It is found that the UWB antenna excited through port-P1 provides a 2:1 VSWR bandwidth from 2.6GHz to 11GHz, meanwhile, the narrowband (NB) antenna excited through port-P2 provides 2:1 VSWR bandwidth from 5 GHz to 5.5 GHz. Thus the integrated antenna meets the VSWR bandwidth requirement for the FCC specified UWB band and for the WLAN spectrum. The trasmission coefficients in Figure 3 shows that, the inter-port isolation is bet‐ ter than 15dB which is a reasonable value to eliminate the cross talk between the antennas. The simulated and measured s-parameters are in reasonable agreement. However, there is a slight discrepancy between the theorectical and experimental results. This is mainly because of the approximation of boundary conditions of computational domain. In addition, as ex‐ plained in [27], RF cables from the vector network analyzer slightly influences the measure‐ ment of small antennas.

edges of NBA are vertical in direction and in turn results in vertical polarization. However,

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it is worth to note that, while estimating the composite current vector, the surface regions

where equal and opposite current vectors exists, indicated by Fc, are not taken into account.

**Figure 5.** Measured and simulated radiation patterns (a) 3.5 GHz [P1] and (b) 5.2GHz [P1] (c) 10.5 GHz [P1] and (d)

5.2GHz [P2]

The isolation mechanism and polarization of the electromagnetic radiation is investigated through simulated surface current analysis. The magnitude and vector plot of surface cur‐ rent density at 5.2 GHz is illustrated in Figure 4.

**Figure 4.** Simulated surface current distribution at 5.2GHz. (a) Magnitude of Jsurf of UWB antenna without integrat‐ ing NB antenna (b) Magnitude of Jsurf with P1-excited, P2=50Ω (c) Magnitude of Jsurf with P2-excited, P1=50Ω (d) Vector of Jsurf with P1-excited, P2=50Ω (e) Vector of Jsurf with P2-excited, P1=50Ω

It is evident from Figure 4a that, the tapered surface regions on both sides of the integrated antenna contributes for the radiation. Meanwhile, the current excited at the top region be‐ tween two tapered slot antennas, indicated by the rectangular dashed box, is almost nil. This region is effectively utilized to integrated the ring slot antenna for narrow band operation. In Figure 4b, the surface currents in the integrated configuration is provided, which shows that the current coupling from UWBA to the NBA and vice versa(figure 4c) is very low. This results in an efficient integration with good inter-port isolation. The vector analysis of sur‐ face current in the integrated antenna is shown in Figures 4 (d-e). It is clear from the plot that the dominant radiating current vector at both the tapering is vertical in direction. This shows that the polarization of the radiated electromagnetic wave from the ultra wideband antenna is vertically polarized. Similarly, the resultant current vector at the vertical slot edges of NBA are vertical in direction and in turn results in vertical polarization. However, it is worth to note that, while estimating the composite current vector, the surface regions where equal and opposite current vectors exists, indicated by Fc, are not taken into account.

the VSWR bandwidth requirement for the FCC specified UWB band and for the WLAN spectrum. The trasmission coefficients in Figure 3 shows that, the inter-port isolation is bet‐ ter than 15dB which is a reasonable value to eliminate the cross talk between the antennas. The simulated and measured s-parameters are in reasonable agreement. However, there is a slight discrepancy between the theorectical and experimental results. This is mainly because of the approximation of boundary conditions of computational domain. In addition, as ex‐ plained in [27], RF cables from the vector network analyzer slightly influences the measure‐

The isolation mechanism and polarization of the electromagnetic radiation is investigated through simulated surface current analysis. The magnitude and vector plot of surface cur‐

**Figure 4.** Simulated surface current distribution at 5.2GHz. (a) Magnitude of Jsurf of UWB antenna without integrat‐ ing NB antenna (b) Magnitude of Jsurf with P1-excited, P2=50Ω (c) Magnitude of Jsurf with P2-excited, P1=50Ω (d)

It is evident from Figure 4a that, the tapered surface regions on both sides of the integrated antenna contributes for the radiation. Meanwhile, the current excited at the top region be‐ tween two tapered slot antennas, indicated by the rectangular dashed box, is almost nil. This region is effectively utilized to integrated the ring slot antenna for narrow band operation. In Figure 4b, the surface currents in the integrated configuration is provided, which shows that the current coupling from UWBA to the NBA and vice versa(figure 4c) is very low. This results in an efficient integration with good inter-port isolation. The vector analysis of sur‐ face current in the integrated antenna is shown in Figures 4 (d-e). It is clear from the plot that the dominant radiating current vector at both the tapering is vertical in direction. This shows that the polarization of the radiated electromagnetic wave from the ultra wideband antenna is vertically polarized. Similarly, the resultant current vector at the vertical slot

Vector of Jsurf with P1-excited, P2=50Ω (e) Vector of Jsurf with P2-excited, P1=50Ω

ment of small antennas.

rent density at 5.2 GHz is illustrated in Figure 4.

208 Advancement in Microstrip Antennas with Recent Applications

**Figure 5.** Measured and simulated radiation patterns (a) 3.5 GHz [P1] and (b) 5.2GHz [P1] (c) 10.5 GHz [P1] and (d) 5.2GHz [P2]

The simulated and measured radiation pattern of both the UWB and NB are presented in Figures 5(a-d). These radiation patterns were measured independently, that is, port-P2 is loaded with 50Ω termination while exciting port-P1 and vice versa. It is clear from the pat‐ tern that the UWB antenna is directional towards 0º and 180º because of the two tapered slot antennas radiating to the corresponding directions. This indicates that, the UWB and NB an‐ tenna has beam maxima at ±X and ±Z directions respectively, which are not highly attractive for applications which utilize the simultaneous utilization of both antennas.

radiation corresponding to the peak gain. It is clear from the measurement results that, the gain variations are within 2.2dBi and 2.4 dBi in the ultra wide band and narrow band spec‐ trum of the integrated antenna, respectively. The radiation efficiency is also measured using wheeler cap method [31]and incorporated in Figure 6. It is found that the average efficiency

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As depicted in the introduction, the UWB antenna need to possess high level of pulse han‐ dling capabilities in order to handle high frequency impulses. In this section the time do‐ main characteristics including group delay, antenna transfer function, implulse response

In order to measure the group delay of the UWB antenna, two identical antenna prototypes were made. As illustrated in the inset of Figure 7, these two identical antennas were kept in in the anechoic chamber at far field(R=1m) with two orientations; face-to-face and side-byside. The time domain measurement capability of the vector network analyser is utilized for this measurement. Prior to the measurement, a full two port calibration is performed to eliminate the effects of cables and connectors. The measurement is performed by exciting the identical antennas through port-P1 while port-P2 is terminated with a broadband 50Ω termination. It is clear from Figure 7 that, the group delay remains constant with variations

**Figure 7.** Measured group delay and normalized antenna transfer function in two different orientations of the UWB

The antenna transfer function of the antenna is also calculated using (2) and incorporated in

of 81% and 75% are observed for UWB antenna and NB antenna, respectively.

*2.2.2. Time domain characteristics*

and fidelity factor were measured and discussed.

less than a nanosecond for both orientations.

antenna (R = 1m)

Figure 7.

However, the radiation patterns are suitable for cognitive radio applications such as IEEE 802.11 wireless rural area networks (WRAN) in which the spectrum sensing take plane dur‐ ing the interval between intra-frame and inter-frame, when the transceiver is switched off [28]. It is also visible from the radiation pattern that, at higher frequencies, the polarization purity is degraded due to the finite ground plane effect. A good agreement between simu‐ lated and measured radiation patterns are observed except for the cross polar patterns in the YZ plane. This is mainly because of the spurious reflections from the SMA connectors and cables that are not incorporated in the computational simulation. In conclusion, the patterns are similar to those observed for antennas used in cognitive radio systems [10, 22] and in wireless system terminals [29]. It is worth to note that, these patterns are also suitable for applications in indoor wireless communication systems including ad-hoc networks, where cross polar performance is not a high priority requirement and channels are dominated by rich Rayleigh fading [30]

**Figure 6.** Separately measured gain and efficiency of UWB (port 1) and NB (port 2) antenna.

The gain of UWB and NB antenna are measured independently in the XZ-plane using the gain comparison method and shown in Figure 6. In the graph 'φ' denotes the direction of radiation corresponding to the peak gain. It is clear from the measurement results that, the gain variations are within 2.2dBi and 2.4 dBi in the ultra wide band and narrow band spec‐ trum of the integrated antenna, respectively. The radiation efficiency is also measured using wheeler cap method [31]and incorporated in Figure 6. It is found that the average efficiency of 81% and 75% are observed for UWB antenna and NB antenna, respectively.

#### *2.2.2. Time domain characteristics*

The simulated and measured radiation pattern of both the UWB and NB are presented in Figures 5(a-d). These radiation patterns were measured independently, that is, port-P2 is loaded with 50Ω termination while exciting port-P1 and vice versa. It is clear from the pat‐ tern that the UWB antenna is directional towards 0º and 180º because of the two tapered slot antennas radiating to the corresponding directions. This indicates that, the UWB and NB an‐ tenna has beam maxima at ±X and ±Z directions respectively, which are not highly attractive

However, the radiation patterns are suitable for cognitive radio applications such as IEEE 802.11 wireless rural area networks (WRAN) in which the spectrum sensing take plane dur‐ ing the interval between intra-frame and inter-frame, when the transceiver is switched off [28]. It is also visible from the radiation pattern that, at higher frequencies, the polarization purity is degraded due to the finite ground plane effect. A good agreement between simu‐ lated and measured radiation patterns are observed except for the cross polar patterns in the YZ plane. This is mainly because of the spurious reflections from the SMA connectors and cables that are not incorporated in the computational simulation. In conclusion, the patterns are similar to those observed for antennas used in cognitive radio systems [10, 22] and in wireless system terminals [29]. It is worth to note that, these patterns are also suitable for applications in indoor wireless communication systems including ad-hoc networks, where cross polar performance is not a high priority requirement and channels are dominated by

for applications which utilize the simultaneous utilization of both antennas.

210 Advancement in Microstrip Antennas with Recent Applications

**Figure 6.** Separately measured gain and efficiency of UWB (port 1) and NB (port 2) antenna.

The gain of UWB and NB antenna are measured independently in the XZ-plane using the gain comparison method and shown in Figure 6. In the graph 'φ' denotes the direction of

rich Rayleigh fading [30]

As depicted in the introduction, the UWB antenna need to possess high level of pulse han‐ dling capabilities in order to handle high frequency impulses. In this section the time do‐ main characteristics including group delay, antenna transfer function, implulse response and fidelity factor were measured and discussed.

In order to measure the group delay of the UWB antenna, two identical antenna prototypes were made. As illustrated in the inset of Figure 7, these two identical antennas were kept in in the anechoic chamber at far field(R=1m) with two orientations; face-to-face and side-byside. The time domain measurement capability of the vector network analyser is utilized for this measurement. Prior to the measurement, a full two port calibration is performed to eliminate the effects of cables and connectors. The measurement is performed by exciting the identical antennas through port-P1 while port-P2 is terminated with a broadband 50Ω termination. It is clear from Figure 7 that, the group delay remains constant with variations less than a nanosecond for both orientations.

**Figure 7.** Measured group delay and normalized antenna transfer function in two different orientations of the UWB antenna (R = 1m)

The antenna transfer function of the antenna is also calculated using (2) and incorporated in Figure 7.

$$H(oo) = \sqrt{\frac{2\pi RcS\_{21}(oo)e^{j a \text{R}/c}}{jao}}\tag{2}$$

Fidelity factor, F is an effective parameter to analyze the distortion between two pulses [33],

where τ is the delay between the input pulse St (t) and the output pulse Sr (t). The fidelity factor of the wideband antenna is also evaluated and presented in Table 2. The fidelity factor remains greater than 0.85 which shows that, the antenna imposes negligible effects on the

**Orientation Fidelity Factor,F**

A parametric analysis of the key antenna prameters which influence the lower cut-off fre‐ quency of the UWB antenna and the resonant frequency of the NB antenna is studied in this section. This will help the antenna engineers to pay more attention to those parameters dur‐

**Figure 9.** Influence of key antenna parameters on reflection coefficient (a) Tapering aprature, AB (b) loop width, w2

The variation of relfection coefficient with tapering aprature AB is the most sensitive param‐ eter which determins the lower cut-off frequency of the UWB antenna. Figure 9a shows the

**Face-to-Face** 0.86 **Side – to –Side** 0.88

*<sup>α</sup>*|*Sr*(*<sup>t</sup>* - *<sup>τ</sup>*)|2*dt*

Dual Port Ultra Wideband Antennas for Cognitive Radio and Diversity Applications

(4)

213

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*<sup>F</sup>* <sup>=</sup> *<sup>∫</sup>*

*∫* -*α <sup>α</sup>*|*St*(*t*)|2*dt<sup>∫</sup>* -*α*


which is defined as,

radiated pulses.

