UWB Technology-Based Devices

#### **Chapter 1**

## Introductory Chapter: Novel Developments in UWB Technology

*Rafael Vargas-Bernal*

#### **1. Introduction**

Like any technology that evolves, UWB systems must reduce their complexity, power consumption, sustainability, and the possibility of reconfiguration, to achieve the highest performance compared to other competitors for implementations of high-accuracy localization systems [1–8]. Despite the advances achieved so far, UWB systems face challenges such as mitigating errors from non-line-of-sight paths and jamming signal interference in dense environments, especially in extreme conditions [1]. In addition, in the pursuit of an upgrade, UWB systems must integrate machine learning capabilities as well as sensor data fusion. The main disadvantages of UWB technology are its high cost and increased power consumption. Until now, it has been established that UWB technology presents interference with the radio frequency systems found in its surroundings and vice versa. The data capacity of UWB systems is restricted because short-duration pulse coding implies longer information synchronization times. The purpose of this chapter is to present the different alternatives that UWB technology is investigating to improve its properties using integrated circuit design as well as materials science and engineering to establish itself as an emerging strategy for its application in high-accuracy radio frequency location systems.

The remainder of the chapter is divided as follows: Section 2 introduces the basic concepts associated with UWB technology. Novel approaches for the use of UWB technology are summarized in Section 3. Some new developments in UWB systems are discussed in Section 4. Finally, the conclusions of the chapter are provided.

#### **2. Basic concepts**

The Federal Communications Commission (FCC) has established that for medical applications, Ultra-Wide Band (UWB) is set in the range of 3.1–10.6 GHz [1–8]. UWB systems represent a technological alternative for the development of applications such as the Internet of Things (IoT), energy harvesting, biomedical, and wireless communication systems [5]. Among the significant advantages that UWB systems have are their 7.5 GHz bandwidth, high data rate, reduced complexity, low power consumption, narrowband interference attenuation, as well as multiple transceiver architectures for different ranges. Also, the bandwidth is greater than 500 MHz or has a value of 20 percent of the center frequency. The power spectral density has a value of less than −41.3 dBm/MHz across the frequency band. For indoor positioning applications, UWB systems have short message lengths, high data rates, and bandwidths, low transmission

powers, as well as high penetration capabilities. UWB signals have multiple frequency components to penetrate obstacles in the signal transmission paths [1]. The spectrum of UWB systems was allocated as free since 2002 for commercial use. Thanks to the low power spectral density, UWB systems do not interfere with other radio frequency signals. Furthermore, high accuracy and good multipath performance are possible due to the short pulse duration that UWB systems have. The specific applications that UWB systems have at the industrial level are smart logistics, the smart city, the smart factory, vehicle tracking, waste management, and robot positioning. The use of UWB technology in internal logistics allows for combining precision, reliability, and scalability in the tracking of goods and people, as well as in the automated control of vehicles. Smart logistics for real-time applications is necessary to track resources, materials, and employees at the same time to plan strategies to optimize the use of UWB technology.

So far six different categories have been developed for UWB signals [1, 8]. In an ultra-wideband system using radio pulses with pulses on the order of nanoseconds, it presents a low-duty cycle for transferring information by varying the phase, pulse shape, duration, and amplitude of the radio signal used [1]. This technology known as IR-UWB is governed by the IEEE 802.15.4z standard. Pseudorandom coding is used for ultra-wideband (UWB) technology through direct sequences called (DS-UWB) which is produced by amplitude modulation of a set of short pulses. Through Orthogonal Frequency Division Multiplexing (OFDM), it is possible to take advantage of the full bandwidth by dividing it into multiple frequency sub-bands using Quadrature Phase Shift Keying (QPSK) modulation to produce multi-bandwidth UWB systems (MB-UWB). The use of frequency-hopping ultra-bandwidth (FH-UWB) systems using variant frequency carriers can be used for periodic narrowband transmission. When frequency hopping involves selection through codes using discrete steps until the bandwidth is reached, it is called the Stepped Frequency Hopping UWB (SFH-UWB) system. The latter category involves the carrier frequency variation being generated by a voltage-controlled oscillator via continuously variable speed which is known as a Swept Frequency UWB (SF-UWB) system.

Typical UWB-based positioning systems include fixed sensors known as anchors, moving targets known as tags, a location server, and a system interface [1]. The location server has the function of storing and processing the data provided by the sensors, while the system interface, commonly a smartphone, computer, or tablet, allows viewing the positioning results. For a two-dimensional positioning system, at least three anchors are required to operate. In the case of a three-dimensional system, it is necessary to use at least four anchors. In addition, more complex systems involving the integration of environments such as the Internet of Things (IoT) or multi-sensor technologies lead to the use of more sophisticated and intelligent user interfaces, network gateways, and navigation frameworks.

#### **3. Novel approaches for the use of ultra-wideband (UWB) technology**

Wearable tracking systems are and will be important for monitoring the physical activity of high-performance athletes through ultra-wideband (UWB) positioning sensors to determine performance parameters such as speed, distance covered, acceleration, and change of direction of travel [3]. Until now, UWB systems achieve a positioning accuracy of up to 10 cm, because this decreases by half to one meter in a three-dimensional location. This positioning tracking is also required to determine the round-trip time of robots indoors or in real-time bus parking and tracking or

#### *Introductory Chapter: Novel Developments in UWB Technology DOI: http://dx.doi.org/10.5772/intechopen.110609*

patient location tracking inside and outside hospitals. The design of UWB devices must address the feasibility of tuning using alternative configurations, different channel frequencies, wide bit rate ranges, and preamble length possibilities.

The adoption of UWB technology will allow the application of distributed robotic systems [1]. In-house robotic applications such as home cleaning or warehouse transportation can offer last-mile delivery solutions. Smart manufacturing in Industry 4.0 must track the entire production process to always make the right decisions in realtime. Internal logistics at the factory floor level should lead to increased transparency, safety, and productivity. Positioning by UWB systems, when reaching precisions in the range of centimeters, uses triangulation or trilateration methods. Devices under UWB technology must be small to be able to develop portable equipment so as not to create fixed infrastructure which would reduce potential applications.

The advances achieved should bring new opportunities such as secure access control, device-to-device communications, as well as location-based services [1]. The automotive industry is implementing key management systems using mobile phones which allow access and start the operations of cars only when the digital key and the precise location of the phone match the user of the vehicle.

UWB systems are continuously introducing new integrated circuits to develop new algorithms and with-it new applications to exploit machine learning, collaborative positioning, and sensor fusion [1]. Sensor fusion seeks to maximize output information by computationally combining measurements from multiple sources. To make more reliable and precise estimates, it is necessary to merge several tracking systems into one UWB system. Machine learning makes complex tasks accessible by allowing computers to learn by themselves to perform tasks autonomously without needing to be programmed. Multilateration techniques use distant observables with direct signal propagation models to estimate the position of an agent. The estimation is more reliable by dynamic state models which use both current observations as well as previous positions using Bayesian statistics.

#### **4. New developments in ultra-wideband (UWB) systems**

The novel components that are being implemented by different research groups around the world for the optimization of ultra-wideband (UWB) systems are outlined in **Figure 1**. The use of integrated circuit design as well as materials science and engineering has a direct influence on the development of these new technological alternatives. These can be used for the implementation of ultra-wideband (UWB) systems.

An optical radar system based on a UWB resonator circuit using a microstrip line (MSL) has been proposed for monitoring the movement of human beings, whether healthy or sick [2]. The basic requirements of the design without degrading the quality factor (*Q*) for full bandwidth are a high signal-to-noise ratio, low power consumption, accuracy, and robustness. The resonator is implemented using an RLC circuit with all its components connected in parallel, having a photodetector at its input and an amplifier at its output, as shown in **Figure 2**. The resonator impedance is expressed according to Eq. 1, it must be kept almost constant at a value of 50 ohms with a bandwidth of 7.2 GHz when tuning the value of the inductor. The use of the microstrip allows a match of approximately 53.5 ohms which is close to the standard impedance in the range of 2–12 GHz. The inductor is implemented using a microstripbased transmission line made of copper layers of a 65 nm process for radio frequency.

$$Z = R \parallel Ls \parallel \frac{1}{Cs} = \frac{RLs}{RLCs^2 + LCs + R} \tag{1}$$

The possibility of designing bandpass filters for UWB systems with cutoff bands at 5.18, 5.86, and 7.92 GHz has been explored [4]. Other filter properties that were achieved such as insertion loss of less than 1.5 dB, return loss of less than 15 dB, as well as high attenuation of unwanted in-band signals were also achieved. The filter structure is based on four stepwise controlled impedance open stubs using uniform transmission lines which provide the required tunability. The stubs have been inserted between two transmission zeros with the central stub in the middle of the uniform transmission line, where the stubs for each of the bands have been branched as illustrated in **Figure 3**.

A transmitter operating in the 3–5 GHz band for ultra-wideband (UWB) impulse radio applications using on-off keying based on a tunable memristor has been

**Figure 1.**

*Novel components for UWB technology.*

**Figure 2.** *Electrical model of a resonator for UWB systems.*

#### **Figure 3.**

*The basic structure of a bandpass filter for UWB systems.*

proposed [5]. The tuning opportunity comes from two external control signals that are used to modify the value of the memristance and the width of the output pulse to control the bandwidth and its center frequency, as depicted in **Figure 4**. The contribution of the memristor is associated with the reduction of power consumption, generating a wide bandwidth and a tunable power spectral density. This transmitter was implemented under standard 0.18-micron CMOS technology using a 1.8 V power supply. This approach is easy to implement and has flexibility that makes it attractive from its design. The output pulse width ranges from 0.8 to 1.74 ns using a control signal, the output excursion is 483 mV peak-to-peak, and it dissipates an energy of 9.48 pJ/pulse applying a pulse repetition frequency of 10 MHz through a 50-ohm load resistor.

**Figure 4.** *Memristor-based transmitter for a UWB system.*

Another element of a UWB system that has been updated is the antenna. A planar monopole antenna operates in the range from 2.76 to 11 GHz in notch sub-bands in intervals from 3.75 to 4.81 and from 5.24 to 6.21 GHz, with a return loss of 10 dB [6]. These sub-bands are strategically placed to eliminate interference from other radio frequency bands. The tuning capability uses loaded stubs with four circular patches and two complementary split ring resonators operating as ground planes to achieve the cutoff bands. The implemented monopole antenna is shown in **Figure 5**.

A flared quasi-Yagi offset-fed monopole UWB antenna operating in the 3.06– 12.37 GHz range has been implemented using an FR-4 dielectric material with dimensions in centimeters [7]. In addition, the antenna has superior bandwidth, reliability, speed, and high resolution, advantages that are usable for UWB technology. The reflection coefficient was less than −10 dB for the previously reported bandwidth. The maximum gain was 10.07 dBi for a frequency of 10.4 GHz with a peak radiation efficiency of 92.64% and with a radiation efficiency of 73%.

The use of microstrips for direct sequence ultra-wideband (DS-UWB) technology design has been raised [8]. This design uses planar structures with a wide bandwidth that exploits the impedance and pattern for applications in the C, X, and Ku bands using short pulses using radio pulse and exploited in multipath cases. This type of antenna is very interesting for systems with the Internet of Things (IoT), multiple inputs and multiple outputs (MIMO), as well as high-speed and short-distance communications.

#### **5. Conclusions**

The success of UWB systems over GPS systems is that in both indoor and outdoor environments, it is the smallest location error of the former. UWB systems perform most effectively under short pulses spread over a wide bandwidth. Narrowband

signals from GPS systems degrade due to the multiple paths present. The accuracy of the GPS is compromised by the availability of repeaters and the time delay between repeaters and receivers.

Researchers worldwide will continue to look for design options that involve reduced complexity, a tendency to decrease power consumption, achieve sustainability, as well as tuning capabilities through reconfigurable options. The use of integrated circuit design as well as materials science and engineering has a direct influence on the development of novel technological alternatives. These can be used for the implementation of ultra-wideband (UWB) systems with better properties.

