ARL-TR-8111 ● AUG 2017

US Army Research Laboratory

Modeling, Simulation, and Measurement of 

Balanced Antipodal Vivaldi (BAV) Antennas for 

Fully Polarimetric Forward-Looking GroundPenetrating Radar (FLGPR) Receive Channels

by Seth A McCormick

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ARL-TR-8111 ● AUG 2017

US Army Research Laboratory

Modeling, Simulation, and Measurement of 

Balanced Antipodal Vivaldi (BAV) Antennas for 

Fully Polarimetric Forward-Looking GroundPenetrating Radar (FLGPR) Receive Channels

by Seth A McCormick

Sensors and Electron Devices Directorate, ARL

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August 2017

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May 2016–January 2017

4. TITLE AND SUBTITLE

Modeling, Simulation, and Measurement of Balanced Antipodal Vivaldi (BAV) 

Antennas for Fully Polarimetric Forward-Looking Ground-Penetrating Radar 

(FLGPR) Receive Channels

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Seth A McCormick

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5e. TASK NUMBER

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7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

US Army Research Laboratory

Sensors and Electron Devices Directorate

ATTN: RDRL-SER-M

2800 Powder Mill Road, Adelphi, MD 20783-1138

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ARL-TR-8111

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

This report documents the design, simulation, and measurement of balanced antipodal Vivaldi (BAV) antenna elements for the 

receive channels of a US Army Research Laboratory fully polarimetric forward-looking ground-penetrating radar (FLGPR) 

system including recommendations for the antenna positioning in a 32-element aperture. The BAV elements are meant to be 

operated from 0.3 to 2.0 GHz in a stepped frequency system. The elements are designed to have improved antenna performance 

compared to the current receive channel antennas below 1.0 GHz. The BAV elements have significantly improved realized gain 

and impedance match over the operational bandwidth. The elements also have an improved transient response with reduced late 

time ringing. Pairs of elements were simulated in different side-by-side configurations to determine effects on individual antenna 

performance and mutual coupling. Simulations showed that the configuration to produce the most compact 32-element aperture

at 2.2 m wide was that of vertical and horizontal elements positioned such that they produce an “L” shape. However, isolation 

between vertical and horizontal elements was considered critical, so a “T”-shaped configuration instead of an L shape would be 

preferred. Such an aperture would be nearly twice as wide at 4 m.

15. SUBJECT TERMS

balanced antipodal Vivaldi, tapered slot, FLGPR, antenna design and simulation, UWB antennas

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Seth A McCormick

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(301) 394-2706

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Contents

List of Figures iv

Acknowledgments vi

1. Introduction 1

2. Problem Statement 1

3. Current Vivaldi Elements and Replacement Antennas Considered 2

4. BAV Design by Simulation 8

5. BAV Measurement and Simulation Comparisons 17

6. Simulations and Measurements of BAV Pairs 23

7. Conclusion 42

8. References 44

Appendix A. Effects of a Wide Stripline Ground, Substrate Thickness, and 

Lens on Reflection Coefficient and Realized Gain 45

Appendix B. Balanced Antipodal Vivaldi (BAV) Schematic 53

List of Symbols, Abbreviations, and Acronyms 55

Distribution List 56
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List of Figures

Fig. 1 Current Vivaldi receive antenna for US Army Research Laboratory 

FLGPR.................................................................................................. 2

Fig. 2 FEKO Vivaldi model a) top view and b) partially transparent view .... 3

Fig. 3 Simulated and measured comparison of Vivaldi a) reflection 

coefficient and b) realized gain vs. frequency ...................................... 4

Fig. 4 Candidate antenna elements for ARL FLGPR: a) antipodal planar 

LPDA, b) cavity-backed UWB planar circular monopole, and c)

balanced antipodal Vivaldi. The radiation patterns are at 0.3, 0.6, and 

1.2 GHz on a 60-dB scale. .................................................................... 5

Fig. 5 Planar LPDA-simulated a) reflection coefficient and b) realized gain 

vs. frequency......................................................................................... 6

Fig. 6 Cavity-backed UWB planar circular monopole a) VSWR and b) 

realized gain vs. frequency compared to the current Vivaldi. Beam 

peak position is given by the theta angle from broadside..................... 7

Fig. 7 Built BAV, FEKO model, and Vivaldi (top), and the connector and 

one of the 3 solder connections (bottom).............................................. 9

Fig. 8 Original BAV from the literature with reduced depth........................ 10

Fig. 9 Reduced depth BAV a) reflection coefficient and b) realized gain vs. 

frequency............................................................................................. 11

Fig. 10 Simulated a) reflection coefficient and b) realized gain vs. frequency 

for percentage increases in flare length without changing taper......... 12

Fig. 11 Simulated a) reflection coefficient and b) realized gain vs. frequency 

for percentage increase in flare length and ending taper width .......... 13

Fig. 12 Comparison of BAV with 60% longer flare and taper width and 

Vivaldi-simulated a) reflection coefficient and b) realized gain vs. 

frequency............................................................................................. 15

Fig. 13 Simulated a) VSWR and b) realized gain vs. frequency for the BAV 

with substrate thickness of 0.3 and 0.25 inch ..................................... 16

Fig. 14 Comparison of simulated and measured a) VSWR and b) realized gain 

vs. frequency for the BAV and Vivaldi .............................................. 18

Fig. 15 Simulated and measured realized gain patterns for the BAV at a) 0.3 

GHz, b) 0.7 GHz, c) 1.5 GHz, and d) 2.0 GHz. E-plane is on the left 

and H-plane is on the right.................................................................. 19

Fig. 16 Comparison of simulated a) F/B, b) 3-dB beamwidth, and c) 

normalized transient response for the BAV and Vivaldi.................... 21

Fig. 17 Recommendation for a) receiver positioning to minimize width with b) 

element spacing and overall dimensions............................................. 24

Fig. 18 CAD models for the BAV receiver pairs............................................ 25
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Fig. 19 Simulated a) reflection coefficient, b) realized gain, c) F/B, and 

d) 0.7-GHz H-plane pattern for the side-by-side vertical BAV pair... 26

Fig. 20 Simulated a) reflection coefficient, b) realized gain, and c) F/B vs. 

frequency for the side-by-side horizontal BAV pair........................... 28

Fig. 21 Simulated a) reflection coefficient, b) realized gain, c) F/B, and d) 

cross-pol isolation vs. frequency for the centered dual-pol BAV 

pair ...................................................................................................... 30

Fig. 22 Electric current for the “flipped VH” simulation at 0.65 and 0.9 GHz

............................................................................................................. 33

Fig. 23 Simulated a) reflection coefficient, b) realized gain, and c) F/B vs. 

frequency for the corner dual-pol BAV pair....................................... 34

