ABSTRACT
In this paper, there is an introduction in c hapter one, there are motivation, modes of operation, analysis of helix and modified helices in chapter two, there are helical antenna wave dispersion and radiation resistance in chapter three about helical antenna. We can see an example for helical antenna in chapter four. In chapter five, there are five topics. First one is feed impedance, second is polarization, third is summary, fourth is conclusions and the last one is references.
1
CHAPTER ONE INTRODUCTION A helical antenna is an antenna consisting of a conducting wire wound in the form of a helix. In most cases, helical antennas are mounted over a ground plane. Helical antennas can operate in one of two principal modes: normal (broadside) mode or axial (or end-fire) mode.
A helical antenna is a specialized antenna that emits and responds to electromagnetic fields with rotating (circular) polarization. These antennas are commonly used at earth-based stations in satellite communications systems. This type of antenna is designed for use with an unbalanced feed line such as coaxial cable. The center conductor of the cable is connected to the helical element, and the shield of the cable is connected to the reflector. To the casual observer, a helical antenna appears as one or more "springs" or helixes mounted against a flat reflecting screen. The length of the helical element is one wavelength or greater. The reflector is a circular or square metal mesh or sheet whose cross dimension (diameter or edge) measures at least 3/4 wavelength. The helical element has a radius of 1/8 to 1/4 wavelengths, and a pitch of 1/4 to 1/ 2 wavelength. The minimum dimensions depend on the lowest frequency at which the antenna is to be used. If the helix or reflector is too small (the frequency is too low), the efficiency is severely degraded. Maximum radiation and response occur along the axis of the helix. Helical antennas are commonly connected together in socalled bays of two, four, or occasionally more elements with a common reflector. The entire assembly can be rotated in the horizontal (azimuth) and vertical (elevation) planes, so the system can be aimed toward a particular satellite. If the satellite is not in a geostationary orbit, the azimuth and elevation rotators can be operated by a computerized robot that is programmed to follow the course of the satellite across the sky.
The helical antenna has a long history and has been the object of much study and development over the last half century centur y since its invention in 1946 [Kraus, 1976]. It is an interesting antenna with unique characteristics, being capable of high gain, wide bandwidth, and circular polarization. As a result, it has been used in a wide range 2
CHAPTER ONE INTRODUCTION A helical antenna is an antenna consisting of a conducting wire wound in the form of a helix. In most cases, helical antennas are mounted over a ground plane. Helical antennas can operate in one of two principal modes: normal (broadside) mode or axial (or end-fire) mode.
A helical antenna is a specialized antenna that emits and responds to electromagnetic fields with rotating (circular) polarization. These antennas are commonly used at earth-based stations in satellite communications systems. This type of antenna is designed for use with an unbalanced feed line such as coaxial cable. The center conductor of the cable is connected to the helical element, and the shield of the cable is connected to the reflector. To the casual observer, a helical antenna appears as one or more "springs" or helixes mounted against a flat reflecting screen. The length of the helical element is one wavelength or greater. The reflector is a circular or square metal mesh or sheet whose cross dimension (diameter or edge) measures at least 3/4 wavelength. The helical element has a radius of 1/8 to 1/4 wavelengths, and a pitch of 1/4 to 1/ 2 wavelength. The minimum dimensions depend on the lowest frequency at which the antenna is to be used. If the helix or reflector is too small (the frequency is too low), the efficiency is severely degraded. Maximum radiation and response occur along the axis of the helix. Helical antennas are commonly connected together in socalled bays of two, four, or occasionally more elements with a common reflector. The entire assembly can be rotated in the horizontal (azimuth) and vertical (elevation) planes, so the system can be aimed toward a particular satellite. If the satellite is not in a geostationary orbit, the azimuth and elevation rotators can be operated by a computerized robot that is programmed to follow the course of the satellite across the sky.