#### **Acknowledgements**

The author appreciates the support of the Instituto Tecnológico Superior de Irapuato to develop this research.

### **Thanks**

The author wants to thank his wife and son for their support and time to edit this book. The author appreciates the support of Ana Cink working for IntechOpen as an author service manager.

### **Author details**

Rafael Vargas-Bernal Higher Technological Institute of Irapuato, Irapuato, Guanajuato, México

\*Address all correspondence to: rvargasbernal@gmail.com

© 2023 The Author(s). Licensee IntechOpen. This chapter is 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.

### **References**

[1] Elsanhoury M, Mäkela P, Koljonen J, Välisuo P, Shamsuzzoha A, Mantere T, et al. Precision positioning for smart logistics using ultra-wideband technology-based indoor navigation: A review. IEEE Access. 2022;**10**:44413- 44445. DOI: 10.1109/access.2022.3169267

[2] Gorre P, Vignesh R, Song H, Kumar S. A 64 dBΩ, 25 Gb/s GFET based transimpedance amplifier with UWB resonator for optical radar detection in medical applications. Microelectronics Journal. 2021;**111**:105026. DOI: 10.1016/j. mejo.2021.105026

[3] Waqar A, Ahmad I, Habibi D, Phung QV. Analysis of GPS and UWB positioning system for athlete tracking. Measurement: Sensors. 2021;**14**:100036. DOI: 10.1016/j.measen.2020.100036

[4] Taibi A, Trabelsi M, Saadi AA. Efficient design approach of triple notched UWB filter. AEU - International Journal of Electronics and Communications. 2021;**131**:153619. DOI: 10.1016/j.aeue.2021.153619

[5] Barraj I, Bahloul MA, Masmoudi M. Design of 3-5 GHz Tunable memristorbased OOK-UWB transmitter. AEU - International Journal of Electronics and Communications. 2021;**132**:153664. DOI: 10.1016/j.aeue.2021.153664

[6] Puri SC, Das S, Tiary MG. UWB monopole antenna with dual-bandnotched characteristics. Microwave and Optical Technology Letters. 2020;**62**(3):1222-1229. DOI: 10.1002/ mop.32112

[7] Nella A, Bhowmick A, Rajagopal M. A novel offset feed flared monopole quasi-Yagi high directional UWB antenna. International Journal of

RF and Microwave Computer-Aided Engineering. 2021;**31**(6):e22653. DOI: 10.1002/mmce.22653

[8] Sarkar T, Ghosh A, Chakraborty S, Singh LLK, Chattopadhyay S. A new insightful exploration into a low profile ultra-wide-band (UWB) microstrip antenna for DS-UWB applications. Journal of Electromagnetic Waves and Applications. 2021;**35**(15):2001-2019. DOI: 10.1080/09205071.2021.1927855

#### **Chapter 2**

## Probe-Fed Polygonal Patch UWB Antennas

*Abhishek Joshi and Rahul Singhal*

#### **Abstract**

The chapter deals with the design of probe-fed planar antennas to operate at wider bands and techniques to improve peak or boresight gain using reflectors. The phenomenon of frequency excitation in dual-band, that is, C-band and X-band using the technique of partial removal of the ground plane, is well demonstrated here. The impedance bandwidth achieved by the sample antenna is 285 MHz and 380 MHz, respectively. The reduced ground plane technique is further exploited along with modifications in the shape of the ground plane to cover the entire ultra-wideband (UWB) range in a probe-fed hexagonal monopole antenna. Due to the existence of higher modes and especially when fed with a probe, UWB antennas are only capable of providing mediocre gain at higher frequencies. An approach to increase the probefed hexagonal UWB antenna's peak gain involves the utilization of an appropriate reflector. The antenna is given an artificial magnetic conductor (AMC)-based reflector, which increases the peak gain as well as boresight gain across a band ≤ UWB. Peak and boresight gains of 3.74 dB and 5.5 dB, respectively, are observed with AMC. The equivalent circuit model and simulated impedance results of the sample antennas are validated with the measurement results.

**Keywords:** probe-fed, polygonal patch, UWB antennas, coaxially fed, AMC reflector

#### **1. Introduction**

Antennas are essential front-end entities of modern wireless communication systems. Today's wireless communication systems utilize planar antennas, which are popular over other types of radiators, especially in personal communication devices for wireless access. The reason for the popularity of planar antennas is essentially credited to their being economical, low profile, and easy integration with portable and personal communication devices. The advantages of planar antenna do accompany some drawbacks too, for example narrow bandwidth, poor radiation efficiency, and low power handling capacity. The limitations of patch antennas that need to be addressed in the present communication system are their intrinsic narrow-band behavior and polarization purity [1]. A signal transmitted by any radio base station cannot maintain its polarization state as it transverses toward the mobile terminal device due to channel properties. Thus, the polarization purity of antennas installed in terminal devices cannot be represented as a very strong design constraint [2]. It is difficult to anticipate the polarization state of the signal received on an antenna, even

with the use of statistical analysis [3], suggesting that antennas should not be constructed based only on polarization assumptions for the reception. An antenna with a high cross-polarization level is a clear choice for polarization diversity applications and does not negatively affect radio-link performance as in cellular or satellite communications [4]. The necessity to keep the antenna dimensions as small as possible destroys the pretense of meeting greater bandwidth requirements. In the earlier generation of communication systems, the task is usually accomplished by techniques that rely on introducing slots or using reactive loads, but in current and future generation systems, subscriber expectation from service providers is extensive, and thus, novel solutions should be explored.

To guarantee that more services are available on various carrier frequencies, the possibility of a multi-frequency operation is expected in a communication link. Both wide-band and multi-frequency operations rely on the stimulation of two or more resonances, which in the case of wide-band antennas must resonate close together, while in the case of multi-frequency operation, they must resonate widely apart. Polygonal patch forms are an intriguing area for investigation among the patch antenna geometries that exhibit many resonances [5–9]. For an antenna designer to investigate and excite many resonances to obtain broadband or multi-resonant characteristics for the antenna, the patch size, the number of edges, the slope of the edges, etc. represent acceptable degrees of freedom [10, 11].

Complex electromagnetic wave interactions may be modeled using supercomputing in the frequency and time domains. It's challenging to create new antenna designs that can carry out demanding duties [12]. Kolundzija et al. [13] proposed an automated meshing of polygonal surfaces to segment a polygonal model into convex quadrilaterals to analyze efficiently as per electromagnetic theory. Sorokosz et al. [14] confirmed that a circular patch can be approximated with an appropriately designed polygon when the model analysis is performed. Many commercial simulation software have emerged during the past two decades, for example, computer simulation technologies (CST), Microwave Studio (MWS), Ansoft HFSS, etc., have supported the rapid advancement of polygonal patch antenna research. They have become fundamental tools in the design and simulation of planar antennas. The excitation and boundary conditions are satisfied via the method of moments (MoM), which makes use of integral equations that are discovered for the fields generated by unidentified currents. Maxwell's equations are transformed into difference equations via the full wave (FW) approach or the finite-difference time-domain (FDTD) method. The Rayleigh–Ritz variational approach is used by the finite element method (FEM) to solve Maxwell's equation as the vector wave equation [15]. Yikai et al. [16] reviewed characteristic modes for radiation problems from antenna design to feeding design and found that with the help of many unique and attractive features of control management, physical understandings of the radiating problems can be much clearer, computation burdens in antenna optimization procedure can be greatly alleviated, and designs with favorite features such as compact and low profile can often be obtained. After a real prototype has been built and measured in a lab, the CST MWS Suite enables virtual prototyping of one's idea, reducing any unpleasant surprises.

Various techniques are available for the fabrication of microstrip patch antenna, but a commonly popular economical fabrication technique such as the wet-etching method will be more suitable in case one of the objectives is technology transfer to the industry shortly. Photolithography technique can be used to transfer the mask image on electroplated copper on a printed circuit board (PCB) using negative photoresist,

and then, it is developed in a developer solution. The unexposed unwanted features are etched out in an etching chemical solution.

A polygon with an odd number of edges as in the case of pentagon geometries may be of a symmetrical shape as that of a regular hexagon with an even number of edges or can be asymmetric too. After the substrate thickness and permittivity are chosen, the resonant frequencies of a regular patch rely on the geometry of the conductor. By using the appropriate degrees of freedom, the resonances along the frequency axis may be controlled [11]. Polygonal patch geometries can be triangular or rectangular as per the conventional definition of the word *polygon,* but in general conception, polygon refers to geometries with edges greater than or equal to five [17]. The text in the chapter will follow this general conception.

The selection of a dielectric substrate for a patch antenna is one of the significant aspects of the antenna design. Many researchers have exploited different dielectric substrates with different permittivities for patch antenna in different applications. Radiofrequency (RF) energy may be provided to microstrip patch antennas using several methods. Contact feed and non-contact feed are two categories into which these approaches may be divided. Microstrip line and coaxial probe feeding are the most often used contact feeding methods, while aperture coupling and proximity coupling feeding are the most widely used non-contact methods. Distinct geometries of patch antenna like a triangular, rectangular, pentagon, hexagon, etc. are well explored by many researchers. By altering the substrate's dielectric constant, the patch's sizer and the conductor strip's metal thickness, any antenna design that is acceptable for operation across a range of impedance bandwidths may be produced. Hexagonal is a popular geometry used to design a stripline-fed monopole antenna [18–21] and is investigated in detail by Ray et al. [22]. There are dozens of research publications about microstrip patch antennas scattered among traditional periodicals. In a 2012 assessment of patch antenna development strategies, Lee et al. [15] discovered that all the ways that described widening the working bands of patch antennas result in increased volume, negating the low-profile benefit of microstrip patch antennas. Due to its broader band yet higher order modes, the hexagonal structure is favored over other geometries [22, 23]. Further use of the hexagonal shape may be used to produce lower modes and produce broader bands or UWBs.

Ground plane geometry plays a vital role in the design of polygonal patch antenna. For contemporary wireless communication systems, hexagonal monopole antennas fed at the edge and the vertex are extensively investigated at lower frequencies [24]. Because CPW-fed antennas cannot be used for the small overall construction, efficient direct probe feeding becomes the best option. However, employing a coaxial probe or connection to feed a direct-fed UWB monopole antenna presents a problem for antenna researchers. Antenna feed plays a significant role in exciting higher order mode and modification of the feed; such as using a larger diameter probe may permit the antenna to generate a higher order mode [25]. Even with a modified connector feed, the design of a probe-fed UWB planar antenna is still a challenge for the antenna research community. According to [26], adding more ground plane structures may raise the boresight gain of planar antennas; however, the strategy also results in larger antennas. For a stable and reliable radiation pattern, a technique for producing a directed pattern in a hexagonal UWB antenna fed via probe must be understood. The UWB monopole antenna's peak gain may be increased using a variety of methods, including a reflector with a frequency-selective surface (FSS) base. The gain of the patch antenna at higher frequencies within the operational range of the antenna may

be greatly increased by defects in the ground plane, such as the insertion of alternative slot geometries or alteration of the ground plane shape.

The literature survey concludes that although many researchers have explored polygonal geometries through their work, a systematic approach to understanding the effect of polygonal geometry over antenna performance has not been undertaken in the past and still is an interesting subject of research. The main limits of polygonal patch antennas in a present communication system are both the intrinsic narrow-band behavior and the polarization purity. The request to keep the antenna's overall dimensions small is often made in conjunction to meet these increased bandwidth requirements.

Every novel patch antenna that should be designed, developed, and characterized should achieve some of the common patch antenna features such as compact antenna size, operating band enhancement, gain enhancements, etc. To reduce the size of the antenna by moving the resonance frequency to the lower side, the ground plane defects and fractal geometries should be investigated. A printed circuit board with FR-4 as a dielectric will be an economic approach for designing the polygonal patch antenna. Recent studies point toward the use of coaxial feed as one of the approaches that may yield multiband or broadband antenna characteristics, which may be further exploited to achieve super wide-band characteristics. The literature review reports various attempts to address polygonal patch antenna(s) and to explore it more.

