GB2403599A

GB2403599A - Antenna combining electric and magnetic fields

Info

Publication number: GB2403599A
Application number: GB0404049A
Authority: GB
Inventors: Peter Normington
Original assignee: Individual
Current assignee: Individual
Priority date: 2003-09-16
Filing date: 2004-02-24
Publication date: 2005-01-05
Also published as: GB0404049D0

Abstract

The two components of an electromagnetic wave in free space or other dielectric media, can be generated separately and when combined in the correct ratio and in the correct phase and physical orientation, a real radiation resistance is observed at the terminals of the antenna. This patent application is the mathematics relating to forming the average of the two field systems over a given region in space and relating this to the basic problem of mixing electric and magnetic fields in the same region in space and equating the ratio of electric and magnetic fields to 120 f to form an antenna. The fundamental problem is to control the relative field strengths, orientation, and relative phase of electric and magnetic fields with a single minimal conductive geometry which is simple enough to analyse. All theory herein is presented on the basis of taking the ratio of average electric to average magnetic fields in a common region in space and equating this the conjugate of the intrinsic impedance of the media through which the EM wave is traveling.

Description

Section 1.1, Description

The basis of the original experimentation around the principle of mixing Electric and Magnetic Fields in the same physical space was carried out with the configuration shown in figure 1. A real radiation resistance was observed, however the antenna was poorly matched and so the following theory was developed.

Since the component of radiation which reaches the fare field of an antenna in free space is in the ratio of 120: 1 E to H. it would seem expedient to follow the proposal of Hately and Kabbery and mix the Fields in the physical aperture of the antenna in precisely this ratio. Also, because the intensity of the fields around the physical aperture are not constant, it would seem reasonable to take an average value of each field in the area where the fields interact and to see if this value has physical meaning.

Another assumption made is that the resulting antenna structure is small compared to the wave length of radiation and so phase related phenomena pertaining specifically to physical size of the antenna can be ignored during the derivation. The validity of this approach is given as a proof by comparison with the accepted equation for characteristic impedance of twin balanced lead transmission line, which is derived by the procedure outlined above. The theory is developed around the conductive geometry as shown in figure 1.

The general case for any dielectric media is: z = Eav Conjugate Equationl Taking this as air we have: 120z =- Equation2 Hav To begin with the average value of electric field, (see figure 6) r It can be shown that: Eav = Jig Equation 3 where v Scaler potential between the straight conductors of figurer s Depth of the aperture as depicted in figure 4 If we define a parameter k such that: Jv sind/2 _ do k _ s Equation 4 Old straight conductors depicted in figurer Equation 2 represents the ratio of the average value of electric field to the max value

of electric field, we can therefore write:

E = kv I d Equation 5 The magnetic field external to the coil can be written as: H(r)=ni.rO= I Equation6 r 2r where n Number of turns on the coil i Current in the coil I Length of the coil r Radial distance from the center of the coil I The equivalent current in a solid conductor with radius equal to the coil r,, Radius of coil The first term on the right of equation 4 is the standard definition of the magnetic field strength a distance r from a cylindrical coil carrying current i. The second term on the right of equation 4 is the definition of magnetic field strength a radial distance r from the center of a solid conductor. In this instance however the Field vector is taken as being rotated by 90 degrees to bring it parallel to the axis of the conductor.

The average value of the H field is then given by:

Hav r +s Equation 7 2= rO Which evaluates to: Han ln(1 ±) Equation 8 2m rO If we now define a characteristic impedance: Za = 120'z- Equation9 This represents the characteristic impedance of the transmission line formed by the outside of the cylindrical coil and the two conductors. If we assume that the average electric and magnetic field over the region of interaction is in a ratio of 120 we can take this value and multiply it by the aspect ratio of antennas physical aperture to form equation 10. The general principle here can be proven using field mapping.

We can now state that: z = _ = an _ = 120;Z- Equation 10 a I HaV I I Equation 8 can then be written as: Hav 240 id ln(1 ± Equation 11 Taking the ratio as stated in equation 2: 120.'z = EaV = kill d Equation 12 Hap Vl 2 ln(1 ± 240'z ds rO Giving us a match condition onto free space of: 2;z =-In(1 ±) Equation 13 ks rO s It can be seen from equation 13 that the depth of the aperture s as shown graphically in figure 4 is finite and that in fact it is a small fraction of r,, . If that is the case we can proceed to an good approximation for the input impedance to the antenna derived from equations 6 and equation 9 as follows.

