Low-Profile UHF Antenna Design Based on an Anisotropic 

Transverse Resonance Condition

by Gregory Mitchell and Wasyl Wasylkiwskyj

ARL-TR-7035 August 2014

Approved for public release; distribution unlimited. 
NOTICES

Disclaimers

The findings in this report are not to be construed as an official Department of the Army position 

unless so designated by other authorized documents.

Citation of manufacturer’s or trade names does not constitute an official endorsement or 

approval of the use thereof.

Destroy this report when it is no longer needed. Do not return it to the originator.
Army Research Laboratory

Adelphi, MD 20783-1138

ARL-TR-7035 August 2014

Low-Profile UHF Antenna Design Based on an Anisotropic 

Transverse Resonance Condition

Gregory Mitchell and Wasyl Wasylkiwskyj

Sensors and Electron Devices Directorate, ARL

Approved for public release; distribution unlimited. 
ii

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the 

data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the 

burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. 

Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid 

OMB control number.

PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS.

1. REPORT DATE (DD-MM-YYYY)

August 2014

2. REPORT TYPE

Final

3. DATES COVERED (From - To)

01/2014–06/2014

4. TITLE AND SUBTITLE

Low-Profile UHF Antenna Design Based on an Anisotropic Transverse Resonance 

Condition

5a. CONTRACT NUMBER

5b. GRANT NUMBER

5c. PROGRAM ELEMENT NUMBER

6. AUTHOR(S)

Gregory Mitchell and Wasyl Wasylkiwskyj

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

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

U.S. Army Research Laboratory

ATTN: RDRL-SER-M

2800 Powder Mill Road

Adelphi, MD 20783-1138

8. PERFORMING ORGANIZATION

 REPORT NUMBER

ARL-TR-7035

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSOR/MONITOR’S ACRONYM(S)

11. SPONSOR/MONITOR'S REPORT

 NUMBER(S)

12. DISTRIBUTION/AVAILABILITY STATEMENT

Approved for public release; distribution unlimited.

13. SUPPLEMENTARY NOTES

14. ABSTRACT

A resonance condition is derived for a tapered rectangular cavity partially loaded with anisotropic magnetic material. This 

resonance condition leads to the design of an extremely low-profile (λo/18) antenna with over an octave of bandwidth and 

positive realized gain from 200–515 MHz. The equation derived for the shape of the partially loaded antenna cavity maintains a 

constant cutoff frequency even as more anisotropic material is introduced to the cavity. Also a method is determined to tailor 

the shape of the cavity as needed using the normal component of the permeability tensor with little to no effect on the 

performance of the antenna.

15. SUBJECT TERMS

anisotropic transverse resonance, low-profile antenna, metamaterials

16. SECURITY CLASSIFICATION OF: 

17. LIMITATION

 OF 

 ABSTRACT

UU

18. NUMBER

 OF 

 PAGES

32

19a. NAME OF RESPONSIBLE PERSON

Gregory Mitchell

A. Report

Unclassified

b. ABSTRACT

Unclassified

c. THIS PAGE

Unclassified

19b. TELEPHONE NUMBER (Include area code)

(301) 394-2322

Standard Form 298 (Rev. 8/98)

Prescribed by ANSI Std. Z39.18
iii

Contents

List of Figures iv

List of Tables v

1. Introduction 1

2. Derivation of a Tapered Cavity Based on an Anisotropic Transverse Resonance 2

2.1 Anisotropic Transverse Resonance Derivation ...............................................................3

2.1.1 Free Space Region (–a/2 ≤ x ≤ –w/2)..................................................................3

2.1.2 Anisotropic Region (–w/2 ≤ x ≤ 0)......................................................................5

2.1.3 Solving the Boundary Conditions for the Impedances in the two Regions.........6

2.1.4 Solving for the Transverse Resonance Condition ...............................................8

3. Low-Profile Antenna Design 10

3.1 Anisotropic Tapered Cavity ..........................................................................................10

3.2 Anisotropic Non-Tapered Cavity ..................................................................................14

3.3 Cascaded Antenna with Feed Structure.........................................................................16

4. Conclusions 19

5. References 20

Appendix. Werlatone 180° Divider/Combiner 21

Distribution List 24
iv

List of Figures

Fig. 1 The cavity geometry derived from the isotropic transverse resonance condition3..............2

Fig. 2 Transmission line representation of parallel plates partially loaded with anisotropic 

material ......................................................................................................................................3

Fig. 3 Plot of Eq. 26 for various ratios of μz/εy with an assumed depth of 3.3 inches.................10

