2-1 Biconical Antenna
A simple broadband antenna which evolved from the dipole antenna is the biconical antenna. The biconical antenna is formed by two infinite extent cone as shown in figure 2.1, and the antenna can be thought to represent a tapered transmission line. We can calculate the radiated field and input impedance by analyzing the current and field distribution. The applied voltage Vi at the input terminal will generate the current I along the surface of the cone and voltage V between the cones, as shown in figure 2.2(a). The voltage and current cause the electromagnetic wave, shown in figure 2.2(b). We assume that the dominant TEM mode (E and H are transverse to the direction of propagation) is excited. From faraday‟s law, we can obtain
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Chapter 2 The basic theory of broadband antenna
Fig. 2.1 Biconical antenna geometry.
Fig. 2.2 (a) Electric and magnetic fields for a biconical antenna. (b) Associated voltages and currents for a biconical antenna.
Which can be expanded in spherical coordinate and assumed that there is only Eθ component independent of φ. Therefore, the above equation can be reduced to
∇ × E = −jωH
(2-1)
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Chapter 2 The basic theory of broadband antenna
It is necessary to form the TEM mode with Eθ so the H only has a Hφ, and then equation (2-2) can be written as
From Ampere‟s law, we can write that
which can be expanded in spherical coordinate and assumed only Eθ and Hφ component independent of φ, and the equation can be reduced to
We substitute (2-6) into (2-3), and it form a different equation for Hφ as
A solution, which meets the condition of (2-5) , (2-7) and represents an outward traveling wave, is
Since the field is TEM mode, the electric field is related to the magnetic field by intrinsic impedance, and we can write is as
Eθ = ηHφ = η H0
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Chapter 2 The basic theory of broadband antenna
The voltage which is produced between two corresponding points on the cones, a distance r from the origin, can be found by
Where α is the cone angle. We can substitute (2-9) into (2-10) to obtain
Moreover, the surface current of the cones, a distance r from the origin, can be found as follows
The voltage and current at a distance r from the origin can be observed in figure 2.2. We can use the voltage of (2-11) and the current of (2-12) to calculate the characteristic impedance as
The input impedance is real because the structure is infinite. If the length of biconical is finite, the discontinuities will cause reflections setting up standing waves, which would show up as a reactive component in the impedance.
The finite biconical antenna is practical in realization. The TEM waves exist with high-order modes created at the ends of the cones, and the high-order modes contribute mainly to the antenna reactance. The reactive part of the input impedance can be held to a minimum over a progressively wider bandwidth by increasing the angle α, and in this way, the real part of the input impedance becomes insensitive to different frequency. The phenomenon is illustrated in figure 2.3, which shows the measured impedance of different angle conical
Zc = V(r)
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Chapter 2 The basic theory of broadband antenna
Fig. 2.3 Measured input impedance of a conical monopole with flare angle versus monopole height Lh.
monopole antenna versus the height Lh. This figure clearly shows that the conical monopole antenna with wider cone angle can easily achieve 2:1 impedance bandwidth, which is one of the definitions of a broadband antenna.
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Chapter 2 The basic theory of broadband antenna
Fig. 2.4 Traveling wave long wire antenna.
2-2 Traveling-wave Antenna
In general case, the wire antenna we have discussed is resonant structure. The wave which travels from the feed point to the end of the wire is reflected, setting up a standing wave current. For example, the current for the top half of the dipole can be written as
The first term in brackets is taken to represent an outward traveling wave while the second term is a reflected wave. However, if there is no apparently reflected wave on an antenna, it is referred to as a traveling wave antenna. A traveling wave antenna is like a guiding structure for traveling waves and it can be created by using matched loads at the ends to prevent reflections. The simplest traveling wave wire antenna is a straight wire carrying a pure traveling wave. The traveling long wire, which is greater than one-half wavelength long, is shown in figure 2.3. In the figure, the long wire is shown being fed from a coaxial
transmission line and with a matched load RL to prevent reflection from the wire end. The radiation pattern of a long wire can be shown as
Imsin β L
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Chapter 2 The basic theory of broadband antenna
Fig. 2.5 Pattern of a traveling wave long wire antenna. (L=6λ)
where K is a normalization constant that depends on the length L. The polar pattern for L=6λ is drawn in figure 2.4, which shows the main beam is a rotationally symmetric cone about the z-axis.
