Open access peer-reviewed chapter

Time Domain Performance Evaluation of UWB Antennas

By Gopikrishna Madanan and Deepti Das Krishna

Submitted: July 10th 2020Reviewed: October 19th 2020Published: December 9th 2020

DOI: 10.5772/intechopen.94546

Downloaded: 148

Abstract

The performance of printed wideband antennas has to be optimized both in frequency and time domains, to qualify for UWB applications. This is especially true in multi-resonant antenna topologies where the excitation of different modes can change phase centers and radiation patterns with frequency. The study presented in this chapter intends to demonstrate the simulation and experimental design for the time domain characterization of UWB antennas. Modeling the antenna as a linear time-invariant system with transfer function and impulse response, distortion caused to a nanosecond pulse is analyzed. Two planar monopole antenna designs are considered for the comparative study: the SQMA and RMA. SQMA is a traditional CPW-fed monopole design with ground modifications for ultra wide-bandwidth. RMA is a rectangular CPW-fed monopole with an impedance transformer arrangement at the antenna feed. RMA maintains constant impedance over the entire UWB and contributes towards maintaining uniformity in the radiation patterns over the entire frequency band by its design. Transfer function measurements are performed for both the azimuthal and elevation planes and the impulse responses are deduced by performing IFFT. Parameters such as FWHM and ringing are computed from the impulse response for the performance comparison. To evaluate the influence of the antenna geometry on a transmitted/received pulse, the impulse responses are convoluted with a standard UWB pulse. The time-domain distortion for the designs is then compared by computing the Fidelity parameter.

Keywords

  • ultra wide band
  • planar monopole antenna
  • antenna transfer function
  • antenna impulse response
  • time domain analysis

1. Introduction

Ultra-wide band systems transmit and receive ultra-short electromagnetic pulses having limited effective radiated power. The system performance is determined primarily by the characteristics of the radiators that have to conform with stringent frequency and time domain requirements in the entire operating band [1]. These requirements are namely, a non-dispersive phase centre; constant radiation and impedance over the frequency range with no excitation of higher order modes [2]. Planar monopole antennas with wide operating bands are most often well matched multi-resonant structures. In [3], Ma et al. have described the time domain performance of a printed dipole antenna employing a tapered slot feed. It is reported that the received pulses are distorted and broadened to more than 1 ns in spite of the antenna being well matched over the entire band. The higher order modes generated tends to shift the antenna phase centers with frequency and can lead to broadening of the radiated pulse. The same authors in [4] reports a much lesser pulse distortion for a tapered slot antenna operating in the 3.1–10.6 GHz UWB band. The present chapter intends to outline the design, simulation and measurement steps followed to characterize UWB antennas in the time domain.

Two monopole antennas with similar design topology is considered for the present analysis: the SQMA with a square radiator and RMA with a rectangular radiator. In both the antennas, the ground plane is optimally designed for a wide impedance bandwidth. The general practice to realize ultra wide-bandwidth in square/rectangular radiating elements is to modify the ground–radiator interface [5, 6, 7, 8, 9, 10]. In SQMA, the inherent resonances of a square patch is matched over the wide band by incorporating cuts in the ground plane at specific locations [11]. The designs proposed in [11, 12] have been contemplated to design the RMA. In RMA, the PCB footprint is greatly reduced and radiation patterns in the 3.1–10.6 UWB is stable without much radiation squinting which is otherise observed in wideband antennas at higher frequencies primarily due to the current distribution on the antenna ground plane [13]. Incase of RMA, this aspect is taken into consideration in the design ensuring broadside radiation all through the band of operation. This is further confirmed from the spatio-temporal transfer characteristics and the transient response analysis, making it suitable for UWB applications.

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2. Time domain analysis

Antennas intended for UWB systems need to possess superior pulse handling capabilities. Analysis of the transient response of the antenna is performed by direct time domain measurements [14, 15] or by a frequency domain measurement followed by Fourier Transformation [16, 17]. Frequency domain measurements take advantage of the high dynamic range and the standardized calibration of the vector network analyzer and is equally accurate to the direct time domain measurements.