Fig. 4 The cavity geometry derived from the anisotropic transverse resonance condition 

with μz/εy = 15 ..........................................................................................................................11

Fig. 5 Return loss at the probe inputs of the single-probe antenna (blue) and the symmetricprobe antenna (red) ..................................................................................................................12

Fig. 6 VSWR at the probe inputs of the single-probe antenna (blue) and the symmetricprobe antenna (red) ..................................................................................................................13

Fig. 7 Far field realized gain of the single-probe antenna (blue) and the symmetric-probe 

antenna (red) ............................................................................................................................13

Fig. 8 The cavity geometry derived from the anisotropic transverse resonance condition 

with μz = 1 and εy = 1 ..............................................................................................................14

Fig. 9 S11 at the probe inputs for the tapered antenna cavity with μz = 15 (blue) and the 

non-tapered antenna cavity with μz = 1 (red)...........................................................................15

Fig. 10 VSWR at the probe inputs for the tapered antenna cavity with μz = 15 (blue) and the 

non-tapered antenna cavity with μz = 1 (red)...........................................................................15

Fig. 11 Realized gain for the tapered antenna cavity with μz = 15 (blue) and the non-tapered 

antenna cavity with μz = 1 (red)..............................................................................................16

Fig. 12 The diagram showing the connectivity between the 180° coupler and the two-port 

antenna .....................................................................................................................................17

Fig. 13 Return loss vs. frequency at for the antenna of Fig. 12 (red) and Fig. 8 (green).............17

Fig. 14 VSWR vs. frequency plots for the antenna of Fig 12 (red) and Fig. 4 (green). ..............18

Fig. 15 Realized gain vs. frequency plots for the antenna of Fig 12 (red) and Fig. 4 (green).....18

Fig. A-1 Picture of the 180° coupler with the ports labeled. Port 1 is the input and ports 2 

and 3 are the outputs. ...............................................................................................................21

Fig. A-2 S11 of the Werlatone 180° hybrid coupler....................................................................22

Fig. A-3 S21 and S31 of the Werlatone 180° hybrid coupler......................................................22

Fig. A-4 Phase difference at ports 2 and 3 of the 180° coupler...................................................23
v

List of Tables

Table 1 The dimensions in inches for the geometry in Fig. 1........................................................2

Table 2 The dimensions in inches for the geometry in Fig. 4......................................................11
vi

INTENTIONALLY LEFT BLANK.
1

1. Introduction

Resonating cavities have been used as a means to achieve stable and unidirectional radiation 

patterns for mounted antenna apertures. Radiation properties such as resonant frequency (fr) and 

realized gain are directly determined by the rectangular cavity dimensions. Generally, the fr is 

defined by the half-free space wavelength at the desired frequency, while the best gain results 

occur for a quarter-wavelength rectangular cavity in the normal direction.

Many applications in wireless communications and radar require antennas that conform to the 

surface of the supporting structure. Whenever applicable, the antenna aperture is approximated 

by a flat plane with the requirement that the dimension normal to the aperture (“profile”) be 

minimized. Low-profile antennas (LPAs) are of special importance within the ultra-high 

frequencies (UHF) band, where they are used as communications antennas on military platforms. 

LPAs reduce platform visibility and decrease antenna weight, which becomes critically 

important in airborne platforms. In addition, many military vehicles contain several protruding 

antennas for multiple communication links at UHF. Therefore, there is great interest in 

developing LPAs with wide bandwidths (BWs). Meeting both requirements at the long 

wavelengths involved poses special difficulties.

Traditionally, magnetic materials have high losses at microwave frequencies above 100 MHz, 

which makes them unsuitable as substrates for UHF antenna structures. The availability of 

artificial magnetic metamaterials has widened the range of possible design approaches. Of 

particular interest are high index magnetic materials (μr ≥ 10) that exhibit low loss in the UHF 

band.

1,2 Furthermore, the development of artificial magnetic metamaterials allows engineers to 

separately control the values of both magnetic permeability and electric permittivity. 

The goal of this report is to derive the anisotropic transverse resonance condition for a parallel 

plate structure partially loaded with anisotropic magneto-dielectric material. This calculation 

allows engineers to design cavity-backed LPAs that maintain a constant fr when loaded with high 

index anisotropic materials. This is important because the refractive index of any material will 

alter fr when placed in a resonant cavity. By maintaining a constant fr, the designer will suppress 

destructive interference from higher-order modes inside the cavity. 