The helical antenna has a long history and has been the object of much study and development over the last half century centur y since its invention in 1946 [Kraus, 1976]. It is an interesting antenna with unique characteristics, being capable of high gain, wide bandwidth, and circular polarization. As a result, it has been used in a wide range 2
of applications including satellite communications, radio astronomy, and wireless networking. This dissertation presents a fundamental advancement of the basic axial mode helix design. This new form of helix antenna, called the Stub Loaded Helix (SLH) antenna, offers the advantage of a significant reduction in helix antenna size with only a relatively small corresponding reduction in performance. The performance reduction in many applications is not relevant a nd the application requirements are still satisfied. The result is a new antenna ant enna design that offers the performance charact eristics and advantages of the conventional axial mode helix but in a much more compact physical size envelope. The original aspects of the work described in this dissertation are covered by U.S. patent #5,986,6 21. All intellectual properties related to this patent are controlled and administered by Virginia T ech Intellectual Properties, Pr operties, Inc. Inc.
The helical antenna is a hybrid of two simple radiating elements, the dipole and loop antennas. A helix becomes a linear antenna when its diameter approaches zero or pitch angle goes to 90 o . On the other hand, a helix of fixed diameter can be seen as a loop antenna when the spacing between the turns vanishes (a (a
!
0o ) .
Helical antennas have been widely used as simple and practical radiators over the last five decades due to their remarkable and unique properties. The rigorous analysis of a helix is extremely complicated. Therefore, radiation properties of the helix, such as gain, far-field pattern, axial ratio, and input impedance have been investigated using experimental methods, approximate analytical techniques, and numerical analyses. Basic radiation properties of helical antennas are reviewed in this chapter.
The geometry of a conventional helix is shown in Figure that describe a helix are summarized s ummarized below. D S
!
diameter of helix
spacing between turns
!
N number of turns !
C
A
!
!
circumference of helix
!
D
total axial length N N S S !
pitch angle a pitch !
3
2.1a.
The parameters
If one turn of the helix is unrolled, as shown in Figure
2.1(b),
between S , C , a and the length of wire per turn, L , are obtained as:
S
L sin a
!
!
C tan
a
=
Figure 1.1 A sk etch of a typical helical antenna
4
the relationships
CHAPTER TWO SURVEY OF HELICAL ANTENNAS
2.1 Motivation
The original motivation for this work came from the desire to develop a reduced size helix antenna for use in satellite communications links for both earth terminals and on space platforms. Although technological trends are toward the use of higher frequencies in the microwave and millimeter regions where greater bandwidths are available, there are still a number of satellite systems that utilize the VHF and UHF frequency bands. The most prominent of these is the U.S. Navy FLTSATCOM system which utilizes a network of geosynchronous satellites to provide worldwide coverage to bases, ships, and mobile ground forces.
At VHF and UHF frequencies, the physical dimensions of a conventional axial mode helix can be large enough to present difficulties, particularly for mobile forces and on the ever 2 increasingly crowded top sides of today's naval ships. A typical helix for FLTSATCOM applications can have a helix diameter on the order of one foot (30.5 cm) and an axial length of 1 2 feet (4 meters) or greater with a ground plane on the order of 4 feet (1.3 meters). Mounting and pointing of such a large structure presents mechanical problems. Any reduction in antenna size without significantly impacting performance would be very desirable.
In every aspect of wireless communications today, there is a desire to minimize antenna size. The technological progress that has produced significant advances in the miniaturization of components and circuitry has not been mirrored by corresponding advancements in antenna miniaturization, for a very fundamental reason. Solid state components are only now approaching structure sizes that are comparable to the wavelength of an electron. Most antennas operate in the size regime where their physical dimensions are on the order of the wavelength of operation. Much theoretical 5
work over the years, as well empirical results, indicate that antenna size reduction results in compromises of some key performance characteristics, most notably efficiency and bandwidth. It is the goal and art of engineering to minimize and optimize these compromises to provide a solution that meets the requirements of each specific application. It is hoped that the Stub Loaded Helix antenna has achieved an appropriate balance between performance and compromises in order to be considered a useful contribution.
2.2 Modes of Operation
2.2.1 Transmission Modes
An infinitely long helix may be modeled as a transmission line or waveguide supporting a finite number of modes. If the length of one turn of the helix is small compared to the wavelength, L , the lowest transmission mode, called the T 0 mode, occurs. Figure 2.2a shows the charge distribution for this mode.