Based on the available literature, the motivation of the chapter is briefed as follows:


Using a survey of reported literature and preliminary work including hexagram design [27], pentaflake antenna [27], and polygonal patch antenna, it is observed that a probe-fed polygonal patch antenna is not much explored, with coaxial feed as one of the approaches that may yield multiband or broadband antenna characteristics, which may be further exploited to achieve super wide-band characteristics.

#### **2. Low cross-polarization vertex-fed hexagonal antenna**

Impedance mismatch affects probe-fed hexagonal patch antennas, particularly when the feed is situated near one of the polygon vertices. High cross-polar levels also affect hexagonal planar antennas. A technique for the low cross-polarization vertexfed hexagonal antenna is demonstrated. To indicate improvement in impedance values, vertex feeding is illustrated in this section. It has an impedance that is excessive when compared to the probe impedance. The suggested approach may be tuned

*Probe-Fed Polygonal Patch UWB Antennas DOI: http://dx.doi.org/10.5772/intechopen.110369*

to match the impedance and obtain excellent return loss. Here, a wide bandwidth (600 MHz) low cross-polarization vertex-fed hexagonal antenna operating at a frequency of 5 GHz is suggested [28]. Therefore, the antenna shown in **Figure 1** is a good fit for unlicensed UNII-1 indoor wireless local area network (LAN) applications. Antennas 1–3 (A1, A2, and A3) are similar in structure as shown in **Figure 1** but differ in their geometrical features, which are listed in **Table 1**. These developed antennas will demonstrate the impact of ground plane miniaturization.

The co- and cross-polarization levels are significantly influenced by the substrate dimension [29]. All three antenna designs'substrate dimensions as presented in **Table 1** are set at a value that is optimal to reduce cross-polarization. The antennas

**Figure 1.**

*Vertex-fed hexagonal antenna with the reduced ground for (a) A1, (b) A2, (c) and A3. (d) Circuit model of the antenna with its probe feeding network.*


#### **Table 1.**

*Parameters used for three antenna designs.*

may be modeled using a simple *RLC* resonant equivalent circuit [17, 30] as shown in **Figure 1d**. According to formulae, lumped elements (*RLC*) may be derived for all the antennas through Eqs. (1)–(3). Eqs. (1)–(3) can be used to calculate patch capacitance (*Cpatch*), patch inductance (*Ln*), and patch resistance (*Rn*) for a given *fn*, and they can also be used to calculate *Z11* and patch impedance (*Zpatch*), which are expressed in Eqs. (4) and (5), respectively.

$$\mathbf{C}\_{patch} = \left(\frac{\varepsilon\_0 \varepsilon\_r}{2h}\right) \left(\frac{\mathbf{3}\sqrt{3}r\_h^2}{2}\right) \left(\mathbf{1} - \frac{G\_p}{l\_\mathrm{g}}\right) \tag{1}$$

$$L\_n = \frac{1}{\left(2\mathfrak{gr}\_n\right)^2 \mathcal{C}\_{patch}}\tag{2}$$

$$R\_n = \frac{Q}{\left(2\pi f\_n\right)C\_{patch}}\tag{3}$$

where *fn* is the working band's center frequency, and *h* and *rh* are the properties of the substrate, respectively. *Gp* affects the overlapping area of the patch with the ground, resulting in the change of patch capacitance (*Cpatch*). The input impedance (*Z*11) as shown in **Figure 1d** with the probe feeding network is given by the following expression.

$$\mathcal{Z}\_{11} = R\_{ph} + j2\pi fL\_{ph} + \frac{1}{R\_T + \frac{1}{\frac{1}{\frac{1}{Z\_{\text{pank}}} + j2\pi fL\_{j1}} + j2\pi fL\_0 + j2\pi fL\_p} + j2\pi fC\_{ph}}\tag{4}$$

An equivalent circuit can be modeled along the same lines as in [30] and is presented in **Figure 1d**. Due to the probe-to-patch junction, the capacitance (*Cj1* and *Cj2*) and inductance (*Lj1*) are present. When the probe is within the substrate, it displays resistance (*Rp*) and inductance (*Lo* + *Lp*). Resistance (*Rph*), inductance (*Lph*), and capacitance (*Cph*) are introduced depending on how high the probe is above the substrate.

$$Z\_{\text{patch}} = \frac{1}{\frac{1}{R\_n} + j2\pi f C\_{\text{patch}} - \frac{j}{j2\pi f L\_n}}\tag{5}$$

then, Eq. (6) may be used to compute the reflection coefficient, S11 (dB).

$$S\_{11}(dB) = 20\log\_{10}\left(\frac{Z\_{11} - Z\_0}{Z\_{11} + Z\_0}\right) \tag{6}$$

where *Z*<sup>0</sup> is the characteristics impedance of the probe, which is 50 Ω. Eq. (6) may be used to generate the |*S*11| (in dB) of the resonant equivalent circuit model shown in **Figure 1d** by simply sweeping the frequency (*f*) for the desired frequency range. The reflection coefficient generated using the resonant equivalent circuit provides a similar result as obtained using simulation software as shown in **Figure 2** for (a) A1, (b) A2, and (c) A3.

The value of *Gp* is varied to analyze its effect on the reflection coefficient of the three-antenna designs used for the analysis and presented in **Figure 2a–c**, respectively. The following can be concluded by observing the results presented in **Figures 2** and **3**, that is, simulated and measured, respectively. A ground reduction method is appropriate for matching the impedance of the demonstrated antenna, thereby suppressing any extra resonance. The suggested antenna impedance (53.37-*j*-5.2) matched at 5 GHz. The Antenna 3 is appropriate for WLAN (UNII-1) applications since it has a 3 dB gain and works at 5 GHz within a 600 MHz bandwidth. Further details regarding low cross-polarization for the vertex-fed hexagonal antenna at the antenna's boresight may be found in [28], which suggests that antenna 3 ground plane reduction suppresses higher order mode.

**Figure 2.** *Simulated reflection coefficient,* S*<sup>11</sup> (dB), for (a) A1, (b) A2, and (c) A3.*

#### **Figure 3.**

*(a) |*S*11| (in dB), measured return loss (Inset: front and back of the developed antennas). Variation in the antennas' input impedance: (b) real part, (c) imaginary part.*

#### **3. Reduced ground plane probe-fed polygonal patch for** *C***- and** *X***-band applications**

This section analyzes and presents the effects of a decreased ground plane on radiation and impedance in a hexagonal antenna that is supplied coaxially. In this study, the measured and simulated impedance findings for an antenna design are compared with the equivalent circuit model. Lower *X*-band and higher *C*-band frequencies that are stimulated by the ground plane are reduced. Here, the antenna displayed in **Figure 1a** and described in an earlier section of the chapter is again used for the analysis. The developed hexagonal antenna makes use of a substrate that measures 32 � 33.5 mm<sup>2</sup> and a smaller ground plane that is 10.44 (*l*<sup>g</sup> – *Gp*) � 24.44 (*wg*) mm<sup>2</sup> as shown in **Figure 4** [31]. **Table 1** for antenna A1 may be referred to for the description and values of all the design variables presented in **Figure 4(a)**. The suggested antenna has an impedance bandwidth in the C-band and X-band of 285 MHz and 380 MHz, respectively. For *C*-band and *X*-band applications, the developed antenna with a smaller ground plane performs well.

As illustrated in **Figure 5**, *RLC* components are employed to mimic the proposed antenna and the corresponding circuit. As mentioned in the third part of the study, the equivalent circuit model is produced for the resonating frequencies of 7 GHz (*f1*) and 8.69 GHz (*f2*) as observed during experiments on a vector network analyzer (VNA). The values of the lumped component *RLC* are derived like that used in [32] for an E-patch. For a hexagonal patch antenna, Eqs. (7)–(9) are found by changing the equation provided in [33].

$$\mathbf{C}' = \mathbf{C}\_{\mathbf{n}} = \frac{\varepsilon\_{o}\varepsilon\_{t}A\_{\varepsilon}}{2\mathbf{h}} \tag{7}$$

$$L\_n = \frac{1}{(2\pi f\_n)C} \tag{8}$$

*Probe-Fed Polygonal Patch UWB Antennas DOI: http://dx.doi.org/10.5772/intechopen.110369*

#### **Figure 4.**

*(a) Reduced ground plane probe-fed polygonal patch for* C *and* X*-band applications. (b) Reflection coefficients (*S*11) when* Gp *and* fr *= 12.6 mm. (c) Simulated* S11 *(dB) of the antenna when* fr *varies when* Gp *= 14 mm.*

**Figure 5.** *Circuit model of the antenna with its probe feeding network.*

$$R\_n = \frac{Q}{(2\pi f\_n)C} \tag{9}$$

where *Ae* is a patch area over the ground plane, *C*<sup>0</sup> and *Cn* are calculated using Eq. (7), and *n* = 1, 2, and so on.

For a complete ground and capacitance of *Cn* = 4.75 pF (for frequencies *f1* and *f2*) as shown in **Figure 5**, the patch area, *Ae*, is 374.12 mm2 . The patch size, *Ae* = 150.03 mm<sup>2</sup> , and capacitance, *C*<sup>0</sup> = 1.90 pF, are for decreased ground (*Gp* = 14 mm). The value of the capacitance for the hexagonal patch, which is represented by its series capacitance (*ΔCrg*), is decreased as a result of the reduction in the ground. The formula in Eq. (10) may be used to get a hexagonal patch's extra series capacitance.

**Figure 6.** *(a) S11 (in dB), the reflection coefficient of the antenna. (b) Measured real and imaginary impedance (Z11).*

$$\frac{1}{C'} = \frac{1}{C\_n} + \frac{1}{\Delta C\_\eta} \tag{10}$$

VNA is used to measure the antenna's reflection coefficient *S11* (dB), which is displayed in **Figure 6**. In **Figure 6**, simulation results utilizing CST MWS and feed probe data from the *RLC* model are compared. By observing the measured, simulated, and circuit model bandwidth, it may be concluded that, due to the inductance introduced by the coaxial feed, the VNA bandwidth is lower (SMA connector).

To analyze the impedance matching, the real and imaginary impedance parts are measured and compared with simulated results as shown in **Figure 6**. By using values simulated of real and imaginary impedance, it is shown that the optimal value of input impedance, *Z*11, at 8.6 GHz is 49.16 - *j* 27.19 in the operational range for the hexagonal form (**Figure 6b**). In the operational range of the designed antenna, measurements observed on a VNA reveal that the value of *Z*<sup>11</sup> measured at 8.62 GHz is 50.06 - *j* 18, which is pretty much like the value described above or observed during simulations.

To attain an *X*-band lower frequency of 8.69 GHz, the impact of the ground reduction in the hexagonal design is investigated and assessed. By raising *Gp* from 0 to 18 mm, the ground is reduced. Due to direct probe feeding, inductance is added, reducing the antenna impedance bandwidth. At 7 GHz and 8.69 GHz, the input impedance, *Z*11, is measured to be 38.6 + *j* 2 and 50.06 - *j* 18, respectively. In the operational bandwidth, the radiation patterns are frequency independent. The antenna shown in this section is suitable and affordable for wireless applications since it has a bandwidth of 285 MHz and 340 MHz at frequencies of the *C*-band and *X*-band, respectively. The study in this section is limited to impedance analysis. Further analysis such as radiation pattern and gain of the presented antenna is given in [31].