This report presents an antenna model where the profile reduction is achieved with high index 

anisotropic magnetic material. The antenna under investigation is a radiating, tapered rectangular 

cavity. An appropriately shaped high index magneto-dielectric material within the cavity 

establishes local resonance conditions with the conducting walls of the cavity. Furthermore, this 

report demonstrates that using anisotropic magnetic metamaterials to load this cavity achieves 

positive realized gain from 220–505 MHz with a return loss (S11) of better than –10 dB with a 
2

cavity profile depth of 0.06λr, where λr is the cutoff free-space wavelength based on the 

dimensions of the aperture. All simulations are performed with CST Studio Suite 2014 and all 

materials are assumed to be lossless.

2. Derivation of a Tapered Cavity Based on an Anisotropic Transverse 

Resonance

A novel idea for a tapered rectangular cavity based on the transverse resonance was proposed in 

a previous report entitled “Comparison of Anisotropic versus Isotropic Metamaterials in a Low

Profile UHF Antenna Design”.3 This report presented an antenna based on a transverse 

resonance condition derived for isotropic materials and demonstrated the ability of this design to 

suppress higher-order modes.

The previous report showed that loading the cavity model shown in Fig. 1 with anisotropic 

material gave the best results, even though the transverse resonance condition that yielded this 

cavity was based on isotropic values of permeability and permittivity. The cavity dimensions that 

correspond to this design are given in Table 1.

Fig. 1 The cavity geometry derived from the isotropic transverse resonance condition3

Table 1 The dimensions in inches for the geometry in Fig. 1

a0 b a1 fr (MHz) d PW L

26.25 11.7 8.3 225 3.3 8.0 8.5

Note that ao = λr/2, b = ao/2.25, and a1 = ao/[(μr/εr)^0.5]. This design yielded a S11 < –6 dB, or a 

voltage-standing-wave-ratio (VSWR) of better than 3:1, from 350–580 MHz, and a 

S11 < –10 dB, or a VSWR of better than 2:1, from 400–575 MHz. Furthermore, a positive 
3

realized gain is achieved from 220–580 MHz. These performance metrics are achieved with 

permeability and permittivity tensors of

15 0 0 100

0 1 0 and 0 1 0

0 01 001

μ ε r r

  

   = =

  .

Section 2.1 shows the results of the derivation of the anisotropic resonance condition for the 

anisotropic case, and its application to the improvement of the previous antenna design from 

Reference 3.

2.1 Anisotropic Transverse Resonance Derivation

At any point z in the tapered cavity shown in Fig. 1, a resonance condition is established by 

material width w(z) and the distance between the two conducting walls a(z). At each point in 

space, this resembles a finite parallel plate waveguide partially loaded with anisotropic material 

with two conducting walls. 

Figure 2 shows a transmission line representation of this parallel plate structure. For a known 

value of w(z), we can determine the value of a(z) in terms of Lg. The following subsections 

describe how to determine Lg from the transverse resonance condition established by the 

conducting walls and the boundaries at the interface between the anisotropic material and free 

space.

Fig. 2 Transmission line representation of parallel plates partially loaded with anisotropic material

2.1.1 Free Space Region (–a/2 ≤ x ≤ –w/2)

Assume Maxwell’s source free equations:
4

∇× = − EjH ωμo , (1a)

∇× = Hj E ωε o . (1b)

Evaluating the curl operator of Eqs. 1a and 1b yields the following transverse components for the 

electric and magnetic fields in the waveguide in terms of Hz and Ez:

2 2

z z

x o zo

o zo

j dH dE E k

k k dy dx ωμ

  = − +   −  , (2a)

2 2

z z

y o zo

o zo

j dH dE E k

k k dx dy ωμ

  =   − −  , (2b)

2 2

z z

x o zo

o zo

j dE dH H k

k k dy dx

ωε

  =   − −  , (2c)

2 2

z z

y o zo

o zo

j dE dH H k

k k dx dy

ωε

  = − +   −   . (2d)

To solve for Hz, we formulate the transverse free space wave equation from Eqs. 1a and 1b as

( ) ( ) 2 ∇ ×∇ × = ∇ × =∇ ∇ ⋅ −∇ T T Hj E H H ωε o T T T Tz ,

( ) 2 0 o oz Tz j jH H ωε ωμ − +∇ = ,

2 2

2

2 2 0 z z

o z

dH dH k H

dx dy

    ++ =

 

. (3)

At the cutoff frequency kzo = 0, which allows us to calculate resonance at cutoff for this structure. 