When the helix circumference, C , is of the order of about one wavelength (C }1 ) , the second-order transmission mode, referred to as the T 1 mode, occurs. The charge distribution associated with the T 1 mode can be seen in Figure
2. 2 b.
Higher-
order modes can be obtained by increasing of the ratio of circumference to wavelength and varying the pitch angle.
2.2.2 Radiation Modes
When the helix is limited in length, it radiates and can be used as an antenna. There are two radiation modes of important practical applications, the normal mode and the axial mode. Important properties of normal-mode and axial-mode helixes are summarized below.
6
Figure 2.1 (a) Geometry of helical antenna; (b) Unrolled turn of helical antenna
Figure 2.2 Instantaneous charge distribution for transmission modes: (a) The lowest-order mode (T0); (b) The second-order mode (T1)
7
2.2.2.1 Normal Mode
For a helical antenna with dimensions much smaller than wavelength ( NL ) , the current may be assumed to be of uniform magnitude and with a constant phase along the helix . The maximum radiation occurs in the plane perpendicular to the helix axis, as shown in Figure
2.3a.
This mode of operation is referred to as the ³normal
mode´. In general, the radiation field of this mode is elliptically polarized in all directions. But, under particular conditions, the radiation field can be circularly polarized. Because of it small size compared to the wavelength, the normal-mode helix has low efficiency and narrow bandwidth.
2.2.2.2 Axial Mode
When the circumference of a helix is of the order of one wavelength, it radiates with the maximum power density in the direction of its axis, as seen in Figure
2.3b.
This radiation mode is referred to as ³axial mode´. The radiation field of this mode is nearly circularly polarized about the axis. The sense of polarization is related to the sense of the helix winding.
In addition to circular polarization, this mode is found to operate over a wide range of frequencies. When the circumference ( C ) and pitch angle (a ) are in the ranges of
< < and 1
2º
a 15º , the radiation characteristics of the
axial-mode helix remain relatively constant. As stated in, ³if the impedance and the
pattern of an antenna do not change significantly over about one octave ( = 2 ) or more, we will classify it as a broadband antenna´. It is noted that the ratio of the upper frequency to the lower frequency of t he axial-mode helix is equal to
. This is close to the definition of broadband antennas. For the
reason that the axial-mode helix possesses a
8
Figure 2.3 Radiation patterns of helix: (a) Normal mode; (b) Axial mode
number of interesting properties, including wide bandwidth and circularly polarized radiation, it has found many important applications in communication systems.
9
2.3 Analysis of Helix
Unlike the dipole and loop antennas, the helix has a complicated geometry. There are no exact solutions that describe the behavior of a helix. However, using experimental methods and approximate analytical or numerical techniques, it is possible to study the radiation properties of this antenna with sufficient accuracy. This section briefly discusses the analysis of normal-mode and axial-mode helices.
2.3.1 Normal-Mode Helix
The analysis of a normal-mode helix is based on a uniform current distribution over the length of the helix. Furthermore, the helix may be modeled as a series of small loop and short dipole antennas as shown in Figure
2.4.
The length of the short
dipole is the same as the spacing between turns of the helix, while the diameter of the loop is the same as the helix diameter.
Since the helix dimensions are much smaller than wavelength, the far-field pattern is independent of the number of turns. It is possible to calculate the total farfield of the normal-mode helix by combining the fields of a small loop and a short dipole connected in series. Doing so, the result for the electric field is expressed as
where
),
is the propagation constant, =
(2.1)
is the intrinsic impedance of the
medium, and I0 is a current amplitude. As noted in ( 2.1), the
and
components of
the field are in phase quadrature. Generally, the polarization of this mode is elliptical with an axial ratio given by
,
(2.2)
10
The normal-mode helix will be circularly polarized if the condition AR
!
1 is satisfied.
As seen from ( 2.2), this condition is satisfied if the diameter of the helix and the spacing between the turns are related as
(2.3)
C
It is noted that the polarization of this mode is the same in all directions except along the z-axis where the field is zero. It is also seen from ( 2.1) that the maximum radiation occurs at
90º ; that is, in a plane normal to the helix axis.
