Design of Very Low Profile Circular UHF Small Antenna Using Characteristic Mode Analysis

This paper presents a very low profile circular UHF small antenna with a radiating body transformed from a monopole. The proposed radiating body is gradually improved by analyzing fundamental modes of the structure with different ground planes via characteristic mode analysis (CMA). CMAs demonstrate operating principles of the radiating body so that a magnetic feeding loop is proposed to excite the radiating body. An equivalent circuit of the radiating body and magnetic feeding loop is then established. The relationships between antenna bandwidth, and eigen value and modal significance are derived through physical insight of the CMA. A prototype of the proposed circular antenna operating at 474MHz is fabricated and measured. It has a radius of 5.2%λc (λc is the operating wavelength), and a profile of 0.5%λc. The CMA of the proposed antenna with testing cable at different lengths is applied to understand the discrepancy between simulations and measurements. The analysis and performance evaluation shows that the proposed antenna can be a strong contender for compact sensors for machine-to-machine (M2M) and Internet of Things (IoT) applications.


Introduction
Small antennas play very important roles for wireless communication devices within limited spaces, but their performance and bandwidth are limited by the electrical size.Wheeler [1] and Chu [2] generally revealed the relationship between bandwidth and electrical size of small antennas.Sievenpiper et al. [3] had summarised the product of bandwidth and efficiency for 110 antenna designs published in the IEEE Transactions on Antennas and Propagation since 2010, extracted experimental validation of performance limits.It is found that most antenna structures approaching the performance limits occupy three-dimensional volumes, and are generally not low profile.
Low-profile small antennas are required and developed with the boom of portable ultra-high frequency (UHF) communication devices built in limited area [4,5].A typical antenna in smart phone is small and low profile, but generally mounted on a relative large ground plane [6].For UHF applications such as radiofrequency identification (RFID) tags, very-low-profile small antennas are necessary [7].There are several ways to design verylow-profile small antennas.A broadband UHF RFID tag was designed by considering the optimum equivalent-circuit network necessary for bandwidth broadening in single resonant tag with conjugate matching [8].New radiating bodies were used and investigated in [9], and relatively high product of bandwidth and efficiency were realised.In addition to RFID applications at UHF frequency bands, recently devices operating at exiting UHF TV frequency bands, termed as TV white space, have attracted much attention from regulators, academia and industry [10][11][12].One of the key applications of TV white space spectrum is the machine-tomachine (M2M) communications to enable emerging internet of things (IoT) applications [13][14][15][16].The small and compact sensors for M2M and IoT applications have resulted in significant challenges for small antennas at UHF TV white space frequency bands, e.g.around 480 MHz.Earlier studies on a circular co-planar inverted-F antenna for M2M communications at TV white space frequency band 480 MHz were presented in [17].The size reduction was achieved by transforming a planar inverted-F antenna.Furthermore, a printed monopole antenna was miniaturised by a magneto-dielectric superstrate for M2M communications [18].However, the superstrate materials are too expensive for the billions of wireless sensors required.Therefore, forming new antenna structures on a printed circuit board (PCB) for such emerging UHF M2M and IoT applications should be a promising approach to design small antennas.
Characteristic mode analysis (CMA) supported by theory of characteristic mode (TCM) becomes an attractive systematic tool to efficiently design antenna structures recently.It was proposed by Garbacz [19] and further developed by Harrington and Mautz [20,21].The CMA makes it possible to obtain full characteristics of a radiating body with arbitrary geometry.Based on insight in fundamental resonance characteristics of antenna geometries and structures to be mounted on, excitation locations and modes of the antenna can be optimised [22].Several small antennas were analysed and designed using CMA.For instance, a multiple-input and multiple-output antenna with enlarged bandwidth and single feed was realised by correlating the characteristic currents and near fields of modes with high modal significance [23].With knowledge of characteristic modes of an electrically small unmanned aerial vehicle body, the desired currents were excited by compact and low-profile feed structures to design integrated antennas [24].Similarly, the metallic chassis of a smart phone was excited by small coupling elements, and compact massive antenna arrays were generated by exciting multiple modes on each array element [25].
In this paper, a very-low-profile circular UHF small antenna is proposed.The CMA is utilised in the process of designing a radiating body and a feeding structure, establishing an equivalent circuit, estimating antenna bandwidth and analysing difference between results of simulation and measurement.With the physical insight from CMA, the proposed antenna ground plane is further optimised to a ring shape with an arc.The substrate is used to further reduce the size of the antenna.The equivalent circuit is established, which is used further to derive the relationship between the antenna bandwidth, and eigen value and modal significance.A prototype antenna operating at 474 MHz is then fabricated, measured and connected to a sensor circuit board for performance evaluations.
The rest of this paper is organised as follows.Section 2 describes the proposed radiating body and CMA.Section 3 presents the magnetic feeding loop for the proposed radiating body.The equivalent circuit and bandwidth estimation methods are also established in this session.A prototype and its measurement results