Fig. 24 a) Built corner dual-pol BAV pair, b) simulated and measured 

reflection coefficient, c) realized gain, d) cross-pol isolation vs. 

frequency, and e) transient response................................................... 36

Fig. 25 Simulated and measured radiation patterns for the corner dual-pol 

BAV with and without a connection at a) 0.3 GHz, b) 0.7 GHz, c) 1.0 

GHz, d) 1.5 GHz, and e) 2.0 GHz. E-plane is shown on the left and 

H-plane is on the right......................................................................... 39

Fig. 26 CAD images and dimensions for aperture with only centered BAV 

pairs. The bottom row consists of horizontal elements, and the top row 

is all vertical........................................................................................ 41

Fig. A-1 Simulated a) reflection coefficient and b) forward realized gain vs. 

frequency of the BAV with and without a wider stripline ground ..... 46

Fig. A-2 Simulated a) reflection coefficient and b) forward realized gain vs. 

frequency of the BAV for different substrate thicknesses.................. 48

Fig. A-3 a) BAV with embedded shaped dielectric lens, b) simulated reflection 

coefficient, and c) realized gain vs. frequency with and without the 

lens...................................................................................................... 49

Fig. B-1 BAV schematic and partially transparent top view. Units are in inches.

............................................................................................................. 54
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vi

Acknowledgments

I would like to acknowledge Arthur C Harrison for assembling the balanced 

antipodal Vivaldi antennas and the foam support structure. I would also like to 

acknowledge William O Coburn for his technical advice in the analysis of the 

balanced antipodal Vivaldi.
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1. Introduction

This report documents the design by simulation of a pair of balanced antipodal 

Vivaldis (BAVs) for the receive channels of an ultra-wideband (UWB) fully 

polarimetric forward-looking ground-penetrating radar (FLGPR). A particular 

challenge when designing a UWB antenna for FLGPR is meeting performance 

requirements in a practical size (i.e., can still be mounted on a commercial vehicle 

and fit within the width of a typical highway lane). Low-frequency performance 

drives antenna size. Operating at lower frequencies improves ground penetration 

and would allow the FLGPR operator to see objects buried deeper within the ground 

as predicted by the skin depth of a lossy half space.1 However, the direct 

relationship between antenna size (performance) and wavelength requires that the 

antenna must be electrically larger to improve the low-frequency performance.2

Often this requires antennas that are large physically, and in the case of material 

loading, produce antennas that are smaller physically with the same electrical size 

but with reduced performance. The metrics by which the antenna performance is 

gauged are efficiency (i.e., realized gain) and the impedance match (i.e., reflection 

coefficient). In addition, both cross polarization (cross-pol) isolation between 

cross-pol receive antennas, which provides a metric for antenna positioning, and 

characterizing the voltage transient of the antenna for a given input pulse (low late 

time ringing) are of concern. Other metrics such as the front-to-back ratio (F/B) and 

half-power beamwidth are also included.

The next section discusses the design requirements for the receive antennas and 

overviews the current receiver to be improved upon. Section 3 shows the measured 

and simulated results for the current Vivaldi and discusses the 3 antennas 

considered as replacements. Section 4 discusses the BAV and the design by 

simulation. Section 5 shows the evaluation of the BAV performance by comparison 

of the measured and simulated results. Section 6 discusses the positioning of paired 

cross-pol BAVs and the impact on performance and isolation, and Section 7 

summarizes and concludes the report with final statements.

2. Problem Statement

The FLGPR system is an in-house-developed system. It is fully polarimetric and 

currently uses 16 Vivaldi antennas for the 16 receive channels, one of which is 

shown in Fig. 1. The transmit channels are switched and use 2 dual-pol ridged horns 

with one on either side of the receive aperture. The Vivaldi has dimensions 4.9 ×

16.8 × 0.3 inches3 (length × width × thickness) with a weight of 2.23 lb. It was 

milled on stacked Rogers Duroid 5880 substrate (εr = 2.2 and tanδe = 0.001). The 
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top and bottom sides are identical. The Vivaldi is fed using a tapered stripline 

ending in a sectoral flare that is centered between the top and bottom surfaces. Brass 

shimming was soldered on the outside for improved structural integrity.

Fig. 1 Current Vivaldi receive antenna for US Army Research Laboratory FLGPR

The Vivaldi was operated over the frequency range of 0.3–2.0 GHz for both vertical 

and horizontal receive channels. The horizontal spacing between elements is about 

5 inches center-to-center. Dual-pol operation is achieved by mechanically rotating 

the elements in between measurements. The small size of the Vivaldi limits the 

low-frequency performance (<1.0 GHz) in terms of the impedance match and the 

realized gain, but just increasing the Vivaldi size alone is not enough. A complete 

new design is necessary as the stripline must also be redesigned and the transient 

response is not particularly smooth with large late-time ringing. Additionally, 

mechanically rotating the elements is impractical for mobile system performance 

(i.e., introduced mechanical delay). The goal of the design process is to improve 

the low-frequency performance while achieving dual-pol operation without 

mechanical means. Additional requirements are to maximize cross-pol isolation 

(i.e., isolation between cross-pol elements) and to maintain a small enough form 

factor to fit 32 elements within a width of 2.2 m; as will be shown, these 2

requirements are in opposition to each other.

3. Current Vivaldi Elements and Replacement Antennas 

Considered

The majority of the design process was conducted through modeling and 

simulation, including comparisons between the designed antennas and the Vivaldi 

to be replaced. The commercial computational electromagnetic software FEKO and 

General Electromagnetic Solver (GEMS) were used for modeling and simulation.3,4

FEKO was the primary computer-aided design (CAD) tool with simulation results 

using the Method of Moments (MoM) to produce the interaction matrix and LowerUpper decomposition for solving the MoM matrix. GEMS was the primary 

simulation tool, as the Finite Difference Time Domain solver was well suited for 

efficiently simulating UWB antennas. FEKO was used as a check for code-to-code 

comparisons. A model for the Vivaldi was built in FEKO from published drawings 
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and is show in Fig. 2.

5 Neither the connector nor the notch around the connector 

was included in the model. The sides of the Vivaldi are metallic; the metal is 

modeled using infinitesimally thin perfectly electrically conducting (PEC) surfaces.