**Table 2.** Fidelity Factor of the wide band antenna

ing the design, optimizaton and prototyping.

**2.3. Parametric analysis**

where c is the velocity of light in free space and R is the distance between two antennas [25].

The antenna transfer function remains fairly stable throughout the UWB spectrum with var‐ iations less than 10dB except for the lower end of the spectrum in the face-to-face orienta‐ tion.

The transient response of the antenna is evaluated using fourth derivative of the Gaussian pulse defined by (3)

$$V\_{\rm int}(t) = A \left( 3 \cdot 6 \left( \frac{4\pi}{T^2} \right) t^2 + \left( \frac{4\pi}{T^2} \right) t^4 \right) e^{-2\pi \left( \frac{t}{T^2} \right)^2} V \left| m \right. \tag{3}$$

The impulse response of the wideband antenna is obtained by convoluting the fourth deriv‐ ative of (3) with the inverse Fourier transform of antenna transfer function (2). The spectrum of this pulse fully covers the FCC band and comply with the emission standards specified when the amplitude constant A = 1.6 and pulse duration parameter T = 67ps. [32]

The input pulse and the output pulses at face-to-face orientation and side-by-side orienta‐ tion are shown in Figure 8. It is evident from the plot that the UWB antenna retains the in‐ formation contained in the impulse with minimum distortion.

**Figure 8.** Input and radiated pulses of the proposed antenna.

Fidelity factor, F is an effective parameter to analyze the distortion between two pulses [33], which is defined as,

$$F = \frac{\underline{\int\_{a}^{a} S\_{t}(t) S\_{r}(t \cdot \tau) d\_{t}}}{\sqrt{\int\_{a}^{a} S\_{t}(t) \|^{2} dt \underline{f}\_{a}^{a} \mid S\_{r}(t \cdot \tau)^{1/2} dt}} \tag{4}$$

where τ is the delay between the input pulse St (t) and the output pulse Sr (t). The fidelity factor of the wideband antenna is also evaluated and presented in Table 2. The fidelity factor remains greater than 0.85 which shows that, the antenna imposes negligible effects on the radiated pulses.


**Table 2.** Fidelity Factor of the wide band antenna

#### **2.3. Parametric analysis**

/

<sup>=</sup> (2)

w

<sup>21</sup> 2 () ( ) *j Rc RcS e <sup>H</sup>*

w

212 Advancement in Microstrip Antennas with Recent Applications

*Vin*(*t*)= *<sup>A</sup>*(3 - 6( <sup>4</sup>*<sup>π</sup>*

formation contained in the impulse with minimum distortion.

**Figure 8.** Input and radiated pulses of the proposed antenna.

tion.

pulse defined by (3)

p

*j*

where c is the velocity of light in free space and R is the distance between two antennas [25].

The antenna transfer function remains fairly stable throughout the UWB spectrum with var‐ iations less than 10dB except for the lower end of the spectrum in the face-to-face orienta‐

The transient response of the antenna is evaluated using fourth derivative of the Gaussian

The impulse response of the wideband antenna is obtained by convoluting the fourth deriv‐ ative of (3) with the inverse Fourier transform of antenna transfer function (2). The spectrum of this pulse fully covers the FCC band and comply with the emission standards specified

The input pulse and the output pulses at face-to-face orientation and side-by-side orienta‐ tion are shown in Figure 8. It is evident from the plot that the UWB antenna retains the in‐

*<sup>T</sup>* <sup>2</sup> )*<sup>t</sup>* 4)*e*-2*π*( *<sup>t</sup>*

*T* )2

*V* / *m* (3)

*<sup>T</sup>* <sup>2</sup> )*<sup>t</sup>* <sup>2</sup> <sup>+</sup> ( <sup>4</sup>*<sup>π</sup>*

when the amplitude constant A = 1.6 and pulse duration parameter T = 67ps. [32]

 w

w

A parametric analysis of the key antenna prameters which influence the lower cut-off fre‐ quency of the UWB antenna and the resonant frequency of the NB antenna is studied in this section. This will help the antenna engineers to pay more attention to those parameters dur‐ ing the design, optimizaton and prototyping.

**Figure 9.** Influence of key antenna parameters on reflection coefficient (a) Tapering aprature, AB (b) loop width, w2

The variation of relfection coefficient with tapering aprature AB is the most sensitive param‐ eter which determins the lower cut-off frequency of the UWB antenna. Figure 9a shows the variation of reflection coefficient with wg2 (and in turn AB). It is clear from the plot that the lower resonance shifts drastically for small variations of wg2. As wg2 increases from 20mm to 24mm the lower cut-off frequency of the UWB antenna moves from 3.2GHz to 2.4 GHz. It is also worth to note that the impedance matching throughout the wide band remains with‐ in the FCC specifications when the tapering aprature varies from 24.8mm to 28.9mm. In nar‐ row band antenna, the variation of resonant frequency with the loop width, w2 is depicted in Figure 9(b). It is found that when the loop width varies from 12mm to 16mm the resonant frequency of the narrow band antenna drifts from 6GHz to 4.6GHz.

#### **2.4. Conclusion**

An integrated dual port antenna with good inter-port isolation in uniplanar configuration for congnitive radio systems is presented in this section. The space between two tapered slot antennas which forms the ultra wideband antenna, is effectively utilized to integrate a narrow band sqare loop slot antenna. The measurement results indicate that, the UWB and NB antenna provides a 2:1 VSWR bandwidth from 2.7 GHz to 11 GHz and 5 GHz to 5.5GHz, respectively. The antenna also provides inter-port isolation better than 15 dB throught the resonant band. Measured readiaton pattern reveals that the wide-band anten‐ na can fulfill the needs of spectrum searching task, and the narrow-band antenna can be used for trasmission in cognitive radio systems. The time domain characteristics of the UWB antenna in the integrated configuration is also studied and the results reveals that it facilitate transmission and reception of pulses with minimum distortion. Therefore, the an‐ tenna can also be a good candidate for future applications, such as medical imaging / weapon detection systems, which are connected to the host system through high speed WLAN link.

**Figure 10.** Geometry of the proposed antenna (a) Top view, (b) Side view

nator facilitates band notch functionality for the diversity antenna.

is approximately half wave length long at the center notch frequency.

The proposed antenna geometry in cartesian coordinate system are shown in Figure 10. The ba‐ sic antenna structure consists of an annulus slot and two orthogonal, identical CPW signal strips at same distance from the annulus center. Compared to dual polarized UWB slot anten‐ nas recently reported in [14, 17], the ground plane of the proposed antenna is modified as an an‐ nulus slot with radius r1 and thickness t, which creatively reduces the antenna footprint. The CPW feedline is exciting two U-shaped elements with geometrical parameter r2, r3. In addition to the the broad impedance bandwidth of this unique design, an impedance transformer with length l4 and gap g2 is also incorporated in the CPW line for further bandwidth enhancement. Since, inter-port isolation is one of the highly desirable characteristics of a diversity antenna, a cross shaped strip with dimensions l1, l2 and l3 is embeded diagonally in the antenna. In order to avoid interferences with the overlaping unlicensed bands in the UWB spectrum, an arc shap‐ ed slot resonator with specifications r4,ts and ls is also integrated in the antenna. This slot reso‐

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**Design:** The antenna is realized on a Rogers® RT/Duroid 6035HTC laminate with permittivity (r) 3.6, loss tangent 0.0013, and thickness (h) 1.524mm. The CPW line with characteristics impe‐ dance 50Ω is first designed using the conventional design procedure [7]. The annulus ground plane parameters (r1) and U-shaped stub dimensions(r2,r3,d) were selected [35]to cover the FCC specified UWB spectrum. In this design the radius r1 of the ground plane determines the first resonant frequency and the radius r2 ensures the impedance matching. In conclusion, the merging of several dominant resonances, which are produced by the annulus ground, the U shaped feeding structure, and the coupling between them provides a broad impedance band width [36]. In order to increase the inter port isolation a cross shaped stub [37] is then inserted at an optimum position diagonally in the ground plane. Finally the semicircular arc shaped reso‐ nators were designed [38] and integrated for notch functionality. The antenna provides de‐ sired notch in the IEEE 802.11a and HIPERLAN/2 bands, when the length of the slot resonator ls

#### **3. Ultra-wideband slot antenna for polarization diversity applications**

In this section an Ultra wideband Antenna for polarization diversity application is present‐ ed. The development, analysis and characterization of this dual port antenna is discussed in detail. Both frequency and time domain analysis of the fabricated prototype reaveals that, this antenna is an attractive element in future wireless communication systems where the challenges such as multipatch fading is a major concern.

#### **3.1. Antenna geometry and design**

The proposed antenna is inspired from the design proposed in [34], where wideband char‐ acteristics is obtained by exciting a compact annulus ground plane with a circular patch. In this work, a polarization diversity antenna is devoloped by feeding an annulus ground plane with dual orthogonal ports. This feeding mechanism is on of the effective technique for diversity antennas [14, 17].

**Figure 10.** Geometry of the proposed antenna (a) Top view, (b) Side view

variation of reflection coefficient with wg2 (and in turn AB). It is clear from the plot that the lower resonance shifts drastically for small variations of wg2. As wg2 increases from 20mm to 24mm the lower cut-off frequency of the UWB antenna moves from 3.2GHz to 2.4 GHz. It is also worth to note that the impedance matching throughout the wide band remains with‐ in the FCC specifications when the tapering aprature varies from 24.8mm to 28.9mm. In nar‐ row band antenna, the variation of resonant frequency with the loop width, w2 is depicted in Figure 9(b). It is found that when the loop width varies from 12mm to 16mm the resonant

An integrated dual port antenna with good inter-port isolation in uniplanar configuration for congnitive radio systems is presented in this section. The space between two tapered slot antennas which forms the ultra wideband antenna, is effectively utilized to integrate a narrow band sqare loop slot antenna. The measurement results indicate that, the UWB and NB antenna provides a 2:1 VSWR bandwidth from 2.7 GHz to 11 GHz and 5 GHz to 5.5GHz, respectively. The antenna also provides inter-port isolation better than 15 dB throught the resonant band. Measured readiaton pattern reveals that the wide-band anten‐ na can fulfill the needs of spectrum searching task, and the narrow-band antenna can be used for trasmission in cognitive radio systems. The time domain characteristics of the UWB antenna in the integrated configuration is also studied and the results reveals that it facilitate transmission and reception of pulses with minimum distortion. Therefore, the an‐ tenna can also be a good candidate for future applications, such as medical imaging / weapon detection systems, which are connected to the host system through high speed

**3. Ultra-wideband slot antenna for polarization diversity applications**

challenges such as multipatch fading is a major concern.

**3.1. Antenna geometry and design**

for diversity antennas [14, 17].

In this section an Ultra wideband Antenna for polarization diversity application is present‐ ed. The development, analysis and characterization of this dual port antenna is discussed in detail. Both frequency and time domain analysis of the fabricated prototype reaveals that, this antenna is an attractive element in future wireless communication systems where the

The proposed antenna is inspired from the design proposed in [34], where wideband char‐ acteristics is obtained by exciting a compact annulus ground plane with a circular patch. In this work, a polarization diversity antenna is devoloped by feeding an annulus ground plane with dual orthogonal ports. This feeding mechanism is on of the effective technique

frequency of the narrow band antenna drifts from 6GHz to 4.6GHz.

214 Advancement in Microstrip Antennas with Recent Applications

**2.4. Conclusion**

WLAN link.

The proposed antenna geometry in cartesian coordinate system are shown in Figure 10. The ba‐ sic antenna structure consists of an annulus slot and two orthogonal, identical CPW signal strips at same distance from the annulus center. Compared to dual polarized UWB slot anten‐ nas recently reported in [14, 17], the ground plane of the proposed antenna is modified as an an‐ nulus slot with radius r1 and thickness t, which creatively reduces the antenna footprint. The CPW feedline is exciting two U-shaped elements with geometrical parameter r2, r3. In addition to the the broad impedance bandwidth of this unique design, an impedance transformer with length l4 and gap g2 is also incorporated in the CPW line for further bandwidth enhancement. Since, inter-port isolation is one of the highly desirable characteristics of a diversity antenna, a cross shaped strip with dimensions l1, l2 and l3 is embeded diagonally in the antenna. In order to avoid interferences with the overlaping unlicensed bands in the UWB spectrum, an arc shap‐ ed slot resonator with specifications r4,ts and ls is also integrated in the antenna. This slot reso‐ nator facilitates band notch functionality for the diversity antenna.