The input impedance of the antenna is given by the ratio of the terminal voltage to the terminal current as: z V Equation 14

- In.

From equation 6 and equation 9 we have that: n rO al Equation 15 2402 From which we have: 240.'z2nr c! Z = 0 Equation 16 In 12 Section 1.2, Significance of the capacitor depicted in figure 1 Figure 5 shows the antennas equivalent circuit. The inductance represents the reactance due to the fields inside the coil. The series reactances of the inductor and the capacitor can impose any relative phase between the electric and the magnetic vectors.

In the case of air dielectric the required phase is around zero and the required condition is produced by: XL = XC Equation 17 Section 1.3, Example of dielectric media other than air (sea water) Evaluating equation I for water at 100MHz: /, \ 1 j2'T. lOOe6.4'Te - 7 Zaire= ^\1 4 conjugate=14arg-45" Ohms From here the derivation proceeds as section 1.1 we arrive again at equation 13 however, equation 10 now reads: TO 7 Z =-= av -= {14 erg45} I Ohms, Equation 19 Equation 15 now reads: nirO al Equation 20 = 1 2'T {14arg- 45 }d And the input impedance is given by: z _ v _ 2'z{14 arg- 45 )durO

Z _ - _

in i 12 Equation 21 Because the input impedance of the antenna is designed as the conjugate of the intrinsic impedance of water, the actual impedance seen at the terminals when the antenna is loaded by this media is then simply given by: z _ 2'z(14)durO inw i 2 Equation 22 Section 1.3, Influence of the factor fir The material inside the coil could have >l without affecting the physics of the derivations as presented, other than to lower the frequency of radiation by a factor given by: In =- Equation 23 This is simply because the phase is established by the series resonance depicted in figure 5.

Section 1.4, Long wire antennas and the proof of the theory developed in section 1.1 Figure 7 shows a section of a long twin lead transmission line. It will be demonstrated is that a contour integral between these two conductors taking the ratio of average electric and average magnetic fields and setting this ratio to 120c results in the equation for the characteristic impedance of balanced twin lead in free space.

Starting with Electric Field, we have the average Electric field as: E = v I s Equation 24

The average Magnetic Field is:

I rOIs 1 Equation25 2rcs

JO

Equation 25 evaluates to: Han = ln(1 + ) Equation 26 rO Since we require a fare field ratio defined by the intrinsic impedance we can write: Eav = | j MU = 120}z Equation27 Hav + j0)ú If we now define a characteristic impedance, which by definition, must conform to the ratio of voltage to current all along the matched (onto free space) transmission line, we can write the following equation: Z0 = V / I Equation 2X SZo rO Equation 29 Now, taking the ratio as stated in equation 27 we have that: Eav V / S Equation 30 120'z = = Hv ln(1 ±) sZO rO Which reduces to: Zig 120 ln(1 + ) Equation 31 With a change of variable into standard form, equation 31 then reads: ZO = 120 In(-) Equation 32 r2 1() This equation was derived on the basis of forming a match onto free space but has resulted in the definition of characteristic impedance of twin lead which represents the load impedance of a transmission line as seen at the terminals. It was proven during practical experimentation that taking Zo=75 Q in equation 32 and arranging the twin lead geometry accordingly does indeed provide a 75Q match onto free space. QED Section 2.1, Discussion of configurations and design equations Configurations 1-2 Configurations 1-2 are connected as per figure 1 and produces radiation which is long in wavelengths compared to the physical size of the antenna. The configuration produces an omnidirectional radiation pattern. To a close approximation the antenna radiation pattern will therefor be that of a Hertzian dipole. Directivity wild be 1.5 numerical, or 1.76dBi balanced and 4.76dBi unbalanced with the E vector normal to ground. The physical geometry of the antenna is determined by equation 16 as Z 240 n,Od Equation 16 Where Number of turns on the coil Radius of coil d Seperation of the E

field rods

I Circumference of antenna 1\ In this instance the length parameter in the denominator is the circumference of the antenna structure.

The approach to constructing these antennas is to pick a reasonable value for the number of turns of the coil and to place a reasonable gap between the turns consistent with keeping the feed through capacitance to a minimum (a reasonable value to pick is around 10 - 20 turns). The number of turns is also consistent with achieving the smallest possible structure. The coil is then bent around to form a toroid. Input impedance is chosen as the system characteristic impedance and from there the remainder of the parameters of the above equation can be solved. The assembly is electrically connected as shown in the electrical schematic of configuration 1. The E- field plates are depicted as C1. The unwanted part of the coils reactance is trimmed out using C2 leaving an in phase E and H field with the radiation resistance of the antenna across the input terminals as required. to meet all conditions for radiation.

