Ultra-Wideband Antennas: Design and Modeling

Abstract

This paper presents an insight into UWB antenna. Aspects regarding design, characterization and modeling of UWB antenna are discussed.

Full text

Ultra-Wideband Antennas: Design and Modeling
(Invited Paper)
Yvan Duroc, Anthony Ghiotto, Tan-Phu Vuong, Smail Tedjini
Grenoble INP – LCIS – Laboratoire de Conception et d’Intégration des Systèmes
Valence, France
Yvan.Duroc@esisar.grenoble-inp.fr
Abstract—This paper presents an insight into UWB antenna.
Aspects regarding design, characterization and modeling of UWB
antenna are discussed.
Keywords-UWB; UWB antenna; UWB antenna
characterisation, UWB antenna modeling
I.
I
NTRODUCTION
For many RF designers the antenna is the most important
piece and its performance will enable the overall characteristic
of the wireless communication system. Five years before
Marconi patented his telegraph experiment in 1900, Popov had
invented a device capable of detecting electromagnetic waves
in the atmosphere [1]. The design of Popov's detector was
similar to that of Marconi's telegraph, but Popov's invention
focused on receiving rather than transmitting signals. Both men
had extrapolated upon the work of earlier physicists, namely H.
Hertz and O. Lodge, but Popov was the first to introduce the
concept of antenna. Many decades after the early investigation
on antennas, these elements are showing very strong evolution
[2] in both their topologies and usages. Research programs on
antennas are driven by several factors.
The first factor deals with the increase of the bandwidth.
Because modern wireless applications are processing more and
more data in different forms, quite larger bandwidths are
needed. So, numerous techniques have been developed in order
to design antennas with large band, in terms of radiation pattern
and impedance matching [2]. Among the most useful
approaches we can notice designs with log-periodic profile,
multiresonant elements and traveling-wave topologies [3].
Because of their simple form, electric dipole and monopole are
the most considered basic structures. Several evolutions are
introduced in order to enlarge their bandwidth [4]-[5].
The second factor deals with field pattern and the ways to
control it. One method is to use a multitude of identical
radiating elements to form an array. The elementary antennas
are fed from a single source through a network of transmission
line and/or waveguides. In such systems the shape of the
radiation pattern is governed by the field pattern of the
elementary antenna (which is chosen to be as simple as
possible) and the power distribution among the elements and
geometric details of their arrangement. Many examples are
available in the literature [6]. Even if arrays are initially
designed for high power purposes and use bulk antennas, their
developments in planar and integrated forms such as microstrip
patchs are attractive [7].
The third factor deals with “isotropric” behavior. Indeed
growing claim for higher mobility in wireless systems raises
the problem of antenna non-isotropy, especially at mobile side.
Ad Hoc sensor networks [8] for human motion capture systems
based on wearable sensors as well as localization of mobile
objects are typical upcoming applications requiring quite
constant received power whatever are the orientations of the
devices relatively to each others. Directions of departure and
arrival of a beam can totally change while in use and fall into
antenna radiating null. Polarization mismatches can also cause
fading of the transmitted power. It is therefore difficult to
maintain the QoS (Quality of Service). Truly isotropic antennas
do not exist [9]. Thus, when space has to be covered in all
directions, smart antennas with pattern and polarization agility
are required. However, for many applications, generalizations
of adaptive smart antenna are still far away, due to their high
cost or power consumption or because of size and integration
issues. Therefore, there is a need for small antennas with
optimized radiation pattern and polarization to provide wide
coverage. One method to obtain a quasi-isotropy behavior is to
associate several elementary antennas in complementary way
in terms of fields and polarization. In [10] the concept of
spatial coverage factor is introduced as well as its application
to a quasi-isotropic antenna.
In addition to the previous factors, and in order to
accurately integrate the antenna performance into the design
off the overall system, specific models compatible with
standard languages like VHDL/VHDL-AMS are highly
desired. Such modeling allows the right design and
optimization of wireless RF front-end (including antenna). An
example of modeling can be found in [11].
Last, but not least, in modern wireless communication
systems, complex signal processing techniques and digital
routines are considered in order to build a device flexible
enough to run every possible waveform, without restrictions on
carrier frequency, bandwidth, modulation format, date rate …
This is philosophy of Software Defined Radio firstly
introduced by Mitola [12].
So, as explained in the previous chapter, the antenna is one
of the most important pieces in a wireless system. In the same
time it is going to be flexible and “intelligent” enough to
perform processing function that can be realized by any other
device.
This paper is divided in two parts. The first part concerns
an overview of UWB and UWB antennas. The second part