**Design:** The antenna is realized on a Rogers® RT/Duroid 6035HTC laminate with permittivity (r) 3.6, loss tangent 0.0013, and thickness (h) 1.524mm. The CPW line with characteristics impe‐ dance 50Ω is first designed using the conventional design procedure [7]. The annulus ground plane parameters (r1) and U-shaped stub dimensions(r2,r3,d) were selected [35]to cover the FCC specified UWB spectrum. In this design the radius r1 of the ground plane determines the first resonant frequency and the radius r2 ensures the impedance matching. In conclusion, the merging of several dominant resonances, which are produced by the annulus ground, the U shaped feeding structure, and the coupling between them provides a broad impedance band width [36]. In order to increase the inter port isolation a cross shaped stub [37] is then inserted at an optimum position diagonally in the ground plane. Finally the semicircular arc shaped reso‐ nators were designed [38] and integrated for notch functionality. The antenna provides de‐ sired notch in the IEEE 802.11a and HIPERLAN/2 bands, when the length of the slot resonator ls is approximately half wave length long at the center notch frequency.

quency end. It also provides a notch band with high band rejection from 4.99 to 6.25GHz. The small differences in the measured and simulated results are due to the approximate boundary conditions in the computational domain. Moreover, RF cable from the vector net‐

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The transmission coefficient shown in Figure 13(a) provides the influence of cross shaped stub throughout the resonant band. It is observed that, the isolation is improved by inserting the stub diagonally between the U-shaped elements. In addition the cross stub improves the

The magnitude of surface current density at 3.5GHz and 8.5 GHz are illustrated in Figure 13(be) which aid better understanding about the isolation performance of the antenna. It is evident from the results that, when P1 is excited without the isolation strip, the current from P1 has a tendency to couple to P2 through the common ground plane. However the integration of the isolation strip drastically reduces the current on the ground plane around P2 (vice-versa when P2 is excited) with a strong current excitation on the strip. This results in better inter-port isola‐ tion and thereby significantly improves the diversity performance. It is also worth to note that the isolation strip has negligible influence over the surface current on the antenna elements con‐

The far-field (2D) radiation pattern of the proposed antenna is also measured and compared with the simulation results at three different frequencies in the UWB band. The patterns are measured in a fully automated anechoic chamber, which is connected to Agilent® E8362b Performance Network Analyzer. A standard horn antenna is connected to the first port of the PNA while the second port is connected to the antenna under test. The radiation pat‐

work analyzer slightly affects the measurements of small antennas [27]

**Figure 12.** Simulated and Measured S-parameters of the diversity antenna.

impedance matching at the lower end of the spectrum.

nected through P1 at both lower and higher end of the UWB spectrum.

**Figure 11.** Photograph of the fabricated prototype

The initial analysis of the geometrical parameters and optimization of the antenna is per‐ formed using the FDTD based CST Microwave Studio®. The optimum parameters are listed in Table 3 which is a tradeoff between wide impedance bandwidth, better isolation, sharp notch and small foot print.


**Table 3.** Geometrical parameters of the diversity antenna shown in Figure.10

#### **3.2. Simulation and experimental results**

After the initial design and optimization of the diversity antenna using 3D full wave electro‐ magnetic solver, a prototype is fabricated using LPKF milling machine. Extreme care is taken during the milling process to ensure fabrication accuracy especially at the most sensing ele‐ ments such as the width of the slot resonator. The fabricated prototype is shown in Figure 11. The measurement results in frequency and time domain are discussed in the following sections.

#### *3.2.1. Frequency domain*

The measured and simulated S-parameters of the proposed dual polarized antenna at port-1 (P1) and port-2 (P2) are presented in Figure 12. Due to geometrical symmetry the simulated results for both ports are identical. The slight difference in the measured S11 and S22is owing to the fabrication inaccuracies. The antenna displays a 2:1 VSWR bandwidth from 2.80 GHz to 11GHz with an inter-port isolation better than 15dB except at the lower and higher fre‐ quency end. It also provides a notch band with high band rejection from 4.99 to 6.25GHz. The small differences in the measured and simulated results are due to the approximate boundary conditions in the computational domain. Moreover, RF cable from the vector net‐ work analyzer slightly affects the measurements of small antennas [27]

**Figure 12.** Simulated and Measured S-parameters of the diversity antenna.

**Figure 11.** Photograph of the fabricated prototype

216 Advancement in Microstrip Antennas with Recent Applications

**Table 3.** Geometrical parameters of the diversity antenna shown in Figure.10

**3.2. Simulation and experimental results**

*3.2.1. Frequency domain*

notch and small foot print.

The initial analysis of the geometrical parameters and optimization of the antenna is per‐ formed using the FDTD based CST Microwave Studio®. The optimum parameters are listed in Table 3 which is a tradeoff between wide impedance bandwidth, better isolation, sharp

> **Parameters Value, mm Parameters Value, mm Parameters Value, mm W** 57 **g1** 0.3 **t** 2.5 **L** 57 **g2** 0.4 **t1** 2 **r1** 23 **d** 0.2 **ts** 0.4 **r2** 10 **lg** 8.5 **l1** 16 **r2** 5 **wg** 7.5 **l2** 5 **r4** 7 **wc** 3.5 **l3** 10

After the initial design and optimization of the diversity antenna using 3D full wave electro‐ magnetic solver, a prototype is fabricated using LPKF milling machine. Extreme care is taken during the milling process to ensure fabrication accuracy especially at the most sensing ele‐ ments such as the width of the slot resonator. The fabricated prototype is shown in Figure 11. The measurement results in frequency and time domain are discussed in the following sections.

The measured and simulated S-parameters of the proposed dual polarized antenna at port-1 (P1) and port-2 (P2) are presented in Figure 12. Due to geometrical symmetry the simulated results for both ports are identical. The slight difference in the measured S11 and S22is owing to the fabrication inaccuracies. The antenna displays a 2:1 VSWR bandwidth from 2.80 GHz to 11GHz with an inter-port isolation better than 15dB except at the lower and higher fre‐ The transmission coefficient shown in Figure 13(a) provides the influence of cross shaped stub throughout the resonant band. It is observed that, the isolation is improved by inserting the stub diagonally between the U-shaped elements. In addition the cross stub improves the impedance matching at the lower end of the spectrum.

The magnitude of surface current density at 3.5GHz and 8.5 GHz are illustrated in Figure 13(be) which aid better understanding about the isolation performance of the antenna. It is evident from the results that, when P1 is excited without the isolation strip, the current from P1 has a tendency to couple to P2 through the common ground plane. However the integration of the isolation strip drastically reduces the current on the ground plane around P2 (vice-versa when P2 is excited) with a strong current excitation on the strip. This results in better inter-port isola‐ tion and thereby significantly improves the diversity performance. It is also worth to note that the isolation strip has negligible influence over the surface current on the antenna elements con‐ nected through P1 at both lower and higher end of the UWB spectrum.

The far-field (2D) radiation pattern of the proposed antenna is also measured and compared with the simulation results at three different frequencies in the UWB band. The patterns are measured in a fully automated anechoic chamber, which is connected to Agilent® E8362b Performance Network Analyzer. A standard horn antenna is connected to the first port of the PNA while the second port is connected to the antenna under test. The radiation pat‐ terns in the XZ and YZ planes at 3.1 GHz, 7.5 GHz and 10.5 GHz seperatly measured for both ports in orthogonal planes are illustrated in Figure 14. Nearly omnidirectional patterns are observed in the lower frequency region of the UWB spectrum meanwhile slight distor‐ tions exists at the higher frequency region. This is partially due to the effect of connecters and cables [39, 40]and magnetic current variations along the circumference of the slot [14]. It is also worth to note that the patterns at P1 and P2 are almost similar with a 90º rotation, which in turn confirms dual polarization. In general, the patters are similar to those ob‐ served for diversity applications [14] and in wireless system terminals [29]

**Figure 14.** Measured and simulated radiation patterns (a) 3.5 GHz [P1] and (b) 7.5GHz [P1] (c) 10.5 GHz [P1] (d) 3.5

In a diversity system the envelope correlation coefficient (ECC) is an important measure of diversity performance. ECC with a value of greater than 0.5 can typically degrade the diver‐ sity performance. The envelope correction coefficient of the proposed antenna is also calcu‐ lated from the simulated and measured S-parameters as described in [41] using (5) and

<sup>11</sup> *<sup>S</sup>*<sup>22</sup> <sup>+</sup> *<sup>S</sup>* \*

It is evident from Figure 15 that, the proposed antenna has a very low value of ECC throughout the operating band which clarifies that the antenna is a good candidate for mod‐

<sup>21</sup> *<sup>S</sup>* <sup>22</sup>|2

(1 - <sup>|</sup>*S*11|2 <sup>+</sup> <sup>|</sup>*S*21|2 )(1 - <sup>|</sup>*S*22|2 <sup>+</sup> <sup>|</sup>*S*12|2 ) (5)

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*<sup>ρ</sup><sup>c</sup>* <sup>=</sup> <sup>|</sup>*<sup>S</sup>* \*

ern wireless communication systems employing polarization diversity.

GHz [P2] and (e) 7.5GHz [P2] and (f) 10.5 GHz [P2]

shown in Figure 15.

**Figure 13.** a) Simulated transmission coefficient, Magnitude of Jsurf (b) at 3.5GHzwithout isolation strip (c) at 3.5GHz with isolation strip (d) at 8.5GHzwithout isolation strip (e) at 8.5 GHz with isolation strip

Dual Port Ultra Wideband Antennas for Cognitive Radio and Diversity Applications http://dx.doi.org/10.5772/52209 219

terns in the XZ and YZ planes at 3.1 GHz, 7.5 GHz and 10.5 GHz seperatly measured for both ports in orthogonal planes are illustrated in Figure 14. Nearly omnidirectional patterns are observed in the lower frequency region of the UWB spectrum meanwhile slight distor‐ tions exists at the higher frequency region. This is partially due to the effect of connecters and cables [39, 40]and magnetic current variations along the circumference of the slot [14]. It is also worth to note that the patterns at P1 and P2 are almost similar with a 90º rotation, which in turn confirms dual polarization. In general, the patters are similar to those ob‐

(a)

(b)

with isolation strip (d) at 8.5GHzwithout isolation strip (e) at 8.5 GHz with isolation strip

**Figure 13.** a) Simulated transmission coefficient, Magnitude of Jsurf (b) at 3.5GHzwithout isolation strip (c) at 3.5GHz

served for diversity applications [14] and in wireless system terminals [29]

218 Advancement in Microstrip Antennas with Recent Applications

**Figure 14.** Measured and simulated radiation patterns (a) 3.5 GHz [P1] and (b) 7.5GHz [P1] (c) 10.5 GHz [P1] (d) 3.5 GHz [P2] and (e) 7.5GHz [P2] and (f) 10.5 GHz [P2]

In a diversity system the envelope correlation coefficient (ECC) is an important measure of diversity performance. ECC with a value of greater than 0.5 can typically degrade the diver‐ sity performance. The envelope correction coefficient of the proposed antenna is also calcu‐ lated from the simulated and measured S-parameters as described in [41] using (5) and shown in Figure 15.

$$\rho\_c = \frac{|\: \mathbb{S}^\*|\: \mathbb{S}\_{22} \star \mathbb{S}^\*|\: \mathbb{S}\_{22}\: \vert^2}{\left(1 \cdot \prod |\: \mathbb{S}\_{11}\:|^2 + \|\: \mathbb{S}\_{21}\:|^2\right)\left(1 \cdot \prod |\: \mathbb{S}\_{22}\:|^2 + \|\: \mathbb{S}\_{12}\:|^2\right)}\tag{5}$$

It is evident from Figure 15 that, the proposed antenna has a very low value of ECC throughout the operating band which clarifies that the antenna is a good candidate for mod‐ ern wireless communication systems employing polarization diversity.