Proposed circular radiating body with disk ground plane
Monopoles are widely adopted for wireless communications during the last decade.It typically has a length of about λ 0 /4 at resonant frequency f 0 , where λ 0 is the wavelength in free space at f 0 .However, the monopole has a high profile because its pole is vertical to the ground plane.In this paper, a small radiating body with very low profile is designed by shape transformations on the monopole.The ground plane in a typical monopole is transformed into a small disk ground plane with a radius of r 3 .The monopole is placed in the same plane of the disk and bent around the disk to become a circular arm with outer radius of r 1 and inner radius of r 2 , as shown in Fig. 1a.The width and average radius of the arm are w 1 = r 1 − r 2 and r 0 = r 1 + r 2 /2, respectively.The arc between open and short end of the arm is defined as θ.
A generic model of the proposed radiating body is established and simulated in the commercial software package FEKO to carry out the CMA.Modal current flows of the first two significant eigen modes are illustrated in Figs.1b and c.In Fig. 1b, the modal current distribution of mode 1 on the circular arm decreases gradually from the short end to the open end, which is similar to that of a typical monopole in its vertical form.However, there are two peaks in the current distribution of mode 2 as shown in Fig. 1c.The mode 1 is therefore selected for the proposed circular radiating body.
The proposed radiating body should tune the resonant frequency of mode 1 at f 0 and suppress the higher modes.TCM implies that modes with eigen value λ n = 0 n = 1, 2, . . .are at resonance and radiate most efficiently [22].Based on extensive CMA simulations, mode 1 can resonate at f 0 when the proposed radiating body is at settings of r 1 : r 2 : r 3 : λ 0 = 0.065: 0.051: 0.03: 1 The effective length of the circular radiating body can be then defined as which is about λ 0 /4 similar to a typical monopole.Eigen values of the first three modes for the radiating body with settings in (1) are illustrated in Fig. 1d, where frequency f is normalised to f N using At f N = 1, λ 1 is equal to 0 while λ 2 and λ 3 are far away from 0, which means that mode 1 is the most significant mode at the resonant frequency.This is consistent with modal current distribution shown in Figs.1b and c.The modal significance is another important quantity to compare the significance of each mode, and defined as Corresponding modal significances of the first three modes are also illustrated in Fig. 1d.At f N = 1, S 1 is equal to 1 while λ 2 and λ 3 are very small and near 0. Therefore, it can be confirmed that the mode 1 should be the desired mode for the proposed radiating body.