focuses on the characterization and modeling of UWB
antennas.
II. U
LTRA
W
IDEBAND
A
NTENNAS
This chapter presents UWB antennas properties and some
typical UWB antennas before introducing a band notched
antenna designed for IR-UWB and to rejects the frequency
band from 5.15GHz to 5.825GHz used by IEEE 802.11a and
HIPERLAN/2.
A. UWB antenna properties
Antennas are an essential part of any wireless system. The
IEEE Standard Definitions of terms for antennas defines an
antenna as a means for radiating or receiving radio waves [14].
An antenna is a device that allows a signal transmits from a
source to a transmission line to be converted into
electromagnetic waves broadcasted into free space.
An UWB antenna is defined, by The Federal
Communications Commission (FCC), has an antenna having a
fractional bandwidth greater than 0.2 and having a minimum
bandwidth of 500 MHz.
MHzffand
ff
ff
BW
LH
LH
LH
5002.02 ≥−≥
+
−
=
(1)
where f
H
is the upper, or high, end of the antenna’s operational
band and f
L
is the bottom, or low, end of the antenna’s
operational band.
An UWB system should comply with the emission mask
and operate within the 3.1-10.6 GHz frequency range allocated
in US. Therefore, the UWB antenna must achieve almost a
decade of impedance bandwidth, spanning 7.5 GHz.
Some other considerations that must be taken into account
are the antenna’s radiation pattern and group delay. The
radiation pattern should be as much constant within the overall
operating frequency in order to guarantee the same pulse
properties in any direction. The group delay is given by the
derivative of the unwrapped phase of an antenna. If the phase is
linear throughout the frequency range, the group delay will be
constant for the frequency range. This is an important
characteristic because it helps to indicate how well an UWB
pulse will be transmitted and to what degree it may be distorted
or dispersed.
B. UWB antenna characteristics
UWB antenna may be categorized into four different types:
frequency independent antennas, small element antennas,
travelling wave antennas and multi-resonant antennas.
1) Frequency independent antennas: Frequency
independent antennas include spiral, log periodic or conical
spiral antennas. These antennas are dependent on variation in
geometry from a smaller-scale portion to larger-scale portion.
The smaller-scale portion contributes higher frequencies while
the larger-scale portion contributes lower frequencies. These
antennas may be dispersive because the effective source of the
radiated fields varies with frequency.
Figure 1. Logarithmic spiral antenna
2) Small element antenna: Small-element antennas include
Lodge’s biconical and bow tie antennas Maters’ diamond
dipole, Stohr’s spherical and ellipsoidal antennas, and
Thomas’s circle dipole. These antennas are small,
omnidirectional and low cost.
Figure 2. UWB compact planar monopole antenna [13]
3) Traveling wave antenna: Traveling wave antenna
includes horn antennas, tapered slot antenna (including Vivaldi
antennas) or dielectric rod antennas: these antennas feature a
smooth transition form guided wave to radiated waves and
have good properties for UWB.
Figure 3. Horn Antenna – SAS 571 from A.H. Systems Inc
4) Multi-resonant antenna: Multi-resonant antennas are
composed of an arrangement of multiple narrowband elements.
This type of antenna includes log periodic antennas or Yagi
antennas. These antenna are UWB but are not convenient for
UWB as they have their phase center is not fixed in frequency
and therefore exhibits dispersion.
Figure 4. Log periodic antenna– SAS 510-7 from A.H. Systems Inc