(a)

(b)

Fig. 2 FEKO Vivaldi model a) top view and b) partially transparent view

The simulated and measured comparisons of the Vivaldi reflection coefficient and 

realized gain are shown in Figs. 3a and 3b, respectively. The excitation is a simple 

wire port in both FEKO and GEMS. The input pulse in the time domain is a 

differentiated Gaussian pulse with a high frequency of 4 GHz. The FEKO results 

are only calculated up to 1.2 GHz because of computational memory limitations 

and time to solution. It is understood that the model comparisons may start to break 

down at higher frequencies because of the mesh. The code-to-code agreement is 

good, but the comparison with measured data is not as good as expected for the 

reflection coefficient. Not including the connector and cutout would be the most 

likely reasons, but increasing the model complexity was not necessary. Material 

losses could also be a reason for the reduction in oscillations (reduced resistance) 

in the impedance as shown by the reflection coefficient, Fig. 3a. The Vivaldi 

impedance may also be sensitive to the metal thickness as it is virtually a slot-type 

antenna under the class of tapered slot antennas. Slot antennas are known to be 

sensitive to the thickness of the metal from which they are constructed, even if the 

metal is thin. The dependency on the slot thickness will become more important as 

the simulation frequency increases. The trend in the simulated reflection coefficient 

and realized gain is similar enough to the measured data to be used as an appropriate 

baseline for model-to-model comparisons. Absolute accuracy was not a concern for 

the model validation in this case for comparing alternative prototypes. 
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Fig. 3 Simulated and measured comparison of Vivaldi a) reflection coefficient and b) 

realized gain vs. frequency
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The antennas considered as alternatives are shown in Figs. 4a–c. The antipodal 

planar logarithmic periodic dipole array (LPDA) antenna element, Fig. 4a, had been 

designed for a previous forward-looking system.6 The LPDA is UWB with 

reasonably stable high gain as shown in the FEKO results, Figs 5a and 5b. This 

particular LPDA is also more compact than typical. As with all LPDAs, it must be 

fed with a coax that is only soldered to the antenna at the end with the short 

elements. While this antenna has desirable gain, the bandwidth that could be 

achieved would fall short of the requirement, and unlike other types of antennas 

where the low-frequency impedance match may gracefully worsen, the LPDA 

impedance match rapidly decays, as can be seen in the reflection coefficient, 

Fig. 5a. Given the size limitations and the fact that the antennas are to function over 

the transmit bandwidth, it is preferred to have an antenna that matches the former 

impedance behavior.

Fig. 4 Candidate antenna elements for ARL FLGPR: a) antipodal planar LPDA, b) cavitybacked UWB planar circular monopole, and c) balanced antipodal Vivaldi. The radiation 

patterns are at 0.3, 0.6, and 1.2 GHz on a 60-dB scale.
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Fig. 5 Planar LPDA-simulated a) reflection coefficient and b) realized gain vs. frequency
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Figure 4b shows a cavity-backed UWB planar circular monopole that had been 

designed for a FLGPR system that operated from 0.3 to 1.2 GHz.7 This antenna is 

advantageous in that its forward dimension is much smaller than that of the Vivaldi 

(i.e., reduced depth), although it requires a cavity backing to produce unidirectional 

radiation. The monopole alone is matched over the near decade bandwidth, but like 

all other planar monopoles, it has an increasing pattern tilt away from the feed, with 

frequency, toward end-fire; this is a consequence of a traveling wave behavior that 

occurs as the monopole becomes electrically longer. The pattern tilt occurs within 

the second octave. At frequencies greater than the second octave, the beam peak 

splits and tilts further, producing a null on boresight and lower gain at broadside. 

Modifications can be made to help reduce the severity of the pattern tilt and increase 

realized gain, but such modifications typically produce positive results up to the 

end of the second octave. The cavity-backed monopole is a significant 

improvement over the Vivaldi, as seen in the voltage standing wave ratio (VSWR), 

Fig. 6a, and realized gain, Fig. 6b, but cannot operate up to 2 GHz because of the 

pattern instability.

Fig. 6 Cavity-backed UWB planar circular monopole a) VSWR and b) realized gain vs. 

frequency compared to the current Vivaldi. Beam peak position is given by the theta angle 

from broadside.
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Fig. 6 Cavity-backed UWB planar circular monopole a) VSWR and b) realized gain vs. 

frequency compared to the current Vivaldi. Beam peak position is given by the theta angle 

from broadside (continued).

Where the LPDA fails to meet the bandwidth requirement and the cavity-backed 

UWB planar circular monopole fails to meet the operational bandwidth due to 

pattern instability, the BAV can supersede on both fronts. The BAV has both a 

more gracefully deteriorating impedance match than the LPDA and a more stable 

radiation pattern than the monopole without requiring a backing to achieve 

unidirectional (or near so) radiation. Another advantage of the BAV versus a 

traditional tapered slot is that it does not need a quarter wave fanned stub terminated 

strip to achieve broadband performance, but instead, the BAV is fed with a tapered 

stripline—a broader band and more simple solution as it does not require a quarter 

wave stub.

4. BAV Design by Simulation

Figure 7 shows the final built BAV and CAD model. It has dimensions of 10 × 17.2 

× 0.25 inches3, which is similar in length and thickness to the Vivaldi but about 

twice as wide. The BAV is a stacked structure with 2 substrates that in total has 3

metal layers. The outer fins are mirror copies of each other and are connected to 

ground. The inner fin flares toward the opposite direction of the outer fins and has 
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a thin strip to connect to the SubMiniature version A center pin. It was milled in 

house from two 150-mil Rogers Duroid 5880 substrates with 0.5-oz copper 

cladding. The antenna was milled in 4 pieces, which were overlapped and attached 

using double-sided 3M adhesive and 22 nylon screws and nuts. A solder connection 

electrically joins the two halves for each of the 3 striplines (i.e., top, bottom, and 

middle). A notch 0.4 inch wide and 0.3 inch deep was cut into the top layer to reveal 

the pin so that it could be soldered to the center stripline after the BAV was 

assembled. A piece of brash shimming was then cut and soldered overtop of the 

notch to cover the center pin and provide a ground contact for the outer fin. 

Simulations showed that the effect of asymmetry at the feed caused by 2 different 

dielectric regions (one air and one Duroid) on opposite sides of the stripline is 

minimal.

Fig. 7 Built BAV, FEKO model, and Vivaldi (top), and the connector and one of the 3 

solder connections (bottom)
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The BAV is based off of a design found in the literature.8 The source paper focused 

on reducing the length of the BAV to make it more compact at the cost of highfrequency performance. The advantage of the BAV versus other tapered slot 

antennas is that it has broader bandwidth, owed to the stripline feed, and improved 

cross-pol rejection.9,10 The larger cross-pol rejection is caused by the mirrored 

ground fins cancelling the cross-polarized electric field component through 

superposition of opposing vectors.10 Figure 8 shows the original BAV with reduced 

depth. The shorter flare length reduces the high-frequency gain but improves the 

low-frequency response and gain by introducing a dipole resonance with its halfwavelength dipole length being the width of the flat edge of the flare. Some of the 

parameters for the BAV were missing in the reference and had to be estimated from 

images provided. After having reproduced the reflection coefficient found in 

Guillanton et al.8, the reduced-profile BAV dimensions were increased by a factor 

of 10

3 to shift the reflection coefficient to lower frequencies. 

