Eingereicht zur GeMIC2009
Equivalent-Circuit Modelling of the
Chassis Radiator
Umut Bulus, Celestine Famdie, Klaus Solbach1
University Duisburg-Essen, Hochfrequenztechnik, Bismarckstr.81,D-47048, Germany
1
klaus.solbach@uni-due.de
Abstract — The comparison of the characteristics of a
flat dipole and the rectangular chassis eigen-mode leads to
the concept of the chassis radiator as a flat dipole with
completely filled, short-circuited terminal area. The
equivalent circuit for the chassis radiator is derived from
the flat dipole equivalent circuit by exclusion of the parasitic
feed inductor and shunt capacitance and by short-circuiting
the de-embedded terminals. In employing equivalent circuit
elements based on measured impedance of a flat dipole, the
partitioning of
parasitic and “dipole” inductance is
achieved by application of the theoretical resonance (eigen-)
frequency of the chassis mode. In a more general equivalent
circuit model the impedance level can be chosen arbitrarily,
only enforcing the theoretical resonance frequency and Qfactor of the chassis mode.
I. INTRODUCTION
Several publications on the design of mobile phone
antennas have reported that the chassis (the PCB board)
of a mobile phone, if of the order of a half wave length in
length dimension, acts as a radiator which is “excited” by
the antenna element, thus increasing bandwidth and
efficiency [1],[2]. Consequently, the chassis has been
interpreted as an antenna structure which can support
resonant current distributions, similar to a wire dipole
antenna; these “chassis modes” have been investigated
and electromagnetic field distributions as well as
resonance frequencies and Q-factors have been presented
in [3]. On the other hand, the interaction of the chassis
and the antenna element has inspired the notion of a
system of coupled resonators and equivalent-circuit
models have been discussed [1], [4].
Furthermore, in an investigation of radiation properties
of a small phased array antenna on a small ground plane
(chassis) it was found that radiation pattern, radiation
resistance of elements and the mutual coupling of the
elements depend strongly on the length and width of the
ground plane [5]. It was concluded then that the ground
plane should be modelled as an additional radiator
element, we can call it the “chassis radiator”, which is
mutually coupled to the radiator elements of the array; in
this concept, the chassis radiator is assumed to be a
dipole antenna with short-circuited terminals in order to
model a flat rectangular conducting plate without
distinguishable terminals.
It is therefore necessary now to understand the chassis
as a dipole-type radiator and reconcile the concept of the
characteristic chassis modes and the concept of the shortcircuited dipole radiator: In this contribution, the
properties of the chassis radiator are discussed based on
measurements and equivalent-circuit modeling of a flat
dipole and it is shown how the chassis mode concept can
be incorporated.
II. EQUIVALENT-CIRCUIT OF FLAT DIPOLE
The chassis-radiator is not directly accessible to a
conventional impedance measurement because of its
structure of a rectangular continuous metal plate which
does not provide any “terminals” for a measurement. A
simple modification leads to a flat dipole which can be
accessed by a transmission line: The rectangular plate is
cut into two halves and the dipole terminals are created
by “tipping” the two halves at the centre. A miniature
balun is connected which allows a small semi-rigid cable
to be attached for measurement of the reflection
coefficient using an automatic network analyzer (ANA),
Fig.1.
Gap
Balun
Coaxial
Feed
Fig.1
Flat dipole of length l = 150 mm and width w = 80 mm fed
in the centre by a semi-rigid cable and a miniature balun
The measured reflection coefficient of the flat dipole,
Fig.2(a), behaves in a similar way as the reflection
coefficient of an electrically thin dipole or monopole:
Both can be approximated by an equivalent-circuit which
models the radiator as a series L-C resonant circuit with a
series radiation resistance and an additional shunt
capacitor to represent the stray electric fields between the
Eingereicht zur GeMIC2009
two halves of the dipole, Fig.2(b). However, the flat
dipole shows considerably reduced resonant frequency
The resulting parasitic inductance adds to the
fundamental series inductance of the dipole equivalent
circuit and thus lowers its series resonant frequency.