Radiating bodies with different ring ground planes
In Fig. 1b, modal current on the disk are flowing mostly along the left edge.There is hardly current flow in the centre and upper right area of the disk ground plane, which hints that the impact of current flow could be slight when these areas are removed.Fig. 2 illustrates three structures with different ring ground planes named as ring 1, ring 2 and ring 3. Ring 1 is formed by only removing the centre area with a radius of r 4 from the disk.Simulations show that when r 4 = 0.022λ 0 , the impacts on current flows between radiating body with disk and ring ground planes are slight.Based on ring 1, ring 2 is formed by removing the upper right part with arc of θ from the whole ring, while ring 3 is formed by removing the upper left part with arc of θ from the whole ring.
As shown in Figs.2a and b, the current flows on both ring 1 and ring 2 are in the opposite rotation direction to the current flows on the arm, which is the same as the radiating body with disk ground plane in Fig. 1b.However, the current flow on ring 3 is forced in the same rotation direction as the current flow on the circular arm when ring 3 has an upper left cut, as shown in Fig. 2c.With the cut on the ring being moved from right to left, the E-field between the arm and ring 3 becomes more uniform, and the ring 3 still serves as the ground plane.
Compared with ring 2, the current flows on ring 3 and the circular arm are in the same rotation direction, and therefore stronger and more uniform near H-field is generated, as shown in Fig. 3. H-fields in Figs.3a-c are very similar, their magnitudes around the arm are strong while those around the centre are weak.However, the H-field for ring 3 in Fig. 3d is nearly uniform from the centre to the outer edge of the structure.Thus, the radiating body with ring 3 is more constructive and efficient.
Eigen value λ 1 for each ground plane is plotted in Fig. 4a.Curves of λ 1 for ring 1 and ring 2 are on the right side and close to the one for the disk ground plane.This verifies again that the effect of cutting the central area of the disk ground plane is slight.The proposed radiating bodies with disk, ring 1 and ring 2 ground planes have similar radiation behaviours and resonant frequency.The blue dash-dot curve of λ 1 for ring 3 is on the left side to the black solid curve for the disk, and both curves have similar trend except that there is a wide gap between them.This indicates that the radiating body with ring 3 not only has the similar radiation behaviour as the disk, but also supports lower resonant frequency.
Radiation patterns for the proposed radiating bodies with different ground planes are given in Fig. 4b.Good agreements are observed in radiation patterns for different ground planes, especially for disk, ring 1 and ring 2. The radiation pattern for ring 3 is slightly more omni-directional on E-plane than the one for other ground planes.These omni-directional radiation patterns in E-plane are primarily resulted from that their circular arm carries current flows with strong magnitudes, and the radiating body generates magnetic field lines passing through the most area surrounded by the circular arm as shown in Fig. 3.
With the aforementioned physical insight via CMA, the radiating body with ring 3 is selected as the radiator for design of the antenna with a feeding structure.3 Proposed circular radiating body with magnetic feeding loop

Proposed radiator on substrate
Although the radiator can be realised by only one thin metal layer, it is more practical to fabricate it on the metal attached to the dielectric substrate by adopting PCB technologies.Therefore, substrate of Rogers 5880 with relative dielectric constant of ϵ r = 2.2 and height of h is used to model a practical design of the proposed radiator.
Value of h is swept to study the performance of radiators on dielectric substrates.The eigen values of radiators with different h are given in Fig. 5, indicating that the radiating body with a substrate has lowered resonant frequency.Thus, a smaller radiator can be achieved at the same frequency with existence of a substrate.The normalised resonant frequencies for different h are directly obtained from Fig. 5 and they are given in Table 1 as f Nc .
The proposed radiator can be generally designed at any desired resonant frequency with the aid of Table 1 and the geometric settings given in (1).Considering the tradeoff between very low profile along z-axis and small size in xy-plane, substrate with height of h = 0.6%λ 0 is selected for design of an example UHF radiator operating at its resonant frequency f c = 474 MHz (λ c = 632 mm).The radiator is designed through the following process.
First, according to (3), the reference resonant frequency f 0 can be determined by (5) when f c = 474 MHz and f Nc = 0.81 for h = 0.60%λ 0 are replaced in (5), f 0 = 585 MHz can be obtained.Then, the corresponding wavelength is calculated as λ 0 = c 0 / f 0 = 512 mm, where c 0 is the light speed in free space.