If we assume a TE10-like resonance, then kyo = 0 for the first resonance at cutoff, which means no 

variation of the fields in the y-direction. This means that d2Hz/dy2 = 0 and

2

2

2 0 z

o

d H k

dx

+ = , (4)

o o β = k . (5)

Solving Eq. 4 for Hz and inserting into Eq. 2b yields

o o jk x jk x H Ae Be z

− + = + , (6a)
5

2 ( )( ) ( ) oo oo o jk x jk x jk x jk x

y o o

o

j E jk Ae Be Z Ae Be k

ωμ −+ −+ =− − = − . (6b)

We can see from Eqs. 2a–2d that based on our resonance conditions on Ez, kzo and kyo that Ex = 0, 

Hx = 0, and Hy = 0.

2.1.2 Anisotropic Region (–w/2 ≤ x ≤ 0)

Again assume Maxwell’s source free equations in the anisotropic region 

∇× = − ⋅ Ej H ωμ μo r , (7a)

∇× = ⋅ Hj E ωε εo r , (7b)

where the permeability and permittivity are now defined by tensors

0 0

0 0

0 0

x

r y

z

μ

μ μ

μ

 

  =  

   

 and 

0 0

0 0

0 0

x

r y

z

ε

ε ε

ε

 

  =  

   

. (8)

Evaluating the curl operator of Eqs. 7a and 7b yields the following transverse components for the 

electric and magnetic fields in the waveguide in terms of Hz and Ez

4,5

2 2 1

1

z z

x oy z

o yx z

j dH dE E k

k k dy dx ωμ μ

μ ε

  = − +   −  , (9a)

2 2 1

1

z z

y ox z

o xy z

j dH dE E k

k k dx dy ωμ μ

μ ε

  =   − −  , (9b)

2 2 1

1

z z

x oy z

o xy z

j dE dH H k

k k dy dx

ωε ε

μ ε

  =   − −  , (9c)

2 2 1

1

z z

y ox z

o yx z

j dE dH H k

k k dx dy

ωε ε

μ ε

  = − +   −  . (9d)

To solve for Hz we formulate the transverse anisotropic wave equation from Eqs. 7a and 7b:

4,5

∇ ×∇ × = ⋅ ∇ × T T Hj E ωε εor T ( )

,

∇ ×∇ × = ⋅ − ⋅ T T Hj j H ωε ε ωμ μ or o r ( ),
6

( ) 1 2

T r T or ε μ Hk H − ∇ × ⋅∇ × = ⋅ ,

2 2 2 2

2

2 22 2 22

1 1

0 o x z z o y

oz z

o xy z o yx z

k d H k d H k H

k k dx k k dy

μ μ

μ

μ ε μ ε

+ += − − . (10)

Now set kz1 = 0, which allows us to calculate resonance at cutoff for this structure. Similarly, we 

can assume that ky1 = 0 for the first resonance at cutoff. This means that d2

Hz/dy2 = 0

2

2

2 0 z

o zy

d H k

dx

+ = μ ε , (11)

1 o zy β με = k . (12)

Solving Eq. 11 for Hz yields

1 1 jx jx H Ce De z

− + β β = + , (13a)

( )( ) ( ) 1 1 1 1

1

o jx jx z jx jx

y o

o y y

jZ E j Ce De Z Ce De k

β β μ β β β

ε ε

− + − + =− − = − . (13b)

We can see from Eqs. 9a–9d that based on our resonance conditions on Ez, kz1 and ky1 that Ex = 0, 

Hx = 0 and Hy = 0.

2.1.3 Solving the Boundary Conditions for the Impedances in the two Regions

The first boundary condition exists at the perfect electric conductor (PEC) boundary at x = –a/2 

where the electric field is known to be zero:

2 2

2

0 o o

a a jk jk

y a x E Ae Be−

=− =→ =

,

o jk a A Be− = . (14)

Plugging Eq. 14 into our Eqs. 6a and 6b yields

2 2 2

oo o

o o o

jk x jk a jk x

y o

a a a jk jk x jk x

o

E ZB e e e

Z Be e e

−− +

  − −+ ++    

=   −  

  =   −

 ,

2 2 sin

2

o

a jk

yo o

a E jZ Be k x −     = − +         . (15a)
7

Similarly,

oo o jk a jk x jk x H Be e Be z

−− + = + ,

2 2 cos

2

o

a jk

z o

a H Be k x −     =   +       . (15b)

Now we can solve for the impedance of the free space region as Z = –Ey/Hz

tan , 0 2 22

y

o oo

z

E a a aw Z jZ k x x

H

 −   =− = + ≤ + ≤         . (16)

The second boundary condition exists at x = –w/2, where the tangential fields at the boundary are 

equal. In this case, there are two tangential fields in Ey and Hz. At the boundary, we have the 

following three conditions:

2 2

y y w w x x E E − +

=− =− =

, (17a)