It its to be pointed out that equation 16 was derived on the basis of reasonable approximations, however the equation gives results which are consistent with the requirements of the antennas industry which is fundamentally founded on trimming any antenna structure to meet a final specification by the use of network analysers.

Many Electromagnetic phenomena cannot be taken into account in the mathematical analysis of a practical radiating structure making the above procedure accepted practice rather than the exception.

Configurations 3-4 Configurations 3-4 are opened out version of configuration 1 and is exactly as depicted in figure 1. Directivity will be slightly higher than Configuration 1 at around 6dBi balanced 9dBi unbalanced respectively. The exact figure will depend on final chosen geometry.

The approach for construction is the same as for configurations 1-2 only this time the denominator of equation 16 is simply taken as the length of the antenna.

Configurations 5-6 Configurations 5-6 are the magnetic version of configuration 1 and will have the same electromagnetic properties. The antennas are configured as a series resonant circuit with an inductor followed by a capacitor followed by a second inductor. The two coils are arranged so that the H field is cumulative in the physical aperture. Directivity will be 1.76dBi balanced and 4.76dBi unbalanced. Fundamentally however the principle of operation is the same with the coils reactance being cancelled by the capacitors reactance which then brings the E and H fields into the required phase and orientation and a real radiation resistance is observed at the terminals of the antenna.

The governing equation for these configurations is not derived in section 1 but is simply stated here as: 1) z 9607z nrOs Equation 33 in 12 Number of Where n turns on one coil Radius of the coils S Separation of the two conductive surfaces of the coils Length of each coil The approach for the construction is to choose reasonable values for the number of turns, the appropriate input impedance, and then to solve the remainder of the parameters in equation 33 consistent with small size as outlined in the description of configuration 1-2 Configurations 7-8 Configurations 7-8 are again an opened out version of configuration 3 and will have 3dB higher directivity than the balanced or unbalanced antennas depicted in configurations 5-6. The antenna will produce a figure of eight pattern in the H-plane with a gain of 4.77dBi when run balanced and 7.77dBi when run unbalanced. The design equation and construction approach are the same as configuration 5-6 however the presence of the ground for unbalanced operation will mean a little network analyser work will invariably be required to match the antenna.

Configurations 9-10 Configurations 9-lO result directly from the proof of the validity of taking averages of electromagnetic fields and in this form they are little more than Beverage antennas with the unique feature that there is no load resistor terminating the end of the antenna.

The antenna structure assumes that several cycles of phase are present over the length of the antenna and under these circumstances placing a load resistor on the end of the antenna actually reduces the gain of the antenna. As long as the above condition is met the antenna's input impedance is fixed and does not vary with Frequency. The only parameter which does change with frequency is the directive gain of the antenna which Is given by: D = 1 OLog1O (121 / i) Equation 34 Where 7 Length of line 1 Wave length of operation And the input impedance of the antenna is given by: Zin = 120 ln(l / r2) Equation 35 These equations relate to the balanced form of the antenna and the symbols for equation 35 are the accepted definition for the characteristic impedance of twin lead.

The unbalanced form of the antenna has design equations: D = lOLog 1O (241 / i) Equation 36 The input impedance of the antenna is given by: Zin 601n(; / r2) Equation 37 Equation 37 is the accepted equation for the characteristic impedance of unbalanced circular mcrostrip. J.

Configuration 11-14 Configurations 11-14 are slow wave version of configuration 5, constructed to prove that the directivity of the long wire antennas is proportional to the number of normalised wavelengths in the meander or delay line as opposed to the length of the antenna. This antenna can also be run in balanced and unbalanced modes. The directivity of the unbalanced mode being 3dB above balanced. The antenna dimensions and input impedance are governed by the above equations for configurations 9-10 as long as the gain equations are calculated with the total electrical length of line. The effect is to reduce the length of the antenna while maintaining gain.