!
2.3.2 Axial-Mode Helix
Unlike the case of a normal-mode helix, simple analytical solutions for the axial mode helix do not exist. Thus, radiation properties and current distributions are obtained using experimental and approximate analytical or numerical methods.
The current distribution of a typical axial-mode helix is shown in Figure
2.5.
As
noted, the current distribution can be divided into two regions. Near the feed region, the current attenuates smoothly to a minimum, while the current amplitude over the remaining length of the helix is relatively uniform. Since the near-feed region is small compared to the length of the helix, the current can be approximated as a travelling wave of constant amplitude. Using this approximation, the far-field pattern of the axial-mode helix can be analytically determined. There are two methods for the analysis of far field pattern. In the first method, an N-turn helix is considered as an array of N elements with an element spacing equal to
S .
The total field pattern is then
obtained by multiplying the pattern of one turn of the helix by the array factor. The result is
(2.4)
11
where c is a constant coefficient and
!
kS .cos
a . Here, a is the phase shift
between successive elements and is given as
In (2.4), cos
(2.5)
is the element pattern and
is the array factor for a uniform
array of N equally-spaced elements. As noted from ( 2.5), the Hansen-Woodyard condition is satisfied. This condition is necessary in order to achieve agreement between the measured and calculated patterns.
In a second method, the total field is directly calculated by integrating the contributions of the current elements from one end of the helix to another. The current is assumed to be a travelling wave of constant amplitude. The current distribution at an arbitrary point on the helix is written as
(l ) = I.exp(-jg
,
(2.6)
Where
l
!
the length of wire from the beginning of the helix to an arbitrary point
g=
= the total length of the helix
p phase velocity of wave propagation along the helix relative to the helix !
relative to the velocity of light , c
12
Figure 2.4 Approximating the geometry of normal-mode helix
Figure 2.5 Measured current distribution on axial-mode helix
=
according to Hansen-Woodyard condition) =2
d
!
!
azimuthal coordinate of an arbitrary point
unit vector along the wire
!
sin
y cos Ö
z sina Ö
13
The magnetic vector potential at an arbitrary point in space is obtained as
( )
=
exp(jdd
(2.7)
Where u
a
k a
!
radius of the helix
B
d
!
B
sin
!
!
g
k a
cos tana
Finally, the far-field components of the electric field, E and E , can be expressed as
= -jw[( cos
=-jw( cos
sin )cos + sin ] ,
- sin ) .
(2.8)
(2.9)
2.3.3 Empirical R elations for Radiation Properties of Axial-Mode Helix
Approximate expressions for radiation properties of an axial-mode helix have also been obtained empirically. A summary of the empirical formulas for radiation characteristics is presented below. These formulas are valid when 1 2ºa 15º ,
<
.
An approximate directivity expression is given as
D=
and
N S ,
(2.10)
are, respectively, the circumference and spacing between turns of the helix
normalized to the free space wavelength ( ) . Since the axial-mode helix is nearly lossless, the directivity and the gain expressions are approximately the same.
14
In 1980, King and Wong reported that Kraus¶s gain formula ( 2.10) overestimates the actual gain and proposed a new gain expression using a much larger experimental data base. The new expression is given as
(2.11)
where
is the free-space wavelength at peak gain.
In 1995, Emerson proposed a simple empirical expression for the maximum gain based on numerical modeling of the helix. This expression gives the maximum gain in dB as a function of length normalized to wavelength (
10. 5 + 1. 2
22
- 0.0726
=
.
. (2.12)
Equation (2.12), when compared with the results from experimental and theoretical analyses, gives the gain reasonably accurately.
Half -Power Beam width
The empirical formula for the half-power beam width is
HPBW =
(degrees) .
(2.13)
A more accurate formula was later presented by King and Wong using a larger experimental data base. T his result is
HPBW =
15
(2.14)
Input Impedance
Since the current distribution on the axial-mode helix is assumed to be a travelling wave of constant a mplitude (Section 2.3.2), its terminal impedance is nearly purely resistive and is constant with frequency. The empirical formula for the input impedance is
R
!