Proposed circular antenna with magnetic feeding loop and its equivalent circuit
The CMA has been utilised to understand the proposed radiating body without considering exciting sources previously.It has been observed that the current flows on the proposed radiating body generate magnetic field lines passing through the most area  surrounded by the circular arm.Given by TCM in [20], a modal solution for the current J on a conducting body defined by S in an impressed electric field E i can be a linear superposition of the modal currents J n , which is expressed as where the modal excitation coefficient (MEC) is When E i is produced by a magnetic current M i and reciprocal theorem is used to (7), we then have where H n is produced by a modal current J n on S.
In xy-plane, a loop structure paralleled with the proposed radiating body is therefore able to generate normal direction equivalent magnetic current, which is in the same directions of the corresponding H-field generated by modal current J 1 .Around the resonant frequency of mode 1 for the proposed radiating body, the eigen values of higher modes would be far away from zero.Also according to (6), if the small loop is placed near the strip connecting the inner ring and the outer circular arm, where the magnitude of the current flow of mode 1 is strongest and the one of mode 2 is weak, J 1 will be the only modal current with significant coefficient.Combining the radiator and magnetic feeding loop on different sides of the substrate, a planar circular antenna is illustrated in Fig. 6a.A typical modal flow of mode 1 for the antenna with feed loop is also given in Fig. 6b.It is clear that the rotation directions of current flows on the radiator and the feeding loop are opposite.This means the feeding loop and the radiator act as an air core transformer, which transfers the power from its feed port to the load by magnetic coupling.Hence, the feeding loop is named as the magnetic feeding loop in this paper.
Based on derivations in [20], when only J 1 is excited in the radiator and the radiated power is unit, the complex power balance for J 1 can be expressed as where j is the imaginary unit.
As shown in Fig. 5, eigen value λ 1 is nearly linear around the resonant frequency, and is zero at resonant frequency, negative below resonant frequency and positive above resonant frequency.This indicates that the frequency response of λ 1 is very similar to the one of reactance of a series LC resonant circuit.Thus, the radiator can be represented by a series resonant circuit comprised of resistor R r , inductor L r and capacitor C r [26].The impedance of the series resonant circuit can be written as where X r is used to simplify the imaginary part of Z r .When the current provided by a source with efficient value of I flows through the series resonant circuit, the complex power balance in the circuit can be expressed as In the case of the source providing unit power on R r , i.e.R r I 2 = 1, if X r /R r = λ 1 are satisfied, (11) and ( 9) are in the same form.Hence, the series resonant circuit becomes the equivalent circuit of the proposed radiator.In order to satisfy X r /R r = λ 1 , R r , L r and C r need to satisfy which can be used to determine the values of L r and C r at the resonant frequency.
The main function of the magnetic feeding loop is to excite mode 1 to transfer the energy from source to the radiator, which is equivalent to realise the impedance matching between source and radiator excited in mode 1.The function can be realised by adjusting the size of the feeding loop.As shown in Fig. 6a, the area of the feeding loop can be controlled by adjusting the length and radian of the feeding loop, indicating as l f and ϕ.When ϕ = π/9, the MECs and normalised resonant frequency ( f Nc ) of mode 1 with respect to l f are extracted from a series of simulations.The results are given in Fig. 6c.When l f increases, resulting in the increase of the magnetic loop coupling area, MEC increases significantly, while f Nc increases slightly.It means that MEC can be directly adjusted by l f , and the effect of the feeding loop on the resonant frequency is small and can be neglected in the equivalent circuit for the sake of simplification.Hence, the small magnetic feeding loop can be used as the excitation structure and its inductance L f is much less than L r , and therefore the effect of L f on the resonant frequency of the radiator is ignored.Now, the equivalent circuit of the proposed antenna combining the radiator and magnetic feeding loop is given in Fig. 6d.Considering the voltage and impedance transformation of the magnetic feeding loop just like the primary coil in an air transformer, the load effect of source impedance R s can be transformed into the series resonant circuit of the radiator as r s , so the original equivalent circuit is transformed into the simplified one as Fig. 6d shows.
If impedance matching between source and radiator are met at the resonant frequency, which can be realised by adjusting l f , the relationship of r s = R r must exist.Commonly, R r nearly remains unchanged around the resonant frequency.Using (10) and (12), the reflection coefficient of the proposed circular antenna is derived as

