4.6 Multiband patch antennasBasic theoryIntroduction Telecommunication technology
is one of technical fields with great interest in military, professional and
also civil sphere. Due to commercial exploitation of complex electrical devices
(e.g. mobile phones), new requirements on their properties appear all the time.
Engineers are compelled to develop novel solutions they match the increasing
demands on both their technical parameters and physical dimensions. Miniature
antennas of modern communication devices have to be able to receive and transmit
electromagnetic waves in different frequency bands related to different communication
services. The
characteristics and analysis of singleband patch antenna was discussed in the previous chapter of the textbook. Now we turn our attention to patch antennas with multiband properties. First, basic
practices for obtaining multiband resonances of patch antennas are introduced.
Second, the modal analysis in the design of planar antennas is discussed. In layer B, example of a simple dualband patch
antenna and its computational model in Ansoft HFSS and CST Microwave Studio is
presented. Via this chapter, we get a short overview about multiband patch
antennas and learn about their design. Beside this, we become familiar with two
wellknown simulation softwares.
Basic types of multiband patch antennas There are
countless numbers of approaches how to obtain multiband resonance of planar
antennas. As example we can name the stacked patch configuration, patches with
slots and cuts of different shapes, antennas with shorting pins or PIFAs
(planar invertedF antennas). The mentioned types of antennas are depicted in fig. 4.6A.1. Considering the
polarization, multiband antennas can have parallel or orthogonal polarization
in working frequency ranges. The orthogonal polarization is preferred in
systems with polarization diversity.

a)
 b) 

c)  d) 
Fig. 4.6A.1  Selected types of multiband planar antennas: stacked patch (a), rectangular patch with slots (b), antenna with shorting pin (c),
PIFA (d). 

Let us now describe the working principle of antennas from fig. 4.6A.1. In the case of
stacked patch, the lower metallic patch is fed directly via connector
(obviously coaxial probe) and the upper metallic patch is in parasitic coupling
with the lower one. The configuration has two resonant frequencies – the lower
one is given by the dimensions of the lower (larger) metallic patch and the
higher one is given by the dimensions of the upper (smaller) metallic patch.
The basic operating mode of rectangular patch is TM_{10}. The current
distribution on rectangular patch can be influenced using slots and cuts of
different shapes. As a result we obtain different antenna modes at the resonant
frequencies. In the case of the structure in fig. 4.6A.1b beside of the basic TM_{10} mode appears another resonant mode TM_{x0} (1 < x < 2) which radiation efficiency is the highest for band angle from 15 deg to 30 deg. The ratio of
patch resonant frequencies f_{1}/f_{2} extends from 1.29 to 1.60. In the case of
antenna with shorting pin good impedance matching can be obtained for the first
two modes positioned along the resonant length of the antenna. If the shorting
pin is placed in the centre of the patch, the resonant frequency f_{1} of the basic TM_{10} mode remains not affected, whereas a new resonance emerges at the frequency f_{2} = 0.5 f_{1}. That means such an antenna can works as halfwave and quarterwave at the same time. Changing the position of the shorting
pin, the ratio f_{1}/f_{2} changes in interval of <2.0; 3.6> PIFAs are widely
used multiband antennas mounted in a broad range of communication devices.
Space between the ground plane and the patch is filed with dielectric. As in
the previous case, good impedance matching in the required frequency bands is
achieved using shorting pins and also cuts and slots (at different frequencies
different portions of the patch are in resonance). PIFAs can be used also for
three and fourband applications, but the design of such antennas is rather
than complicated. Detailed
description of the abovementioned antennas and other variants can be found in
the literature [33], [34]. To get fundamental physical insight into the working
principle of multiband planar antennas, the basics of the modal analysis is
discussed in the next section. The modal analysis describes the field
distribution of particular antenna modes. It simplifies the design process and
final tuning because we are able to do a good estimation about the shape and
dimensions of the metallic patch to achieve resonances at required frequencies. Modal analysis In the case of the
modal analysis the planar antenna is modeled as a resonant cavity with perfect
electric walls at the top and bottom. The main restriction is that the
thickness of the dielectric substrate must be much smaller than the wavelength.
Due to this, the variance of the electric field in the plane perpendicular to
the patch (axis z) is negligible. Because of the applied boundary conditions
the electric field is nonzero only along the axis z, whereas the magnetic
field has nonzero components only in the xy plane. Along the boundaries of
the metallic patch the Neumann condition for electric field is valid. It expresses the fact that the derivative of the
electric field intensity vector normal to the perfect magnetic conductor has to
be zero (∂E/∂n = 0). It implies the boundaries of the patch can be considered as perfect magnetic conductor. The component of the
electric field intensity perpendicular to the plane of the patch satisfies the
scalar wave equation

$\text{\Delta}{E}_{z}+{k}^{2}{E}_{z}=0$.

( 4.6A.1 )
 The magnetic field
vector H which is proportional to the current density J on the patch surface, can expressed as the gradient of the electric field intensity E_{z} using the equation 
$\mathbf{H}=\frac{1}{j\omega {\mu}_{0}}{\mathbf{z}}_{0}\times \nabla {E}_{z}$.

( 4.6A.2 )
 To solve the wave
equation (4.6A.1), the finite element method software Comsol Multiphysics can be exploited. The patch is modeled as
homogenous dielectric waveguide with the permittivity the same as the
permittivity of the antenna substrate. The boundaries of the waveguide are
considered to be perfect magnetic conductor. The cutoff frequencies of the
computed transverse magnetic modes correspond to the antenna resonance
frequencies (note that for this case it is necessary to set the value of the
propagation constant near to zero, for example 0.001 rad.m^{1}). In fig. 4.6A.2
amplitude of the magnetic field intensity for a dualband planar antenna with
rectangular patch and doubleU slot is depicted. The antenna is designed for
frequency bands 2.45 GHz and 3.60 GHz. The working principle is as follows: at
lower frequency resonates the whole patch, whereas at higher frequency only the
smaller inner portion. In tab. 4.6A.1 the calculated resonant frequencies are
summarized. Clearly, the third and fifth resonant frequencies are very close to
the required ones. Parameters of the designed antenna are introduced in layer B
together with the simulation results from Ansoft HFSS and CST Microwave Studio.
Tab. 4.6A.1  Resonant frequencies of the antenna from fig. 4.6A.2 – results of the modal analysis. 

Resonance number 
1. 
2. 
3. 
4. 
5. 

Frequency [GHz] 
1.055 
1.100 
2.348 
2.985 
3.585 

 
a)  b) 
Fig. 4.6A.2  Antenna modes on a rectangular patch with doubleU slots – amplitude of the magnetic field intensity: 2.348 GHz (a), 3.585
GHz (b). Red color – high intensity, blue color – low intensity. 

Using the above described modal analysis, basic characteristics of the designed antenna as
resonator can be obtained in a very short time. That is because in Comsol
Multiphysics we draw the longitudinally homogenous waveguide (i.e. our antenna)
as a twodimensional structure. This fact significantly reduces the computational
time in comparison to threedimensional model.