140
(ohms).
(2.15)
The input impedance, however, is sensitive to fe ed geometry. Our numerical modeling of the helix indicated that ( 2.15) is at best a crude approximation of the input impedance.
Bandwidth
Based on the work of King and Wong, an empirical expression for gain bandwidth, as a frequency ratio, has been developed:
(2.16)
where and are the upper and lower frequencies, respectively, from equation ( 2.11), and
G
is the peak gain
is the gain drop with respect to the peak gain.
2.3.4 Optimum Performance of Helix
Many different configurations of the helix have been examined in search of an optimum performance entailing largest gain, widest bandwidth, and/or an axial ratio closest to unity. The helix parameters that result in an optimum performance are summarized in Table 2.1. There are some helices with para meters outside the ranges in Table 2.1 that exhibit unique properties. However, such designs are not regarded as optimum, because not all radiation characteristics meet desired specifications. A
16
summary of the effects of various parameters on the performance of helix is presented below.
Table 2.1 Parameter ranges for optimum performance of helix
Circumf erence
As shown in Figure 2.6, it is noted that the optimum circumference for ac hieving the peak gain is around 1.1 and is relatively independent of the length of the helix. Other results show that the peak gain smoothly drops as the diameter of the helix decreases (Figure 2.7). Since other parameters of the helix also affect its properties, a circumference of 1.1 is viewed as a good estimate for an optimum performance.
Pitch Angle
Keeping the circumference and the length of a helix fixed, the gain increases smoothly when the pitch angle is reduced, as seen in Figure reduction
17
2.8.
However, the
Figure 2.6 Gain of helix for diff erent lengths as f unction of normalized circumf erence (C )
Figure 2.7 Peak gain of various diameter as D and a varied (circles), D f ixed and a varied
of pitch angle is limited by the bandwidth performance. That is, a narrower bandwidth is obtained for a helix with a smaller pitch angle. For this reason, it has been generally agreed that the optimal pitch angle for the axial-mode helix is about 18
.
Number of Turns
Many properties, such as gain, axial ratio, and beam width, are affected by the number of turns. Figure 2.9 shows the variation of gain versus the number of turns. It is noted that as the number of turns increases, the gain increases too. The increase in gain is simply explained using the uniformly excited equally-spaced array theory. However, the gain does not increase linearly with the number of turns, and, for very large number of turns, adding more turns has little effect. Also, as shown in Figure 2.10,
the beam width becomes narrower for larger number of turns. Although adding
more turns improves the gain, it makes the helix larger, heavier, and more costly. Practical helices have between 6 and 16 turns. If high gain is required, array of helices may be used.
Conductor Diameter
This parameter does not significantly affect the radiation properties of the helix. For larger conductor diameters, slightly wider bandwidths are obtained. Also, thicker conductors can be used for supporting a longer antenna.
Ground Plain
The effect of ground plain on radiation characteristics of the helix is negligible since the backward traveling waves incident upon it are very weak. Nevertheless, a ground plane with a diameter of one-half wavelength at the lowest frequency is usually recommended.
19
Figure 2.8 Gain versus f requency of 30.8-inch length and 4.3-inch diameter helix for diff erent pitch angles.
Figure 2.9 Gain versus f requency for 5 to 35-turn helical antennas with 4.23-inch diameter 20
Figure 2.10 Radiation patterns for various helical turns of helices with a
!
and C
!
10cm. at
3Hz GHz.
2.4 Modif ied Helices
Various modifications of the conventional helical antenna have been proposed for the purpose of improving its radiation characteristics. A summary of these modifications is presented below.
2.4.1 Helical Antenna with Tapered End
Nakano and Yamauchi have proposed a modified helix in which the open end section is tapered as illustrated in Figure
2.11.
This structure provides significant
improvement in the axial ratio over a wide bandwidth. According to them, the axial ratio improves as the cone angle
is increased. For a helix with pitch angle of
and 6 turns followed by few tapered turns, they obtained an axial ratio of 1:1.3
over a frequency range of 2.6 to 3.5 GHz.