Bandwidth estimation
For small antenna, the product of bandwidth and efficiency Bη is the most important performance indicator, and its theoretical limit for linearly polarised or single-mode antennas with voltage standing wave ratio, VSWR = 2 is given in [3] as where B is the fractional bandwidth with VSWR = 2, η is the radiation efficiency, k is the wave number and r is the radius of the smallest sphere enclosing the antenna.Replacing Γ in the relationship of VSWR and Γ with the expression given in (13), the VSWR of the antenna can be derived as Using the condition of VSWR = 2 to (15), we can obtain the solutions of λ 1 as λ 1 is a function of frequency, once it is obtained by CMA two horizontal lines with constant values of −0.7 and 0.7 cut a certain curve of λ 1 at two normalised frequency points denoted as f Nl and f Nh , respectively, as shown in Fig. 5 for example.Then, the fractional bandwidth is estimated as Reading from Fig. 5, the estimated fractional bandwidths for different h are evaluated and given in Table 2.

Simulated and measurement results and analyses
An example of the proposed circular antenna operating at 474 MHz is also modelled and simulated in software CST microwave studio with parameters of r 1 = 33 mm, r 2 = 26 mm, r 3 = 15.5 mm, r 4 = 11.5 mm and h = 3.1 mm.The antenna is fabricated and measured at Queen Mary University of London.The prototype is shown in Figs.7a and b.A customised subminiature version A (SMA) connector is soldered on the probe pads through holes.Fig. 7c presents the VSWR and total efficiency of the proposed antenna.Resonant frequency and VSWR < 2 bandwidth are about 474 and 2.2 MHz in simulation, and 471 and 3.3 MHz for measurement.The simulated total efficiency is 84% at 474 MHz.
The measured VSWR has a lower centre frequency and a wider bandwidth than the simulated one.The radiation patterns of the proposed antenna is also simulated by CST and given in Fig. 7d.It is clear that the radiation patterns of the proposed antenna agree well with the ones of the radiator given by CMA.This means the radiation patterns of the CMA can be used to predict the radiation behaviour of the proposed antenna.
As shown in Fig. 7a, the antenna prototype is measured with a SMA connector and test cable, which generally affects the near field around the radiating body for such a UHF band compact antenna with small ground structure although calibration is carried out.Cables with different lengths of l are located in the centre of the proposed radiator shown in Figs.7a and b.The corresponding λ 1 are obtained and shown in Fig. 8a.It can be observed that the resonant frequency of the antenna decreases when the length of cable increases.When l < λ c /8 , only resonant frequency decreases slightly while the fractional bandwidth remains unchanged, reflecting by the unchanged slope around the resonant frequency.When l > λ c /4 , resonant frequency still decreases while the fractional bandwidth begins to increase, because the slope around the resonant frequency decreases.When l ≃ λ c /2 , the cable becomes a dipole with strong radiation at the operating frequency, it will strongly affect the desired radiation mode of the proposed small antenna.Hence, the proposed circular antenna can keep its performance for compact devices without a feeding cable, e.g.directly connecting to a small sensor.
To evaluate the performance of the proposed circular antenna, the relevant performance data versus kr of various antennas are illustrated in Fig. 7b.The antennas for comparison purposes include the proposed antennas with different thickness of the substrate h, an ideal dipole with same kr and resonant frequency as the proposed prototype, and several small antennas reported in the open literature.The performance data contain Bη of each compared antenna, ratio of Bη of each antenna to the theory limit with same kr, experimental limit of Bη for planar antennas which is defined   by the best planar antennas cited in the literature [3], and are named as (Bη) a , (Bη) L , (Bη) a /(Bη) L and (Bη) E , respectively.
In Fig. 8b, solid and hollow symbols with same kr represent (Bη) a and (Bη) a /(Bη) L of the same antenna.(Bη) a labelled with h = pλ 0 are directly based on Table 2, where p is a percentage.The change trend of gap between (Bη) L and (Bη) E reflects that the smaller the kr is, the more difficult the design of planar small antenna is.(Bη) a /(Bη) L of the proposed antennas are not as high as the antennas in [9], but corresponding to smaller kr.All (Bη) a are below the polyline defined by (Bη) E .For the proposed antenna, the thicker the substrates is, the closer (Bη) a to (Bη) E is.Changes of (Bη) a /(Bη) L of the proposed antennas are very small when the height of substrate increases.It implies that the proposed antenna is suitable for very small antenna designs and has the potential to extend the experimental limit for planar antenna when the antenna is fabricated on substrate with high relative dielectric constant and height.
It is worth mentioning that (Bη) a of the antenna in Fig. 7a is based on results of the model with the same parameters as the prototype and a SMA connector simulated in CST, and it is a little larger than the estimated one (corresponding to h = 0.6%λ 0 ) due to the existence of feeding structure and SMA connector.Therefore, the derived bandwidth estimation in this paper is verified and can be generally used, being faster than electromagnetic simulations as it only needs the information of λ 1 with respect to frequency provided by CMA.