The efficiency of the antenna for both ports is measured using Wheeler cap method [31] and is also incorporated in Figure 16. The antenna provides efficiency better than 70% in the

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Advanced UWB systems are realized using an impulse-based technology in which the time domain performance are equally as important as frequency domain properties. The time do‐ main characteristics including group delay, antenna transfer function, impulse response and

The group delay of the antenna for face to face orientation is measured using the time do‐ main measurement facility of Anritsu Ms4647A network analyzer by exciting two identical antennas kept in the far field (when P1 is excited P2 is terminated with 50 Ω load and viceversa).The antenna provides a group delay (Figure 17) which remains almost constant with variations less than 1ns except at the notch band. The antenna transfer function defined by (2) is also calculated and incorporated in Figure 17.It shows fairly flat magnitude variations for each port of the antenna, which is less than 10dB throughout the band. The impulse re‐ sponse of the antenna is evaluated by convoluting the modulated Gaussian monocycle de‐ fined in (3) with h(t), the inverse Fourier transform of antenna transfer function. The spectrum of this impulse fully covers the FCC band and comply with the emission stand‐ ards specified when, the amplitude constant A = 1.6 and pulse duration parameter T = 67ps. The input and output waveforms for both ports are shown in Figure 18. It can be seen that the radiated pulse through two ports of the proposed antenna retain the information with

UWB spectrum while it drops to 25% in the notch band.

fidelity are measured, analyzed and discussed in this section.

**Figure 17.** Measured group delay and antenna transfer function between identical antennas

*3.2.2. Time domain analysis*

minimum dispersion.

**Figure 15.** Measured and simulated envelope correlation coefficients from S parameters

The gain of the antenna for both ports are measured independently (when P1 is excited, P2 is terminated with 50Ω load and vice-versa) using gain comparison method. In this the gain is measured in both the planes of the radiation pattern and the peak gain is selected from either plane which gives the larger value. It is clear from the Figure 16 that, the antenna has moderate gain with variations less than 2.23dBi throughout the operating band while the gain drops up to -9.3dBi in the notch frequency.

**Figure 16.** Measured peak gain and radiation efficiency

The efficiency of the antenna for both ports is measured using Wheeler cap method [31] and is also incorporated in Figure 16. The antenna provides efficiency better than 70% in the UWB spectrum while it drops to 25% in the notch band.

#### *3.2.2. Time domain analysis*

**Figure 15.** Measured and simulated envelope correlation coefficients from S parameters

gain drops up to -9.3dBi in the notch frequency.

220 Advancement in Microstrip Antennas with Recent Applications

**Figure 16.** Measured peak gain and radiation efficiency

The gain of the antenna for both ports are measured independently (when P1 is excited, P2 is terminated with 50Ω load and vice-versa) using gain comparison method. In this the gain is measured in both the planes of the radiation pattern and the peak gain is selected from either plane which gives the larger value. It is clear from the Figure 16 that, the antenna has moderate gain with variations less than 2.23dBi throughout the operating band while the

Advanced UWB systems are realized using an impulse-based technology in which the time domain performance are equally as important as frequency domain properties. The time do‐ main characteristics including group delay, antenna transfer function, impulse response and fidelity are measured, analyzed and discussed in this section.

The group delay of the antenna for face to face orientation is measured using the time do‐ main measurement facility of Anritsu Ms4647A network analyzer by exciting two identical antennas kept in the far field (when P1 is excited P2 is terminated with 50 Ω load and viceversa).The antenna provides a group delay (Figure 17) which remains almost constant with variations less than 1ns except at the notch band. The antenna transfer function defined by (2) is also calculated and incorporated in Figure 17.It shows fairly flat magnitude variations for each port of the antenna, which is less than 10dB throughout the band. The impulse re‐ sponse of the antenna is evaluated by convoluting the modulated Gaussian monocycle de‐ fined in (3) with h(t), the inverse Fourier transform of antenna transfer function. The spectrum of this impulse fully covers the FCC band and comply with the emission stand‐ ards specified when, the amplitude constant A = 1.6 and pulse duration parameter T = 67ps. The input and output waveforms for both ports are shown in Figure 18. It can be seen that the radiated pulse through two ports of the proposed antenna retain the information with minimum dispersion.

**Figure 17.** Measured group delay and antenna transfer function between identical antennas

(a) (b)

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A compact uniplanar dual polarized UWB antenna with notch functionality is developed for diversity applications. The antenna features a 2:1 VSWR band from 2.8-11 GHz while show‐ ing the rejection performance in the frequency band 4.99-6.25 GHz along with a reasonable isolation better than 15dB. The measured radiation pattern and the envelop correlation coef‐ ficient indicate that the antenna provides good polarization diversity performance. Time do‐ main analysis of the antenna shows faithful reproduction of the transmitted pulse even with

The authors would like to acknowledge Rogers Corporation for providing high frequency

[1] FCC, "First Report and Order: Revision of Part 15 of the Commissions Rules Regard‐

ing Ultra-Wideband Transmission Systems," ET Docket 98-153, Apr. 2002.

**Figure 19.** Effect of major antenna parameters on antenna characteristics (a) r1 (b) ls

**3.4. Conclusions**

a notch band.

**Acknowledgements**

**Author details**

**References**

laminates through university program.

Gijo Augustin , Bybi P. Chacko and Tayeb A. Denidni

National Institute of Scientific Research (INRS), Montreal QC, Canada

**Figure 18.** Input and output impulses through P1 and P2 of the antenna

The cross correlation between the source pulse St (t) and the radiated pulse Sr(t) is then eval‐ uated by the fidelity factor, F using (4). As shown in Table 4, high value of Fidelity reveals that the antenna imposes negligible effects on the transmitted pulses [42].


**Table 4.** Fidelity Factor of the proposed antenna for both ports.

#### **3.3. Parametric analysis**

In order to provide more information to the antenna engineers during the design and opti‐ mization process, a parametric analysis of important antenna parameters which influence the lower cutoff frequency (r1) and notch band (*l*s) are conducted and presented.

Figure 19a shows that the first resonant frequency of the antenna drifts down when the ground radius r1 is increased from 22 to 25 mm. This clarifies the initial assumption that, the first resonance frequency is determined by the radius r1. It is also clear that the ground strip length has a slight influence on the isolation characteristics. An optimum value r1=23mm is selected for required performance. The tuning of notch band with slot length ls is shown through the parametric analysis in Figure 19b. As the ls varies from 16mm to 20mm, the peak notch frequency shifts from 6.1 GHz to 5GHz. These parameters are very sensitive to the overall performance of the antenna and therefore it is required to provide extreme care during the fabrication process.

**Figure 19.** Effect of major antenna parameters on antenna characteristics (a) r1 (b) ls

#### **3.4. Conclusions**

**Figure 18.** Input and output impulses through P1 and P2 of the antenna

222 Advancement in Microstrip Antennas with Recent Applications

**Table 4.** Fidelity Factor of the proposed antenna for both ports.

**3.3. Parametric analysis**

during the fabrication process.

The cross correlation between the source pulse St (t) and the radiated pulse Sr(t) is then eval‐ uated by the fidelity factor, F using (4). As shown in Table 4, high value of Fidelity reveals

In order to provide more information to the antenna engineers during the design and opti‐ mization process, a parametric analysis of important antenna parameters which influence

Figure 19a shows that the first resonant frequency of the antenna drifts down when the ground radius r1 is increased from 22 to 25 mm. This clarifies the initial assumption that, the first resonance frequency is determined by the radius r1. It is also clear that the ground strip length has a slight influence on the isolation characteristics. An optimum value r1=23mm is selected for required performance. The tuning of notch band with slot length ls is shown through the parametric analysis in Figure 19b. As the ls varies from 16mm to 20mm, the peak notch frequency shifts from 6.1 GHz to 5GHz. These parameters are very sensitive to the overall performance of the antenna and therefore it is required to provide extreme care

**Orientation Fidelity Factor**

that the antenna imposes negligible effects on the transmitted pulses [42].

**P1** 0.88 **P2** 0.85

the lower cutoff frequency (r1) and notch band (*l*s) are conducted and presented.

A compact uniplanar dual polarized UWB antenna with notch functionality is developed for diversity applications. The antenna features a 2:1 VSWR band from 2.8-11 GHz while show‐ ing the rejection performance in the frequency band 4.99-6.25 GHz along with a reasonable isolation better than 15dB. The measured radiation pattern and the envelop correlation coef‐ ficient indicate that the antenna provides good polarization diversity performance. Time do‐ main analysis of the antenna shows faithful reproduction of the transmitted pulse even with a notch band.

#### **Acknowledgements**

The authors would like to acknowledge Rogers Corporation for providing high frequency laminates through university program.

#### **Author details**

Gijo Augustin , Bybi P. Chacko and Tayeb A. Denidni

National Institute of Scientific Research (INRS), Montreal QC, Canada

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**Section 4**

**Circular Polarization**


**Section 4**

**Circular Polarization**

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**Chapter 10**

**Axial Ratio Bandwidth of a**

**Circularly Polarized Microstrip Antenna**

Microstrip antenna has been widely used due to its many advantages, such as, small volume, light weight, easy to get various polarization and easy to be integrated (Dang & Liu, 1999). Microstrip antenna can adopt many methods to obtain circular polarization (Xue and Zhong, 2002). And some technologies can achieve the miniaturization of the microstrip antenna (Xue and Zhong, 2002). Also there are some methods to enhance the impedance bandwidth of the

In this chapter, we focus on the axial ratio bandwidth of a circularly polarized microstrip antenna. The previous reference books discussed the axial ratio bandwidth less, always said that the axial ratio bandwidth of a circularly polarized microstrip antenna was limited, and it was less than the impedance bandwidth of a linearly polarized microstrip antenna (Lin & Nie, 2002). The group of Professor Ahmed A. Kishk has done a lot of research work on the circularly polarized microtrip antenna recently (Yang et al., 2008); (Yang et al., 2007); (Yang et al., 2006); (Chair et al., 2006); (Kishk et al., 2006). We adopt theoretical analysis and simulation by CST Microwave Studio to give out the method of improving the axial ratio bandwidth of the

First, we briefly introduce the basic methods which can form the circular polarization for a microstrip antenna, including the single-feed and the multiple-feed. When using multiple-feed for one patch, the sequential rotation technology (Hall et al., 1989) can be adopted. Starting from the mechanism of circular polarization obtaining from multiple-feed method, the multiple-feed can improve the axial ratio bandwidth of a microstrip antenna effectively than the single-feed microstrip antenna is demonstrated by theoretical analysis and simulation. The

> © 2013 Sun et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use,

© 2013 Sun et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

distribution, and reproduction in any medium, provided the original work is properly cited.

miniaturized microstrip antenna (Liu et al., 2002) ; (Wang & Gao, 2003).

Li Sun, Gang Ou, Yilong Lu and Shusen Tan

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/54664

circularly polarized microstrip antenna.

more feeds, the better the axial ratio bandwidth is.

**1. Introduction**

### **Chapter 10**

## **Axial Ratio Bandwidth of a Circularly Polarized Microstrip Antenna**

Li Sun, Gang Ou, Yilong Lu and Shusen Tan

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/54664

#### **1. Introduction**

Microstrip antenna has been widely used due to its many advantages, such as, small volume, light weight, easy to get various polarization and easy to be integrated (Dang & Liu, 1999). Microstrip antenna can adopt many methods to obtain circular polarization (Xue and Zhong, 2002). And some technologies can achieve the miniaturization of the microstrip antenna (Xue and Zhong, 2002). Also there are some methods to enhance the impedance bandwidth of the miniaturized microstrip antenna (Liu et al., 2002) ; (Wang & Gao, 2003).

In this chapter, we focus on the axial ratio bandwidth of a circularly polarized microstrip antenna. The previous reference books discussed the axial ratio bandwidth less, always said that the axial ratio bandwidth of a circularly polarized microstrip antenna was limited, and it was less than the impedance bandwidth of a linearly polarized microstrip antenna (Lin & Nie, 2002). The group of Professor Ahmed A. Kishk has done a lot of research work on the circularly polarized microtrip antenna recently (Yang et al., 2008); (Yang et al., 2007); (Yang et al., 2006); (Chair et al., 2006); (Kishk et al., 2006). We adopt theoretical analysis and simulation by CST Microwave Studio to give out the method of improving the axial ratio bandwidth of the circularly polarized microstrip antenna.

First, we briefly introduce the basic methods which can form the circular polarization for a microstrip antenna, including the single-feed and the multiple-feed. When using multiple-feed for one patch, the sequential rotation technology (Hall et al., 1989) can be adopted. Starting from the mechanism of circular polarization obtaining from multiple-feed method, the multiple-feed can improve the axial ratio bandwidth of a microstrip antenna effectively than the single-feed microstrip antenna is demonstrated by theoretical analysis and simulation. The more feeds, the better the axial ratio bandwidth is.