21
2.4.2 Printed R esonant Quadrif ilar Helix
Printed resonant quadrifilar helix is a modified form of the resonant quadrifilar helix antenna first proposed by Kings. The structure of this helix consists of 4 micro strips printed spirally around a cylindrical surface. The feed end is connected to the opposite radial strips as seen in Figure 2.12. The advantage of this antenna is a broad beam radiation pattern (half-power beam width "
). Additionally, its compact
size and light weight are attractive to many applications especially for GPS system.
2.4.3 Stub-Loaded Helix
To reduce the size of a helix operating in the axial mode, a novel geometry referred to as stub-loaded helix has been recently proposed. Each turn contains four stubs as illustrated in Figure
2.13.
The stub-loaded helix provides comparable
radiation properties to the conventional helix with the same number of turns, while offering an approximately 4:1 reduction in the physical size.
2.4.4 Monopole-Helix Antenna
This antenna consists of a helix and a monopole, as shown in Figure
2.14
. The
purpose of this modified antenna is to maintain operation at two different frequencies, applicable to dual-band cellular phone systems operating in two different frequency bands (900 MHz for GSM and 1800 MHz for DCS1800).
22
Figure 2.11 Tapered helical antenna conf iguration.
Figure 2.12
turn half -wavelength printed resonant quadrif ilar helix .
23
Figure 2.13 Stub-loaded helix conf iguration .
Figure 2.14 Monopole-helix antenna .
24
CHAPTER THREE
3.1 Helical Antenna Current Density
To calculate the current density of the helical antenna a simplified geometry was assumed with infinitely thin wire and a single complete loop around the tube at either end to complete the circuit. Thus the generalized antenna model used to calculate the current density consists of two helical windings, each making one rotation in a distance and displaced by 0.5 radius of the antenna is
.
. The total length of the antenna is L, and the
This is the simplified antenna configuration employed by
the numerical model when making a comparison with the experimental results in section 3.2. With the origin in the middle of the antenna the
component of the
current density can be written as
(3.1)
where
=
,
, and F is defined by equation 2.4 Equation ( 2.17) can
be Fourier transformed into the more useful coordinates of the azimuthal mode number m, and the wave number k.
(3.2)
25
This has the property
(3.3)
When the parallel wave number is close to the peak in the current density spectrum, the azimuthal wave number is predominately m =
. This antenna has
positive helicity, in the positive k direction m = +1 is dominant, while in the negative k direction m = -1 is predominant. The dominance of m = +1 in the positive k direction is shown in figure 3.1(b). Figure 3.1(a) shows how the k spectra becomes more selective as the length of t he antenna is increased. The total length of the antenna used for Basil was L = 1.5
3.2 Helical Antenna Wave Dispersion and Radiation R esistance
A helical antenna was constructed in the hope of producing plasma with the m = -1 azimuthal mode. It would be expected that if a plasma were produced in the
<0
direction that the wave mode responsible for the plasma production would be m = 1. It was immediately clear from the light emission that the helical antenna only produced plasma in the direction of positive azimuthal modes. Measurements in both directions of the wave were taken by reversing the direction of the static magnetic field. Azimuthal magnetic wave field measurements confirmed that the mode in the direction of strong plasma was m = 1. The plasma extended a short
26
Figure 3.1 The current density spectrum of the simple helical antenna, r = 0.0225 m, = 0.18 m. (a) Axial spectra for azimuthal mode number m = +1 for diff erent antenna lengths, L , L = 2 (dotted), L = 1.5 (solid), L = 1
(dashed), and L = 0.5
(dot-dash). (b) Azimuthal mode number spectra for parallel wave number 35 L = 1.5
, and
.
Distance, approximately 10cm, in the negative k direction as can be seen in figure 3.2(a). Measurements of the azimuthal fields in this plasma revealed a low amplitude
m = +1 mode probably coupled by the end sections of the antenna. The
wave propagating in the direction of right hand rotation of the antenna travels from under the antenna along the discharge.