In the latter method, the antenna is considered as a linear time invariant system described by its transfer function (gain and phase) and the associated impulse response [18, 19]. Transfer function and impulse response of UWB antennas are modeled as spatial vectors as the antenna characteristics depend on the signal propagation direction [16, 17]. Figure 1 shows the model for the analysis which consists of a radio link made up of two antennas in free space under the approximation of far–field and line-of-sight propagation. In this model, the transmitting and receiving antennas are characterized by eliminating channel effects [20].

Figure 1.

The UWB channel model.

2.1 Transient reception

The time domain relation between the received voltage pulse URxωrθφand the incident electric field pulse Eradωrθφis [17],

URxωrθφzc=hRxωθφEradωrθφz0E1

In the time domain, the corresponding relation is,

uRxtrθφzc=hRxtθφeradtrθφz0E2

zcand z0are the antenna port and free–space characteristic impedance respectively, while indicates convolution operation. If θφrepresents the elevation and azimuth angles, the receive antenna transfer function hRxωθφand its impulse response hRxtθφare considered as a function of the angle of arrival of the received pulse.

An ideal receiving antenna should receive a voltage pulse of the same shape as the one incident on it from any direction. This means that it should have a Dirac–delta impulse response which is also be independent of the angle of arrival. In other words, the antenna transfer function should have a uniform amplitude and a linear phase response (or constant group delay). However, in practice, the receiving antenna transfer function is always band limited.

2.2 Transient radiation

The frequency domain relation between the transmitted electric field pulse and the applied voltage pulse is,

Eradωrθφz0=hTxωθφejωr/crUTxωrθφzcE3

and,

hTxωθφ=2πchRxωθφE4

The time domain relation between the transmitted electric field pulse eradtrθφand the applied voltage pulse uTxtrθφat the transmitting antenna is,

eradtrθφz0=1rtrc12πcthRxtθφuTxtrθφzcE5

where,

hTxtθφ=12πcthRxtθφE6

The convolution with the delta function in Eq. (5) represents the time delay attributed to the finite speed of light, denoted by c. Eq. (6) indicates that the transmit impulse response hTxtθφis a time derivative of the receive impulse response hRxtθφ. As a result, an ideal antenna (with hRxtθσ=δt) will radiate an electric field pulse which would be a first–order time derivative of the input voltage pulse.

2.3 Model of transient transmission

The full input-to-output characteristics, in both frequency and time domains is deduced from 1 and 3 as below,

URxωrθφUTxωrθφ=ATx,Rxejωr/crhRxωθφ=2ωcATx,Rxcejωr/c22ωchRxωθφE7

where,

ATx,Rx=2πchRxωθφ
S21ω=URxωrθφUTxωrθφ=HTxωθφHChωHRxωθφE8

where,

HTxωθφ=2ωcATx,RxE9
HChω=cejωr/c2E10
HRxωθφ=2ωchRxωθφE11

In the time domain, 7 reads,

uRxtrθφuTxtrθφ=hTxtθφhChthRxtθφE12

2.4 Simulation

For the time domain characterization of the antennas, the fourth derivative of the Gaussian pulse given in Eq. (13) and shown in Figure 2(a) is chosen as the input pulse, as this pulse conforms to the FCC spectral mask as shown in Figure 2(b) when A = 0.333 and T = 0.175 nS.

Figure 2.

(a) Input pulse (b) power spectral density.

sit=A364πT2tτ2+4πT22tτ4e2πtτT2VmE13

For the antennas discussed in the later sections of this chapter, the input voltage uTxt(= sit) is specified in CST Microwave Studio and the radiated pulse eradtrθφis calculated on a sphere of radius 25 cm. Fourier transforms of these two quantities are then calculated and the transfer function HRxωθφis deduced from Eq. (4). An IFFT operation on this would generate the pulse response hRxtθφ.

2.5 Measurement

A scattering parameter S21measurement in the frequency domain can be used to deduce the transfer functions of both the transmitting and receiving antennas. Two identical standared horn antennas oriented in the bore sight direction is used, and considering Eq. (7), the corresponding transfer functions are found out from

HTxωθφ=j2πωc2S21ωθφHChωθφm1E14
HRxωθφ=2πjcω2S21ωθφHChωθφmE15

where the free space transfer function is,

HChω=c2expjωdcE16

Once the reference antenna (Tx Antenna) is characterized, transfer function of the AUT is found for multiple orientations using,

HAUTωθφ=S21ωθφHTxωHChωE17

2.6 Data processing, windowing

S21is measured with frequency resolution 15.25 MHz and Eqs. (14)(17) are used to compute the corresponding transfer functions. The data is further appended with zero padding for 0–2 GHz and 12–62.47 GHz range with 4096 points in the pass band. The conjugate of this signal is is then reflected to the negative frequencies to get a double sided spectrum of a real signal which is then transformed to the time domain using IFFT.