Fig. 8 Original BAV from the literature with reduced depth

Figure 9a shows the simulated reflection coefficient for the reduced-profile BAV 

after scaling using GEMS and FEKO. The simulated results show that the antenna 

does not quite meet the standard –10-dB reflection coefficient definition for 

bandwidth, but this reflection coefficient translates to a VSWR less than 2.5, which 

is acceptable. The realized gain, Fig. 9b, shows up to 4 dB more gain below 0.7 

GHz than the Vivaldi, comparable gain between 0.7 and 1.7 GHz, and at least 2 dB 

less gain than the Vivaldi above 1.7 GHz. While the reduced-profile BAV is shorter 

in length than the Vivaldi by 6–7 inches, the lower gain above 1.7 GHz caused by

the shorter flare was not acceptable. Simulations comparing reflection coefficient 

and realized gain for the reduced-profile BAV with percentage increases in flare 

length and percentage increases in both flare length and flare width were performed 

in GEMS to determine the combination that achieved the overall best impedance 

match and realized gain.
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Fig. 9 Reduced depth BAV a) reflection coefficient and b) realized gain vs. frequency
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Figures 10a and 10b show the simulated reflection coefficient and realized gain 

versus frequency for percentage increases in flare length while maintaining the 

same exponential taper (i.e., start and end opening widths do not change). 

Increasing the flare length shifts the low-frequency match at 0.5 GHz closer to 

0.35 GHz and improves the impedance match above 0.6 GHz. The increased length 

also improves the realized gain above 0.6 GHz but reduces the gain below 0.6 GHz 

and produces minimal improvement in the gain above 1.7 GHz. Figures 11a and 

11b show the same simulations but with the taper end width increased by the same 

percentage as the flare length. Again, the low-frequency match is shifted to near 

0.3 GHz and the match is improved above 0.6 GHz. Unlike the increase in flare 

length–only simulations, the gain is improved by 2–3 dB above 1.7 GHz while 

giving up some gain below 0.7 GHz. The flare length and taper width increase of 

60% was chosen as it has the best impedance match and gain over the frequency 

band.

Fig. 10 Simulated a) reflection coefficient and b) realized gain vs. frequency for percentage 

increases in flare length without changing taper
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Fig. 10 Simulated a) reflection coefficient and b) realized gain vs. frequency for percentage 

increases in flare length without changing taper (continued)

Fig. 11 Simulated a) reflection coefficient and b) realized gain vs. frequency for percentage 

increase in flare length and ending taper width
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Fig. 11 Simulated a) reflection coefficient and b) realized gain vs. frequency for percentage 

increase in flare length and ending taper width (continued)

Figures 12a and 12b show the comparison between the BAV with a 60% longer 

flare and taper width and the Vivaldi-simulated reflection coefficient and realized 

gain vs. frequency. The final simulated design has a significant improvement in the 

impedance match, which will translate to a much better VSWR and either 

comparable or greater gain than the Vivaldi. A final change to the BAV was to 

reduce the substrate thickness so that it could be built using standard boards. 

Custom substrate thicknesses could be bought but would increase cost. The final 

design has a thickness of 0.25 inch instead of 0.3 inch. The reduced substrate 

thickness negatively effects the impedance match but improves the gain as shown 

in Figure 13a and 13b. The stripline width was adjusted to accommodate the change

in substrate thickness. See the Appendix A for simulation results of the reducedprofile BAV performance versus substrate thickness and Appendix B for the BAV 

schematic.
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Fig. 12 Comparison of BAV with 60% longer flare and taper width and Vivaldi-simulated 

a) reflection coefficient and b) realized gain vs. frequency
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Fig. 13 Simulated a) VSWR and b) realized gain vs. frequency for the BAV with substrate 

thickness of 0.3 and 0.25 inch
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5. BAV Measurement and Simulation Comparisons

This section shows the simulation and measurement comparisons for the fabricated 

BAV. Figures 14a and 14b show the measured and simulated VSWR and realized 

gain for the BAV and the measured results for the Vivaldi. The VSWR of the BAV 

is below 3.0 only for frequencies greater than 0.7 GHz. Below 0.7 GHz, the VSWR 

is as large as 5.0, but the Vivaldi VSWR is asymptotically large at those same 

frequencies. Except for 1.5–1.7 GHz and 1.8–2.0 GHz, the BAV has lower VSWR 

compared to the Vivaldi. The measured realized gain, Fig. 14b, confirms that the 

BAV has up to 8 dB more gain below 0.5 GHz and up to 5 dB more gain above 

0.7 GHz. Between 0.5 and 0.7 GHz, the gain is comparable to the Vivaldi. Gain 

measurements with 2 different horns were required to cover 0.3–2.0 GHz. The data 

name “BAV Previous Measurement” was taken using a ridged SATIMO horn,

which is spec’d to cover 0.4–6.0 GHz. It gives the best results, as it is small enough 

to be placed in the back of the tapered anechoic chamber apex. The data above 

1.8 GHz are spurious because of chamber effects.

The other 4 measurements were taken with a ridged horn spec’d from 0.18 to 

2.15 GHz. Because of the horn’s size, it had to be positioned far out of the chamber 

apex, which worsened the spurious data points in the gain measurements. The 

E- and H-plane realized gains were taken to observe polarization dependencies of 

the artifacts. The 2 data sets were averaged together in linear space to attempt to 

average out some of the artifacts, but there are still serious spurious data points 

particularly between 1.3 and 1.7 GHz, where the gain is measured to be up to 2 dB 

lower than the previous measurement with the SATIMO. The low-frequency gain 

is in good agreement with simulation, confirming the improved gain, albeit with 

some inaccurate data.
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(a)

(b)

Fig. 14 Comparison of simulated and measured a) VSWR and b) realized gain vs. frequency 

for the BAV and Vivaldi
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Figures 15a–c show the comparison of the simulated and measured realized gain 

patterns at 0.3, 0.7, 1.5, and 2.0 GHz. The data and simulations are in good 

agreement. The measurements confirm a dipole-like radiation pattern at 0.3 GHz 

with a more directive pattern at frequencies greater than 0.4 GHz. The radiation 

pattern is stable in the H-plane, but the E-plane pattern shows a tendency to favor 

the side with 2 fins in the mid band and comes back to the forward direction at high 

frequencies. The F/B of the BAV, Fig. 16a, becomes greater than 2 dB above 

0.5 GHz and is up to 11 dB larger than the Vivaldi F/B for almost the entire 

frequency band. The 3-dB beamwidths, Fig. 16b, show that the BAV has a slower 

reduction with increasing frequency as compared to the Vivaldi. The frequency 

range covers only 0.7–2.0 GHz as both antennas start to approach beamwidths of 

greater than 180° below 0.7 GHz. Figure 16c shows the simulated normalized 

transient response for the BAV and Vivaldi, respectively. The results show that the 

BAV has reduced late time ringing compared to the Vivaldi, which would be ideal 

for a pulsed or even for stepped frequency systems, such as the FLGPR system the 

BAV is designed for. Removing the short metallic sides on the Vivaldi does not 

help the late time ringing, but removing the duplicate tapered slot side does help as 

shown in Fig. 16c. Still, the Vivaldi has larger late time ringing than the BAV.