#### **4. Flangeless SMA connector hexagonal UWB antenna fed via probe**

This section of the chapter introduces a UWB antenna that is supplied via a flangeless standard SMA connection close to one of the hexagonal patch's vertices as reflected in **Figure 7**. **Figure 7a** uses the same notation as described in **Table 1** to describe the design variables. To accomplish UWB with monopole radiation characteristics, the antenna has a ground plane that is half elliptical but truncated and has a rectangular slot. The antenna prototype has a WLAN band rejection of 1.6 GHz from 4.9 GHz to 6.5 GHz and an impedance bandwidth of 8.3 GHz from 2.3 GHz to 10.6 GHz [34]. The removal of flanges transforms a *C*-band antenna into a UWB

*Probe-Fed Polygonal Patch UWB Antennas DOI: http://dx.doi.org/10.5772/intechopen.110369*

**Figure 7.**

*UWB hexagonal antenna: (a) Dimensions and layout (c) Simulated |*S*11| (in dB), when the feed point (*fr*) is at 17 mm, and the hexagonal slot radius* (rcut*) is 3 mm, for various values of slot width (*sgw*) and slot length (*sgl*). (d) Simulated scattering parameter, |*S*11| (in dB) vs. frequency, for various* fr *value slot points (*fr*) is at 17 mm, and* rcut *is 3 mm when slot length (*sgl*) is 2 mm and slot width (*sgw*) is 10 mm.*

antenna, according to antenna tests. The proposed method may be used with a probefed antenna to obtain UWB radiation. Measurement results are consistent with what is anticipated based on simulation outcomes.

It is shown how an antenna presented in this section responds to SMA connection flanges in terms of impedance bandwidth. The suggested antenna displays *C*-band characteristics when fed via a connector with a flange, but a flangeless connector is a good option to obtain UWB characteristics in a direct-fed antenna. The designed antenna prototype shown in **Figure 8** exhibits WLAN band rejection between 4.9 GHz and 6.5 GHz. The designed antenna prototype has a 1.6 GHz WLAN spectrum rejection and is suited for UWB applications between 2.3 GHz and 10.6 GHz.

**Figure 8.** *Probe-fed hexagonal monopole UWB antenna. (a) Measured |*S*11| (in dB) and (b) gain (dB).*

#### **5. Determination of band edge frequencies of probe-fed printed hexagonal monopole antenna**

The calculation of the lowest edge resonance frequency of a printed monopole antenna is not addressed much as done for the resonant frequency of a dipole antenna. It is well known that expressions available for the calculation of the resonant frequency of a dipole antenna cannot be used for the calculation of a lower edge frequency of a printed monopole antenna. Resonant modes in a dipole antenna are generated due to half-wave variation along its horizontal and vertical axis, but printed monopole antennas have negligible patch capacitance. In this chapter, an empirical formula is proposed to calculate the lower and higher edge frequencies of a probe-fed printed monopole antenna as it possesses band-pass impedance characteristics. Three types of printed monopole antennas have been studied and simulated for validation of the empirical formula proposed utilizing full-wave simulation software. It is observed that the probe-fed hexagonal antenna exhibits a wider band, which motivated us to validate the empirical formula through an experiment. Experimental results validated the results obtained from the proposed empirical formula. Percentage error magnitude is also calculated and presented in the section for each case studied in this work.

The empirical formulas for the calculation of the lower edge frequency of the impedance bandwidth (*fL*) for a rectangular monopole antenna, a hexagonal monopole antenna, and a circular monopole antenna are given in [22, 35, 36], respectively. A stripline-fed quarter-wave hexagonal monopole antenna is modeled in [22], and the empirical formula to calculate the *fL* (in GHz) of a stripline-fed hexagonal monopole antenna is given in [22]. Reference [36] exploits a modified trapezoid-based empirical formula given in [37] to derive the formula for a circular monopole antenna. The expressions given in [22, 35–37] can be used to calculate the *fL* (GHz) of the designed antenna with a stripline feed when fed at the vertex of the printed monopole antenna. As the area of a hexagon is treated as an equivalent circular area, the empirical value of 1.15 is multiplied in the denominator to calculate the *fL* of the vertex-fed hexagonal monopole. Also, instead of a quarter wavelength, that is, 0.25 λ, 0.24 λ is used in the expression, which results in a constant of 7.2 in the numerator [22]. Antenna configurations with different patch geometries, that is, rectangle, hexagonal, and circular monopole antenna with dimensions as given in [22, 35, 36], are used to calculate *fL* and indicated in **Table 2**.

The expressions given in [22, 35–37] are modified by changing the parameters to avoid loss of generality, and *fL* can be calculated near practical results. In the case of a printed monopole antenna, the lower edge frequency is a significant parameter rather than the resonant frequency. The lower edge frequency of a printed monopole antenna is given by


**Table 2.**

*Comparison of* fL *of various monopole antenna configurations.*

*Probe-Fed Polygonal Patch UWB Antennas DOI: http://dx.doi.org/10.5772/intechopen.110369*

$$\|f\|\_{L} = \frac{c}{\lambda\sqrt{\varepsilon\_{\mathcal{G}}}}\tag{11}$$

where *c* is the speed of light.

But here, quarter-wave monopole antennas are used and compared. Thus, the length will be *L* = λ/4, which results in λ = 4*Leff*; therefore,

$$f\_L = \frac{c}{4L\_{\sharp\sharp}\sqrt{\varepsilon\_{\sharp\sharp}}}\tag{12}$$

$$f\_L = \frac{7.5}{L\_{\text{eff}} \sqrt{\varepsilon\_{\text{eff}}}} \tag{13}$$

In the case of a stripline-fed monopole antenna, the effective length will be *Leff* = *L+Ls,* and hence, the lower edge frequency is given by

$$f\_L = \frac{7.5}{(L + L\_s)\sqrt{\varepsilon\_{\rm eff}}}\tag{14}$$

where effective dielectric constant, *εeff* = (*ε<sup>r</sup>* - 1)/2, *ε<sup>r</sup>* is the permittivity of the substrate material, and *Ls* is the length of the stripline.

The empirical formula for the calculation of the *fL* for circle and hexagonal monopole antenna is modified by considering *L* = 2 � *R and L* = 2 � *hr,* respectively, where *R* (in cm) is the circle radius and *hr* (in cm) is the circumradius of the hexagon; the final form of the expression is as given in Eq. (15).

$$f\_L(\text{GHz}) = \begin{cases} \frac{7.5}{(L+L\_s)\sqrt{\varepsilon\_{\text{eff}}}}; \text{for rectangle} \\ \frac{7.5}{(2h\_r+L\_s)\sqrt{\varepsilon\_{\text{eff}}}}; \text{for hexagon} \\ \frac{7.5}{(2R+L\_s)\sqrt{\varepsilon\_{\text{eff}}}}; \text{for circle} \end{cases} \tag{15}$$

The empirical formula for *fL* calculation of the circular monopole antenna as given in [36, 37] is modified for the hexagonal monopole antenna by considering circumradius *W1* = *W2* = 3 � *hr* and *L* = 2 � *hr*, and the final expression for rectangle, hexagon, and circle are given by Eq. (16). Measured and calculated values are displayed in **Table 3**.


**Table 3.**

*Comparison of* fL *of various monopole antenna configurations using modified formula.*

$$f\_L(\text{GHz}) = \begin{cases} \frac{904}{4\pi L + W\_1 + W\_2}; \text{for rectangle} \\ \\ \frac{904}{8\pi h\_r + 6h\_r}; \text{for hexagon} \\ \frac{904}{10\pi R + 120h}; \text{for circle} \end{cases} \tag{16}$$

For the formulation of probe-fed hexagonal monopole antenna, the empirical value, that is, *k* (dielectric constant), is avoided by assuming it as '1', which is earlier used in stripline-fed hexagonal monopole antennas, due to the fringing extension and the effective dielectric constant (1 < *ɛeff* < *ɛ<sup>r</sup>* [38]). The additional effective *hreff* and feed line length are also avoided since a direct probe is used to feed the vertex of the hexagon. Another reason for choosing *k* = 1 is that due to the negligible capacitance of the patch because of a monopole configuration and purely inductive patch, the effective dielectric constant leads to 1. The hexagonal monopole configuration is conventionally modeled as an equivalent circular monopole antenna. For a vertex-fed hexagonal monopole antenna, the length of the hexagon will be twice the circumradius of the hexagon, that is, *L* = 2 � *hr*; substituting it in Eq. (12) results in Eq. (17).

$$\,\_{L}f\_{L} = \frac{c}{4(2h\_{r})\sqrt{1}}\tag{17}$$

Although expressions for vertex-fed hexagonal monopole have been explored earlier and empirically [22], derived for a stripline-fed antenna, here an empirical formula that is more suited to a probe-fed hexagonal monopole antenna when fed at the vertex of the hexagon is presented:

$$f\_L = \frac{7.5}{2h\_r} \text{ or } \frac{3.75}{h\_r} \tag{18}$$

where *hr* is in cm. The empirical expression can be justified by the fact that the monopole can be modeled as a pure inductance with negligible capacitive effect.

Moreover, the higher edge frequency of the impedance bandwidth (*fH*) of the probe-fed hexagonal antenna can also be estimated using the following empirical formula, that is, Eq. (18). A similar technique is used in [21] for the calculation of the *fH* of an irregular hexagon. The higher edge frequency empirical formula is because the smallest edge of the patch will contribute to the wavelength; that is, the lowest radiating wavelength will be equal to the edge of the patch with the smallest dimension. But, in a regular hexagon, the edge dimension is the same as the circumradius of the hexagon. The estimation of *fH* using Eq. (18) for the probe-fed hexagonal monopole antenna overlooks weakly rejected bands. Although the monopole antenna exhibits high pass impedance characteristics [35], the calculation of *fH* is sometimes appreciated while designing UWB monopole antennas.

$$f\_H = \frac{c}{h\_r \sqrt{\varepsilon\_{\ell\overline{\mathcal{Y}}}}} \tag{19}$$

where *c* is the light speed in free space, *hr* is in meters, and *ɛeff* = (*ɛ<sup>r</sup>* + 1)/2.

The effective dielectric constant in Eqs. (18) and (19) is estimated from enormous simulations, experiments, and analyses to achieve an appropriate empirical formula

#### *Probe-Fed Polygonal Patch UWB Antennas DOI: http://dx.doi.org/10.5772/intechopen.110369*

for a probe-fed hexagonal monopole antenna. Eq. (18) is used to calculate the *fL* for three planar monopole antennas, that is, square, circle, and hexagon. All three antenna configurations are assumed to have the same circumradius of 16.5 mm. The calculated values of *fL* are indicated in **Table 4**. The values of *fL* are further verified through CST MWS simulation results.

Three different probe-fed monopole antenna configurations, that is, rectangle, circle, and hexagon with feed position at the vertex of the polygon, are designed in CST microwave studio as shown in the inset of **Figure 9a** and simulated for *S*<sup>11</sup> characteristics of the designed antenna as reflected in **Figure 9a**. The probe at the vertex of the polygon helps in designing the monopole antenna by avoiding overlapping with the ground. The patch has been modeled as a regular design with the circumradius *hr*. The three designed configurations consist of an FR-4 substrate of <sup>46</sup> 46 mm<sup>2</sup> , a ground plane with dimensions 3 40 mm<sup>2</sup> , and a patch with a circumradius of 16.5 mm. The ground dimensions of the antenna configurations are chosen such that the designed probe-fed hexagonal monopole antenna has a minimum size. All three antennas have almost the same lowest edge frequency as may be observed from **Figure 9** at 10 dB and as indicated in **Table 4**.

Eq. (18) is found to be more suitable for a probe-fed hexagonal monopole antenna, especially when fed at the vertex of the hexagon, which yields *fL* = 2.27 GHz, which provides an error of 1.3% as indicated in **Table 4**. As observed from **Figure 10**, the probe-fed hexagonal monopole antenna possesses wideband characteristics and was further chosen for fabrication to design a probe-fed UWB monopole antenna. The hexagon monopole antenna shows weak rejection at 4.3 GHz as depicted in **Figure 10**.