© 2013 Sun et al.; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 Sun et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Then, the detail analysis of the axial ratio bandwidth including when the amplitudes have some difference and the phase excitation of the feed point has an offset according to the designed central frequency in manufacture are described.

At last, the example of circularly polarized microstrip antenna design and test are in the section 5. Due to the volume limited in the project, we choose two feeds for the microstrip antenna.

**Figure 2.** Patch shape

**Figure 3.** Feed methods

feed, etc.

**2.2. Single-feed realization method**

**Figure 4.** Patch shape of single-feed circularly polarized microstrip antenna

Single-feed for the patch to form circular polarization is based on the cavity model of microstrip antenna. The two orthogonal polarized degenerate modes which can formed the circular polarization can be obtained by corner cut, quasi-square, slot, etc, and the patch shape (Lin & Nie, 2002) can be seen in Fig.4. The feed methods can adopt coaxial probe feed, aperture couple

Axial Ratio Bandwidth of a Circularly Polarized Microstrip Antenna

http://dx.doi.org/10.5772/54664

231

The axial ratio 3dB bandwidth of the circularly polarized microstrip antenna is much less than the impedance bandwidth of the linearly polarized microstrip antenna. Via application, the axial ratio 3dB bandwidth the single-feed circularly polarized microstrip antenna is limited at

### **2. Circularly polarized method**

#### **2.1. Simple microstrip antennas**

Generally, the configuration of the simple microstrip antenna (Ung, 2007) is showed as in Fig. 1. It can be simply formed by a dielectric substrate through photoetching technology or etching process. In the configuration, there are the metallic patch of certain shape on the top, the substrate layer of certain thickness and the ground plane on the bottom. The dielectric constant and the thickness of the dielectric substrate material, the shape and size of the top patch and the feeding method determine the performance of the microstrip antenna.

**Figure 1.** Configuration of the microstrip antenna

The shape of the top metallic patch can be various. Such as square, rectangle, circle, triangle, ellipse and unconventional shape, etc. The feed methods include coaxial probe feed, microstrip line feed, aperture couple feed, etc (Ung, 2007); (stutzman & Thiele, 1997). The simple micro‐ strip antenna is usually linearly polarized. The bandwidth of the linearly polarized microstrip antenna is described by the impedance bandwidth.

#### Axial Ratio Bandwidth of a Circularly Polarized Microstrip Antenna http://dx.doi.org/10.5772/54664 231

**Figure 3.** Feed methods

Then, the detail analysis of the axial ratio bandwidth including when the amplitudes have some difference and the phase excitation of the feed point has an offset according to the

At last, the example of circularly polarized microstrip antenna design and test are in the section 5. Due to the volume limited in the project, we choose two feeds for the microstrip antenna.

Generally, the configuration of the simple microstrip antenna (Ung, 2007) is showed as in Fig. 1. It can be simply formed by a dielectric substrate through photoetching technology or etching process. In the configuration, there are the metallic patch of certain shape on the top, the substrate layer of certain thickness and the ground plane on the bottom. The dielectric constant and the thickness of the dielectric substrate material, the shape and size of the top patch and

The shape of the top metallic patch can be various. Such as square, rectangle, circle, triangle, ellipse and unconventional shape, etc. The feed methods include coaxial probe feed, microstrip line feed, aperture couple feed, etc (Ung, 2007); (stutzman & Thiele, 1997). The simple micro‐ strip antenna is usually linearly polarized. The bandwidth of the linearly polarized microstrip

the feeding method determine the performance of the microstrip antenna.

designed central frequency in manufacture are described.

**2. Circularly polarized method**

230 Advancement in Microstrip Antennas with Recent Applications

**Figure 1.** Configuration of the microstrip antenna

antenna is described by the impedance bandwidth.

**2.1. Simple microstrip antennas**

#### **2.2. Single-feed realization method**

Single-feed for the patch to form circular polarization is based on the cavity model of microstrip antenna. The two orthogonal polarized degenerate modes which can formed the circular polarization can be obtained by corner cut, quasi-square, slot, etc, and the patch shape (Lin & Nie, 2002) can be seen in Fig.4. The feed methods can adopt coaxial probe feed, aperture couple feed, etc.

**Figure 4.** Patch shape of single-feed circularly polarized microstrip antenna

The axial ratio 3dB bandwidth of the circularly polarized microstrip antenna is much less than the impedance bandwidth of the linearly polarized microstrip antenna. Via application, the axial ratio 3dB bandwidth the single-feed circularly polarized microstrip antenna is limited at about 35%of the difference of the two resonant frequencies (Lin & Nie, 2002). So we must find methods to improve the axial ratio bandwidth of the circularly polarized microstrip antenna.

#### **2.3. Multiple-feed realization method**

A circularly polarized electromagnetic wave can be divided into two equal amplitudes linearly polarized components both in space and in time. Suppose that the two orthogonal polarized components are

$$
\vec{E}\_{\,\,\,x} = E\_{\,\,\,\nu} \quad \vec{E}\_{\,\,y} = E \, e^{\frac{\pi}{2}} \, \,\_{\,\,\nu}
$$

then we have

$$
\bar{E}\_y = E e^{j\frac{\pi}{2}} = j\bar{E}\_x.\tag{1}
$$

Suppose that

so the two orthogonal components are

2 *pπ <sup>M</sup>* cos <sup>2</sup>*p<sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> *Ee <sup>j</sup>*

2 *pπ <sup>M</sup>* sin 2*pπ*

According to the following formula,

sin(*<sup>x</sup>* <sup>+</sup> <sup>1</sup>

cos(*<sup>x</sup>* <sup>+</sup> <sup>1</sup>

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> cos 2(*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup>*

<sup>2</sup> (*<sup>M</sup>* <sup>−</sup><sup>1</sup> <sup>+</sup> 1)

*<sup>M</sup>* <sup>+</sup> cos <sup>4</sup>*p<sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> cos <sup>4</sup>*p<sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> sin<sup>2</sup> (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> cos<sup>2</sup> (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup>*

4*pπ <sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> sin

*<sup>M</sup>* <sup>+</sup> cos<sup>2</sup> <sup>2</sup>*p<sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> *Ee <sup>j</sup>*

sin 1 <sup>2</sup> *<sup>n</sup><sup>α</sup>* sin 1 2 *α*

4*pπ <sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> sin

> sin 1 <sup>2</sup> (*<sup>M</sup>* <sup>−</sup><sup>1</sup> <sup>+</sup> 1)

sin 1 <sup>2</sup> *<sup>n</sup><sup>α</sup>* sin 1 2 *α*

cos <sup>1</sup>

*<sup>M</sup>* <sup>+</sup> cos<sup>2</sup> <sup>2</sup>*p<sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> sin<sup>2</sup> <sup>2</sup>*p<sup>π</sup>*

<sup>2</sup> (cos <sup>2</sup>*p<sup>π</sup>*

<sup>2</sup> (cos <sup>2</sup>*p<sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> *<sup>E</sup>* ⇀

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> cos<sup>2</sup> (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> *Ee <sup>j</sup>*

<sup>2</sup> (*<sup>n</sup>* <sup>+</sup> 1)*α*),

2(*M* −1)*pπ M*

> 2*pπ <sup>M</sup>* <sup>=</sup>

<sup>2</sup> (*<sup>n</sup>* <sup>+</sup> 1)*α*),

*M*

2*pπ <sup>M</sup>* <sup>=</sup>

*M*

*M*

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> cos 2(*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> cos 2(*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup>*

2(*M* −1)*pπ*

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> *Ee <sup>j</sup>*

*<sup>M</sup>* <sup>+</sup> <sup>1</sup>

(*M* −1) *pπ*

*<sup>M</sup>* <sup>+</sup> *<sup>j</sup>* sin<sup>2</sup> *<sup>p</sup><sup>π</sup>*

sin (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup> M* sin *<sup>p</sup><sup>π</sup> M*

sin( *<sup>p</sup><sup>π</sup>* <sup>−</sup> *<sup>p</sup><sup>π</sup> <sup>M</sup>* )

> sin *<sup>p</sup><sup>π</sup> M*

> > *<sup>M</sup>* ) <sup>=</sup> *<sup>M</sup>*

*<sup>M</sup>* ) <sup>=</sup> *<sup>M</sup>*

*<sup>M</sup>* sin (*<sup>M</sup>* <sup>−</sup>1)*P<sup>π</sup> M*

(*M* −1) *pπ M*

*<sup>M</sup>* cos (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup> M*

(*M* −1) *pπ*

<sup>2</sup> *<sup>j</sup>* sin

*<sup>M</sup>* sin (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup> M*

*<sup>M</sup>* cos (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup> M*

*<sup>M</sup>* <sup>+</sup> sin<sup>2</sup> <sup>2</sup>*p<sup>π</sup>*

sin(*pπ*)=0,

cos(*pπ*)= −1.

2 ,

2 ,

4*pπ <sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> sin

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> sin<sup>2</sup> (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup>*

2(*M* −1)*pπ M*

Axial Ratio Bandwidth of a Circularly Polarized Microstrip Antenna

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233

*M*

2*pπ <sup>M</sup>* <sup>+</sup> sin

*E* ⇀ <sup>1</sup> =*E*, *E* ⇀ <sup>2</sup> <sup>=</sup>*Ee <sup>j</sup> pπ <sup>M</sup>* , *E* ⇀ <sup>3</sup> <sup>=</sup>*Ee <sup>j</sup>* 2 *pπ <sup>M</sup>* , ......, *E* ⇀ *<sup>M</sup>* <sup>=</sup>*Ee <sup>j</sup>*

*Ex* =*E* ⇀ <sup>1</sup> + *E* ⇀ 2cos *<sup>p</sup><sup>π</sup> <sup>M</sup>* <sup>+</sup> *<sup>E</sup>* ⇀ <sup>3</sup>cos <sup>2</sup>*p<sup>π</sup>*

*Ey* =*E* → 2sin *Pπ <sup>M</sup>* <sup>+</sup> *<sup>E</sup>* ⇀ 3sin 2*Pπ <sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> *<sup>E</sup>* ⇀

= *Ee <sup>j</sup> pπ <sup>M</sup>* sin *<sup>p</sup><sup>π</sup>*

= 1 <sup>2</sup> sin 2*pπ <sup>M</sup>* <sup>+</sup> sin

∑ *k*=1 *n*

sin 2*pπ <sup>M</sup>* <sup>+</sup> sin

=

∑ *k*=1 *n*

sin(*x* + *kα*)=

we can get

sin (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup> M* sin *<sup>p</sup><sup>π</sup> M*

and according to

*<sup>M</sup>* <sup>+</sup> cos <sup>4</sup>*p<sup>π</sup>*

sin (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup> M* sin *<sup>p</sup><sup>π</sup> M*

cos(*x* + *kα*)=

we can get

cos <sup>2</sup>*p<sup>π</sup>*

<sup>1</sup> <sup>+</sup> cos<sup>2</sup> *<sup>p</sup><sup>π</sup>*

<sup>=</sup> *<sup>M</sup>* <sup>2</sup> <sup>+</sup> <sup>1</sup> <sup>2</sup> <sup>+</sup> <sup>1</sup>

<sup>=</sup> *<sup>M</sup>* <sup>2</sup> <sup>−</sup> <sup>1</sup> 2 − 1

sin<sup>2</sup> *<sup>p</sup><sup>π</sup>*

=

=*E* + *Ee <sup>j</sup>*

=1 <sup>+</sup> cos<sup>2</sup> *<sup>p</sup><sup>π</sup>*

*pπ <sup>M</sup>* cos *<sup>p</sup><sup>π</sup>*

Multiple-feed for one patch can adopt the sequential rotation technology. The technology of sequential rotation is successfully used in circularly polarized antenna array design (Hall et al., 1989). Multiple-feed has an appropriate phase difference between excitations, and this can improve the axial ratio bandwidth and reduce the cross-polarization. The mode exited by each feed for one patch can be regarded as the mode exited by each element in the array. So, in the case of using *M* feed points, the *mth* feed point's phase *φem* can be expressed as

$$
\varphi\_{em} = (m-1)\frac{p\pi}{M}1 \le m \le M\_\prime \tag{2}
$$

where *P* is an integer.