Fig. 15 Simulated and measured realized gain patterns for the BAV at a) 0.3 GHz, b) 0.7 

GHz, c) 1.5 GHz, and d) 2.0 GHz. E-plane is on the left and H-plane is on the right.
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Fig. 15 Simulated and measured realized gain patterns for the BAV at a) 0.3 GHz, b) 0.7 

GHz, c) 1.5 GHz, and d) 2.0 GHz. E-plane is on the left and H-plane is on the right (continued).
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Fig. 15 Simulated and measured realized gain patterns for the BAV at a) 0.3 GHz, b) 0.7 

GHz, c) 1.5 GHz, and d) 2.0 GHz. E-plane is on the left and H-plane is on the right (continued).

Fig. 16 Comparison of simulated a) F/B, b) 3-dB beamwidth, and c) normalized transient 

response for the BAV and Vivaldi
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Fig. 16 Comparison of simulated a) F/B, b) 3-dB beamwidth, and c) normalized transient 

response for the BAV and Vivaldi (continued)
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6. Simulations and Measurements of BAV Pairs

This section presents the simulated and measured reflection coefficient, realized 

gain, and cross-pol isolation between pairs of BAV elements to determine positiondependent coupling effects on individual element performance as well as to 

maximize cross-pol isolation. Simulation tools were leveraged after model 

validation in lieu of measurements to ensure that performance effects were dictated 

by antenna-to-antenna interactions and not the environment. Cross-pol isolation 

was measured for validation to ensure accuracy as the simulation environment is 

idealized. Figure 17a shows the recommended configuration for 32 BAV receivers 

to minimize the overall width dimension. The center-to-center element spacing is 

0.5 inches, Figure 17b, which gives an overall height of 21.2 inches, a depth of 17.2 

inches, and a width of 86.7 inches, which is within 2.2 m. The fin matching for the 

cross-pol elements was not initially considered and was found to be preferred to 

maintain antenna performance through simulating the different paired geometries. 

Figure 18 shows the 9 paired combinations. Pairs with matching fins have one 

antenna excited and the other terminated into 50 Ω, resulting in only one simulation. 

Pairs that do not have matching fins are simulated twice, interchanging the 

excitation and termination between the pair. 
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Fig. 17 Recommendation for a) receiver positioning to minimize width with b) element

spacing and overall dimensions
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Fig. 18 CAD models for the BAV receiver pairs

Figure 19a shows the simulated reflection coefficient for the side-by-side vertical

pair. Since the pair are mirror opposites of each other, only one simulation was 

performed. As can be seen by the reflection coefficient and the realized gain, Fig.

19b, this configuration has little effect on both the impedance match and realized 

gain. The biggest impact is on the 0.3-GHz realize gain, where the pair shows a 

1-dB reduction. The F/B, Fig. 19c, shows that there is a decrease in the back lobe,

which improves the F/B up to 1.1 GHz. The cause of the 7-dB improvement in the 

F/B at 0.7 GHz is shown in the H-plane radiation pattern, Fig. 19d. The side-byside vertical arrangement has produced a null in the back lobe, which improves the 

F/B. The vertical configuration does not produce any observable negative 

performance effects that are of concern beyond the 1-dB gain loss at 0.3 GHz.
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Fig. 19 Simulated a) reflection coefficient, b) realized gain, c) F/B, and d) 0.7-GHz H-plane 

pattern for the side-by-side vertical BAV pair
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Fig. 19 Simulated a) reflection coefficient, b) realized gain, c) F/B, and d) 0.7 GHz H-plane 

pattern for the side-by-side vertical BAV pair (continued)
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Simulated results for the side-by-side horizontal pair are shown in Figs. 20a–c. The 

naming convention is as follows: The term “gnd” means that grounded fins are next 

to each other; “hot” refers to center fins next to each other; “flipped” refers to a 

grounded fin next to a center fin; “left” and “right” refer to which BAV is excited. 

Directional reference is taken to be in the direction of propagation. From the 

simulated reflection coefficient, Fig. 20a, the gnd, hot, and flipped left 

configurations show similar results, although the flipped-left case has the poorest 

impedance match below 0.4 GHz. The flipped-right configuration shows that the 

reflection coefficient is significantly influenced by the antenna to the left. The 

realized gain, Fig. 20b, shows a similar trend. The forward realized gain is similar 

for the gnd, hot, and flipped-left configurations, but the flipped-right simulation 

shows degraded realized gain above 1.0 GHz. There is more variation between the 

4 cases in the F/B, Fig. 20c. The hot and flipped-left simulations have similar F/B 

results but are different compared to the gnd and flipped right simulations. All 4

simulations show degraded F/B between 0.6 and 0.9 GHz and improved F/B above 

1.8 GHz. 

Fig. 20 Simulated a) reflection coefficient, b) realized gain, and c) F/B vs. frequency for the 

side-by-side horizontal BAV pair
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Fig. 20 Simulated a) reflection coefficient, b) realized gain and c) F/B vs. frequency for the 

side-by-side horizontal BAV pair (continued)
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Simulated results for the centered dual-pol pair are shown in Figs. 21a–d. The

naming convention is as follows: The term “flipped” refers to the vertical element 

with its grounded fins positioned toward the underlying horizontal element; “HV” 

and “VH” denote which antenna is excited and which is terminated; the first letter 

references the excitation and the second letter the termination. The centered 

configuration shows the greatest degradation in reflection coefficient besides the 

previous “flipped right” simulation, Fig. 21a, particularly below 0.6 GHz. The 

curves for the VH and flipped HV cases are also not as smooth as the other 2 with 

some additional local maxima and minima introduced. The realized gain, however, 

is not as poorly degraded, if at all, Fig. 21b. The F/B, Fig. 21c, has been 

significantly affected with the exception of the HV simulation. A 10-dB dip has 

been introduced between 0.6 and 0.7 GHz in the VH and flipped VH configurations,

and a 4-dB increase has been introduced between 0.7 and 1.1 GHz in the VH 

configuration. The flipped HV has a 3-dB dip between 1.0 and 1.1 GHz and a 4-dB 

larger peak between 1.4 and 1.6 GHz. Between 1.7 and 2.0 GHz the flipped HV 

configuration sees the largest variation of all configurations. 