2 2

z z w w x x H H − +

=− =− =

, (17b)

1

2 2

w w o x x Z Z − +

=− =− = . (17c)

Plugging Eqs. 13 and 15 into Eqs. 17a and 17b yields the following set of equations:

1 1 2 2 2 2 sin

2

o

a w w jk j j z

o

y

a w jBe k Ce De μ β β

ε

−  −   − +   − =−            , (18)

1 1 2 2 2 2 cos

2

o

a w w jk j j

o

a w Be k Ce De −  − − + β β     = −       . (19)

This gives us two equations to solve for three unknowns. In order to solve for the third unknown, 

we can match Eq. 16 to the impedance in the anisotropic region at x = –w/2. Again we solve for 

Z = –Ey/Hz from Eqs. 15a and 15b:

1 1 1

1 1 1

2

1 2

1 , 0 1 2

jx jx j x

z z

o o jx jx j x

y y

De Ce e w Z Z Z x

De Ce e

β β β

β β β

μ μ ρ

ε ε ρ

+ − −

+ − −

   − − = = − ≤≤       + + , (20a)

1

z

o

y

Z Z μ

ε =

, (20b)
8

C

D ρ = . (21)

Now applying boundary condition Eq. 17c to Eqs. 16 and 20

1

1

1

tan

1 2

j w

z

o j w o o

y

e a w Z jZ k

e

β

β

μ ρ

ε ρ

  −  −     =       +     ,

1

1

1

tan

1 2

j w

y

j w o

z

e a w j k j X

e

β

β

ρ ε

ρ μ

  −  −   =   =       +     ,

1 1 1 j w j w e jX jX e β β − =+ ρ ρ ,

1 1 1 jw jw jX jX e e β β −= + ρ ρ ,

1

2

1 tan

1

1

1 tan

z y

y

w j j w z

y

z

a w j j X e e

j X a w j

π με β λ

ε

π

μ λ

ρ

ε

π

μ λ

− −

   −     −     −     = =  

+    −   +          

. (22)

Substituting Eq. 22 into Eq. 21 gives us our third equation along with Eqs. 18 and 19 to solve for 

the three unknowns B, C, and D.

2.1.4 Solving for the Transverse Resonance Condition

If we view Fig. 2 as a transmission line representation of our problem, we can solve for Lg in 

terms of w for a given wavelength (λo). For instance, at 200 MHz, λo = 1.5 m. We can use the 

input impedance transformations of transmission line theory to calculate Zin

 at x = 0. Then by 

symmetry the transverse resonance condition simplifies to Zin = 0  or Yin = 0  .

Starting at x = –a/2, we can calculate Zin

 at x = –w/2 by 

tan Z jZ k L o og α =    



. (23)

We can now calculate Zin

 at x = 0 as

1 1

1

1 1

tan

2

tan

2

w Z jZ

Z Z

w Z jZ

α

α

β

β

Ω

  +     =   +    







. (24)

The transverse resonance condition simplifies Eq. 24 to
9

1 1 tan 0

2

w Z jZ α β   + =    



. (25)

Plugging Eqs. 20b and 23 into Eq. 25 yields the following equation for Lg:

tan tan ( ) 0

2

z

o o og o zy

y

w Z Z kL k μ μ ε

ε

  − =     ,

1 1 tan

2 tan

z

g y

z y

L

w

μ

ε

λ π π

μ ε λ

−

 

 

  =               . (26)

In Reference 3, Lg depended on both μr and εr, which means all six permittivity and permeability 

tensor elements affected the return loss of the antenna. We know that ultimately the permeability 

value in the direction of the magnetic field at the aperture is what determines the best return loss 

for our antenna in Fig. 1.

3 Now we see that as we change this tensor value (μx), there will be no 

effect on the taper of the cavity.

Figure 3 shows the relationship between the ratio of μz/εy and the shape of the cavity. Note that 

for a ratio of 1, we have a purely linear taper. Now that we have an explicit expression for the 

cavity taper based on anisotropic permittivity and permeability, we apply it to antenna design in 

Fig. 1 to see if we can further optimize the performance.
10

Fig. 3 Plot of Eq. 26 for various ratios of μz/εy with an assumed depth of 3.3 inches

3. Low-Profile Antenna Design

Now we can use Eq. 26 to design an optimum cavity taper for our LPA. We start out by 

comparing a tapered cavity based on our anisotropic transverse resonance condition to that of an 

antenna in Fig. 1.

3.1 Anisotropic Tapered Cavity

Figure 1 has a cavity shape based on a ratio of μr/εr = 15.