#### **Table 4.**

*Comparison of* fL *of proposed probe-fed monopole antenna configurations using proposed formula.*

#### **Figure 9.**

*(a) Scattering parameter, |S11| (in dB) of different monopole antenna configurations (Inset: pictures of antennas). (b) Variation in* fL *with* hr *of probe-fed hexagonal monopole antennas.*

**Figure 10.** *|*S*11| (in dB) for probe-fed hexagonal monopole antennas.*

The value of *fL* is calculated for different values of *hr* using Eq. (18) and observed using CST software for probe-fed hexagonal monopole antennas. The optimized value of *hr* of probe-fed hexagonal monopole antennas demonstrates maximum bandwidth, for a given *fL*, and is displayed in **Figure 9b**. The probe-fed hexagonal monopole antenna, especially when fed at the vertex of the hexagon, demonstrates maximum bandwidth because of the best transition of impedance bandwidth.

*fL* is found to be 1.72 GHz when *hr* = 1.65 cm using Eq. (14). The dimensions of the hexagon mentioned earlier are chosen to accommodate the entire *S*-band along with the UWB band. But, after fabrication, the *fL* calculated using Eq. (14) provides an error of 25.21%, because probe feeding is used for the excitation of the hexagonal monopole antenna. A more suitable expression for the calculation of *fL* for probe-fed hexagonal monopole antenna is presented in Eq. (17), and it provides an error of only 1.3% (**Figure 10**).

A simple empirical formula has been proposed and presented to accurately calculate the lower edge frequency of probe-fed regular hexagonal monopole antennas. The antenna is fed at the vertex of the hexagon and found that the values obtained for lower edge frequency are quite close to the simulated and measured |*S*11| results of the designed and developed antennas. Lower edge frequency dependency of the probe feeding on the square, circle, and hexagon monopole antenna has been studied using simulation for maximum bandwidth, and the *S*<sup>11</sup> results have been demonstrated. The lower edge frequency of the probe-fed hexagonal monopole antenna also depends on the hexagon circle radius, and its variation is also presented. The probe-fed antenna designed using the presented expression demonstrates UWB performance, which ranges from 2.3 GHz to 10.6 GHz with a weak rejection between 5 GHz and 6.5 GHz. The calculated lower and higher edge frequencies of the designed antenna are found to be 2.27 GHz and 11.2 GHz, respectively, which provide an error of only 1.3% and 3.4%, respectively, when compared with the measured *S*11(dB) results.

#### **6. Gain boosting of a probe-fed hexagonal UWB antenna using an AMC reflector**

Due to the existence of higher modes, particularly when fed with a probe, UWB antennas are restricted to having weak gain at higher frequencies. In this section, a technique for increasing the peak gain of a hexagonal UWB antenna fed via probe is presented. An artificial magnetic conductor (AMC)-based reflector is added to the antenna shown in **Figure 11**, enhancing both the peak gain for UWB antennas and the

#### **Figure 11.**

*Probe-fed hexagonal UWB antenna using an AMC reflector: (a) Design; (b) |*S*11| (dB); (c) boresight gain (dB); (d) peak gain (dB).*

boresight gain to a broader band. Peak and antenna boresight gain improvements on average are 3.74 dB and 5.5 dB [39], respectively. In the presence of an AMC-based reflector, the boresight gain increases, becoming positive for a 1 GHz broader band. The UWB antenna measures 46 by 46 mm<sup>2</sup> , while the AMC reflector increases the antenna's overall size to 100 by 100 mm<sup>2</sup> . The suggested antenna configuration is suitable for UWB applications and may provide a directed and steady radiation pattern.

The presented antenna's boresight and peak gain are compared and shown in **Figure 11c** and **d**, respectively, to help comprehend the gain enhancement phenomena brought on by the AMC reflector. In **Figure 11c**, it is apparent. In the simulation, the AMC reflector increases the average boresight gain by around 5.46 dB. Without an AMC reflector, the antenna's positive boresight gain is visible between 2.2 GHz and 4.3 GHz, whereas with an AMC, a broader band between 2 GHz and 5.8 GHz is seen. The observation of a large increase in boresight gain across a broader band emphasizes the need for an AMC reflector. The boresight gain of the antenna is measured and shown in **Figure 11** to better understand how AMC affects the augmentation of boresight gain. During testing, the antenna's boresight gain seems to be positive across broadband that spans from 2 GHz to 6 GHz as opposed to 2.2 GHz to 4.5 GHz when no AMC reflector is used. During testing, it is shown that applying AMC to a hexagonal monopole antenna increased the average boresight gain by a factor of 5.5 dB.

The use of an AMC reflector with a square-shaped loop unit cell to convert a monopole-like radiation pattern into a directional pattern increases the gain of the presented antenna. To increase the peak gain and gain of the UWB antenna, an AMC reflector with a 20 by 20 array of unit cells is built at the rear of the hexagonal radiator. After using an AMC reflector, the antenna's boresight and peak gain are both greatly improved by around 5.5 dB and 3.74 dB, respectively. The antenna that has been put together with AMC may be used for UWB applications.

#### **7. Conclusions**

Polygonal patch antenna is the keystone of modern wireless communication systems and services. In the development of contemporary wireless communication systems, an antenna with a wide radiation bandwidth is demanded to cater to such a demand. These concerns encourage the antenna researcher to design an antenna with a wide radiation bandwidth.

Hexagon is chosen here to fulfill the requirement of modern wireless communication systems and services while maintaining a fundamental mode. Feed is an important part of the antenna; the impedance and the gain will influence the antenna performance. To increase the antenna's bandwidth, the specified antenna probe feed point is altered. According to the probe feed analysis, a polygonal patch antenna's wideband performance is optimal when the feed point is maintained closer to the polygon's vertex.

Hexagonal patch antennas with probes show narrow band behavior. It is shown how a vertex-fed slotted hexagonal antenna with a truncated half elliptical ground plane responds to SMA connection flanges in terms of impedance bandwidth. The suggested antenna displays C-band characteristics when fed via a connection with a flange, but a flangeless connector may be used to obtain UWB characteristics in a direct-fed antenna. A ground plane reduction approach is also employed that changes the dipole configuration to a monopole configuration to obtain UWB using a hexagonal patch. The ground plane slot enabled the antenna's bandwidth to be increased. Multiple modes in the UWB band are excited using a rectangular slot and a ground plane reduction approach. The antenna has broadband between 2.4 GHz and 10 GHz.

The use of an AMC reflector with a square-shaped loop unit cell to convert a monopole-like radiation pattern into a directional pattern increases the gain of the hexagonal UWB antenna. To increase the peak gain and gain of the UWB antenna, an AMC reflector may be mounted at the rear of a hexagonal radiator. After using an AMC reflector, the presented antenna's boresight and peak gain are greatly improved by around 5.5 dB and 3.74 dB, respectively. The antenna that has been put together with AMC may be used for UWB applications.

#### **Acknowledgements**

This research work was funded by the Department of Science and Technology, New Delhi, India (Reference Number: SR/FST/ETI-346/2013) for equipment.

*Probe-Fed Polygonal Patch UWB Antennas DOI: http://dx.doi.org/10.5772/intechopen.110369*

### **Author details**

Abhishek Joshi\* and Rahul Singhal Department of Electrical and Electronics Engineering, Birla Institute of Technology and Science, Pilani, Rajasthan, India

\*Address all correspondence to: abhishek.joshi@pilani.bits-pilani.ac.in

© 2023 The Author(s). Licensee IntechOpen. This chapter is 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.

### **References**

[1] Pozar DM, Schaubert D. Microstrip Antennas: The Analysis and Design of Microstrip Antennas and Arrays. Piscataway NJ: Institute of Electrical and Electronics Engineers; 1995. pp. 57-104. DOI: 10.1109/9780470545270.ch2

[2] Collins G. Effect of reflecting structures on circularly polarized Tv broadcast transmission. IEEE Transactions on Broadcasting. 1979;**BC-25**:5-13. DOI: 10.1109/TBC.1979.266307

[3] Saleh AAM, Valenzuela R. A statistical model for indoor multipath propagation. IEEE Journal on Selected Areas in Communications. 1987;**5**: 128-137. DOI: 10.1109/JSAC.1987. 1146527

[4] Lee W, Yeh Y. Polarization diversity system for mobile radio. IEEE Transactions on Communications. 1972; **20**:912-923. DOI: 10.1109/TCOM.1972. 1091263

[5] James JR, Hall PS, editors. Handbook of Microstrip Antennas. U.K: Peregrinus; 1989. p. 25-27

[6] Wang YJ, Lee CK, Koh WJ, et al. Design of small and broad-band internal antennas for IMT-2000 mobile handsets. IEEE Transactions on Microwave Theory and Techniques. 2001;**49**:1398-1403. DOI: 10.1109/22.939919

[7] Sabban A. A new broadband stacked two-layer microstrip antenna. In: Proceedings of the 1983 IEEE Antennas Propagation Symposium; 23-26 May 1983; Houston, TX, USA. 1983. pp. 63-66. DOI: 10.1109/APS.1983.1149074

[8] Yang F, Zhang X-X, Ye X, et al. Wide-band E-shaped patch antennas for wireless communications. IEEE Transactions on Antennas and

Propagation. 2001;**49**:1094-1100. DOI: 10.1109/8.933489

[9] Tunski Z, Fathy AE, McGee D, Ayers G, Kanamaluru S. Compact multiband planar antenna for mobile wireless terminals. In: Proceedings of the 2001 IEEE Antennas and Propagation Symposium; 08-13 July 2001; Boston, MA, USA. 2001. pp. 454-457. DOI: 10.1109/APS.2001.959496

[10] Bilotti F, Vegni C. MOM entire domain basis functions for convex polygonal patches. Journal of Electromagnetic Waves and Applications. 2003;**17**:1519-1538. DOI: 10.1163/156939303772681398

[11] Bilotti F, Alù A, Manzini M, Vegni L. Design of polygonal patch antennas with a broad-band behavior via a proper perturbation of conventional rectangular radiators. In: Proceedings of the International Symposium on 2003 IEEE Antennas Propagation; June 2003; Columbus OH. 2003. pp. 268-271. DOI: 10.1109/APS.2003.1219229

[12] Balanis CA. Antenna theory: A review. Proceedings of the IEEE. 1992; **80**:7-23. DOI: 10.1109/5.119564

[13] Kolundzija B, Tasic M, Petrovic N, Mikavica M. Efficient electromagnetic modeling based on automated meshing of polygonal surfaces. In: Proceedings of the International Symposium on Antennas and Propagation Society; 16-21 July 2000. Held in conjunction with: USNC/URSI National Radio Science Meeting (C, Salt Lake City, UT, USA). IEEE; 2000. pp. 2294-2297. DOI: 10.1109/APS.2000.874952

[14] Sorokosz L, Zieniutycz W. On the approximation of the UWB dipole

*Probe-Fed Polygonal Patch UWB Antennas DOI: http://dx.doi.org/10.5772/intechopen.110369*

elliptical arms with stepped-edge polygon. IEEE Antennas and Wireless Propagation Letters. 2012;**11**:636-639. DOI: 10.1109/LAWP.2012.2203575

[15] Lee K-F, Tong K-F. Microstrip patch antennas—Basic characteristics and some recent advances. Proceedings of the IEEE. 2012;**100**:2169-2180. DOI: 10.1109/JPROC.2012.2183829

[16] Chen Y, Wang C-F. From antenna design to feeding design: A review of characteristic modes for radiation problems (invited paper). In: Proceedings of the International Symposium on Antennas & Propagation (ISAP); 23-25 Oct. 2013; Nanjing. China. 2013. pp. 68-70

[17] Garg R. Microstrip Antenna Design Handbook. Boston London: Artech House Publishers; 2001. pp. 9-10

[18] Zhao D, Yang C, Zhu M, et al. Design of WLAN/LTE/UWB antenna with improved pattern uniformity using ground-cooperative radiating structure. IEEE Transactions on Antennas and Propagation. 2016;**64**:271-276. DOI: 10.1109/TAP.2015.2498939

[19] Li D, Mao J. Coplanar waveguide-fed Koch-like sided Sierpinski hexagonal carpet multifractal monopole antenna. IET Microwaves, Antennas & Propagation. 2014;**8**:358-366. DOI: 10.1049/iet-map.2013.0041