S(2,2)
S(1,1)
III. CHASSIS MODE CHARACTERIZATION
freq (351.2MHz to 1.200GHz)
Fig.2(a) Measured reflection coefficient (red) of the flat dipole and
the simulated characteristic from an ADS model (blue)
Fig.2(b)
Equivalent circuit model for the flat dipole
compared to a dipole of equal length, which can be
explained mainly by a parasitic inductance at the feed
point terminals: As indicated in the sketch, Fig.3, the
dipole current is forced to travel from the centre feed
points to the outer edges of the flat dipole halves, thus
creating parasitic magnetic field energy which would not
be created if the current could flow uniformly.
The investigation of the characteristic current modes of
a rectangular flat metallic plate (chassis) has led to
solutions which can be understood as resonant modes of
a radiating conductor, [3],[5], the so-called Chassis
Modes. Field plots show that the lowest frequency
chassis mode can be compared to the fields of a halfwavelength linear dipole, Fig.4. At higher frequencies,
modes with current distributions similar to harmonic
current distributions, i.e., one wavelength, etc. are found.
If we reduce the width of the flat chassis plate, we
approach the homogeneous solution of the thin, linear
dipole. It is therefore admissible to apply the term halfwavelength dipole mode to the lowest chassis mode.
Fig.4
Surface current density of lowest chassis mode representing
the λ/2-mode of the chassis radiator
This term then lets us think of the chassis as a flat dipole
which is short-circuited at the centre, by covering and
virtually eliminating the feed terminals of the dipole. As
such, it is no longer possible to determine where the feed
terminals have been originally, e.g., at the centre or offset
from the centre. This explains why the chassis mode
theory cannot yield the radiation resistance of the chassis
radiator, but rather gives its resonant frequency and the
quality factor only. Fig. 5 shows the theoretical Q-factor
and the resonant length l/λ for a chassis of 150mm length
as a function of its widths.
Fig.5
Quality factor and resonant length of the chassis radiator
with l = 150 mm based on chassis mode theory [3]
Fig.3
Flat dipole layout with indication of current flow and
parasitic inductance and shunt capacitance
It is seen that the broader the chassis the lower the Qfactor and that the resonant length varies only slightly
with the width.
Eingereicht zur GeMIC2009
IV. EQUIVALENT CIRCUIT OF CHASSIS MODE RADIATOR
The concept of the chassis radiator as a short-circuited
flat dipole can now be applied to our flat dipole: In a first
step, the flat dipole is short-circuited at the terminal
points, Fig.6(a), causing a strongly non-uniform current
distribution close to the terminals.
of the area between the two dipole halves. Therefore, in a
third step, the equivalent circuit of the chassis radiator is
developed from the short-circuited dipole equivalent
circuit by excluding the parasitic shunt capacitor and the
series parasitic inductance, Fig.7(b). This is to say that
the chassis radiator is just embedded in the full
equivalent circuit of the flat dipole, “hidden” behind the
parasitic elements. The only problem is: We do not know
the size of the series inductance LS !
Fig.7(b)
Fig.6(a)
Flat dipole with short-circuit
This situation is described by the dipole equivalent
circuit with a short-circuit connected to the dipole
terminals, Fig.6(b). The equivalent circuit shows the
inductance separated into the parasitic part LS and a
partial inductance LCh which would be the inductance of
a fictitious dipole with uniform current distribution (no
parasitic inductance).
We can solve this problem by determining the
inductance of the dipole or chassis radiator LCh instead,
such that the R-L-C series circuit resonance frequency is
equal to the frequency predicted by chassis mode theory:
f0 =
Equivalent circuit of short-circuited flat dipole
In a second step, this is contrasted to the short-circuited
chassis radiator which has no terminals and thus can
provide a practically uniform current distribution across
its width at the center, Fig.7(a), and thus does not suffer
from a parasitic inductance.