Each feed point's physical position must have some symmetry, seen in fig.5. Through simu‐ lation, finding that fixing the first feed point position, other feed points rotate the correspond‐ ing phase differences between itself and the first feed point. The center is the disc center. In the case of *P<M*, and the last feed point does not rotate to the first feed point, it can improve axial ratio bandwidth.

**Figure 5.** Feed position of multiple-feed

Suppose that

about 35%of the difference of the two resonant frequencies (Lin & Nie, 2002). So we must find methods to improve the axial ratio bandwidth of the circularly polarized microstrip antenna.

A circularly polarized electromagnetic wave can be divided into two equal amplitudes linearly polarized components both in space and in time. Suppose that the two orthogonal polarized

> <sup>2</sup> . *<sup>j</sup> y x E Ee jE* p

Multiple-feed for one patch can adopt the sequential rotation technology. The technology of sequential rotation is successfully used in circularly polarized antenna array design (Hall et al., 1989). Multiple-feed has an appropriate phase difference between excitations, and this can improve the axial ratio bandwidth and reduce the cross-polarization. The mode exited by each feed for one patch can be regarded as the mode exited by each element in the array. So, in the

case of using *M* feed points, the *mth* feed point's phase *φem* can be expressed as

j

( 1) 1 , *em <sup>p</sup> m mM M* p

Each feed point's physical position must have some symmetry, seen in fig.5. Through simu‐ lation, finding that fixing the first feed point position, other feed points rotate the correspond‐ ing phase differences between itself and the first feed point. The center is the disc center. In the case of *P<M*, and the last feed point does not rotate to the first feed point, it can improve

= = v v (1)

= - ££ (2)

**2.3. Multiple-feed realization method**

232 Advancement in Microstrip Antennas with Recent Applications

components are

*<sup>x</sup>* =*E*, *E* ⇀ *<sup>y</sup>* <sup>=</sup>*Ee <sup>j</sup> π* 2 ,

then we have

where *P* is an integer.

axial ratio bandwidth.

**Figure 5.** Feed position of multiple-feed

*E* ⇀

$$
\vec{E}\_1 = E, \,\,\,\vec{E}\_2 = E \,\,e^{\,\,\frac{\rho\pi}{M}}, \,\,\,\vec{E}\_3 = E \,\,e^{\,\,\frac{2\rho\pi}{M}}, \,\,\,\dots, \,\,\,\vec{E}\_M = E \,\,e^{\,\,\frac{(M-1)\rho\pi}{M}}
$$

so the two orthogonal components are

$$\begin{split} &E\_{x} = \tilde{E}\_{1} + \tilde{E}\_{2}\cos\frac{p\pi}{M} + \tilde{E}\_{3}\cos\frac{2p\pi}{M} + \dots + \tilde{E}\_{M}\cos\frac{(M-1)p\pi}{M} \\ &= E + E \cdot e^{\frac{p\pi}{M}}\cos\frac{p\pi}{M} + E \cdot e^{\frac{2p\pi}{M}}\cos\frac{2p\pi}{M} + \dots + \dots + e^{\frac{(M-1)p\pi}{M}}\cos\frac{(M-1)p\pi}{M} \\ &= 1 + \cos^{2}\frac{p\pi}{M} + \cos^{2}\frac{2p\pi}{M} + \dots + \cos^{2}\frac{(M-1)p\pi}{M} + \frac{1}{2}f\Big[\sin\frac{2p\pi}{M} + \sin\frac{4p\pi}{M} + \dots + \sin\frac{2(M-1)p\pi}{M}\right] \\ &E\_{y} = \tilde{E}\_{2}\sin\frac{p\pi}{M} + \tilde{E}\_{3}\sin\frac{2p\pi}{M} + \dots + \tilde{E}\_{M}\sin\frac{(M-1)p\pi}{M} \\ &= \tilde{E}e^{\frac{p\pi}{M}}\sin\frac{p\pi}{M} + \tilde{E}e^{\frac{2p\pi}{M}}\sin\frac{2p\pi}{M} + \dots + \tilde{E}e^{\frac{(M-1)p\pi}{M}}\sin\frac{(M-1)p\pi}{M} \\ &+ \frac{1}{2}\Big[\sin\frac{2p\pi}{M} + \sin\frac{4p\pi}{M} + \dots + \sin\frac{2(M-1)p\pi}{M}\right] + f\Big[\sin^{2}\frac{p\pi}{M} + \sin^{2}\frac{2p\pi}{M} + \dots + \sin^{2}\frac{(M-1)p\pi}{M}\Big] \\ \end{split}$$

According to the following formula,

$$\sum\_{k=1}^{n} \sin(\alpha + k\alpha) = \frac{\sin\frac{1}{\mathfrak{D}} n\alpha}{\sin\frac{1}{\mathfrak{D}}\alpha} \sin\left(\alpha + \frac{1}{\mathfrak{D}}(n+1)\alpha\right).$$

we can get

$$\begin{aligned} & \left[ \sin \frac{2p\pi}{M} + \sin \frac{4p\pi}{M} + \dots + \sin \frac{2(M-1)p\pi}{M} \right] \\ & - \frac{\sin \frac{(M-1)p\pi}{M}}{\sin \frac{p\pi}{M}} \sin \left[ \frac{1}{2} (M-1+1) \frac{2p\pi}{M} \right] \approx \frac{\sin \frac{(M-1)p\pi}{M}}{\sin \frac{p\pi}{M}} \sin (p\pi) = 0, \end{aligned}$$

and according to

$$\sum\_{k=1}^{n} \cos(\alpha + k\alpha) = \frac{\sin\frac{1}{2}n\alpha}{\sin\frac{1}{2}\alpha} \cos\left(\alpha + \frac{1}{2}(n+1)\alpha\right),$$

we can get

$$\begin{aligned} &\frac{2p\pi\tau}{M} + \cos\frac{4p\pi}{M} + \dots + \cos\frac{2(M-1)p\pi}{M} \\ & -\frac{\sin\frac{(M-1)p\pi}{M}}{\sin\frac{p\pi}{M}}\cos\left[\frac{1}{2}(M-1+1)\frac{2p\pi}{M}\right] - \frac{\sin\left(p\pi-\frac{p\pi}{M}\right)}{\sin\frac{p\pi}{M}}\cos(p\pi) = -1. \end{aligned}$$

$$\begin{aligned} &1 + \cos^2\frac{p\pi}{M} + \cos^2\frac{2p\pi}{M} + \dots + \cos^2\frac{(M-1)p\pi}{M} \\ &= \frac{M}{2} + \frac{1}{2} + \frac{1}{2}\left(\cos\frac{2p\pi}{M} + \cos\frac{4p\pi}{M} + \dots + \cos\frac{2(M-1)p\pi}{M}\right) - \frac{M}{2}, \\ &\sin^2\frac{p\pi}{M} + \sin^2\frac{2p\pi}{M} + \dots + \sin^2\frac{(M-1)p\pi}{M} \\ &= \frac{M}{2} - \frac{1}{2} - \frac{1}{2}\left(\cos\frac{2p\pi}{M} + \cos\frac{4p\pi}{M} + \dots + \cos\frac{2(M-1)p\pi}{M}\right) - \frac{M}{2}, \end{aligned}$$

so

$$1 + \cos^2\frac{p\pi}{M} + \cos^2\frac{2p\pi}{M} + \dots + \cos^2\frac{(M-1)p\pi}{M} = \sin^2\frac{p\pi}{M} + \sin^2\frac{2p\pi}{M} + \dots + \sin^2\frac{(M-1)p\pi}{M} = \frac{M}{2}$$
 Therefore we can get

$$E\_y = \mathbf{j}E\_x.\tag{3}$$

where *OA* is the half major axis of the polarization ellipse, and the *OB* is the half minor axis of

The elliptical polarization of electromagnetic wave can be divided into two linearly polarized components. One's orientation is along x-axis, and the other is along y-axis. Suppose that the

where *E1* is the amplitude of the linear polarization along x-axis *Ex*, and *E2* is the amplitude of the linear polarization along y-axis *Ey*. δis the phase difference between *Ex* and *Ey*. Based on the above, we will analyze the axial ratio bandwidth of the multiple-feed microstrip antenna

Assume that the amplitudes excitation of each feed are equal, mutual coupling is small, and it can be neglected. Only the frequency changes the phase excitation relationship between the feed points. In the real case, usually using power splitter with separation to realize the equal amplitude excitation, and using different microstrip line length to realize the phase excitation

> <sup>1</sup> sin( ), *<sup>x</sup> EE t z* = w b

<sup>2</sup> sin( ). *<sup>y</sup> EE t z* = -+ wb

> <sup>1</sup> sin , *<sup>x</sup> EE t* = w

<sup>2</sup>(sin cos cos sin ), *<sup>y</sup> EE t t* = wd

 d

 wd

(5)

Axial Ratio Bandwidth of a Circularly Polarized Microstrip Antenna

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235

(6)

(7)

+ (8)

2 2 1, *x xy y aE bE E cE* - += (9)

two linearly polarized components are *Ex* =*E*1sin(*ωt* −*βz*), *Ey* =*E*2sin(*ωt* −*βz* + *δ*),

the polarization ellipse.

in the next section.

At *z=0*,

where sin*ω<sup>t</sup>* <sup>=</sup>*Ex*

*E*1

Substitute (7) into (8), we can get

, cos*ωt* = 1−(

*Ex E*1 ) 2

**3.2. Axial ratio bandwidth of two feeds**

difference. So the assumption is reasonable.

Two feeds: *M=2, P=1*. The two orthogonal electric fields are

That is (1), so the multiple-feed method above has realized the circular polarization.

#### **3. Theoretical analysis of the axial ratio bandwidth**

#### **3.1. Axial ratio**

We can use the polarization ellipse to describe the elliptical polarization. The instantaneous electric field orientation can figure out an ellipse in the space, seen in Fig.6.

**Figure 6.** Polarization ellipse

The axial ratio is defined as

$$AR = \bigvee\_{\mathsf{OB}} \{ \mathbf{1} \le AR \le \infty \} \tag{4}$$

where *OA* is the half major axis of the polarization ellipse, and the *OB* is the half minor axis of the polarization ellipse.

The elliptical polarization of electromagnetic wave can be divided into two linearly polarized components. One's orientation is along x-axis, and the other is along y-axis. Suppose that the two linearly polarized components are *Ex* =*E*1sin(*ωt* −*βz*), *Ey* =*E*2sin(*ωt* −*βz* + *δ*),

where *E1* is the amplitude of the linear polarization along x-axis *Ex*, and *E2* is the amplitude of the linear polarization along y-axis *Ey*. δis the phase difference between *Ex* and *Ey*. Based on the above, we will analyze the axial ratio bandwidth of the multiple-feed microstrip antenna in the next section.

#### **3.2. Axial ratio bandwidth of two feeds**

Assume that the amplitudes excitation of each feed are equal, mutual coupling is small, and it can be neglected. Only the frequency changes the phase excitation relationship between the feed points. In the real case, usually using power splitter with separation to realize the equal amplitude excitation, and using different microstrip line length to realize the phase excitation difference. So the assumption is reasonable.

Two feeds: *M=2, P=1*. The two orthogonal electric fields are

$$E\_{\pm} = E\_1 \sin(\alpha t - \beta z),\tag{5}$$

$$E\_y = E\_2 \sin(\alpha t - \beta z + \delta). \tag{6}$$

At *z=0*,

so

<sup>1</sup> <sup>+</sup> cos<sup>2</sup> *<sup>p</sup><sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> cos<sup>2</sup> <sup>2</sup>*p<sup>π</sup>*

234 Advancement in Microstrip Antennas with Recent Applications

Therefore we can get

**3.1. Axial ratio**

**Figure 6.** Polarization ellipse

The axial ratio is defined as

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> cos<sup>2</sup> (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup>*

**3. Theoretical analysis of the axial ratio bandwidth**

electric field orientation can figure out an ellipse in the space, seen in Fig.6.

*<sup>M</sup>* =sin<sup>2</sup> *<sup>p</sup><sup>π</sup>*

That is (1), so the multiple-feed method above has realized the circular polarization.