C. Band notched UWB antenna
A compact band-rejected U-slotted planar antenna for IR-
UWB is presented here. The concept of this antenna design is
introduced in [13].
Fig. 5 shows the geometry of the antenna. A U-Slot filter
was added to reject the undesired frequency bandwidth. The
antenna is feed by a 50Ω microstrip line printed on a partial
ground plane.
Figure 5. Geometry of the reported antenna (front view)
The antenna design’s parameters are: Lsub=35mm,
Wsub=30mm, Lf=12.5mm, Wf=3.2mm, Lp=14.5mm,
Wp=15mm, Wc=1mm, Lst1=1mm, Wst1=1.5mm,
Lst2=1.5mm, Wst2=1.5mm, Lsl1=5mm, Lsl2=7mm,
Wsl=0.5mm.
Techniques applied to match the antenna over the UWB
frequency band are: the use of two steps and of a partial ground
plane. The antenna was first studied without the U-Slot filter to
operate in the overall UWB frequency band.
Once the antenna was designed for operation within the
overall UWB frequency band, we added the U-Slot filter to
reject the undesirable 5.15GHz to 5.825GHz frequency band
(Fig. 6).
4 6 8 10
-25
-20
-15
-10
-5
0
f [GHz]
|
Γ
| [dB]
Measured
Simulated
Figure 6. Measured and simulated reflection coefficient |Γ|
Fig. 7 shows the surface current distribution at different
frequencies.
(a)
(b)
Figure 7. Simulated current distributions. (a) 5.5GHz. (b) 7GHz.
It can be observed on Fig. 7(a) that the current concentrated
on the edges of the interior and exterior of the U-Slot are
opposed at 5.5GHz. The rejected frequency occurs where the
total U-slot length is equal to half a wavelength. Therefore the
antenna impedance changes at this frequency due to the
resonant properties of the U-Slot. This leads to a high
attenuation of the undesired frequencies. For other frequencies,
the addition of the U-Slot filter had few effects.
III. C
HARACTERIZATION AND
M
ODELING
A. State-of-art
An antenna can be considered as a transducer transforming
guided electromagnetic waves into electromagnetic waves
propagating in free space, and vice versa. Standard definitions
may be employed to define antennas characteristics [14].
Considering an antenna as an electromagnetic radiator, a
Radio Frequency (RF) engineer will be interested by its
radiation pattern, directivity, gain, aperture, efficiency and
polarization. However, considering an antenna as a circuit
element, an RF circuit designer will be more interested by its
input impedance, reflection coefficient and voltage standing
wave ratio. When considering narrowband systems, all of these
characteristics can be considered as frequency independent, i.e.
constant within the used frequency band. In wideband systems,
conventional properties become strongly frequency dependent.
Therefore, one important feature of UWB antennas is that they
introduce some pulse dispersion due to its frequency sensitive
characteristics. Notably concerning impulse radio applications,
antennas are critical components since the emitted and received
pulse shapes are distorted.
In [15]-[16] the antenna effective lengths are considered to
specify impulse radiation and reception characteristics of
antennas. More recently with the emergence of the UWB
technology, the frequency-domain transfer functions and the
associated time-domain impulse response, which derived from
antenna effective lengths, have been preferred to describe these
characteristics. Different definitions of the parameters involved
in obtaining transmit and receive transfer functions have been
proposed [17]-[19]. In practice, the transfer functions are
deduced from the simulated or measured complex scattering
parameter, i.e. transmission coefficient, S
21
. A vector network
analyzer (VNA) is generally used in the frequency domain and

a post-treatment allows the assessment of time domain
measures [20]. It should be noticed that the time domain
measurement is possible but the corresponding calibration is
not always well established, although the two approaches were
demonstrated to be quasi-equivalent [21]. In the literature, the
papers which present new UWB antennas propose not only
design aspects and conventional characteristics but also, more
and more, a time domain characterization in order to validate
the antenna ability to transmit short pulses and to receive these
pulses with low distortion [22]-[25]. Moreover performance
parameters (e.g., the fidelity factor, the full width at half
maximum), issued to transfer function or impulse response,
were introduced to quantify and analyze the pulse-preserving
performances of UWB antennas [26]-[27]. One issue with
many published propagation measurements was that the
antenna effect is implicitly included in the measurement but not
explicitly allowed for in the channel analysis, e.g., the IEEE
802.15.3a standard model [28]. Thus, the consideration of the
antenna effects in order to analyse or evaluate the performance
of an UWB system implied also the introduction of antenna
models based on transfer function (or pulse response) [29]-
[31]. Otherwise, several researches were presented approaches
for the modeling of UWB antennas directly in RF circuit
simulators in order to enable simulations of circuit performance
with the antennas included. In [32], a transient model using
cascaded ideal transmission lines for UWB antennas is
presented. In [33], a bilateral equivalent model for the UWB 2-
antenna network which allows notably the modeling of
multipath channels in the circuit domain was proposed. Finally,
recent studies shown that the use of a parametric modeling can
enhance the modelling [34]-[36]. Analytical and compact
expressions of transfer functions and impulse responses can be
computed from simulations or measurements. The parametric
methods are based on the Singularity Expansion Method
(SEM) which provides a set of poles and residues.
Considerations about measurement setup were presented in
[37]-[38] to guarantee accurate models.
B. Interests of the Use of Parametric Models
Several applications of the use of parametric models are
summarily presented from the small U-slotted planar antenna
presented in part II. More details of part B2, B3, B4 are
exposed in [11].
1) Preambule : brief summury of the SEM: Two of the
most popular linear methods are the polynomial method (first
developed by Prony in 1795) and the Matrix Pencil Method,
more recent and more computationally efficient because the
determination of the poles is a one-step process [39]. These
methods use the same projection in a base of exponential
functions. The model is given by:
( ) ( )
∑
=
=
N
1i
ii
tsexpRtx
(2)
where {R
i
} are the residues (complex amplitudes), {s
i
} are the
poles and N is the order of the model. Then after sampling,
and with the poles defined in the z-plane as z
i
= exp(s
i
T
e
) the
sequence can be written as:
( )
∑
=
=
N
1i
k
ii
zRkx
(3)
The knowledge of the poles and the residues allows the direct
determination of the impulse response and the transfer
function. The frequency representation is also a direct function
of the poles and residues and is written in the Fourier plane
and z-plane respectively, as:
( ) ( )
[ ]
∑
=
−
==
N
1i
i
i
sjf2
R
txTFfX
π
(4)
( ) ( ){ }
∑∑
==
−
−
=
−
==
N
1i
i
i
N
1i
1
i
i
zz
zR
zz1
R
kxTzzX
(5)
where the operator “TF” corresponds to the Fourier transform
and the operator “Tz” corresponds to the z-transform.
Using an inverse Fourier transform, the impulse response
x(t) of the antenna is determined from the transfer function
X(f). The parametric modeling applied to the impulse response
determines the poles and the residues. The quality of the
modeling is a compromise between accuracy and complexity,
i.e. the order of the model N.
2) Directional Time-Frequency Parametric Model: Fig. 8
presents the antenna radiation characteristics in the time
domain for 4 orientations of the azimuth plane. The impulse
responses were deduced from the measured parameter S21.
The computed model present a good agreement with 30
complex couples of poles, and for any orientation 30 associated
couples of residues.
90°
45°
-
45°
φ
0°
Figure 8. Antenna radiation characterization in the time domain
3) Equivalent Circuit of UWB Antenna Input Impedance:
The parametric approach can also be applied to the antenna
input impedance and associated to the Foster’s passive filter