The measured dispersion shown in figure 3.3(a) gives an indication of the higher selectivity of the helical antenna, with a smaller range of parallel wavelengths being observed than with the double saddle coil antenna. It was found that attempts to significantly vary the wavelength by increasing the power resulted in unstable discharges. An example of this is shown in figure 3.4, which shows the ion saturation current of a Langmuir probe in a fix position as a function of time for increasing power. As the power is increased the discharge becomes unstable. However, eventual an equilibrium condition is established where further increases in power do not increase the on axis density significantly. Thus, for a helical antenna with a total length equal to, or larger than the wavelength of the antenna, the operating regime is limited to the region of the preferred parallel wavelength of the antenna.
27
Figure 3.3(b) compares the measured radiation resistance with that calc ulated by the numerical model which used the measured radial density profiles shown in figure 3.5. The radiation resistance measured for the helical antenna is more peaked than that of the double saddle coil, which is consistent with the higher selectivity of the helical antenna as indicated by the current density spectrum. The radiation resistance reaches
a maximum at approximately
dispersion curve correspondsto
, which from the
. This is in agreement with figure
3.1 where the current density
Figure 3.2 Longitudinal measurements of (a) electron density (b) and temperature on axis (c) axial magnetic wavef ield amplitudes and (c) phase and (d) 3 azimuthal magnetic wave f ield amplitudes and (e) phase 30msec into an Argon discharge with a helical antenna at a static f ield of 960 Gauss and f illing pressure of 30mTorr.
28
The position of the antenna is indicated by the vertical dashed lines and the end of the static field coils by the solid line.
Figure 3.3 Comparison of measured and calculated dispersion and radiation resistance of the helicon wave launched by the helical antenna in argo.
29
Figure 3.4 Power scan with a helical antenna,
=
576 Gauss, pressure = 30 mTorr.
Spectrum reaches a maximum at approximately the same value. It also agrees with the numerical model which also reaches a maximum at approximately the sa me value.
It is noticeable that the radiation resistance of the helical antenna is much higher than the double saddle coil antenna. However there is a significant discrepancy between the measured and calculated radiation resistance for the higher values of
. As discussed in section the results from the numerical model can be strongly
influenced by systematic errors in the density profiles. This is especially the case with the helical antenna which has a higher selectivity of parallel wavelength. However, Kamenski demonstrated that by altering the maximum in the density profiles only slightly higher radiation resistances could be obtained, which are not as high as the experimental results. The peak value of the radiation resistance for the helical antenna
30
is 4 times higher than for the double saddle coil antenna. Below the peak the radiation resistance drops off sharply, consistent with the current density spectrum and is in reasonable agreement with the model. Above the peak there appears a systematic discrepancy between the measured and model results which is not presently understood.
In figure 3. 2, which show longitudinal measurements for neon and krypton, it is clear that the plasma extends in the direction of left hand rotation of the antenna beyond the region of power deposition by the wave. This is due to ionization by electrons travelling from the region of power deposition. As expected the distance the plasma extends in this direction is strongly dependent on the gas, with the collision cross section, and thus the mean free path of the electrons being a function of the gas type and filling pressure. In an measurement at similar conditions to those in figure 3.2, but with a filling pressure of 13mTorr, the plasma extended 35cm past the antenna compared to
Figure 3.5 Radial density prof iles of Argon plasmas produced with a helical antenna as a f unction of applied f ield.
31
10cm as in the figure, demonstrating the dependence on pressure. Also noticeable in the axial density profiles is the peak in the density near the end of the discharge where the plasma reaches the end of the field. This is believed to be due to depletion of neutrals along the length of the discharge and supply of neutrals from the end of the tube and will be studied.
By comparing the radial density profiles obtained with the helical antenna (see figure 3.5 and those obtained with the double saddle coil antenna it can be seen that the densities obtained in both cases are similar in magnitude. However, comparing the corresponding plots of power coupled to the plasma for the helical antenna profiles and double saddle coil antenna profiles (see figure 3.4) it is clear that the power required to produce discharges of similar densities was much lower for the helical antenna. This is not surprising, as with only half the plasma, the plasma losses have also been halved. Thus if a plasma on only one side of the antenna is sufficient the helical antenna is far more efficient, but has a less flexible operating regime.