We can use the polarization ellipse to describe the elliptical polarization. The instantaneous

*<sup>M</sup>* <sup>+</sup> sin<sup>2</sup> <sup>2</sup>*p<sup>π</sup>*

*<sup>M</sup>* <sup>+</sup> <sup>⋯</sup> <sup>+</sup> sin<sup>2</sup> (*<sup>M</sup>* <sup>−</sup>1)*p<sup>π</sup>*

. *y x E jE* = (3)

*AR OA* (1 ) *AR OB* = £ £¥ (4)

*<sup>M</sup>* <sup>=</sup> *<sup>M</sup>*

2

$$E\_{\pm} = E\_1 \sin \alpha t \,\prime \tag{7}$$

$$E\_y = E\_2(\sin\alpha t \cos\delta + \cos\alpha t \sin\delta),\tag{8}$$

$$\text{where } \sin\omega t = \prescript{E\_\chi}{\begin{vmatrix} E\_{1'} & \cos\omega t = \sqrt{1 - \binom{E\_\chi}{E\_1}} \end{vmatrix}} $$

Substitute (7) into (8), we can get

$$\left| aE\_x \right|^2 - bE\_x E\_y + cE\_y \, ^2 = 1,\tag{9}$$

where

$$a = \frac{1}{E\_1 ^2 \sin^2 \delta}, \ b = \frac{2 \cos \delta}{E\_1 E\_2 \sin^2 \delta}, \ c = \frac{1}{E\_2 ^2 \sin^2 \delta}.$$

Construct an ellipse equation

$$\frac{E\_{\text{x}}\,^{\text{2}}}{A^{2}} + \frac{E\_{\text{y}}\,^{\text{2}}}{B^{2}} = 1,\tag{10}$$

In other words, the phase excitation difference is 90°. At *z=0*, the two orthogonal electric

 wd

> w

> > d

 d

> dw

2 2 1, *x xy y aE bE E cE* - += (17)

2 2 3 3 2 2 ( ) 1 2cos . 1 2cos ( )

d

d

(18)

(14)

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237

Axial Ratio Bandwidth of a Circularly Polarized Microstrip Antenna

(15)

(16)

1 3 sin sin( 2 ), *<sup>x</sup> E E tE t* =- + w

2 4 sin( ) sin( 3 ), *<sup>y</sup> EE t E t* = +- + wd

2 4 2 4 ( cos cos3 )sin ( sin sin 3 )cos . *<sup>y</sup> E E E tE E t* = - +-

 dw

d

2

fields are

where

cos*ωt* =

where

*<sup>a</sup>* <sup>=</sup> <sup>1</sup> 4*E*<sup>1</sup> 2sin<sup>4</sup> *δ* ,

*<sup>c</sup>* <sup>=</sup> cos<sup>2</sup>

4*E*<sup>1</sup> 2sin<sup>4</sup> *δ* +

So

*<sup>b</sup>* <sup>=</sup> cos*δ*cos2*<sup>δ</sup> E*1 2sin<sup>4</sup> *δ* +

*δ*

sin*ωt* = 1−(

In the case of *E1=E2=E3=E4*,

2*Ex*cos*δ* −*Ey* −2*E*1sin*δ*

Substitute into (16), we can get

2*Ex*cos*δ* −*Ey* <sup>−</sup>2*E*1sin*<sup>δ</sup>* )

> cos*δ E*1 2sin<sup>2</sup> *δ* ,

1 4*E*<sup>1</sup> 2sin<sup>2</sup> *δ* .

> *<sup>A</sup> ac ac b AR B ac ac b*

+- - + - = = <sup>=</sup>

++ - + +

where

*Ex* '=*Ex*cos*θ* −*E s <sup>y</sup> inθ*, *Ey* '= *Ex*sin*θ* + *E c <sup>y</sup> osθ*.

Thus (10) becomes,

$$\text{Li}(\frac{\cos^2\theta}{A^2} + \frac{\sin^2\theta}{B^2})E\_x^2 - (\frac{\sin 2\theta}{A^2} - \frac{\sin 2\theta}{B^2})E\_x E\_y + (\frac{\sin^2\theta}{A^2} + \frac{\cos^2\theta}{B^2})E\_y^2 = 1. \tag{11}$$

Through (9) and (11), we can get

$$A = \sqrt{\frac{2}{a+c+\sqrt{\left(a-c\right)^2+b^2}}},$$

$$B = \sqrt{\frac{2}{a+c-\sqrt{\left(a-c\right)^2+b^2}}}.$$

So

$$AR = \frac{A}{B} = \sqrt{\frac{(E\_1/E\_2)^2 + 1 - \sqrt{(E\_1/E\_2)^4 + 1 + 2\cos 2\delta(E\_1/E\_2)^2}}{\left(E\_1/E\_2\right)^2 + 1 + \sqrt{(E\_1/E\_2)^4 + 1 + 2\cos 2\delta(E\_1/E\_2)^2}}}.\tag{12}$$

Two feeds, when *E1/E2=1*, we can get (13) from (12).

$$AR = \text{tg}\frac{\delta}{2}.\tag{13}$$

#### **3.3. Axial ratio bandwidth of four feeds**

We analyze the axial ratio bandwidth of multiple-feed antenna, in the case of ampli‐ tude excitations are equal, and mutual coupling is neglected. Four feeds, when *M=4, P=2*.

In other words, the phase excitation difference is 90°. At *z=0*, the two orthogonal electric fields are

$$E\_{\pm} = E\_1 \sin \alpha t - E\_3 \sin(\alpha t + 2\delta),\tag{14}$$

$$E\_y = E\_2 \sin(\alpha t + \delta) - E\_4 \sin(\alpha t + 3\delta),\tag{15}$$

where

where

*<sup>a</sup>* <sup>=</sup> <sup>1</sup> *E*1 2sin<sup>2</sup>

where

*Ex*

*<sup>δ</sup>* , *<sup>b</sup>* <sup>=</sup> 2cos*<sup>δ</sup> <sup>E</sup>*1*E*2sin<sup>2</sup>

236 Advancement in Microstrip Antennas with Recent Applications

Construct an ellipse equation

'=*Ex*cos*θ* −*E s <sup>y</sup> inθ*, *Ey*

qq

<sup>2</sup> + *b* <sup>2</sup> ,

<sup>2</sup> + *b* <sup>2</sup> .

**3.3. Axial ratio bandwidth of four feeds**

Two feeds, when *E1/E2=1*, we can get (13) from (12).

Through (9) and (11), we can get

Thus (10) becomes,

*<sup>A</sup>*<sup>=</sup> <sup>2</sup>

*<sup>B</sup>* <sup>=</sup> <sup>2</sup>

So

*a* + *c* + (*a* −*c*)

*a* + *c* − (*a* −*c*)

*<sup>δ</sup>* , *<sup>c</sup>* <sup>=</sup> <sup>1</sup> *E*2 2sin<sup>2</sup> *δ* .

'= *Ex*sin*θ* + *E c <sup>y</sup> osθ*.

'2 '2 2 2 1, *<sup>y</sup> <sup>x</sup> <sup>E</sup> <sup>E</sup> A B*

2 2 2 2

qq

22 22 22 cos sin sin 2 sin 2 sin cos

*<sup>A</sup> EE EE E E AR B EE EE E E*

++ ++

.

We analyze the axial ratio bandwidth of multiple-feed antenna, in the case of ampli‐ tude excitations are equal, and mutual coupling is neglected. Four feeds, when *M=4, P=2*.

<sup>2</sup> *AR tg* d

+- ++ = =

( )( ) ( )1. *<sup>x</sup> x y <sup>y</sup> E E E E AB AB AB*

2 2

24 2 1 2 1 2 1 2 24 2 1 2 1 2 1 2 ( ) 1 ( ) 1 2cos2 ( ) . ( ) 1 ( ) 1 2cos2 ( )

d

(12)

d

= (13)

 q

+ -- ++ = (11)

+ = (10)

 q

$$E\_y = (E\_2 \cos \delta - E\_4 \cos 3\delta) \sin at + (E\_2 \sin \delta - E\_4 \sin 3\delta) \cos at. \tag{16}$$

In the case of *E1=E2=E3=E4*,

$$\cos\omega t = \frac{2E\_x\cos\delta - E\_y}{-2E\_1\sin\delta}$$

$$\sin\omega t = \sqrt{1 - \left(\frac{2E\_x\cos\delta - E\_y}{-2E\_1\sin\delta}\right)^2}$$

Substitute into (16), we can get

$$\left| a\mathbf{E}\_x \right|^2 - b\mathbf{E}\_x \mathbf{E}\_y + c\mathbf{E}\_y \mathbf{j}^2 = \mathbf{1},\tag{17}$$

where

$$\begin{aligned} a &= \frac{1}{4E\_1 2\sin^4\delta}, \\ b &= \frac{\cos\delta\cos 2\delta}{E\_1 2\sin^4\delta} + \frac{\cos\delta}{E\_1 2\sin^2\delta}, \\ c &= \frac{\cos^2\delta}{4E\_1 2\sin^4\delta} + \frac{1}{4E\_1 2\sin^2\delta}. \end{aligned}$$

So

$$AR = \frac{A}{B} = \sqrt{\frac{a+c-\sqrt{(a-c)^2+b^2}}{a+c+\sqrt{(a-c)^2+b^2}}} = \sqrt{\frac{1-2\cos^3\delta}{1+2\cos^3\delta}}.\tag{18}$$

That is

$$AR = \sqrt{\frac{1 - 2\cos^3\delta}{1 + 2\cos^3\delta}}.\tag{19}$$

#### **3.4. Comparison of the two feeds and the four feeds**

Next we give out the expression for phase excitation difference δ between the two feeds. The feed network substrate's relative dielectric constant is ε*r*, the substrate thickness is *h*, and the width of the microstrip line is *W*. With the theory of the microstrip line, the effective dielectric constantε*re* is (Lin & Nie, 2002)

$$
\varepsilon\_{re} = \frac{\varepsilon\_r + 1}{2} + \frac{\varepsilon\_r - 1}{2} (1 + \frac{12h}{W})^{-\frac{1}{2}}.\tag{20}
$$

**Figure 7.** Simulation files of two feeds and four feeds

**Figure 8.** Axial ratio bandwidth comparison between two feeds and four feeds

different ratio of E1 and E2, showing in Fig.9.

**4. Axial ratio bandwidth analysis when manufacture error exist**

When two feeds, assume that the amplitudes excitation are equal at every frequency. But if we substitute (22) into (12), we can get the changing of the axial ratio bandwidth according to the

Axial Ratio Bandwidth of a Circularly Polarized Microstrip Antenna

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239

The phase velocity's wavelength λ*p* of the quasi-TEM wave propagated in the micro‐ strip line is

$$
\lambda\_p = \frac{c}{f\sqrt{\varepsilon\_{re}}},
\tag{21}
$$

where *c* is the velocity of light in the vacuum, and *f* is frequency.

Assume that the microstrip line length *x* which providing 90° phase excitation according to the central frequency, provide δ phase excitation in fact due to the changing of the frequency, *δ/x* = 360*/λp*, then

$$
\delta = \frac{360 \text{xf} \sqrt{\varepsilon\_{re}}}{c}.
\tag{22}
$$

The phase excitation difference of each feed in the feed network is designed according to the central frequency. The phase excitation difference which provided by the microstrip line is changing according to the changing frequency. This will affect the circular polarization out side the central frequency.

We use the CST microwave studio to simulate the multiple-feed microstrip antenna. The simulation files are showed in Fig.7. Thorough simulation and calculation, we give out the axial ratio bandwidth comparison between two feeds and four feeds in Fig.8. Through the theoretical computation, we demonstrate that multiple-feed for one patch can effectively improve the axial ratio bandwidth. The axial ratio 3dB bandwidth of two feeds can achieve 42.6%, and four feeds can achieve 74%.

**Figure 7.** Simulation files of two feeds and four feeds

That is

3 3 1 2cos . 1 2cos

Next we give out the expression for phase excitation difference δ between the two feeds. The feed network substrate's relative dielectric constant is ε*r*, the substrate thickness is *h*, and the width of the microstrip line is *W*. With the theory of the microstrip line, the effective dielectric

<sup>2</sup> 1 1 <sup>12</sup> (1 ) . 2 2

The phase velocity's wavelength λ*p* of the quasi-TEM wave propagated in the micro‐

, *<sup>p</sup> re*

*c f*

e

Assume that the microstrip line length *x* which providing 90° phase excitation according to the central frequency, provide δ phase excitation in fact due to the changing of the frequency,

> <sup>360</sup> . *re xf c* e

The phase excitation difference of each feed in the feed network is designed according to the central frequency. The phase excitation difference which provided by the microstrip line is changing according to the changing frequency. This will affect the circular polarization out

We use the CST microwave studio to simulate the multiple-feed microstrip antenna. The simulation files are showed in Fig.7. Thorough simulation and calculation, we give out the axial ratio bandwidth comparison between two feeds and four feeds in Fig.8. Through the theoretical computation, we demonstrate that multiple-feed for one patch can effectively improve the axial ratio bandwidth. The axial ratio 3dB bandwidth of two feeds can achieve

+ - -

*r r*

l

d

where *c* is the velocity of light in the vacuum, and *f* is frequency.

 e d

(19)

d

1

=+ + (20)

<sup>=</sup> (21)

= (22)

*h W*

*AR*

**3.4. Comparison of the two feeds and the four feeds**

238 Advancement in Microstrip Antennas with Recent Applications

*re*

e

e

constantε*re* is (Lin & Nie, 2002)

strip line is

*δ/x* = 360*/λp*, then

side the central frequency.

