1.2.1 Some antenna concepts and definitions Antenna bandwidth
Antennas can transmit and receive over a range of frequencies, or bandwidth (BW), from the lowest frequency (flow) to the highest frequency (fhigh) of the bandwidth. Depending on their functions, antennas are designed to operate in a narrow or a large bandwidth. An example of a very narrowband antenna is the dipole. On the other hand, there are antennas with a large bandwidth, for instance the helix or spirals. In order to compare them, the bandwidth can be defined in three main ways (Haupt, 2010):
• Percent of center frequency (fcenter):
BW = fhigh−flow
fcenter ×100 (1.1)
• Ratio of high to low frequencies, (fhigh :flow):
BW = fhigh
flow
(1.2)
• Range of frequencies:
BW =f −f (1.3)
Figure 1.1: Curve described by a circularly polarized wave with AR=3 dB, or XpolR = 15 dB.
Broadband or wideband antennas present a 25% (∼1.3 : 1) or higher bandwidth (Stutzman and Buxton, 2000). The limits of the bandwidth (flow, fhigh) depend on the parameters considered.
In this work we will consider two main parameters of the antenna: impedance matching and polarization.
Impedance matching
For an antenna, usually, good impedance matching means a reflection coefficient,|S11|, under -10 dB. This represents a loss in the power driven to the antenna of about 10%. It is also common to find the Voltage Standing Wave Ratio (VSWR) as an indicator of impedance matching. A good impedance matching has a VSWR≤ 2. The relations between theS11 and the VSWR are presented in Eq. 1.4 and 1.5.
S11= Zin−Zref
Zin+Zref
(1.4) V SW R= 1 +|S11|
1− |S11| (1.5)
Polarization
For an electromagnetic wave radiated from an antenna, the electric field vector has a magnitude and orientation that depend on time and space. For linearly-polarized antennas, the electric field describes a line, as in a dipole. Other antennas, like spirals, present a circular polarization, which means that the electric field rotates in such a way that it describes a circle, the ideal case, or an ellipse, the most realistic case. This rotation is called “right hand” (“left hand”) if it is clockwise (counterclockwise) when looking at the transmitted wave in the direction of propagation. The Axial Ratio (AR) of a wave is an indicator of the ellipticity of the polarization. According to IEEE (IEEE Standard, 1993), the AR is the ratio (expressed in dB) between the major and the minor axes of a polarization ellipse. Usually, good AR values are less than 3 dB (in linear scale
√2, cf. Fig. 1.1). For the case of a linearly-polarized wave, it is easy to see that the AR will be infinite.
Another common indicator of the AR is the Rejection of Cross Polarization (XpolR), usually expressed in dB. Good XpolR values are larger than 15 dB. Eq. 1.6 shows the relation between
the AR and the XpolR, both expressed in dB.
XpolR = 20log10
10AR20 + 1
10AR20 −1 (1.6)
Gain
The gain of an antenna (G) is the ratio between the power delivered by the antenna in a certain direction versus the power delivered to the antenna. The directivity of the antenna (D) is the power density in a certain direction versus the average power density created by the antenna. The directivity will be always larger than the gain since the latter includes the losses, such as losses in the substrate, losses due to loads in the antennas, etc. Eq. 1.7 relates these two parameters by the radiation efficiency (δe) (Haupt, 2010).
D=δeG (1.7)
Another interesting parameter is the theoretical maximum gain of an aperture. If the gain of the antenna achieves this value, it is said that it has a 100% aperture efficiency. This maximum gain is shown in Eq. 1.8.
Gmax= 4πA
λ2 (1.8)
where Gmax is the maximum gain, A is the area of the radiant element expressed in m2 and λ the wavelength expressed in m.
1.2.2 Broadband antennas
The use of broadband antennas can be traced back to the days of telegraphy. By the end of the 19th century, Lodge proposes new improvements to a system known at that time as “Hertzian- wave telegraphy” (Lodge, 1898). In his invention, he explains that the system uses “capacity areas” (antennas) to transmit and receive the signals. Lodge cites many antennas, among them
“cones or triangles or other such diverging surfaces with the vertices adjoining and their larger areas spreading out into space”. Fig. 1.2 shows some of his designs. The biconical antenna has been revisited by Carter and Schelkunoff (Schantz, 2004). Many other antennas have been proposed, such as Vivaldi, helix, spiral antennas and four square antennas.
Biconical or conical with ground plane
If the biconical antenna were infinite its bandwidth would also be infinite. But in practice the bandwidth is limited to about 50:1 (Sandler and King, 1994). The input impedance of this antenna is mostly real and it depends on the angular aperture. It can be easily designed to be adapted to an input impedance of 50Ω. The polarization of the antenna is linear, parallel to the axis of the antenna. The radiation pattern is omnidirectional, in the perpendicular plane of the axis of the antenna, as in the case of the dipole.
Horn
By adapting the aperture edges of the horn, it is easy to obtain an octave bandwidth (Burnside
Figure 1.2: Biconical antenna described by Lodge in US Patent 609154 (Lodge, 1898).
(a) Quad-ridge horn antenna (Van der Merwe et al., 2012).
(b) Four square antenna (Stutzman and Buxton, 2000).
Figure 1.3: Examples of broadband antennas.
coaxial cable. With the addition of ridges, this antenna can be dual linearly-polarized and its bandwidth can go up to 15.7:1 of bandwidth (Van der Merwe et al., 2012) (cf. Fig. 1.3(a)).
Vivaldi, tapered slot or flared notch antenna
The Vivaldi antenna produces an endfire directive linearly polarized radiation. This antenna can easily achieve a bandwidth of 20:1 (Gazit, 1988). Its tapered profile provides a good impedance match to a 50Ω coaxial cable.
Archimedean and equiangular spiral
Commercial spiral antennas can achieve bandwidths larger than 20:1. Its input impedance in free space is about 188Ω. An impedance transformer is needed to adapt to a 50Ω coaxial cable.
They exhibit excellent circular polarization (Kaiser, 1960), thanks to their rotational symmetry.
Four square
The four square antenna was patented in 1999 by the Virginia Tech Antenna Group (cf. Fig.
1.3(b)). It provides dual orthogonal linear polarization. Its bandwidth goes up to 1.8:1 (Stutz- man and Buxton, 2000). Its input impedance can be designed to be around 100Ω.
For airborne applications, planar structures have some advantages, such as the possibility to be mounted in the skin of an aircraft. In this case the biconical, horn and Vivaldi antennas can be too cumbersome. Additionally, if we want circular polarization the spiral antenna provides it naturally.