1. Fig. 2. Single element EM model
Fig. 1. Test antenna measurements at RFS Meriden, CT, USA
Advanced Modeling Method for UHF Broadcast
Slotted Coaxial Antennas
Brandon George
Senior Electrical Engineer
RFS Meriden, USA
Myron Fanton
Antenna Systems Engineer
RFS Meriden, USA
Nick Wymant
CTO Broadcast/Defense
RFS Meriden, USA
Yan Cao
Senior Electrical Engineer
RFS Kilsyth, Australia
Abstract—Advances in electromagnetic simulation software
and rigorous design methods allow for faster and more accurate
UHF broadcast coaxial slot antenna manufacturing.
Keywords—Antenna Arrays, slot antennas, iterative algorithms,
UHF antennas, FCC spectrum repack, incentive auction.
I. INTRODUCTION
Slotted coaxial array antennas have been in use for UHF
TV broadcasting for many decades. While these antennas are
essentially single-channel antennas, they are still enjoying high
popularity because of the features they offer [2].
Historically, slotted coaxial antenna design techniques
involve approximate methods. The use of relatively crude and
simple spreadsheets is quite common. This makes it necessary
to iterate the design during production resulting in
modifications and adjustments that are time consuming.
Upcoming high demand for replacement slotted coaxial
antennas as a consequence of the UHF spectrum repack,
requires fast and accurate design and production methods with
the aim of short delivery time [1]. Modern full wave
electromagnetic analysis tools are available and produce
accurate results. However, these tools are relatively slow when
it comes to simulation of large antenna structures, particularly
when used for design optimization tasks. The design problem
is not new. When electromagnetic design tools first appeared,
CPU speed was below 250 MHz and the simulation time was
long with negative impact on the design time. This resulted in
the development of techniques aimed at minimizing the
number of electromagnetic simulation runs by adopting clever
methods. We can now benefit from this work and instead of
using “brute-force but slow” EM design, employ smart
methods.
The fundamental idea of the method presented is to use
highly accurate EM simulation models in tandem with very fast
lower level equivalent models. By linking the fast lower level
model to a slower but highly accurate full wave EM model,
both goals of fast design time and highly accurate results are
achieved. The result: short time design time, accurate antenna
design, reduced tuning time on the test range, and short lead
times for slot antennas.
To date, the method described in this paper has been used
at RFS to design and build multiple production antennas. Side
mounted and top mounted center-fed antennas with
omnidirectional and directional patterns have been produced
using the technique described. The example in this paper is
based on a full size 24 bay directional side mounted slot
antenna that required almost zero tuning effort in production.
II. CURRENT DESIGN METHODS USED IN INDUSTRY
Slotted coaxial antenna array design methods were created
long before the powerful analysis tools of today were
imaginable. Many of these processes such as spreadsheet tools,
circuit model analysis, or test data from single element
measurements are still in use today. The goal when using these,
or other, approximate design methods is to generate a design
that is “close enough” to tune during the production phase.

2. Fig. 3. Example of an archer correcting for an error
A slotted coaxial antenna created with these current design
methods will often require extensive tuning or re-design before
the specifications are compliant due to its high Q factor and
other real world effects not included in the simple models, such
as the interactions between radiation elements [4]. Any
required design change to coupling structures or slot lengths
during production or post-production can be time consuming
and costly.
One solution to avoid design changes during production, is
to verify the design using an industry standard 3D EM
simulation tool, such as ANSYS HFSS. It is generally thought
in industry that full EM analysis and design of slotted coaxial
antennas is not possible due to their complexity, size, and tight
tolerances.
EM solvers have grown exponentially more powerful since
slotted coaxial antenna design became mature, both in accuracy
and in solver time reduction. When using modern simulation
techniques and suitable computer hardware we are able to
accurately analyze a 32-bay slotted coaxial antenna in a full
wave 3D EM model in less than three hours. This is a
reasonable amount of time for analysis, but not fast enough to
use the full EM model to optimize the design parameters.
The upcoming FCC spectrum repack requires a new slotted
coaxial antenna design methodology which will allow for
accurate designs in short lead times. Space mapping [3] is one
technique that can make use of moderately accurate models for
intermediate designs in conjunction with very accurate full EM
models for analysis. This design method is already used at RFS
for RF filters. By adopting a similar approach we have
combined the accuracy of 3D EM analysis with the fast
iteration time of simpler models to create slotted coaxial
antenna arrays which require little to no design changes during
production. Removing design changes from production
shortens the lead time of an antenna dramatically.
III. APPLICATION OF SPACE MAPPING
Often the evaluation of a problem becomes so costly in
either resources or time that traditional optimization techniques
become impractical. In these cases a computationally cheaper,
less accurate model can be used to find the ideal design
parameters. The problem can therefore be separated into two
models
1. A “fine” model which has high accuracy, but has a long
computation time. Gradients of the model function with
respect to the design parameters cannot be calculated in a
reasonable amount of time.
2. A “coarse” model which can be quickly evaluated and
parameters can be optimized effectively, but lacks the
accuracy of the fine model.
The space mapping technique involves forming a
connection between the fine and coarse models to optimize the
set of parameters in the fine model. If the desired response
from the fine model is y*
with parameters x, the current best
guess from the coarse model is c(xi), and the evaluated fine
model is ƒ(xi), then the current fine model error is
 ƒ(xi) - y* 
To correct for the fine model error , the next set of
parameters xi+1 need to be found by the following equation
 y* - = c(xi+1) 
With the next set of fine model parameters, xi+1, found the
fine model can be evaluated again with the entire process
continuing until the required fine model goals are achieved [3].
Fig. 3 illustrates an example of the tuning process in which
an archer would correct for a missed shot by aiming in the
opposite direction of the error. Aiming for y*
and hitting f(x0),
the archer would next aim for y* -  to correct for the miss [3].
IV. DESIGN METHOD AND RESULTS
A 24 element coaxial slot antenna was designed for ATSC
channel 26 with 0.5 degrees of beam tilt and a smooth null free
elevation pattern. The required antenna VSWR specification
was 1.08 across the channel. From the specified elevation
pattern, required slot illuminations were derived. Slot
illuminations are defined by the amplitude and phase of the
electric field at the center of each slot. In RFS’s design, each
slot length and coupler penetration can be independently
adjusted to select the specific slot amplitude and phase. This
allows for a flexible design that accommodates a wide range of
elevation patterns.
In this process, the coarse model is a simplified model of a
single slot element. The fine model is a full EM model of the
slotted coaxial antenna including centering pins, tee section,
vertical radiating dipoles, radomes and any other parts that may
have an effect on the design. The single element coarse model
characterized data are shown in Fig. 4 and Fig. 5.
To start the design process, we start with design amplitude
and phase
 A0 = Arequired 
 0required 