[20] Tripathi S, Mohan A, Yadav S. Hexagonal fractal ultra-wideband antenna using Koch geometry with bandwidth enhancement. IET Microwaves, Antennas & Propagation. 2014;**8**:1445-1450. DOI: 10.1049/ietmap.2014.0326

[21] Dastranj A. Low-profile ultrawideband polarisation diversity antenna with high isolation. IET Microwaves, Antennas & Propagation. 2017;**11**: 1363-1368. DOI: 10.1049/ietmap.2016.0937

[22] Ray KP, Tiwari S. Ultra wideband printed hexagonal monopole antennas. IET Microwaves, Antennas & Propagation. 2010;**4**:437-455. DOI: 10.1049/iet-map.2008.0201

[23] Joshi A, Singhal R. Performance comparison of probe-fed polygonal patch antennas for L-band applications. In: Proceedings of the 2016 IEEE Region 10 Conference (TENCON); 22-25 November 2016; Singapore. 2016. pp. 1307-1311. DOI: 10.1109/ TENCON.2016.7848224

[24] Kumar G, Ray KP. Broadband Microstrip Antennas. Boston London: Artech House; 2003. pp. 368-370

[25] Emadeddin A, Salari MA, Zoghi M, et al. A compact ultra-wideband multibeam antenna system. IEEE Transactions on Antennas and Propagation. 2018;**66**:125-131. DOI: 10.1109/TAP.2017.2776342

[26] Thajudeen C, Zhang W, Hoorfar A. Boresight gain enhancement of planar stair-like UWB monopole antenna. Microwave and Optical Technology Letters. 2014;**56**:2809-2812. DOI: 10.1002/mop.28710

[27] Joshi A, Pal D, Singhal R. Vertex-fed hexagram patch wideband antenna. In: Proceedings of the 2014 International Conference on Signal Propagation and Computer Technology (ICSPCT 2014); 12-13 July 2014; Ajmer. 2014. pp. 218-221. DOI: 10.1109/ICSPCT.2014. 6885011

[28] Joshi A, Singhal R. Vertex-fed hexagonal antenna with low

cross-polarization levels. Advances in Electrical and Electronic Engineering. 2019;**17**:138-145. DOI: 10.15598/aeee. v17i2.3004

[29] Kishk A, Shafai L. The effect of various parameters of circular microstrip antennas on their radiation efficiency and the mode excitation. IEEE Transactions on Antennas and Propagation. 1986;**34**:969-976. DOI: 10.1109/TAP.1986.1143939

[30] Joshi A, Singhal R. Probe-fed regular hexagonal narrow-slot antenna with reduced ground plane for WLAN applications. In: Proceedings of the 2016 IEEE Region 10 Conference (TENCON); 22-25 November 2016; Singapore. 2016. pp. 1312-1316. DOI: 10.1109/ TENCON.2016.7848225

[31] Joshi A, Singhal R. Coaxially fed hexagonal patch antenna for C- and Xband applications with reduced-ground plane. ECTI Transactions on Electrical Engineering, Electronics, and Communications. 2019;**17**:136-143. DOI: 10.37936/ecti-eec.2019172. 219184

[32] Malekpoor H, Jam S. Analysis on bandwidth enhancement of compact probe-fed patch antenna with equivalent transmission line model. IET Microwaves, Antennas & Propagation. 2015;**9**:1136-1143. DOI: 10.1049/ietmap.2014.0384

[33] Joshi A, Singhal R. Lower mode excitation in vertex-fed slotted hexagonal S-band antenna. AEU - International Journal of Electronics and Communications. 2018;**87**:180-185. DOI: 10.1016/j.aeue.2018.02.008

[34] Joshi A, Singhal R. Probe-fed hexagonal ultra wideband antenna using flangeless SMA connector. Wireless Personal Communications. 2019;**110**:

973-982. DOI: 10.1007/s11277-019- 06768-2

[35] Ray KP, Thakur SS, Deshmukh RA. Broadbanding a printed rectangular monopole antenna. In: Proceedings of the 2009 Applied Electromagnetics Conference (AEMC); Kolkata. 2009. pp. 1-4. DOI: 10.1109/AEMC.2009. 5430695

[36] Yang Z, Li L, Wang H. Investigation on ultra-wideband printed circular monopole antenna with frequencynotched. In: 2008 International Conference on Microwave and Millimeter Wave Technology; Nanjing. 2008. pp. 1858-1861. DOI: 10.1109/ ICMMT.2008.4540844

[37] Evans JA, Amunann MJ. Planar trapezoidal and pentagonal monopoles with impedance bandwidths in excess of 10:1. In: Proceedings of the IEEE Antennas and Propagation Society International Symposium1999 Digest. Held in conjunction with USNC/URSI National Radio Science Meeting (Cat. No.99CH37010); Orlando FL. 1999. pp. 1558-1561. DOI: 10.1109/APS.1999. 788241

[38] Balanis CA. Antenna Theory Analysis and Design. 3nd ed. Wiley; 2008. pp. 816-820

[39] Joshi A, Singhal R. Gain enhancement in probe-fed hexagonal ultra wideband antenna using AMC reflector. Journal of Electromagnetic Waves and Applications. 2019;**33**: 1185-1196. DOI: 10.1080/09205071. 2019.1605939

## **Chapter 3** Wideband True Time Delay Cells

*Ahmad Yarahmadi*

#### **Abstract**

True-time delay (TTD) cells are used in timed array receivers for wideband multiantenna topologies. TTD cells are divided into two major categories: silicon-based and non-silicon-based structures. Non-silicon-based structures have very good bandwidth but are bulky in the below 10 GHz frequency band. Silicon-based TTD cells are much more compact and better candidates for integrated circuit (IC) design. Passive and active approaches are the two ways to have a silicon-based TTD cell. Passive TTD cells are built by transmission lines (TL), artificial transmission lines (ATL), and LC ladder networks. Their power consumption is very low, and the delay bandwidth is good, but they are still bulky at low frequencies like below 5 GHz applications. Active all-pass filters as TTD cells are presented for these issues. In this chapter, we will discuss the challenges of inductor-based TTD cells. Then, inductor-less TTD cells are presented to address some of the previous structure's issues. Finally, we will talk about these structures' challenges as well. Then, the nonidealities effects on the TTD cell's performance are investigated, and the body bias technique is presented to address these issues.

**Keywords:** true time delay, inductor-less structure, all-pass filter, timed array structure, inverter-based design, wide band filter

#### **1. Introduction**

Nowadays, linearity and dynamic range are critical issues for radars, A/D conversion, multi-standard applications like IoT or 5G/6G communications, receiver chains in communication systems, data processing, and imaging sensors [1–6]. Multiantenna systems like phased array topologies are suitable for this matter since they can do analog beamforming with very good performance in narrow-band applications [7]. They can do the beamforming task with an approximation of the incident signal. They approximate the delay of the signal with phase change in the phased array multiantenna system [8]. This approximation is one by phase shifters as the core block of a phased array system. They are quite good for narrow-band signals, but for wideband applications, they suffer from the beam squint phenomena [9].

Unfortunately, other problems arise in wide-band applications like intrinsic narrow-band characteristics, spatial interferences, pulse dispersion, and inter-symbol interference (ISI) [10]. So, another topology must be considered for this matter, leading to the timed array receiver. This structure replaces phase shifters with TTD cells as the system's core in wide-band applications. The TTD cells delay the

received signal in contrast to phase shifters which approximate the delay time with a phase shift.

There are two approaches to creating a TTD cell, silicon-based and non-siliconbased TTD cells [2]. Non-silicon-based TTD cells have better performance than silicon-based TTD cells but have some limitations like considerable production cost concerning the rival. So, although the silicon-based TTD cells have a significant loss and high footprint, they are preferable for mass production and low-cost purposes [10]. Silicon-based TTD cells have two separate categories. Passive TTD cells are based on transmission lines (real or artificial) and LC ladders [11, 12]. These topologies have great performance for high frequencies (10 GHz and beyond). But they are very bulky for low frequencies. Active TTD cells are a solution for below 5 GHz applications. in these topologies, all-pass filters are used to create an active TTD cell, and passive inductors are used to ensure the wideband performance of the structure [4, 13].

**Figure 1** shows the literature review of TTD cells, and the state-of-the-art design in this area is depicted. This chapter discusses the reason for the high DV (delay-

**Figure 1.**

*The diagram of the literature review of TTD cells.*

variation) for larger delay amounts in the inverter-based inductor-less active TTD cell. Also, the mechanism of the body biasing scheme for improving the performance of the TTD cell is presented, too.

#### **2. CMOS low-frequency design considerations**

Based on the above discussion, an active all-pass filter can be a good solution for designing a true time delay cell. However, there are some design considerations about the low frequency (below 10 GHz) wideband design of TTD cells. In the following paragraphs, we will discuss why an inductor-less TTD cell is needed and why Padé approximation is used to create an all-pass transfer function from the TTD transfer function. Also, we will see the minimum and maximum available delay amounts for a TTD cell with proper characteristics.

#### **2.1 Inductor-less design**

In this chapter, we have focused on low-frequency wideband applications. Most of this band's applications demand a very compact structure. Also, the integration ability of circuits is necessary because these cells will be used in the mass production of different devices. So, the chip area and production cost are very important issues, too. On the other hand, the structure must work in various applications. For example, it could be a part of a multi-input multi-output structure like a smartphone, drone, or even an automobile.

An inductor is a bulky and limiting element, and this issue is critical for low frequencies like 1–5 GHz applications because they are large enough in this band. As a result, there is a trade-off here in choosing an inductor [4, 14]. If high-quality off-chip inductors are used, the total cost will increase dramatically. Furthermore, the system's performance will be impacted and bounded if the on-chip inductor is used.

This trade-off could be minimized with advancing technology because on-chip high-quality inductors are available for the advanced chip technologies. Another benefit of these technologies is their smaller parasitic capacitances, which lead us to use inductor-less designs with acceptable wideband performance.

Another issue for inductor-based designs is that the design transformation from one technology node to another (mostly to an advanced one) has a complex procedure. In contrast, it is very simple for an inductor-less design to be transformed into another technology node. This issue is so important concerning the technology improvement speed. Since we almost need to redesign an inductor-based structure, design cost, and total cost are more in these topologies.

However, the chip production cost is higher for more advanced technology nodes. So, there are better choices than bulky elements like inductors below 5 GHz applications. They will impact the total budget of the design dramatically. On the other side, mass production demands production costs as low as possible in most applications.

In the layout and tape-out steps of the chip design, we need to use a trial-and-error procedure to find the proper performance of an inductor-based structure since there is no exact model for them. It forces us to need more design time and lead us to more design cost. Although off-chip inductors are a good candidate to eliminate some of the above issues, they will increase the total cost dramatically, which eventually leads us to a lower yield.

Recently inductor-less active TTD cells have been presented in the literature to address these issues. In these active TTD cells, the transfer function of the cell will be approximated with an all-pass filter, usually with Padé or Taylor approximation. Nevertheless, these topologies suffer from high DV (delay variations) in their wideband performance [4, 11, 13]. Inverter-based active TTD cells are presented to overcome their DV issue of them in the 1–5 GHz band [15]. This TTD cell delays the incident signal with 10 ps and 3% DV. However, for larger delay values, the DV of the TTD cell will drop dramatically (for example, for a 50 ps delay amount). The body bias technique can be applied to the TTD cell to address this issue.

#### **2.2 Minimum and maximum required delay amount**

Delay systems consisted of several delay cells to create a timed array receiver. In a timed array receiver and for a lined antenna topology based on the number of antenna elements, their topology, the distance between the elements, operational frequency, etc. A minimum and maximum required delay can be calculated for a specific purpose [16]. Assume the system has an *N*-element antenna, the operational frequency is from *fmin* to *fmax*, the maximum steering angle concerning boresight is �*θ*, and *b*-bit spatial resolution is required. The noise figure (*NF*) is set to be better than *NFmax*; there is no grating lobe and 40 dB depth for sidelobe is available.