Fig. 21 Simulated a) reflection coefficient, b) realized gain, c) F/B, and d) cross-pol isolation 

vs. frequency for the centered dual-pol BAV pair
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Fig. 21 Simulated a) reflection coefficient, b) realized gain, c) F/B, and d) cross-pol isolation 

vs. frequency for the centered dual-pol BAV pair (continued)
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Fig. 21 Simulated a) reflection coefficient, b) realized gain, c) F/B, and d) cross-pol isolation 

vs. frequency for the centered dual-pol BAV pair (continued)

The simulated and measured cross-pol isolation is shown in Figure 21d. 

Simulations show 22 dB or greater isolation, but measurements show only 15 dB 

or better, the worse occurring between 0.6 and 0.65 GHz. It is important to note 

that the isolation measurement can be sensitive to the measurement environment. 

For that reason, the measurement was done within the onsite near-field 

measurement range where the walls are RF absorber lined. The absorber is not rated 

below L-band but can still reduce reflections from the walls. The anechoic room 

also has less metallic artifacts to produce reflections. For this reason, the centered 

configuration should be spec’d at 15-dB minimum isolation. The electric current 

distribution for the VH simulation at the dip frequency 0.65 GHz and peak 

frequency of 0.9 GHz in the F/B is shown in Fig. 22. There is a strong interaction 

between the center fin of the vertical element and the horizontal element beneath it 

at 0.65 GHz and a much weaker interaction at 0.9 GHz.
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Fig. 22 Electric current for the “flipped VH” simulation at 0.65 and 0.9 GHz

Simulated results for the corner dual-pol pair are shown in Figs. 23a–c. The naming

convention is as follows: “gnd” specifies that the grounded fins for the 2 antennas 

are next to each other; “hot” refers to side-by-side center fins; “flipped” refers to 

the grounded fin next to the center fin; “VH” and “HV” specify which antenna is 

excited and which is terminated, the same as the previous centered cases. Effects 

on the impedance match are mostly negligible for all cases except for the “corner 

flipped VH” configuration, which has the worst impedance match as seen from the 

simulated reflection coefficient, Fig. 23a. The realized gain, Fig. 23b, shows that 

the gain remains virtually unchanged for all frequencies above 0.6 GHz. Below 

0.6 GHz, the gain is reduced by 0.5–1.0 dB because of the impedance match at 

those frequencies. Again, the flipped VH case has the poorest gain. The largest gain 

reduction is 1 dB at 0.3 GHz. The F/B is affected similarly amongst all 

configurations, Fig. 23c. Above 0.8 GHz, the F/B above the 4 configurations are 

within 1–2 dB of the single BAV, but they all lose up to 5 dB or more between 0.55 

and 0.8 GHz.
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Fig. 23 Simulated a) reflection coefficient, b) realized gain, and c) F/B vs. frequency for the 

corner dual-pol BAV pair
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Fig. 23 Simulated a) reflection coefficient, b) realized gain, and c) F/B vs. frequency for the 

corner dual-pol BAV pair (continued)

A critical question to answer pertaining to the 32 element aperture was whether all 

of the BAV elements needed to be electrically connected together, and if so, what 

effect on performance would electrically connecting them have? It is suggested in 

the literature that nearby tapered slot antennas that are not connected can have 

reduced performance due to radiation from neighboring edge currents between the 

fins, and that electrically connecting the fins can reduce such effects.11 A pair of 

BAV elements were built, as shown in Fig. 24a, to test performance effects caused 

by electrically connecting and disconnecting the neighboring fins for the “corner” 

configurations. Measurements of the reflection coefficient, realized gain, and crosspol isolation were made and compared to simulation with the elements both 

soldered together at the grounded fins and disconnected. The same element 

positioning and spacing were maintained for both measurements. To connect the 2

elements, one of the BAV elements had a notch removed from one layer of the 

substrate so that the other BAV could rest on top. A copper strip was placed in 

between the newly formed right angle joint overlapping the grounded fins of both 

elements and connected with a continuous solder joint. In simulation, the PEC 

surfaces are joined by a perfect connection.
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The simulated and measured reflection coefficient results are shown in Fig. 24b. 

The terms “C” and “NC” stand for connected and not connected, respectively. 

Agreement between simulation and measurement is not exact, particularly above 

1.1 GHz; however, the trend between simulations and the trend between 

measurements are in agreement. That is, electrically connecting the elements has

little effect on the impedance match as compared to not connecting them. The same 

is true for the realized gain shown in Fig. 24c. The dual-pol measurements have 

similar if not the same chamber artifacts as the lone BAV. Electrically connecting 

the elements does have an appreciable effect in the mutual coupling shown by the 

isolation data in Fig. 24d. Not connecting the elements can improve the cross-pol 

isolation by up to 10 dB at frequencies above 1.2 GHz, 5–10 dB between 0.6 and 

1.2 GHz, and a modest improvement of 1–2 dB below 0.6 GHz. 

Fig. 24 a) Built corner dual-pol BAV pair, b) simulated and measured reflection coefficient, 

c) realized gain, d) cross-pol isolation vs. frequency, and e) transient response
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Fig. 24 a) Built corner dual-pol BAV pair, b) simulated and measured reflection coefficient, 

c) realized gain, d) cross-pol isolation vs. frequency, and e) transient response (continued)
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Fig. 24 a) Built corner dual-pol BAV pair, b) simulated and measured reflection coefficient, 

c) realized gain, d) cross-pol isolation vs. frequency, and e) transient response (continued)
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Measured and simulated radiation patterns at 0.3, 0.7, 1.0, 1.5, and 2.0 GHz are 

shown in Figs. 25a–c. The E-plane patterns are on the left, and the H-plane on the 

right. Having 2 elements near each other would, expectedly, influence the radiation

pattern, particularly in the side lobes. While connecting the antennas had little effect 

on the forward gain, it could be argued that connecting them is more detrimental to 

the side lobe structure than not connecting them. Also, the pair have a larger 

measured back lobe at 0.7 GHz, which confirms the simulated results of a much 

smaller F/B between 0.55 and 0.8 GHz. The transient response, Fig. 24e, shows 

that the neighboring BAV will produce additional ringing in the transient response 

at a later point in time because of the additional current path to the neighboring 

BAV termination. Connecting the BAVs produces identical late time ringing. 

Fig. 25 Simulated and measured radiation patterns for the corner dual-pol BAV with and 

without a connection at a) 0.3 GHz, b) 0.7 GHz, c) 1.0 GHz, d) 1.5 GHz, and e) 2.0 GHz. 

E-plane is shown on the left and H-plane is on the right.
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Fig. 25 Simulated and measured radiation patterns for the corner dual-pol BAV with and 

without a connection at a) 0.3 GHz, b) 0.7 GHz, c) 1.0 GHz, d) 1.5 GHz, and e) 2.0 GHz. 