3. Fig. 4. Coarse model for coupler penetration characterization
Fig. 5. Coarse model for slot length characterization
Fig. 6. Iterative error convergence
And assuming Ai and i represent the current design
illuminations, then the current antenna slot design parameters,
coupling structure penetration (Pi) and slot length (Li) are
found by the following equations
 PiƒPi, Ai 
 LiƒLi, Ai 
Where the functions ƒP and ƒL represent the data in Fig. 4
and Fig. 5, respectively.
Now the ith EM fine model can be evaluated with the
antenna slot design parameters Pi and Li. Next the EM fine
model’s slot illuminations are compared with the required slot
illuminations. From this, individual slot amplitude and phase
errors can be computed.
 AAfine – Arequired 
 finerequired 
Then the next set of design illuminations will be adjusted
by the current illumination errors.
 Ai+1 = Ai –A 
 ii 
The process in steps (5) through (10) is continued until the
elevation pattern in the fine model meets the required
specifications. Fig. 6 shows how the errors have converged
after only three iterations for this antenna. Current industry
practice is that the manufactured antenna would initially be
built to the specifications of design iteration 1. This would
require the engineer to tune or re-design the antenna into
compliance. The proposed RFS design method allows the
antenna to be optimized in software before a single part is
ordered. The resulting design only needs minor adjustments
during production, if at all. This will cut days or weeks off lead
time.
After the final iteration, the simulation results showed a
compliant elevation pattern and VSWR. Next the full size 24
bay coaxial slot antenna was built (Fig. 8) to the exact
specifications of the model. Fig. 7 compares the final design
computed elevation pattern and the measured elevation pattern
of the completed slotted coaxial antenna. The elevation pattern
of the manufactured antenna met specification without the need
for any post-production tuning. Achieving a compliant
elevation pattern without any design changes allows us to build
slot antennas quickly and free engineering resources during
production.
As with the elevation pattern, the technique described also
allows the designer to ensure that the VSWR of the antenna
will be compliant to specifications with minimal or no tuning.
Incompliant VSWR can be corrected in a number of ways, but

4. Fig. 7. Measured antenna and EM model comparison Fig. 9. Measured VSWR results of as- built antenna
Fig. 8. Finished antenna at RFS Meriden
these can be just as time consuming as correcting the slot
antenna’s elevation pattern. Using an EM model to ensure that
the VSWR will be compliant before building the antenna can
save days or weeks of time during production.
Fig. 9. shows the built antenna’s VSWR performance. This
test confirmed that the VSWR with the antenna radomes fitted
was compliant to the required specification.
Azimuth patterns of the antenna are generally designed
using the EM model, and then verified on a full scale single or
dual layer antenna test section. Fig. 1 shows a typical pattern
measurement inside the test chamber. Similarly, if the antenna
includes vertically coupled fields, these are designed in the EM
model, verified in the test chamber, and finally confirmed
during full antenna testing on the outdoor test range.
V. CONCLUSIONS
We have shown that EM modeling tools can be used to
analyze and verify slotted coaxial antenna array designs. By
verifying slot array antennas before construction, we can avoid
some of the delays due to array tuning issues currently present
in industry.
We have also presented that these EM tools, in conjunction
with Space Mapping techniques, allow for optimization of full
model coaxial slotted antennas in a short amount of time. This
allows for antennas to be built “pre-tuned” in contrast to
current industry antenna design methods.
These design and verification methods will allow for fast
and accurate designs during the FCC UHF spectrum repack.
ACKNOWLEDGEMENTS
The fine design work and many important contributions of
our colleagues: Dieter Pelz, Simon Bauwens, Chad Van
Vlierden, Jay Alessi, and Ray Testo are thankfully
acknowledged.
REFERENCES
[1] N. Wymant, "Future Proofing Your DTV Transmission Facility", NAB
Broadcast Engineering Conference proceedings, 2014.
[2] M. D. Fanton, “Slotted Coaxial Arrays Provide Lightweight,
Economical Antenna Alternatives to Panel Arrays,” ERI Technical
Series, Vol. 6, April 2006.
[3] J. Søndergaard, “Optimization Using Surrogate Models by the Space
Mapping Technique”, Ph.D. thesis, IMM, DTU, Lyngby, 2003.
[4] S. Silver, ed., Microwave Antenna Theory and Design, London,
England: Peter Peregrinus, Ltd, 1984.