For this preferred system, the distance between antenna elements, maximum delay amount, delay step (minimum delay), and noise figure of each channel can be calculated as follows [17, 18]:

To avoid grating lobes, *d*, the distance between antenna elements should be less than half of the wavelength of *fmax*:

$$d \le \frac{\lambda\_{f,\max}}{2} \tag{1}$$

The maximum required delay amount of a timed array system is equivalent to the maximum steering angle of the system (*θmax*). It depends on three terms: the number of antenna elements (*N*), the distance between antenna elements (*d*), and the maximum steering angle (*θmax*). Concerning these terms, the maximum required delay amount of the channel will be [10]:

$$\tau\_{\text{max}} = (N - 1)\frac{d \sin(\theta\_{\text{max}})}{c} \tag{2}$$

In this equation, *c* is the speed of light in a vacuum. From this equation, and for the incident signal angle concerning bore sigh (*θin*), the delay step can be calculated as follows:

$$
\Delta \tau = (N - 1) \frac{d \sin(\theta\_{in})}{\sigma} \tag{3}
$$

This delay step in a timed array receiver equals a 4-bit resolution in a phased array receiver system. The minimum delay of the timed array system also can be calculated as the following equation:

$$\tau\_{\min} = \frac{\sin(\theta\_{\min})}{\mathfrak{F}} \tag{4}$$

*Wideband True Time Delay Cells DOI: http://dx.doi.org/10.5772/intechopen.111474*

Based on the above discussion, four antenna elements in a lined topology are required for an assumed 1–5 GHz application and 60 degrees of steering angle with a 4-bit resolution. The distance between them will be *d* = 3 cm, the maximum delay amount will be 260 ps, and the minimum delay amount will be 12.5 ps.

With this information, we can design the required delay system as shown below, so the delay block, which means a true time delay cell, can be designed for this system (**Figure 2**).

#### **2.3 Delay approximation accuracy analysis**

The two most common approaches to approximating true time delay transfer function (*TF*) are the Padé approximation and Taylor approximation. The Taylor expansion of ideal delay *TF* can be written as follows [19]:

$$e^{-sT} \simeq \mathbf{1} - \frac{(sT)}{\mathbf{1}!} + \frac{sT^2}{2!} + \dots + (-\mathbf{1})^n \frac{sT^n}{n!} \tag{5}$$

However, this *TF* does not meet the physical requirements to create a filter. To make it feasible for filter design, we must modify this equation with the following one:


**Table 1.**

*The Taylor approximation for the time delay transfer function.*

$$e^{-sT} = e^{-s\left(\frac{T}{2} + \frac{T}{2}\right)} = e^{-s\frac{T}{2}}e^{-s\frac{T}{2}} = \frac{e^{-s\frac{T}{2}}}{e^{s\frac{T}{2}}}\tag{6}$$

As a result, this modification improves the approximation's accuracy, so the Taylor approximation is applicable for delay approximation for below 4th-order approximations. The fifth order and above approximations will face instability issues and are not available for filter design. The Taylor approximation for 1 to 5-order approximations is shown in **Table 1**.

Based on these five transfer functions, the MATLAB simulation for their step response concerning true time delay is done, and the results as the order of approximation increases, the precision increases, too.

Another approach to creating the *TF* of an all-pass filter is the Padé approximation. In this case, the *TF* of true timed delay will approximate with this eq. [20]:

$$e^{-sT} \simeq \sum\_{i=0}^{n+m} (-1)^i \frac{sT^i}{i!} = \frac{\sum\_{i=0}^m p\_i (sT)^i}{\sum\_{i=0}^n q\_i (sT)^i} \tag{7}$$

**Table 2** shows the *TF* of the approximation for one to five orders. Furthermore, **Figure 3** depicts their frequency response versus the ideal step response. It is worth mentioning that in practical designs, because of unstable zeros of *TF*, below 10-order approximations are feasible. This approximation does not need any modifications for lower orders. So, it can be a better choice for simple designs. Based on these five transfer functions, the MATLAB simulation for step response of them concerning true time delay is done, and the results are shown in **Figure 3**.

The simulations of both approximations show that the Padé approximation has a more accurate response concerning Taylor approximation. For example, for the 5 th-order approximation, the accuracy of Padé is 30 times better than Taylor's approximation.

So, the first step to designing a TTD cell is to use a Padé approximation with proper order for an intended purpose. Because lower orders are simple, but higher orders are *Wideband True Time Delay Cells DOI: http://dx.doi.org/10.5772/intechopen.111474*


#### **Table 2.**

*The Padé approximation for the time delay transfer function.*

#### **Figure 3.**

*The step response of equal order numerator and denominator of the TF's fraction for Padé approximation versus TTD for a 5-second delay.*

more accurate. For our TTD cell, we have focused on simplicity, So the lower orders are chosen.

Another important issue that is remained here is the difference between true time delay (*τd*) and group delay (*τg*). To investigate more about them, first, the phase response of both first and second-order approximations are calculated here:

$$\rho\_{1st,order}(\alpha) = -2\tan^{-1}\frac{\alpha T}{2} \tag{8}$$

$$\,\_2\phi\_{2ud, order}(o) = -2\tan^{-1}\frac{\mathsf{G}oT}{\mathbf{1}2 - o^2T^2} \tag{9}$$

From these two equations, the delay amount of both approximations can be calculated:

$$\pi\_{d1}(\alpha) = -\frac{\rho\_{1t,order}(\alpha)}{\alpha} = \frac{2\tan^{-1}\frac{\alpha T}{2}}{2} \tag{10}$$

$$\pi\_2(o) = -\frac{q\_{2ud, ordr}(o)}{o} = \frac{2\tan^{-1}\frac{6oT}{12 - o^2T^2}}{2} \tag{11}$$

Furthermore, from these equations, the group delay of both approximations can be calculated:

$$\pi\_{\rm g1}(o) = -\frac{d}{d o \nu} \left( \wp\_{1st, order}(o) \right) = \frac{2}{\mathbf{1} + \frac{o \cdot T}{2}} \tag{12}$$

$$\pi\_{\rm g2}(\alpha) = -\frac{d}{d\alpha} \left( \wp\_{2nd, order}(\alpha) \right) = \frac{2\left(73 + \alpha^3 T^3\right)}{\left(12 + 35\alpha^2 T^2\right)\left(12 - \alpha^2 T^2\right)}\tag{13}$$

#### **2.4 Maximum available flat delay amount**

From these four equations, the group delay and true time delay are equal when the phase changes are linear, i.e., linear phase response. This matter can be calculated from these equations:

$$\begin{aligned} \tau\_{\xi} &= \tau\_{d} \\ \Rightarrow -\frac{\rho(\boldsymbol{\alpha})}{\boldsymbol{\alpha}} &= -\frac{d\rho(\boldsymbol{\alpha})}{d\boldsymbol{\alpha}} \\ \Rightarrow \frac{d\boldsymbol{\alpha}}{\boldsymbol{\alpha}} &= \frac{d\rho(\boldsymbol{\alpha})}{\rho(\boldsymbol{\alpha})} \end{aligned}$$

$$\Rightarrow \int \frac{d\boldsymbol{\alpha}}{\boldsymbol{\alpha}} = \int \frac{d\rho(\boldsymbol{\alpha})}{\rho(\boldsymbol{\alpha})}$$

$$\Rightarrow \ln\left(\rho(\boldsymbol{\alpha})\right) = \ln\left(\boldsymbol{\alpha}\right) + \boldsymbol{\varepsilon}$$

$$\Rightarrow \rho(\boldsymbol{\alpha}) = e^{\ln\left(\boldsymbol{\alpha}\right) + \boldsymbol{\varepsilon}} = e^{\ln\left(\boldsymbol{\alpha}\right)}\boldsymbol{\varepsilon}^{\varepsilon}$$

$$\Rightarrow \rho(\boldsymbol{\alpha}) = \mathbf{C}.\rho\tag{14}$$

From the above calculations, and concerning the value of phase, we can write the below equation for both first and second-order approximations:

$$\log(\phi) = -2\arctan\left(\frac{\alpha T}{2}\right) \stackrel{Linear}{=} \text{Co}\tag{15}$$

$$\varphi(\alpha) = -2\arctan\left(\frac{6\alpha T}{12 - \left(\alpha T\right)^2}\right) \stackrel{Linear}{=} \mathcal{C}\alpha \tag{16}$$

Both equations are arctangent-based. As shown in **Figures 4**–**6**, the response will be linear up to 23 degrees (0.4 radians) which means, until the phase argument reaches this amount, the output of the TTD cell will remain linear.

#### **Figure 4.**

*The comparison between* y = arctan (x) *and* y = x.

**Figure 5.** *The comparison between* y = arctan (x) *and* y=x *in magnified mode.*

So, for the 5 GHz application, this maximum delay can be calculated from the previous Eqs. (15) and (16). For the first-order approximation, the delay amount will be *T* = 25 ps, and for the second-order approximation, the delay amount will be *T* = 24 ps. Up to this amount, the TTD cell will remain in a linear area, and the group delay and true time delay are equal.

It is why most active TTD cells with larger delay values suffer from DV in lower frequencies. For example, [13, 14] tried to provide 24 ps and 59 ps delays, but they have 30% and 50% DV. [11, 21] also have a borderline 10% DV for their bandwidth.

So, for having larger delays, it is inevitable to use circuit-level or system-level approaches like master-save, DLL (delay lock loop), and phase linearizer to address this issue [10, 22, 23].

**Figure 6.** *The inverter-based inductor-less TTD cell is proposed in [15].*

#### **2.5 Inductor-less TTD cell with COMS inverter cell**

As mentioned above, the ideal transfer function of a TTD cell can be approximated with Padé approximation [15]. The equation of this approximation can be written as follows:

$$H(\mathbf{s}) = e^{-s\tau} \approx \frac{2 - s\tau}{2 + s\tau} = \frac{\mathbf{1} - s\left(\frac{\tau}{2}\right)}{\mathbf{1} + s\left(\frac{\tau}{2}\right)} = -\left(\frac{-2}{\mathbf{1} + s\left(\frac{\tau}{2}\right)} + \mathbf{1}\right) \tag{17}$$

This equation shows that the all-pass filter can be created with a low pass filter and a gain stage. The inverter-based structure for a TTD cell is proposed in [15] as shown in **Figure 6**.

In this TTD cell, the second path is the gain stage with a gain of 2. It consists of M4 and M5. The first pass is the low pass filter section which consists of M1, M2, M3, *R*, and *C*. To investigate the structure's performance, first, we must calculate the low-frequency gain of the cell. The overall gain of the structure ignoring parasitic capacitances comes from this equation:

$$\frac{\upsilon\_{out}}{\upsilon\_{in}} = A\_{v1} + A\_{v2}$$

$$A\_{v1} = \frac{\frac{\mathcal{g}\_{m3}}{\mathcal{g}\_{m4} + 1/R\_L} \left(1 - R\left(\mathcal{g}\_{m1} + \mathcal{g}\_{m2}\right)\right)}{1 + \varepsilon \mathcal{CR}},\\A\_{v2} = \frac{\mathcal{g}\_{m5}}{\mathcal{g}\_{m4} + 1/R\_L} \tag{18}$$

In this equation, *Av*<sup>1</sup> and *Av*<sup>2</sup> are the low-frequency gains of the first and second stages. The overall gain is the summation of these two gains since the two paths are parallel. In this equation, *R* and *C* are the feedback resistor and second-stage capacitances of the TTD cell. *RL* is the output load (usually 50 ohms). *gm*1, *gm*2, *gm*3, *gm*4, and *gm*<sup>5</sup> are the M1 to M5 transconductances. This gain can be rewritten as follows if we made some assumptions:

*Wideband True Time Delay Cells DOI: http://dx.doi.org/10.5772/intechopen.111474*

$$\frac{v\_{out}}{v\_{in}} = A\_{v1} + A\_{v2} = \frac{1 - sRC}{1 + sRC}$$

$$\text{if}$$

$$\mathbf{g}\_{m5} = \mathbf{g}\_{m4} + \mathbf{1}/R\_L, \frac{\mathbf{g}\_{m3}\left(\mathbf{1} - R\left(\mathbf{g}\_{m1} + \mathbf{g}\_{m2}\right)\right)}{\mathbf{g}\_{m4} + \mathbf{1}/R\_L} = -2\tag{19}$$

With this assumption, the all-pass filter with equal frequency for the left-handed pole and right-handed zero is created. From the previous discussion, the true time delay of this TTD cell can be calculated as follows:

$$\pi\_d(\rho) = \frac{2\tan^{-1}\alpha RC}{\rho} \tag{20}$$

This equation means that the delay of the TTD cell can be manipulated just with the *R* and *C* of the TTD cell. Although all parasitic parameters can change the value, *R* and *C* are the dominant parameters for this matter. While *R* is used as the feedback resistor and ensures the wideband application of the structure, capacitor *C* is relaxed to create an arbitrary delay amount. There are many trade-offs and non-idealities in the TTD cell design, like input capacitance of the stage, parasitic zero and pole, limited bandwidth, finite output impedance, noise, and nonlinearity of the structure. They are deeply discussed in [15]. The TTD cell must have input/output impedance matching since it may work in a delay line.