E-plane is shown on the left and H-plane is on the right (continued).
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From the study through simulation of the 9 BAV pairs, the corner and side-by-side 

vertical pairs have the least effect on antenna performance, with the exception of 

cross-pol isolation. The centered pair—albeit not the preferred arrangement from 

the viewpoint of individual antenna performance—has the superior low-frequency 

cross-pol isolation. Between 0.3 and 0.6 GHz, the centered BAV has 30–15 dB of 

isolation, whereas the corner pair has 6–20 dB of isolation. Low-frequency 

performance is of critical importance, and with the realized gain being within 1–2 

dB of the lone BAV below 1.0 GHz, it could be advantageous to use the centered 

configuration for all BAVs with neighboring fins matched, Fig. 26, as opposed to 

mixed pairs, Fig. 17. Doing so would nearly double the width to 4 m. Such an 

aperture would require further mechanical considerations for construction, as it 

could be too wide for use in the field.

Fig. 26 CAD images and dimensions for aperture with only centered BAV pairs. The bottom 

row consists of horizontal elements, and the top row is all vertical.

An important point to make as this section closes is the potential cost for producing 

32 elements. While the design and analysis for the BAV was done, assuming 

standard 125-mil-thick Rogers Duroid 5880, the cost for a single board can 

approach $500 or more. Each BAV would require 2–3 boards and including the 

cost of tooling hardware and assembly, could cost $1,200–$1,800 to be built inhouse. Outsourcing may or may not significantly decrease the unit cost. Switching 

to a cheaper substrate with similar performance is preferred, but finding such a 

substrate that also comes in a standard thickness of 125 mil was challenging. The 

Arlon substrates, sold by Rogers Corp, were the closest in terms of loss and 

permittivity. The AD350A substrate, εr = 3.5 and tanδ = 0.003, was the closest and 

would reduce the total cost by a factor of 7.3 at the cost of a 1-dB gain loss above 

1.5 GHz due to an 8° and 4° increase in azimuthal and elevation beamwidth,

respectively, and a small frequency shift caused by the higher permittivity.
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7. Conclusion

This report documents the design by simulation and validation of a balanced 

antipodal Vivaldi antenna for use as a potential receiving element replacement in 

US Army Research Laboratory 32-element stepped-frequency ground-penetrating 

radar within the frequency range of 0.3–2.0 GHz. The initial design process focused 

on maximizing impedance matching, forward gain, and cross-pol isolation 

performance. Additional metrics such as half-power beamwidth, F/B, and transient 

response are compared against the current receiver. The focus of the design was to 

maximize low-frequency performance, particularly below 1.0 GHz. The current 

receiver is a Vivaldi type as well but is constructed more akin to a traditional design 

where the tapered slot is on one side of a single substrate and a stubbed microstrip 

runs across the gap. Such Vivaldis tend to have –10 dB impedance bandwidths that 

are limited by the fanned quarter-wave stub on the microstrip; BAV antennas, on 

the other hand, can have a much broader impedance bandwidth because of the 

stripline transition and improved cross-pol rejection. However, given the size 

constraint of this application, neither design will achieve the desired impedance 

match and bandwidth. Increasing the Vivaldi size can help, but it does not maximize 

the realized gain below 0.4 GHz and has a poor transient response. 

The BAV has 8- to 5-dB larger gain between 0.3 and 0.5 GHz and 2–3 dB above 

0.7 GHz. The VSWR is better, though not less than 3.0 across the band, with a max 

VSWR of 5:1 at 0.3 GHz; the Vivaldi, on the other hand, has a VSWR greater than 

10:1 below 0.5 GHz. The transient response is also superior to the Vivaldi with 

reduced late time ringing. The radiation pattern, as the aperture electrical size 

increases, is unstable versus frequency. The instability causes frequency variations 

in the gain and is seen in the E-plane pattern of the BAV but not in the H-plane. 

The BAV is comparable in length and thickness to the Vivaldi but is about twice as 

wide. While the built BAV substrate is Rogers Duroid 5880, to reduce unit cost, it 

is recommended to use the AD350A substrate as the cost is reduced by a factor of 

7.3 at the expense of a 1-dB gain loss above 1.5 GHz and a small frequency shift

caused by the larger permittivity.

Simulations to predict performance effects of BAV pairs in different arrangements 

shown in Fig. 18 were documented. It was found that most arrangements had 

negligible effects on realized gain and impedance match with the exception of the 

side-by-side horizontal and T-shaped pairs. The horizontal pair showed appreciable 

effects on performance when opposing fins are next to each other (i.e. grounded fin 

of one BAV next to the center fin of the other BAV). The T-shaped pair showed 

that regardless the fin orientation, there was one excitation/termination case for 

each orientation where the performance was degraded. Overall, the worst effects 
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produced artifacts in the realized gain of 1 dB (loss or increase) at some frequencies. 

The cross-pol isolation measurements and simulation showed that although the 

corner configuration produces the best individual BAV performance, its isolation 

is in fact worse than the T-shaped below 0.6 GHz. Because cross-pol isolation is 

critical to the polarimetric array and low-frequency performance was the focus of 

the design, it is recommended that an aperture configuration like that shown in Fig.

26 be used even though its width is nearly double the 2.2-m requirement.
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8. References

1. Balanis CA. Advanced engineering electromagnetics. 2nd ed. Hoboken (NJ): 

John Wiley and Sons; 2012. p. 143.

2. Stutzman WL, Thiele GA. Antenna theory and design. 3rd ed. Edison (NJ): 

John Wiley and Sons; 2013. p. 488–498.

3. FEKO. Stellenbosch (South Africa): Altair Engineering Inc.; 2017 [accessed 

2017 Apr 7]. www.feko.info.

4. GEMS. Fairfax (VA): 2COMU; 2009 [accessed 2017 July 7]. 

www.2comu.com.

5. Smith GD, Harris RW, Ressler MA, Stanton B. Wideband Vivaldi notch 

antenna design for UWB SIRE VH/UHF/Radar. Adelphi (MD): Army 

Research Laboratory (US); 2008 March. Report No.: ARL-TR-4409.

6. Coburn WO, McCormick SA. Antenna array development for the radio 

frequency enabled detection, location, and improvised explosive device (IED) 

neutralization evaluation (REDLINE) system. Adelphi (MD): Army Research 

Laboratory (US); 2016 July. Report No.: ARL-TR-7712.

7. McCormick SA, Zaghloul AI, Harrison AC. A rugged ultra-wideband (UWB) 

circular planar monopole for multichannel radar. Adelphi (MD): Army 

Research Laboratory (US); 2016 March. Report No.: ARL-TR-7630.

8. Guillanton E, Dauvignac JY, Pichot C, Cashman J. A new design tapered slot 

antenna for ultra-wideband applications. Microwave and Optical Technology 

Letters. 1998;(19)4:286–289.