1
(1)
CCh LCh
This approach was checked using the equivalent circuit
elements found for the measured dipole impedance and
using the resonance length data from Fig.5. The element
values of the optimized equivalent circuit can be taken
from Fig.8
Term
Term2
Num=2
Z=50 Ohm
Fig.6(b)
Equivalent circuit of the chassis radiator
Fig.8
R
R1
R=27.5
C
C2
C=1.28128 pF
L
L1
L=17.8785 nH
R=
C
C1
C=3.00404 pF
Equivalent circuit for flat dipole (ADS optimization)
The inductance of 17.8 nH was divided into a parasitic
inductance of LS = 7.8 nH and a chassis radiator
inductance LCh =10.1 nH in order to create a resonance
frequency of 913 MHz for the chassis length of l = 150
mm. From the series resistance RCh and the inductance or
capacitance we can calculate the Q-factor at resonance of
the chassis mode R-L-C circuit as Q = 2.1 while theory
predicts about 2.5. This is a satisfactory agreement
considering the measurement inaccuracies and the crude
equivalent circuit approximation used.
VI. CONCLUSION
Fig.7(a)
Short-circuited chassis radiator
Comparing the geometry of the chassis radiator to the
short-circuited dipole radiator it becomes clear that the
chassis short circuit can be thought of as a conducting fill
The comparison of the characteristics of a flat dipole
and the rectangular chassis mode has lead to the concept
of the chassis radiator as a flat dipole with completely
filled terminal area. The equivalent circuit for the chassis
radiator was shown to derive from the flat dipole
equivalent circuit by cancellation of the parasitic feed
inductor and shunt capacitance and by a short-circuiting
at the de-embedded terminals.
In employing equivalent circuit elements based on
measured impedance of a flat dipole, the partitioning of
Eingereicht zur GeMIC2009
parasitic and “dipole” inductance was achieved by
enforcing the theoretical resonance (eigen-) frequency of
the chassis mode.
Since opposite to the flat dipole, in our concept of the
chassis radiator the feed terminals are covered by the
conductor and are not identifiable, they can be assumed
to be anywhere along the plate. This means that also the
impedance level (e.g., the radiation resistance) is not
defined and can in principle be set to an arbitrary value.
It is only necessary to define the chassis radiator
equivalent circuit elements such that the resonance
frequency and quality factor agree with the theoretical
chassis mode results.
The chassis radiator model is a necessary step in the
modelling of the interaction of radiators placed on a
small ground plane, as outlined in [5]; the investigation and
modelling of mutual coupling of a monopole antenna and the
ground plane (chassis radiator) will be presented elsewhere [7].
REFERENCES
[1]
[2]
[3]
P.Vainikainen, J.Ollikainen, O.Kivekäs, I.Kelander,
“Resonator-based analysis of the combination of mobile
handset antenna and chassis”, IEEE Trans.AP, vol.50,
no.10, Oct.2002, 1433 – 1444
P.Lindberg, E.Öjefors, “A bandwidth enhancement
technique for mobile handset antennas using wavetraps”,
IEEE Trans.AP, vol. 54, no.8, August 2006, 2226-2233
C.T.Famdie, W.L.Schroeder, K.Solbach, ”Numerical
analysis of characteristic modes on the chassis of mobile
phones”, EuCAP2006, Nice, France, Nov.2006
[4] L.Huang, W.L.Schroeder, P.Russer,”Estimation of
Maximum Attainable Antenna Bandwidth in
Electrically Small Mobile Terminals”, EuMC2006,
Manchester, 2006, pp.630-633
[5] K.Solbach, C.T.Famdie, ”Mutual Coupling and Chassis[6]
[7]
Mode Coupling in Small Phased Array on Small Ground
Plane”, EuCAP2007, Edinburgh, November 2007
C.T.Famdie, W.L.Schroeder, K.Solbach, ”Optimal
antenna location on mobile phones chassis based on the
numerical analysis of characteristic modes”, EuMC2007,
Munich, October 2007
U.Bulus, K.Solbach,”Modelling of the Monopole
Interaction with a small Chassis”, submitted to
EuCAP2009, Berlin, March 2009