3 Therefore, for an accurate comparison 

using the same cavity shape, we use a ratio of μz/εy = 15. Furthermore, we know that a value of 

μx = 15 gives our best broadband return loss.

3 This results in the following permeability and 

permittivity tensors for our anisotropic material:

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

0

0.05

0.1

0.15

0.2

0.25

w/λo

Lg/

λo

Space between Conductor and Dielectric

μz

/ε

y=.1, a1= 0.16λ

μz

/ε

y

=.2, a1= 0.22λ

μz

/ε

y=1, a1= 0.25λ

μz

/ε

y=5, a1= 0.22λ

μz

/ε

y

=10, a1= 0.16λ

μz

/ε

y

=15, a1= 0.13λ

μz

/ε

y

=20, a1= 0.11λ
11

15 0 0

010

0 0 15

μr

 

  =  

   

and 

100

010

001

r ε

 

  =  

   

. (27)

Figure 4 shows a cavity that is very similar to Fig. 1. The dimensions of the tapered cavity are 

given in Table 2. Note that now a1 = ao/[(μz/εy)^0.5]. In order to achieve the best wideband return 

loss, fr has been lowered to 150 MHz. This results in a much larger aperture; however, the profile 

of the antenna remains d = 3.3 inches.

Fig. 4 The cavity geometry derived from the anisotropic transverse resonance 

condition with μz/εy = 15

Table 2 The dimensions in inches for the geometry in Fig. 4

a0 b a1 fr (MHz) d PW L

39.4 17.5 10.2 150 3.3 0.25λr 0.35λr

This antenna model is now a two-port system with two symmetric probes. This differs from the 

one-port probe shown in Fig. 1. Feeding the two probes 180° out of phase provides a continuous 

current path across a positive-to-negative voltage potential across the walls of the cavity in the 

y-direction. This should provide a better impedance match at the input to both ports.

Figure 5 shows the return loss versus frequency for the single-port antenna of Fig. 1 and the 

symmetric-port antenna of Fig. 4. This shows a S11 < –6 dB from 230–505 MHz, which is about 

an 80-MHz improvement in BW at the upper end of the frequency range. We also have a much 

flatter S11 response from 250–420 MHz even though the return loss is better for the single-probe 

antenna. Figure 6 shows the VSWR versus frequency for the single-port antenna of Fig. 1 and 

the symmetric-port antenna of Fig. 4. This shows better than a 3:1 VSWR from 230–505 MHz,
12

which is about an 80-MHz improvement in bandwidth at the upper end of the frequency range of 

the single probe antenna. Figure 7 shows the realized gain versus frequency for the single-port 

antenna of Fig. 1 and the symmetric-port antenna of Fig. 4. This shows the most dramatic 

difference in performance. Due to the flat return loss response of the symmetric-probe antenna 

over 420–500 MHz, the deep trough in the realized gain for the single-probe antenna is 

eliminated. This gives us a positive realized gain in excess of the entire BW 180–515 MHz. 

The combination of realized gain and return loss yields over an octave of BW for the antenna 

design in Fig. 4 with tensor values of Eq. 27. However, we have forced the μz component of the 

permeability tensor to be 15. However, the μz component should have little effect on the overall 

performance of the antenna.3 Section 3.2 investigates how setting μz = 1 affects the shape of the 

cavity and the performance of the antenna.

Fig. 5 Return loss at the probe inputs of the single-probe antenna (blue) and the symmetric-probe antenna (red)

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

0.18 0.22 0.26 0.3 0.34 0.38 0.42 0.46 0.5 0.54

dB

Frequency (GHz)

Best Case |S11| for Single Port Antenna

Single Probe

Symmetric Probe
13

Fig. 6 VSWR at the probe inputs of the single-probe antenna (blue) and the symmetric-probe antenna (red)

Fig. 7 Far field realized gain of the single-probe antenna (blue) and the symmetric-probe antenna (red)

0

2

4

6

8

10

0.18 0.22 0.26 0.3 0.34 0.38 0.42 0.46 0.5 0.54

Frequency (GHz)

Best Case VSWR for Single and 

Symmetric Probe Antenna

Single Probe

Symmetric Probe

-4

-2

0

2

4

6

8

10

0.18 0.22 0.26 0.3 0.34 0.38 0.42 0.46 0.5 0.54

dB

Frequency (GHz)

Best Case Realized Gain for Single Port 

Antenna 

Single Probe

Symmetric Probe
14

3.2 Anisotropic Non-Tapered Cavity

This section explores how setting μz = 1 affects the cavity shape of the antenna design. The 

results of Reference 3 suggest that this should have little effect on the return loss of the antenna. 