Conclusions
The paper presented a very-low-profile circular UHF small antenna with radiating body transformed from a monopole.CMA was used to analyse and design the proposed antenna.After the comparison of radiation behaviours and sizes of several radiating bodies with different ground planes, the one with an improved ring ground plane was selected as the radiator for the proposed antenna.The omni-directional radiation patterns of the radiator were achieved on E-plane due to the natural almost full-round current flow of mode 1. CMA pointed out that the size of radiator fabricated on a substrate can be smaller than the one with only conductor, and the normalised resonant frequency for the radiator fabricated on substrate was a scale factor of the geometric length.A magnetic feeding loop was integrated with the radiator to construct the proposed small antenna, where an equivalent circuit was established and used to estimate its bandwidth based on the physical insight of CMA.
An example of the proposed low-profile circular antenna was practically designed and fabricated at 474 MHz with a radius of 33 mm (5.2%λ c , λ c is the operating frequency wavelength), and a profile of 3.1 mm (0.5%λ c ).There was a discrepancy between simulated and measured VSWR of the prototype.The CMA of the proposed antenna with a test cable at lengths was applied to examine the difference.Based on the analysis and performance evaluation, the proposed antenna can be a strong contender for compact sensors at UHF TV white space for M2M and IoT applications.

Fig. 1
Fig. 1 Proposed planar circular radiating body with a disk ground plane transformed from a monopole (a) Geometry of the radiating body, (b) current flow of mode 1, (c) current flow of mode 2, and (d) eigen values λ n and modal significance S n for the first three modes

Fig. 6
Fig. 6 Circular radiating body with magnetic feeding loop (a) Structure layout of the proposed circular antenna with magnetic feeding loop, (b) Modal current flows of mode 1 for the antenna with feeding loop, (c) MECs and f Nc with respect to the length of the feeding loop l f , (d) Equivalent circuit of the proposed circular antenna with magnetic feeding loop

Fig. 7
Fig. 7 Prototype of the proposed circular antenna (a) Radiator side view, (b) Magnetic feeding loop side view (r 1 = 33 mm, r 2 = 26 mm, r 3 = 15.5 mm, r 4 = 11.5 mm and h = 3.1 mm corresponding to parameters in Fig. 1a), (c) VSWR and total efficiency of the proposed antenna, (d) Radiation patterns

Fig. 8
Fig. 8 Eigen value λ1 of the proposed circular radiator

( a )
Eigen value λ 1 of the proposed circular radiator with a test cable at different lengths, (b) Comparison of Bη and Bη /(theory limit) between the proposed and other antennas IET Microw.Antennas Propag., 2017, Vol.11 Iss.8, pp.1113-1120 This is an open access article published by the IET under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/)