Measurements using two identical wide band horns are shown in Figure 3. While Figure 3(a) represents the measured antenna transfer functions, Figure 3(b) shows the real and imaginary parts of the transfer functions. Transmitting and receiving antenna impulse responses are shown in Figure 3(c) which clearly indicates that hTxtis a derivative of hRxt.

Figure 3.

(a) Transmitting and receiving transfer functions of identical wide band horn antennas (b) transmitting and receiving transfer functions after conjugate reflection (c) impulse response of the transmitting antenna and receiving antenna.

2.7 Time domain parameters

The time domain evaluation of the antenna effects on the transmitted/received signals is carried out by analyzing the envelope of the analytic response for co–polarization. The real valued antenna’s transient response is,

hnt=hntE18

The peak output voltage from an incident wave form depends on the peak value pθφof the antenna’s transient response:

pθφ=maxthntθφE19

A measure for the linear distortion of the antenna is the envelope width, which is defined as the full width at half maximum (FWHM) of the magnitude of the transient response envelope.

FWHM0.5θφ=t2p/2t1p/2,t1<t2E20

The duration of the ringing is defined as the time until the envelope has fallen from the peak value below a fraction αof the main peak.

RINGINGα=t2αpt1p,t1<t2E21

The lower bound for αis chosen according to the noise floor of the measurement. In order to compare the ringing of antennas with different gains under the condition of a constant noise floor, the fraction αis chosen to be 0.22 (−13 dB).

2.8 Pulse distortion analysis

The antenna effects on the received signal is evaluated by convoluting the analytic response hntθφwith the input pulse sit.

sot=hntθφsitE22

For UWB systems, receivers are in general based on the pulse energy detection or correlation with the template waveform. Therefore, the pulse distortions can be examined by calculating fidelity factor which is defined as [21],

F=max+sitsotτdt+sit2dt+sot2dtE23

where τis the delay parameter varied in a sense to maximize the numerator. The fidelity parameter measurement is performed for different spatial orientations of the test antenna and is evaluated as the maximum of the cross–correlation function. It compares only shapes of the waveforms, not amplitudes.

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3. Performance comparison of UWB antennas

To demonstrate the necessity of the time domain analysis of UWB antennas, two topologies shown in Figure 4 is considered.

Figure 4.

Design and parameters of (a) SQMA (b) RMA.

3.1 Antenna designs

Figure 4(a) depicts the design of the SQMA. The overall length of the element determines the lower end of the operational band and the upper end by the feed gap ‘d’. It is the ground plane which determines the impedance bandwidth of a monopole antenna. In the present design, the cuts engraved in the ground plane match the multiple resonances, making the antenna operate over the specified ultra wide band. The SQMA has the following dimensions with units of lengths in mm: s= 2.3, g= 0.48, l_patch= 16, l= 14.57, b= 13, d= 0.5, w= 1.4, L= 32, W= 30, εr= 4.4, tanδ= 0.02, h= 1.6.

The topology of the RMA comprises of a rectangular monopole of area l1×b1as shown in Figure 4(b). This antenna is evolved from a basic printed monopole design shown in the same Figure. To facilitate ultra wide band performance, an impedance transformer is embedded in the CPW transmission line with increasing slot widths g1, g2, g3and g4. The special design of the transformer provide gradual transformation of the 50 Ωline impedance and at the same time, result in a new current path for radiation. The coupling of the guided waves to the radiator is strongly dependent on parameter dand the resonances in the structure can be matched by suitably choosing d. For the RMA, the geometric parameters are: s= 2.3, g= 0.28, d= 4.25, l1= 9, b1= 10, lg= 17.75, l2= 6, b2= 7.3, g1= 0.45, g2= 1.35, g3= 2, g4= 2.7, t= 1, sf= 2, lf= 3, L= 30, W= 12, εr= 4.4, tanδ= 0.02, h= 1.6. Unit of all lengths are in mm.