Figure 3 suggests that a ratio of μz/εy = 1 will result in a linearly tapered cavity. However, for the 

special case of μz/εy = 1, where both μz and εy are unity, the walls of the cavity do not need to be 

tapered at all.

Figure 8 shows the cavity geometry given by Eq. 26 for the following permeability and 

permittivity tensors

15 0 0

0 10

0 01

μr

 

  =  

   

 and 

100

010

001

r ε

 

  =  

   

. (28)

Fig. 8 The cavity geometry derived from the anisotropic transverse resonance condition with 

μz = 1 and εy = 1

The cavity shape is a rectangular cavity with no taper. This is a very different result from those 

of Figs. 1 and 4. This indicates that regardless of the anisotropic tensor values, as long as μz = 1 

and εy = 1, any amount of loading will result in the same cavity shape and a constant fr even at 

the material to free space boundary. We now see if changing the value of μz from 15 to 1 has any 

effect on the return loss or realized gain of the antenna.

Figures 9–11 show very good agreement in the return loss, VSWR, and realized gain plots. 

Therefore, we conclude that the non-tapered cavity shape of Fig. 8 has no noticeable effect on 

the overall performance of the antenna. This is a very useful result, because it means the shape of 
15

the cavity can be changed to fit in different environments as long as the designer has some 

amount of control over the μz component of the permeability tensor.

Fig. 9 S11 at the probe inputs for the tapered antenna cavity with μz = 15 (blue) and the non-tapered antenna cavity 

with μz = 1 (red)

Fig. 10 VSWR at the probe inputs for the tapered antenna cavity with μz = 15 (blue) and the non-tapered antenna 

cavity with μz = 1 (red)

-12

-10

-8

-6

-4

-2

0

0.18 0.22 0.26 0.3 0.34 0.38 0.42 0.46 0.5 0.54

dB

Frequency (GHz)

Best Case |S11| for Tapered and 

Non-tapered Cavity Antenna

tapered cavity

non-tapered cavity

0

2

4

6

8

10

0.18 0.22 0.26 0.3 0.34 0.38 0.42 0.46 0.5 0.54

Frequency (GHz)

Best Case VSWR for Tapered and Nontapered Antenna Cavity

tapered cavity

non-tapered cavity
16

Fig. 11 Realized gain for the tapered antenna cavity with μz = 15 (blue) and the non-tapered antenna cavity with 

μz = 1 (red)

3.3 Cascaded Antenna with Feed Structure

The results of the symmetric-probe-fed antenna models from Sections 3.1 and 3.2 were driven 

using two separate ports that are 180° out of phase with an equal magnitude. This is an optimized 

way to drive the antenna, but in reality we would want a feed structure with a single input port 

and two output ports with –3.0 dB insertion loss (this is a one-half power split) as well as a 180°

phase shift. The following subsections show the results for two different feed structures.

The following are the results for a commercial 180° hybrid coupler and the non-tapered antenna 

of Fig. 8. The commercial splitter is the Werlatone 2-Way 180° Combiner/Divider H7971-102. 

The pertinent S-parameter and phase difference information pertaining to this device is found in 

the Appendix.

Figure 12 shows how the two output ports 2 and 3 of the coupler connect to the two antenna 

input ports 1A and 2A. All antenna dimensions are consistent with Table 2.

-4

-2

0

2

4

6

8

10

0.18 0.22 0.26 0.3 0.34 0.38 0.42 0.46 0.5 0.54

dB

Frequency (GHz)

Best Case Realized Gain for Tapered and 

Non-tapered Cavity

tapered cavity

non-tapered cavity
17

Fig. 12 The diagram showing the connectivity between the 180° coupler and the two-port antenna

Figures 13–15 compare the performance of the system shown in Fig. 12 to those of the antennas 

shown in Fig. 8 to see if there is any improvement when using the commercial coupler. It should 

be noted that for the antenna with no coupler, the return loss is calculated at the input to port 1A 

in Fig. 12, and for the antenna with the coupler, the return loss is calculated at the input to port 1. 

There is better than a 4-dB improvement in S11 due to the presence of the coupler and up to 

0.75-dB degradation in realized gain due to the added insertion loss in S21 and S31 of the 

coupler. 

Adding a commercial 180° hybrid coupler has improved the return loss at the input to the system 

and increased the bandwidth with very little degradation in the realized gain. The antenna system 

now has better than a 2:1 VSWR from 220–505 MHz and better than a 3:1 VSWR from 

200–515 MHz. The return loss of the antenna design was good enough that the 0.75-dB 

degradation in the return loss is due almost solely to the insertion loss of the coupler and not due 

to any mismatch between the output port of the coupler and the input port of the antenna.