synthesis method allows the determination of an equivalent
circuit of this impedance (Fig. 9). Fig. 10 shows the measured
real and imaginary parts of the antenna input impedance
compared to results from the parametric model and the circuit
equivalent model (simulated with SPICE).
(
)
12112
2
12
BA2/A −
α
(
)
2222
BA2/A
2
−
α
(
)
111
2
1
BA2/A −
α
B
1
/M
1/A
1
A
1
/M
B
2
/M
1/A
2
A
2
/M
B
12
/M
1/A
12
A
12
/M
Figure 9. Equivalent electric circuit of antenna input impedance
2 4 6 8 10 12
-200
-100
0
100
200
Za-Real Part [
Ω
]
Measured Impedance
Parametric Model
Circuit Model
2 4 6 8 10 12
-200
-100
0
100
200
Za-Imaginary Part [
Ω
]
f [GHz]
Figure 10. Real and imaginary parts of antenna input impedance
4) VHDL-AMS Modeling of an UWB Radio Link Including
Antennas: The UWB radio link model including antennas can
be written in VHDL-AMS (Very High Speed integrated circuit
hardware Description Language – Analog and Mixed-Signal
Extension) from the parametric model of the transmission
parameter S21. Fig. 11 and Fig. 12 illustrate the modeled UWB
communication chain (non-coherent reception technique) and
the obtained signals. In Fig. 12c is the received signal in which
we can notice the attenuation and delay propagation, and
antennas filters effects.
Data
Data
Pulses
Generator
On-
Off keying
Modulator
Clock
Square-
law
device
(b)
(c) (d) (e ) (a)
Comparator
Mono-
stable
Figure 11. UWB communication chaine
5) State Representation of UWB Antennas: The transfer
function of the LTI system characterizing the antenna can be
considered as N elementary (with an order equal to 1) parallel
systems (Fig. 13):
( ) ( )
∑
=
=
N
1i
aa
zHzH
i
(6)
with the following elementary transfer functions:
( ) ( )
{
}
1
i
i
a
i
a
zz1
R
khTzzH
i
−
−
==
(7)
(a)
(b)
(c)
(d)
(e)
0 20 40 60 80 100 120
Time [ns]
Figure 12. UWB transmission chronogram
y(n)
y
1
(n)
z
-
1
u
1
(n)
R
1
z
1
y
2
(n)
z
-
1
u
2
(n)
R
2
z
2
y
N
(n)
z
-
1
u
N
(n)
R
N
z
N
u(n)
Figure 13. Illustration of the elementary systems associated in parallel
In the field of filter theory, it is classically possible to
extract an internal representation of the system (here the
antenna), called the state representation. This state
representation is given by the following matrix expression:
( )
( )
( )
( )






⋅


















=






+
∑
nu
nX
Rzzz
Rz00
0
R0z0
R00z
ny
1nX
i
iN21
NN
22
11
L
L
MOMM
L
L
(8)
(
)
( )
(
)
( )






⋅






=






+
nu
nX
ny
1nX
dC
BA
(9)
where the vector X(n) represents the state variables (i.e. the
state vector), u(n) is the input of the system, y(n) is the output,

A is the state matrix, B is the input matrix, C is the output
matrix, and d is the feedforward coefficient. It should be
noticed that the state matrix A is diagonal. In consequence, the
observable and controllable states are directly accessed.
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