3.2 Performance evaluation in the frequency domain

Measured and simulated return losses of the two antennas are shown in Figure 5. The prominent resonances in the SQMA are at 3.8 GHz, 8 GHz and 13 GHz while that for the RMA are at 3.5 GHz, 5 GHz, 7 GHz and 11 GHz. Both antennas cover the 3.1-10.6 GHz UWB.

Figure 5.

Measured and simulatedS11dBof the (a) SQMA and (b) RMA.

3-D radiation patterns of the two antennas obtained from CST are shown in Figure 6. In SQMA, the pattern degradation at the higher frequencies were found to be effective from 8 GHz onwards. SQMA also shows pattern squinting as in Figure 6(a). For the RMA, the pattern degradation at the higher frequencies are minimum; radiation is stable and directed towards the bore-sight at all frequencies. The cross–polar level exhibited by both the antennas remain better than −20 dB in the 3.1–10.6 GHz band. Both antennas have linear polarization, oriented in the Z direction. Peak gains of the antennas were measured by gain transfer method. Average value of the peak gain in the 3.1–10.6 GHz UWB is found to be 3.75 dBi for SQMA and 2.6 dBi for the RMA.

Figure 6.

Simulated radiation patterns at different frequencies for the the antennas (a) SQMA (b) RMA.

3.3 Performance evaluation in the time domain

As an UWB signal is transmitted or received, the pulse shape is altered. This distortion is reflected in the transfer function (in the frequency domain) or impulse response (in the time domain) of the antenna. The antenna transfer function, a complex quantity, would have a constant amplitude and linear phase response while the impulse response would be a delta function, in cases when the antenna has no effect on the pulse transmitted.

3.3.1 Results of simulation in CST

Magnitude of the transfer function hRxωθφsimulated in CST for the x-y plane of the antennas are shown in Figure 7(a) (Using Eq. (3)). It is seen that the intensity plots for hRxωθφand hTxωθφdiffer only in their relative amplitudes. Magnitude of the transfer function decay gradually as a function of frequency over most of the azimuth angles (x-y plane). The loss of omni-directionality of the pattern of SQMA at frequencies above 8 GHz is reflected in its transfer function as relatively low intensities at at certain angles. Sharp nulls are seen between 300500, 13001500, 21002300and 32003300. Transfer function in the x-z plane of the SQMA is shown in Figure 7(b). The nulls in the radiation pattern at 1800can be seen in the transfer functions which show intensity variations.

Figure 7.

Computed transfer functions of the SQMA in the (a) x-y (b) x-z planes; computed impulse responses the SQMA in the (c) x-y (d) x-z planes.

Impulse response in the x-y plane is well formed with good peak value over almost all the angular regions as shown in Figure 7(c). Amplitude degradation beyond 8 GHz in the SQMA impulse response is reflected between 3001200and 20003300. Impulse response in the x-z plane of the SQMA is shown in Figure 7(d).

Figure 8(a) indicates that the antenna transfer function of the RMA in the x-y plane is fairly constant throughout the entire UWB. Even though computed transfer function in the x-z plane shown in Figure 8(b) has variations, it remains within the acceptable limits. The nulls observed in the transfer function in Figure 8(b) can be attributed to the monopole pattern of RMA. Impulse responses computed in the x-y and x-z planes for the RMA is shown in Figure 8(c) and 8(d). In the x-y plane, the impulse response preserves the expected Dirac-delta shape, unlike that in the SQMA. Even though not in the perfect shape, impulse response of the RMA in the x-z plane has more resemblance to a Dirac-delta, when compared to SQMA.

3.3.2 Experimental results

For the measurements, the transmitting and receiving antennas were positioned in their far field, at a distance of 25 cm. Source power level in the VNA was set at 10 dB to improve signal to noise ratio in the measured data.

Figure 8.

Computed transfer functions of the RMA in the (a) x-y (b) x-z planes; computed impulse responses the RMA in the (c) x-y (d) x-z planes.

Figure 9(a) and (b) indicate the measured antenna transfer functions in the x-y and x-z planes for the SQMA. The measurements seem to follow simulations indicated in Section 3.3.1. Figure 9(c) and (d) indicate the transfer functions in the x-y and x-z planes for the RMA. While the transfer functions in the x-y planes remain constant with variation within 10 dB, the measured values for the x-z plane shows large variations at particular frequencies.