9. Gazit E. Improved design of the Vivaldi antenna. IEEE Proceedings. 

1988;(135)2:89–92.

10. Langley JDS, Hall PS, Newham P. Novel ultrawide-bandwidth Vivaldi

antenna with low crosspolarisation. Electronics Letters. 1993;(29)23:2004–

2005.

11. Schaubert DH. Wide-band phased arrays of Vivaldi notch antennas. 10th 

International Conference on Antennas and Propagation. 1997;(436):1.6–1.12.
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Appendix A. Effects of a Wide Stripline Ground, Substrate 

Thickness, and Lens on Reflection Coefficient and Realized 

Gain
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This Appendix documents the simulated results for the effects of a wider stripline 

ground, thicker substrate, and an imbedded shaped dielectric lens on balanced 

antipodal Vivaldi (BAV) performance. Figures A-1a and A-1b show the simulated 

reflection coefficient for the BAV shown in Fig. 8 of the main text with a wider 

ground. The ground for the BAV is the flared fins near the feed (i.e., grounded 

strips for the stripline). Two cases were simulated: one with the ground as built and 

one with the width the same as the substrate width. Widening the ground 

exponential taper till it is the same width as the substrate improves the impedance 

match across the band, including the low frequencies, as seen in Fig. A-1a. 

However, this improved match does not necessarily translate to an improved 

forward realized gain, Fig. A-1b. With the exception of frequencies near 0.5 GHz 

where the gain is about 2 dB larger, the gain sees practically no improvement, and 

it is nearly 2 dB less at 0.7 GHz where the pattern splits. The focus of the design 

was to improve the low-frequency performance, in particular the realized gain, as 

it takes into consideration the impedance match. Because the wider ground 

produced reduced gain at some frequencies, it was not included in the final design.

Fig. A-1 Simulated a) reflection coefficient and b) forward realized gain vs. frequency of the 

BAV with and without a wider stripline ground
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Fig. A-1 Simulated a) reflection coefficient and b) forward realized gain vs. frequency of the 

BAV with and without a wider stripline ground (continued)

Figures A-2a and A-2b show the simulated reflection coefficient and realized gain 

versus frequency of the BAV shown in Fig. 8 for varying substrate thickness; the 

stripline width is adjusted for the change in thickness to maintain the same input 

impedance. Substrate thicknesses of 60, 180, 300, 420, and 480 mils were 

considered. As expected, increasing the substrate thickness can help to improve the 

impedance match up to a point, Fig. A-2a. From the shown results, the substrate

thickness for the best impedance match would be around 420 mils as it gives the 

lowest frequency match while maintaining a near –10-dB reflection coefficient up 

to 3.0 GHz and beyond. The realized gain results, Fig. A-2b, show the expected 

behavior of worsening gain for too thick a substrate owing to surface waves. Where 

the 420 mils thickness is best for the impedance match, the 180 mils thickness 

would be the best for the realized gain as it has the flattest gain behavior vs. 

frequency. Just like with the impedance match, if the substrate is too thick or too 

thin the gain is not optimal. Considering both the impedance match and the forward 

realized gain, 300 mils would be the preferred substrate thickness.
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Fig. A-2 Simulated a) reflection coefficient and b) forward realized gain vs. frequency of the 

BAV for different substrate thicknesses
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Figure A-3a shows the computer-aided design (CAD) BAV model with an 

embedded shaped dielectric lens. The lens permittivity is 6.0 and is lossless. The 

shape was taken from the literature and was not modified to achieve the best 

performance possible.1 The permittivity was chosen to conform to what can be 

found readily available from commercial printed circuit board substrate 

manufactures. The lens is the same thickness as the BAV and extends about 1.5 

inches past the BAV edge. The purpose of the shaped lens is to produce a uniform 

(or near uniform) phase front radiating from the tapered slot region by introducing 

a spatially varying phase delay. The varying phase delay is achieved by shaping the 

lens such that fields nearer the center of the tapered slot are delayed the most 

compared to those fields farthest away from the slot (i.e., all radiating paths are 

equal).2 The embedded lens functions similar to a director in that it concentrates 

the aperture field within the slot.

Fig. A-3 a) BAV with embedded shaped dielectric lens, b) simulated reflection coefficient, and 

c) realized gain vs. frequency with and without the lens

 

1 Bourqui J, Okoniewski M, Fear EC. Balanced antipodal Vivaldi antenna with dielectric director for near-field 

microwave imaging. IEEE Transactions on Antennas and Propagation. 2010;(58)7:2318–2326.

2 Volakis JL. Antenna engineering handbook. 4th ed. New York (NY): McGraw-Hill; 2007. p. 18–2.
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Fig. A-3 a) BAV with embedded shaped dielectric lens, b) simulated reflection coefficient, and 

c) realized gain vs. frequency with and without the lens (continued)
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Embedded dielectric lenses are most commonly seen in waveguides and horns,

which also serve as a means to reduce the size of the aperture. If successful, the 

embedded lens should give modest improvements in realized gain as well as added 

benefits of material loading, such as reduced electrical size. For the BAV, the 

embedded lens achieves both in addition to an improved impedance match as seen 

in Fig. A-3b and A-3c. The cause of the improved impedance match was not 

explored, but a hypothesis would be that a reduction in the wave impedance (i.e.,

improved impedance match to free space) has been achieved and so there is a better 

transmission of fields out of the substrate away from the feed and into free space. 

The lens improves the gain across the frequency band with modest 1-dB increases 

at frequencies below 1.0 GHz, to a more appreciable improvement of 2 dB at 

frequencies above 1.0 GHz. The unwanted side effect of a thicker, higher 

permittivity medium on gain can be seen above 3.0 GHz where there is a 1- to 2-

dB reduction; this could, however, be due to the lens not extending far enough into 

the tapered slot to work for those higher frequencies.
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INTENTIONALLY LEFT BLANK.
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Appendix B. Balanced Antipodal Vivaldi (BAV) Schematic
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This Appendix presents a BAV schematic (Fig. B-1). Specifications for the cutout 

and connector are given in Section 4 of the main text.

Fig. B-1 BAV schematic and partially transparent top view. Units are in inches. 
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List of Symbols, Abbreviations, and Acronyms

BAV balanced antipodal Vivaldi

CAD computer-aided design

cross-pol cross polarization

F/B front-to-back ratio

FLGPR forward-looking ground-penetrating radar

GEMS General Electromagnetic Solver

LPDA logarithmic periodic dipole array

MoM Method of Moments

PEC perfectly electrically conducting

UWB ultra-wideband

VSWR voltage standing wave ratio
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1 DEFENSE TECHNICAL

(PDF) INFORMATION CTR

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(PDF) RDRL DCM

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RDRL DCL

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