42.6%, and four feeds can achieve 74%.


**Figure 8.** Axial ratio bandwidth comparison between two feeds and four feeds

#### **4. Axial ratio bandwidth analysis when manufacture error exist**

When two feeds, assume that the amplitudes excitation are equal at every frequency. But if we substitute (22) into (12), we can get the changing of the axial ratio bandwidth according to the different ratio of E1 and E2, showing in Fig.9.

**Figure 9.** Axial ratio bandwidth of different amplitudes excitation of the two feeds

We can get the conclusion that the amplitude difference between the two feeds affects the axial ratio badly. When the amplitude ratio of the two feeds is 3dB, the axial ratio 3dB bandwidth has already disappeared.

Next we have a look at the axial ratio bandwidth changing when the phase excitation designed at the central frequency has an offset. In the feed network, change the microstrip line length *x* which provides 90° phase excitation to the length which provides 85.8° phase excitation. Using the same process, we can give out the changing of the axial ratio bandwidth when two feeds amplitudes are equal in Fig.10. When two feeds amplitudes ratio is 2dB in Fig.11.

**Figure 11.** Axial ratio bandwidth of phase excitation has an offset at the central frequency in case of E1/E2=2dB

limited in the project.

**5.1. Design**

realize.

**5. Antenna design example**

in antenna manufacture. The feed network is in Fig.13.

We can see that there is an offset on the axial ratio bandwidth when the phase excitation designed at the central frequency has an offset. From our theoretical analysis, we can get the conclusion that the multiple-feed technology can improve the axial ratio bandwidth of the microstrip antenna effectively. To get a wide band circularly polarized microstrip antenna, first, we must determine the most feed points we can use in the design according to the size

Axial Ratio Bandwidth of a Circularly Polarized Microstrip Antenna

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The more feeds, the better the axial ratio bandwidth of the circularly polarized microstrip antenna. But the feed network is more complicated and the feed network needs more space to

We design a small antenna, using two feeds. Two linearly polarized components which are equal amplitude and 90°phase difference form the circular polarization. The patch shape is in Fig.12 (Hall et al., 1989), and the stubs on the patch are used to debug the resonant frequency

**Figure 10.** Axial ratio bandwidth of phase excitation has an offset at the central frequency in case of E1/E2=0dB

**Figure 11.** Axial ratio bandwidth of phase excitation has an offset at the central frequency in case of E1/E2=2dB

We can see that there is an offset on the axial ratio bandwidth when the phase excitation designed at the central frequency has an offset. From our theoretical analysis, we can get the conclusion that the multiple-feed technology can improve the axial ratio bandwidth of the microstrip antenna effectively. To get a wide band circularly polarized microstrip antenna, first, we must determine the most feed points we can use in the design according to the size limited in the project.

#### **5. Antenna design example**

#### **5.1. Design**

**Figure 9.** Axial ratio bandwidth of different amplitudes excitation of the two feeds

240 Advancement in Microstrip Antennas with Recent Applications

has already disappeared.

We can get the conclusion that the amplitude difference between the two feeds affects the axial ratio badly. When the amplitude ratio of the two feeds is 3dB, the axial ratio 3dB bandwidth

Next we have a look at the axial ratio bandwidth changing when the phase excitation designed at the central frequency has an offset. In the feed network, change the microstrip line length *x* which provides 90° phase excitation to the length which provides 85.8° phase excitation. Using the same process, we can give out the changing of the axial ratio bandwidth when two feeds

amplitudes are equal in Fig.10. When two feeds amplitudes ratio is 2dB in Fig.11.

**Figure 10.** Axial ratio bandwidth of phase excitation has an offset at the central frequency in case of E1/E2=0dB

The more feeds, the better the axial ratio bandwidth of the circularly polarized microstrip antenna. But the feed network is more complicated and the feed network needs more space to realize.

We design a small antenna, using two feeds. Two linearly polarized components which are equal amplitude and 90°phase difference form the circular polarization. The patch shape is in Fig.12 (Hall et al., 1989), and the stubs on the patch are used to debug the resonant frequency in antenna manufacture. The feed network is in Fig.13.

**5.2. Simulation analysis**

microstrip antenna.

feeds microstrip antenna are showed in Fig.14.

**Figure 14.** Simulation configuration of the single-feed and the two feeds

**Figure 15.** Axial ratio simulation results of the single-feed and the two feeds

Simulate the two feeds microstrip antenna we design in the above section using the CST microwave studio. We compare the difference in the axial ratio bandwidth between the singlefeed and the two feeds through simulation. The configurations of the single-feed and the two

Axial Ratio Bandwidth of a Circularly Polarized Microstrip Antenna

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243

The simulation results of the axial ratio of the single-feed and the two feeds at zenith are showed in Fig.15. We can see that the axial ratio bandwidth of the single-feed is very limited. For the two feeds, the phase difference of the two equal amplitudes and 90° phase difference linearly polarized components according to the centre frequency change slowly and smoothly with the frequency band. This can improve the axial ratio bandwidth of a circularly polarized

**Figure 12.** Patch shape

**Figure 13.** Feed network

#### **5.2. Simulation analysis**

**Figure 12.** Patch shape

242 Advancement in Microstrip Antennas with Recent Applications

**Figure 13.** Feed network

Simulate the two feeds microstrip antenna we design in the above section using the CST microwave studio. We compare the difference in the axial ratio bandwidth between the singlefeed and the two feeds through simulation. The configurations of the single-feed and the two feeds microstrip antenna are showed in Fig.14.

**Figure 14.** Simulation configuration of the single-feed and the two feeds

The simulation results of the axial ratio of the single-feed and the two feeds at zenith are showed in Fig.15. We can see that the axial ratio bandwidth of the single-feed is very limited. For the two feeds, the phase difference of the two equal amplitudes and 90° phase difference linearly polarized components according to the centre frequency change slowly and smoothly with the frequency band. This can improve the axial ratio bandwidth of a circularly polarized microstrip antenna.

**Figure 15.** Axial ratio simulation results of the single-feed and the two feeds

#### **5.3. Test result**

The manufactured two feeds microstrip antenna is tested in the anechoic chamber. The test result of the axial ratio is showed in Fig.16.

**Author details**

, Gang Ou2

, Yilong Lu3

1 Beijing Satellite Navigation Center, China

tronics industry, 7-50537-495-8

Stanford University. March, 2007

2002) page numbers (331-336), 17(4)

*search*, PIER 80, page numbers , 45-61.

978-0-47102-590-0US

*nautics*, February. 2000) page numbers (15-18), 26(1)

and Shusen Tan1

2 College of Electronic Science and Engineering, National University of Defense Technology,

Axial Ratio Bandwidth of a Circularly Polarized Microstrip Antenna

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245

3 School of Electrical and Electronic Engineering, Nanyang Technological University,

[1] Dang, H. S, & Liu, Y. G. (1999). The analysis and design of a microstrip antenna. (in Chinese). *Journal of Detection and Control*, March. 1999) page numbers (35-39), 21(1)

[2] Hall, P. S, Dahele, J. S, & James, J. R. (1989). Design principles of sequentially fed, wide bandwidth, circularly polarized microstrip antennas, *Proceedings of IEE Micro‐ waves. Antennas and Propagation*, 0095-0107X, October, 1989, IEE, 136(5), 381-389.

[3] Lin, C. L, & Nie, Z. P. (2002). *Antenna engineering handbook*, Publishing house of elec‐

[4] Liu, Z. F, Lu, S. W, & Li, S. Z. (2002). Improved Method for Designing Wideband Mi‐ crostrip Antennas. (in Chinese). *Journal of Beijing University of Aeronautics and Astro‐*

[5] Stutzman, W, & Thiele, G. (1997). *Antenna theory and design*, Wiley,

[6] Ung Suok Kim(2007). Mitigation of signal biases introduced by controlled reception pattern antennas in a high integrity carrier phase differential GPS system, *dissertation*.

[7] Wang, C. M, & Gao, X. J. (2003). Technologies of broadband microstrip antenna. (in Chinese). *Electronic Warfare Technology*, September. 2003) page numbers (23-26), 18(5)

[8] Xue, R. F, & Zhong, S. S. (2002). Survey and progress in circular polarization technol‐ ogy of microstrip antennas. (in Chinese). *Chinese Journal of Radio Science*, August.

[9] Yang, S. S, Lee, K. F, Kishk, A. A, & Luk, K. M. (2008). Design and study of wideband single feed circularly polarized microstrip antennas. *Progress In Electromagnetics Re‐*

Li Sun1

China

Singapore

**References**

**Figure 16.** Axial ratio test result

In simulation, the two feeds are ideal equal amplitudes and 90° phase difference. In the manufacture, the microstrip line feed network provides the two equal amplitudes and 90° phase difference excitations. Due to the dielectric constant error of the substrate material and error of manufacture, the axial ratio bandwidth of the microstrip antenna get worse compared to the simulation result. The axial ratio 3dB bandwidth tested of the microstrip antenna is about 10MHz.

#### **6. Conclusion**

Microstrip antenna has been used in every field, due to its many advantages. Our main research topic in this chapter was how to improve the axial ratio bandwidth of a circularly polarized microstrip antenna. Multiple-feed method can realize the circular polarization for a microstrip antenna. Circularly polarized microstrip patch antenna designed by the multiple-feed method adopting the sequential rotation technology can improve the axial ratio bandwidth effectively. In this chapter, we demonstrate it by theoretical analysis.

Through simulation by CST Microwave Studio and theoretical computation, the axial ratio 3dB bandwidth of two feeds can achieve 42.6%, and four feeds can achieve 74%.

In engineering, choosing the most feed points according to the feed network space limited in the project can improve the axial ratio bandwidth of a circularly polarized microstrip antenna. And it is at the price of a complicated feed network compared to the few feed points design.

#### **Author details**

**5.3. Test result**

**Figure 16.** Axial ratio test result

10MHz.

**6. Conclusion**

result of the axial ratio is showed in Fig.16.

244 Advancement in Microstrip Antennas with Recent Applications

The manufactured two feeds microstrip antenna is tested in the anechoic chamber. The test

In simulation, the two feeds are ideal equal amplitudes and 90° phase difference. In the manufacture, the microstrip line feed network provides the two equal amplitudes and 90° phase difference excitations. Due to the dielectric constant error of the substrate material and error of manufacture, the axial ratio bandwidth of the microstrip antenna get worse compared to the simulation result. The axial ratio 3dB bandwidth tested of the microstrip antenna is about

Microstrip antenna has been used in every field, due to its many advantages. Our main research topic in this chapter was how to improve the axial ratio bandwidth of a circularly polarized microstrip antenna. Multiple-feed method can realize the circular polarization for a microstrip antenna. Circularly polarized microstrip patch antenna designed by the multiple-feed method adopting the sequential rotation technology can improve the axial ratio bandwidth effectively.

Through simulation by CST Microwave Studio and theoretical computation, the axial ratio

In engineering, choosing the most feed points according to the feed network space limited in the project can improve the axial ratio bandwidth of a circularly polarized microstrip antenna. And it is at the price of a complicated feed network compared to the few feed points design.

3dB bandwidth of two feeds can achieve 42.6%, and four feeds can achieve 74%.

In this chapter, we demonstrate it by theoretical analysis.

Li Sun1 , Gang Ou2 , Yilong Lu3 and Shusen Tan1

1 Beijing Satellite Navigation Center, China

2 College of Electronic Science and Engineering, National University of Defense Technology, China

3 School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore

#### **References**


[10] Yang, S. L. S, Kishk, A. A, & Lee, K. F. (2008). Wideband Circularly Polarized Anten‐ na with L-shaped Slot. *IEEE Transactions on Antennas and Propagations*, June. 2008) page numbers 1780-1783, 56(6)

**Section 5**

**Recent Advanced Applications**