Figure 9.

Measured antenna transfer functions: (a) SQMA, x-y plane (b) SQMA, x-z plane (c) RMA, x-y plane (d) RMA, x-z plane.

The Figure 10(a)(d) shows the corresponding impulse responses, obtained by performing an IFFT on the measured transfer functions and they resemble delta functions across all the angles in the x-y plane.

Figure 10.

Measured impulse responses: (a) SQMA, x-y plane (b) SQMA, x-z plane (c) RMA, x-y plane (d) RMA, x-z plane.

Figures 11 and 12 shows the time domain performance indicators of the antennas for x-y and y-z planes. For the RMA, as the Figure 11(a) shows, the FWHM is constant and ringing is minimum at all angles in the x-y plane. The SQMA however shows variations, though within acceptable limits, which could be attributed to its relatively larger size. Computations also futher confirms that fidelity of the received pulses in the case of RMA is constant and better compared to the SQMA. The performance indicators show variations in the x-z plane in tune with the corresponding radiation patterns. Impulse responses are convoluted with the pulse form given in Eq. (13) to study the effect of the antenna geometry on a transmitted the baseband pulse. Computed fidelity of the received pulses of the RMA is constant and better compared to the SQMA. Variation in Fidelity in the θ=00ϕ=00and θ=1800ϕ=00directions could be attributed to the nulls in the radiation patterns at those angles.

Figure 11.

Computed (a) FWHM (b) ringing and (c) Fidelity measured in the x-y plane.

Figure 12.

Computed (a) FWHM (b) ringing and (c) Fidelity measured in the x-z plane.

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4. Conclusion

Printed UWB antennas are multi-resonant structures that operate over a wide frequency range. Even if the radiators designed for UWB exhibit excellent bandwidth, efficiency, etc., traveling phase centers present in the geometry can impair their use in time-domain applications. Changes in the antenna phase centers are reflected in the time domain as a dispersion in the transmitted/received pulses. A variation in antenna phase center can be quantified in terms of group delay or antenna transfer function, a curb on the former being 1nS over the entire band and that on the latter is to remain within 10 dB.

In this work, we have demonstrated this point by comparing the time-domain performance of two similar antenna geometries: the SQMA and the RMA. PCB area occupied by the SQMA is approximately 2.7 times that of the RMA and resonances in the geometry are inherent due to the square patch itself. Because of the different modes that are excited in the geometry, its peak radiation points are disoriented in the higher side of the UWB. Severe pattern degradation has also been observed at these frequencies. In RMA, the radiation patterns are found to be stable with minimum degradation at the higher frequencies. The design of RMA has achieved this virtue by manipulating the surface currents in the geometry. Abrupt discontinuities that can cause reflections in the geometry are avoided by the impedance transformer designed in the ground plane.

As frequency domain characterizations hardly throw light into the pulse handling capabilities UWB antennas, a method to characterize them in the time domain is presented in this work. Temporal characterizations of the two antennas performed by the method outlined here reveal a close correspondence between the geometry of the antenna with its performance in the time domain. From the study, it is concluded that for good time-domain performance, excitation of multiple modes within the operating band of the UWB antennas has to be taken care of during the designing of the antennas itself and its physical dimension has to remain to a minimum. The first condition minimizes internal reflections and the subsequent cancelations in the antenna geometry while the second one ensures that there are no changes in the phase center of the antenna.

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Acknowledgments

Simulations and measurements of the present work were done at the Govt. Victoria College, Palakkad and Cochin University of Science and Technology, Cochin. The authors acknowledge DST SERB, DST-FIST, UGC and KSCSTE for funding the facilities for simulation and measurement.

The authorship criteria are listed in our Authorship Policy: https://www.intechopen.com/page/authorship-policy.

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Conflict of interest

The authors declare no conflict of interest.

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Abbreviations

FCC
FWHMFull Width Half Maxima
IFFT
RMA
SQMA
UWB

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.0 License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Gopikrishna Madanan and Deepti Das Krishna (December 9th 2020). Time Domain Performance Evaluation of UWB Antennas, Innovations in Ultra-Wideband Technologies, Albert Sabban, IntechOpen, DOI: 10.5772/intechopen.94546. Available from:

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