The input impedance of a traveling-wave antenna is almost real. By recalling the impedance of a pure traveling wave on a low-loss transmission line is equal to the characteristics impedance (real) of the transmission line. Antennas that support traveling waves operate in a similar manner. The termination resistance should equal the value of the radiation resistance. The radiation resistance of a traveling long wire antenna is 200 to 300Ω.
Since the termination resistance is always independent of frequency, the bandwidth of a well-matched long wire antenna can be very wide.
F θ = K sin θsin[(βL 2 )(1 − cosθ)]
βL 2 (1 − cosθ)
(2-15)
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Chapter 2 The basic theory of broadband antenna
Fig. 2.6 The geometry of the circle disc monopole antenna.
2-3 UWB Antenna Review
In previous section, we have introduced the prototype of the wide-band antennas and its basic analyzing. In order to further understand the operating mechanism of the UWB antenna, two kinds of UWB antenna is reviewed and discussed in this section.
2-3-1 A Disc Monopole Antenna
The most common UWB antenna is various shaped metal plate monopole antenna which is modified from wire monopole antennas. In [13], a disc metal plate fabricated on 0.5 mm copper is mounted on a 300×300 mm2 ground plane as shown in figure 2.6. In order to design lowest frequency 3GHz, the diameter of the disc is 25 mm which is quarter wavelength at this frequency. The measured return loss can be observed in figure 2.7. The antenna bandwidth covers from 2.5 GHz to 20 GHz while the upper is out of the frequency range.
In this paper, a method to further improve impedance matching of the disc monopole is cutting angle α at lower portion of the disc near the ground plane. The cutting angle is
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Chapter 2 The basic theory of broadband antenna
Fig. 2.7 The measured return loss of the circle disc monopole antenna.
removing stray capacitance between the disc and the ground plane, so the impedance matching can be improved. For cutting angle α=20∘, the return loss less than -15dB is obtained at least from 2.5 GHz to 12 GHz.
In addition to the circular disc monopole antenna, the elliptical disc monopole can be also an UWB antenna. In [14], different ellipticity ratios disc antenna are compared and discussed. It concludes that the disc antenna with ellipticity ratio equal to 1.1 has the maximum bandwidth (bandwidth ratio 1:10.7), and the bandwidth decrease as the ratio becomes to 1.4. The lowest operating frequency of these antennas can be predicted by the equation
where L is the antenna length, and r is equivalent radius obtained by 2πrL = πab (a and b are the semi-major axis and the semi-minor axis respectively), the all units are in mm.
Moreover, the square, rectangular and hexagonal shapes monopole antennas represent rather narrow bandwidth compared to the disc monopole antenna, which is also validated in [14].
The radiation patterns of the disc monopole antenna are similar to the vertical linear monopole antenna where the E plane is conical shaped and the H plane is omni-directional.
f =c
λ= 3 ∗ 1011 (L + r) 0.24
(2-16)
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Chapter 2 The basic theory of broadband antenna
Fig. 2.8 The geometry of the planar UWB monopole antenna and its S11.
2-3-2 planar monopole UWB antenna
The general UWB monopole can be further expanded to a planar one. The planar
monopole UWB antenna is fabricated on a Printed Circuit Board with micro-strip feed line. In [15], three methods are applied for good impedance matching of planar UWB monopole antenna: 1. Tapered connection between the rectangular patch and the feed line. 2. The dual slots on the patch. 3. A partial ground plane flushed with feed line. According to the paper, the geometry parameters of the three structures can be adjusted to tune the return loss over wide range of frequency. The final geometry of the planar UWB monopole antenna and its return loss are shown in figure 2.8. It is noted the tapered connection between rectangular patch and the feed line is the key factor of the antenna design. The similar geometry of a UWB planar antenna is proposed in [16], which also has a tapered profile in antenna structure. Radiation patterns of the planar UWB monopole antenna are omni-directional in H plane and roughly dumbbell shape in E plane.
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