Fig. 13 Return loss vs. frequency at for the antenna of Fig. 12 (red) and Fig. 8 (green)
18

Fig. 14 VSWR vs. frequency plots for the antenna of Fig 12 (red) and Fig. 4 (green).

Fig. 15 Realized gain vs. frequency plots for the antenna of Fig 12 (red) and Fig. 4 (green)
19

4. Conclusions

This report details the derivation of a LPA based on an anisotropic resonance condition of a 

partially loaded rectangular cavity. Results show that the shape of the cavity taper can be 

changed as needed with no degradation to the overall antenna performance through control of the 

permeability in the normal direction (μz). Research in this area has yielded a LPA design that has 

a profile of d = 0.055λo (λo /19) at 200 MHz or d = 3.3 inches with μx = 1. This antenna design 

has more than an octave of bandwidth from 200–515 MHz. This is a 78% reduction in antenna

profile compared to the traditional λo /4 separation between radiating element and ground plane. 

The design has a positive realized gain from 180–515 MHz, a 3:1 VSWR from 200–515 MHz, 

and a 2:1 VSWR from 220–505 MHz. The 3:1 VSWR BW exceeds the design goals of 

200–500 MHz. 

Further investigation into matching techniques for larger values of μx is needed to try and reduce 

the profile of the antenna further.
20

5. References

1. Lagarkov AN, Semeneko VN, Kisel VN, Christyaev VA. Development and Simulation of 

Microwave Artificial Magnetic Composites Utilizing Non-magnetic Inclusion. 2003.

2. Maslovski S, Ikonen P, Kolmakov I, Tretyakov S. Artificial Magnetic Materials Based on 

the New Magnetic Particle Metasolenoid. Progress in Electromagnetics Research (PIER).

2005;54:61–81.

3. Mitchell G. Comparison of Anisotropic versus Isotropic Metamaterials in Low Profile UHF 

Antenna Design; Adelphi (MD): US Army Research Laboratory (US); 2104. Report No.: 

ARL-TR-7012.

4. Meng F-Y, Wu Q, Fu Jai-H. Miniaturized Rectangular Cavity Resonator Based on 

Anisotropic Metamaterials Bilayer. Microwave and Optical Technology Letters. August 

2008;50(8).

5. Meng F-Y, Wu Q, Li L-W. Transmission characteristics of wave modes in a rectangular

waveguide filled with anisotropic metamaterial. Applied Physics A: Material Science. 

2009;94:747–753.
21

Appendix. Werlatone 180° Divider/Combiner

This appendix shows the pertinent S-parameters of the 180° hybrid coupler discussed in Section 

3.3. This is in actuality a four-port device, but the fourth port is terminated inside the metal box.

Figure A-1 shows a picture of the device. There is one input port and two output ports with a 

180° phase difference. Its operational frequency range is 100–1000 GHz, but we are interested 

mostly in the 200–500 MHz range. Figure A-2 shows the return loss at the input port of the 

coupler as measured on a network analyzer. Here we see a better than –20 dB return loss across 

the entire frequency range of interest. Figure A-3 shows the insertion loss at the output ports of 

the coupler as measured on a network analyzer. There is a 0.25-dB difference between the two 

outputs. These plots show a 0.55–0.75 dB difference in insertion loss from a perfect –3.0 dB 

split. Figure A-4 shows the phase difference at the output ports of the coupler as measured on a 

network analyzer. This device maintains a phase separation of 180.5° across frequency.

Fig. A-1 Picture of the 180° coupler with the ports labeled. Port 1 is the input and ports 2 and 3 are the outputs.
22

Fig. A-2 S11 of the Werlatone 180° hybrid coupler

Fig. A-3 S21 and S31 of the Werlatone 180° hybrid coupler
23

Fig. A-4 Phase difference at ports 2 and 3 of the 180° coupler
24

1 DEFENSE TECH INFO CTR

(PDF)ATTN DTIC OCA (PDF)

2 US ARMY RSRCH LABORATORY

(PDF) ATTN IMAL HRA MAIL & RECORDS MGMT

ATTN RDRL CIO LL TECHL LIB

1 GOVT PRNTG OFC

(PDF) ATTN A MALHOTRA

6 US ARMY RSRCH LAB

(PDF) ATTN RDRL SER M A ZAGHLOUL

ATTN RDRL SER M E ADLER

ATTN RDRL SER M G MITCHELL

ATTN RDRL SER M S WEISS

ATTN RDRL SER M T ANTHONY

ATTN RDRL SER M W O COBURN