32
CHAPTER FOUR EXAMPLE FOR HELICAL ANTENNA
A helical antenna operating in the normal mode has N turns with diameter 2b and interturn spacing s. Both 2 b and
s
are very small in comparison to P / N and
are adjusted to radiate circularly polarized waves.
Find :
(a) its directive gain and directivity,
(b) its radiation resistance.
(Sol.)
(a)
X N [Q0 I e j F R E ( )[ aU js aN FT b 2 ] sin U 4T R
!
Ö
Ö
X , H !
1
a v Ö
L0
X
!
F I e j F ( )[aJ js aU FT b2 ]sinU 4T Ö
Ö
Circularly polarized: s = b 2
U !
P r !
(b)
2
a P av ! Ö
2T
´ ´ 0
T
0
r
!
2
X X F 2L 0 a Re[ v H ] ! ( N Is ) 2 sin 2 U 2 2 16T
1
Ö
U sin Ud Ud J !
2 P r 2
I
!
F 2L 0
L 0 ( N Is ) 2 3T
bT
( N Is) 2 G D !
! 40( N F 2T b 2 ) 2
33
4T U P r
!
3 2
T sin 2 U , D ! G D ( ) ! 1.5 2
CHAPTER FIVE
5.1 Feed impedance
A typical helical antenna has an input impedance of around 140 ohms. Kraus3 gives a nominal impedance of Z = 140C - with axial feed. This is a resistive impedance only at one frequency, probably near the center frequency. Matching the impedance to 50 ohms over a broad bandwidth would be more difficult than simply matching it well for a ham band. A simple quarter-wave matching section with a Zo ~ 84 ohms should do the trick for a single band. The matching section10 is often part of the helix: a quarter-wave of wire close to the ground plane before the first turn starts. It could also be on the other side of the ground plane, to separate impedance matching from the radiating element.
5.2 Polarization Circular polarization has two possible senses: right-hand ( HCP) and lefthand (LHCP). Since a helix cannot switch polarization, it is important to get it right: by the IEEE definition3,
HCP results when the helix is wound as though it were to fit in the
threads of a large screw with normal right-hand threads. Note that the classical optics definition of polarization is opposite to the IEEE definition. More important for a feed is that the sense of the polarization reverses on reflection, so that for a dish to radiate HCP polarization requires a feed with LHCP. For EME, reflection from the moon also reverses circular polarization, so that the echo returns with polarization reversed from the transmitted polarization. A helical feed used for EME would not be able to receive its own echoes because of cross-polarization loss.
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5.3 Summary
The helical antenna is an excellent feed for circular polarization. It is broadband and dimensions are not critical, and the patterns are well-suited to illumination of offset dishes. It is a particularly good feed for small offset dishes for satellite applications.
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CONCLUSION
A helical antenna for the capsule endoscope is designed. To encase the system in the capsule module and to obtain the omni-directional radiation pattem, the small sized normal mode helical antenna is designed. To enhance the bandwidth of the ant enna for transmitting the high data rate information, the end of the helix is connected to the ground. From the measured return loss and the radiation pattem, it is found that the designed antenna is suitable to use for the capsule endoscope. The shape and the size of the ground conductor can significantly influence the helical antenna performance. The ground conductor in the form of truncated cone has the highest favorable impact on the antenna gain, which was demonstrated both computationally and experimentally. The geometrical parameters of the conical ground conductor were optimized with the goal to maximize the antenna gain. The details of the optimization procedure were outlined. The obtained optimal parameters (cone diameters and height) are in good agreement with those used in our computations and experiments. The performed optimization of the conical ground conductor improves the antenna performance.
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R ef erances
1.] http://ourworld.compuserve.com/homepages/demerson/helix.htm or
2.
] http://www.tuc.nrao.edu/~demerson/helixgain/helix.htm
3. ] http://www.zeland.com
4. ] http://www.ansoft.com
5. ] http://www.qsl.net/wb6tpu/swindex.html
6. ] http://en.wikipedia.org/wiki/Helical_antenna
7.]http://related:scholar.lib.vt.edu/theses/available/etd-02102000 19330046/unrestricted/07chapter 2.PDF 2. Survey of Helical Antennas
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