From **Figure 7**, the TTD cell provides a 10.6 ps delay amount with 3% DV in the 1–5 GHz. The loss of TTD cells is acceptable, and *S*<sup>21</sup> is better than �3.9 dB. The TTD cell has input/output impedance matching, and *S*<sup>11</sup> and *S*<sup>22</sup> are below �10 dB. This TTD cell works well to provide a 10 ps delay amount. However, a larger delay will have a bounded delay bandwidth, and the DV will arise, as discussed earlier. Another issue for this novel structure is its performance against process variations, aging effects, field variations, and other non-idealities. We need a solution to ensure its performance against these issues.

#### **2.6 The TTD cell improvement**

There are two major issues in inductor-less TTD cells. The High value of DV for large delay amounts and non-ideality issues like process, supply voltage, and temperature (PVT) variations, aging effects, and mismatch between TTD cell's devices. A few approaches to address these issues are discussed in the introduction section. Here we will discuss another approach to improve the TTD cell's performance.

As the semiconductor industry develops, the size of the transistors decreases. This size reduction causes some stability issues for transistors, especially for highfrequency applications. Due to this size reduction, the transistors are more sensitive to PVT variations, aging effects, and field variations.

The effect of these non-idealities will show on the change in threshold voltage of the transistor, which changes the transistor's transconductance and noise parameters of the device. The threshold voltage can be defined as a function of three parameters as follows:

$$\mathbf{V}\_t = \mathbf{V}\_{t0} + \eta \left( \sqrt{(|2\Phi\_F| - \mathbf{V}\_{\rm BS})} - \sqrt{|2\Phi\_F|} \right) \tag{21}$$

**Figure 7.** *The* S*11,* S*22, gain, and delay of the TTD cell.*

In this equation, *Vt* is the threshold voltage when the body bias is available (*VBS*, not zero), *Vt0* is the threshold voltage when the body bias (*VBS* = 0 V) is zero, *Ф?* is the Fermi potential, and usually is 0.3–0.4 V1/2. *γ* is the body parameter, also known as the body coefficient, and comes from the below equation:

$$\gamma = \frac{\mathbf{t}\_{\text{ox}}}{\varepsilon\_{\text{ox}}} \left( \sqrt{2 \mathbf{q} \varepsilon\_{\text{Si}} \mathbf{NA}} \right) \tag{22}$$

In this equation, tox is oxide thickness, *εox* is the permittivity of oxide,*ε*Si is the permittivity of silicon, *NA* is the doping density, and *q* equals the electrical charge. *γ* is always positive.

From Eq. (21), Process variations change the body coefficient, which leads to *Vt* variation. Temperature variations and field effects change the Fermi potential level, which leads to *Vt* variation, too. Fortunately, from Eq. (21), another phenomenon can be observed. If the threshold voltage faces any change by the non-idealities, we can manipulate it by *VBS* to compensate for that variation deliberately.

With this technique, we can provide a larger delay with the proposed TTD cell since any delay variation can be tuned by the body bias of the TTD cell's devices. Moreover, the structure will be robust against any non-ideality from PVT, again effects or field effects.

The results of the body bias technique are depicted in **Figure 8**. Delay, *S*11, *S*22, and *S*<sup>21</sup> with and without body bias techniques are depicted in this figure. The delay

**Figure 8.** *The Results of TTD cell with and without body bias technique.*

amount of the TTD cell is 50.95 ps with only 2% DV in the 1–5 GHz band. The TTD shows a flat delay response compared to the TTD without body bias. The loss (*S*21) of the TTD cell is improved, and we have a flatter *S*<sup>21</sup> parameter. *S*<sup>11</sup> and *S*<sup>22</sup> are below 10 dB and improved with the body bias technique.

#### **3. Conclusion**

In this chapter, we have discussed wide-band TTD cells. There are two major TTD cells, silicon-based and non-silicon-based TTD cells. In this chapter, we studied why silicon-based TTD cells are used in today's IC design. Then we faced two major approaches for designing a silicon-based TTD cell. Active TTD cells are used for high frequencies (upper than 10 GHz), and active TTD cells are used for low frequencies (below 5 GHz). Active TTD cells have two topologies, inductor-based TTD cells, and inductor-less TTD cells. This chapter deeply discussed why we do not prefer inductors in our designs. Also, active TTD cells suffer from high DV, which its roots are discussed here. Finally, we have presented an inductor-less inverter-based TTD cell. This cell works well, but if we need large delay amounts, it will face high DV, too. The body bias technique is applied to the TTD cell to overcome the DV issue. The results are fruitful, and the structure provides larger amounts of delay with a flat frequency response. Moreover, the TTD cell is robust against non-idealities like PVT variations, aging effects, and field effects.

#### **Author details**

Ahmad Yarahmadi Tarbiat Modares University, Tehran, Iran

\*Address all correspondence to: ahmad.yarahmadi@modares.ac.ir

© 2023 The Author(s). Licensee IntechOpen. This chapter is 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.

*Wideband True Time Delay Cells DOI: http://dx.doi.org/10.5772/intechopen.111474*

#### **References**

[1] Jeong J, Collins N, Flynn MP. A 260 MHz IF sampling bit-stream processing digital beamformer with an integrated array of continuous-time band-pass ΔΣ modulators. IEEE Journal of Solid-State Circuits. 2016;**51**(5):1168-1176

[2] Elamien MB, Maundy BJ, Belostotski L, Elwakil AS. Ultra-lowpower compact single-transistor all-pass filter with tunable delay capability. AEU-International Journal of Electronics and Communications. 2021;**132**:153645

[3] Spoof K, Unnikrishnan V, Zahra M, Stadius K, Kosunen M, Ryynänen J. True-time-delay beamforming receiver with RF re-sampling. IEEE Transactions on Circuits and Systems I: Regular Papers. 2020;**67**(12):4457-4469

[4] Paul A, Ramírez-Angulo J, Lopez-Martin AJ, Carvajal RG. CMOS firstorder all-pass filter with 2-Hz pole frequency. IEEE Transactions on Very Large Scale Integration (VLSI) Systems. 2019;**27**(2):294-303

[5] Guo B, Wang H, Wang H, Li L, Zhou W, Jalali K. A 1–5 GHz 22 mW receiver frontend with active-feedback baseband and voltage-commutating mixers in 65 nm CMOS. IET Circuits, Devices & Systems. 2022;**16**(7):543-552

[6] Nejadhasan S, Zaheri F, Abiri E, Salehi MR. PVT-compensated lowvoltage and low-power CMOS LNA for IoT applications. International Journal of RF and Microwave Computer-Aided Engineering. 2020;**30**(11):e22419

[7] Mondal I, Krishnapura N. A 2-GHz bandwidth, 0.25–1.7 ns true-time-delay element using a variable-order all-pass filter architecture in 0.13 μm CMOS. IEEE Journal of Solid-State Circuits. 2017;**52**(8):2180-2193

[8] Spoof K, Zahra M, Unnikrishnan V, Stadius K, Kosunen M, Ryynänen J. A 0.6–4.0 GHz RF-resampling beamforming receiver with frequencyscaling true-time-delays up to three carrier cycles. IEEE Solid-State Circuits Letters. 2020;**3**:234-237

[9] Gao F, Wang B, Xing C, An J, Li GY. Wideband beamforming for hybrid massive MIMO terahertz communications. IEEE Journal on Selected Areas in Communications. 2021;**39**(6):1725-1740

[10] Garakoui SK, Klumperink EAM, Nauta B, van Vliet FE. Compact cascadable gm-C all-pass true time delay cell with reduced delay variation over frequency. IEEE Journal of Solid-state Circuits. 2015;**50**(3):693-703

[11] Chen Y, Li W. An ultra-wideband pico-second true-time-delay circuit with differential tunable active inductor. Analog Integrated Circuits and Signal Processing. 2017;**91**(1):9-19

[12] Kim J, Park J, Kim J-G. CMOS truetime delay IC for wideband phased-array antenna. ETRI Journal. 2018;**40**(6): 693-698

[13] Aghazadeh SR, Martinez H, Saberkari A. 5GHz CMOS all-pass filterbased true time delay cell. Electronics. 2018;**8**(1):16

[14] Aghazadeh SR, Martinez H, Saberkari A, Alarcon E. Tunable active inductor-based second-order all-pass filter as a time delay cell for multi-GHz operation. Circuits, Systems, and Signal Processing. 2019;**38**(8):3644-3660

[15] Yarahmadi A, Jannesari A. Wideband inductorless true time delay cell based on CMOS inverter for timed

array receivers. Circuits, Systems, and Signal Processing. 2021;**40**(8):3703-3726

[16] Cho M-K, Song I, Kim J-G, Cressler JD. An active bi-directional SiGe DPDT switch with multi-octave bandwidth. IEEE Microwave and Wireless Components Letters. 2016; **26**(4):279-281

[17] Visser HJ. Array and Phased Array Antenna Basics. England: John Wiley & Sons; Chichester; 2005

[18] De Oliveira AM, Perotoni MB, Garay JRB, Barboza SHI, Justo JF, Kofuji ST. A complete CMOS UWB Timed-Array Transmitter with a 3D vivaldi antenna array for electronic highresolution beam spatial scanning. In: 2013 SBMO/IEEE MTT-S International Microwave & Optoelectronics Conference (IMOC), 4–7 August 2013. Rio de Janeiro, Brazil: IEEE; 2013. pp. 1-6

[19] Makundi M, Valimaki V, Laakso TI. Closed-form design of tunable fractional-delay allpass filter structures. In: ISCAS 2001, the 2001 IEEE International Symposium on Circuits and Systems, 6–4, 2001. Vol. 4. Sidney, Australia: IEEE; 2001. pp. 434-437

[20] Kashmiri SM, Haddad SAP, Serdijn WA. High-performance analog delays: surpassing Bessel-Thomson by Pade-approximated Gaussians. In: 2006 IEEE International Symposium on Circuits and Systems, 21–24 May 2006. Kos, Greece: IEEE; 2006. pp. 2349-2352

[21] Chang Y-W, Yan T-C, Kuo C-N. Wideband time-delay circuit. In: 2011 6th European Microwave Integrated Circuit Conference, 10–11 October 2021. Manchester, UK: IEEE; 2021. pp. 454-457

[22] Chen Y, Li W. Compact and broadband variable true-time delay line with DLL-based delay-time control.

Circuits, Systems, and Signal Processing. 2018;**37**(3):1007-1027

[23] Nauta B. Analog CMOS Filters for Very High Frequencies. New York, USA: Springer; 1993

Section 2