Configurations 15-16 Configurations 15-16 represent the next logical step in the slow wave concept. The unique feature of this antenna configuration however is that the phase length of the line is imposed on the transmission line by employing phase shifters with an input and output impedance equal to the characteristic impedance of the transmission line. This configuration gave very high directivity. The directivity of the unbalanced mode being 3dB above balanced. The practical form of the antenna used pi network phase shifters as shown in diagrams for configurations 15-18. The advantage offered here is that the phase delay of a pi phase shifter operated with input and output impedance equal to the load impedance is that a fixed 90 of phase occurs across the network and with many such shifters low frequency operation and high gain becomes possible.

Configuration 13-14 can produce gains in excess of 18dBi at HF frequency with a physical size of less than 0.5 by.035 by.010 meter. This antenna can also be run in balanced or unbalanced modes.

Design equations for the balanced antenna are: D = lOLogl0(12 360 ) + lOLog(121/) Equation 38 Where n Number of phase shifters / Length of Ime Wavelength of operation Zin 1201nr1 /r2) Equation39 The design equation for unbalanced antenna are: D = lOLogl0(24 360 ) + lOLog(241/) Equation40 Zin 60 1n(r1 / r2) Equation 41 Configurations 17- 18 Configurations 17-18 are basically the same as configuration 9-10 but is curled round to form an omnidirectional antenna radiation pattern. This antenna can also be run in balanced and unbalanced modes. The directivity of the unbalanced mode being 3dB above balanced. Directive gain of the antenna will be 1.76dBi balanced and 4.76dBi unbalanced. Input impedance to the antenna will be given by: Balanced Zin 1201n(r1 /r2) Equation42 Unbalanced Zin 601n(r1 / r2) Equation43 Configuration 19, Minimum antenna configuration This antenna configuration has a field system which is not clearly defined being dependent on a very variable antenna geometry. This fact makes the radiation pattern and input impedance undefined, however the configuration represents the absolute minimum component and materials aerial presented. The final form of this antenna must be iteratively defined using a network analyser. Gain will be approximately 4.76dBi. The first step in the design procedure is to assume configuration 8 and related design equations hold then the antenna will have to be iteratively altered from this

point to meet specification.

Section 2.2, General statement on the subject of characteristic impedance With all the long wire antennas ( configurations 9-14) the equations stated as input impedance are identical to the equations for characteristic impedance for the stated type of line. The phenomena described ie radiating balanced or microsrip lines (straight, meander, or delay) is general. Any balanced or microstrip line of any geometry ( ie flat or circular or rectangular) separated with any dielectric material what so ever will radiate and operate as described. The equations presented need only be altered to take into consideration the effective phase length of the line. 1)

Claims

Section 3.1 Claims (1) A minimal antenna structure as depicted in figure I

which allows a mathematical analysis to be developed which can be used to predictably and reliably mix electric and magnetic fields in the same region in space in the required proportion and the required phase and the required physical orientation.

(2) A mathematical technique as described in section 1 which is based on taking volumetric averages of the field structures over the region of interaction of the

electric and magnetic fields.

(3) As claimed in claim(1) and claim(2), antenna structures referred as configurations I to 8 and configuration 19 and the related design equations.

(4) As claimed in claim(3) any antenna structure referred to in claim(3) with relative permeability above unity inside the coil.

(5) As claimed in claim(3) and claim(4) any antenna structure referred to in claim(3) with any material with relative permitivity above unity andor relative permeability above unity in the region where the fields are mixed.

(6) Any antenna structure with conductor cross sections other than round conforming generally to the lay out of antennas referred to in claim(3), claim(4) and claim(5).

(7) The proof of the general mathematical technique of taking volumetric averages as described in section 1.

(8) As claimed in claim(l), claim(2), and claim(7), antenna structures referred to as configurations 9 to 18 and related design equations.

(9) As claimed in claim(l), claim(2), claim(7), and claim(8), any antenna structure referred to in claim(8) with any material with relative permitivity above unity and-or relative permeability above unity in the region where the fields are f mlxea.

(10) Any antenna structure with a conductor cross section other than round conforming generally to the lay out OF antennas referred to in claim(8) and claim(9) f (1 1) As claimed in all above claims, anything similar. . À À

À À . . À .. ' À as À . À 1 À À Amendments to the claims have been filed as follows (1) A minimal antenna structure as depicted in figure 1 which allows a mathematical analysis to be developed which can be used to predictably and reliably mix electric and magnetic fields in the same region in space in the required proportion and the required phase and the required physical orientation (2) A mathematical technique as described in section 1 which is based on taking volumetric averages of the field structures over the region of interaction of the

electric and magnetic fields

(3) As claimed in claim(l) and claim(2) the antenna structures referred as configurations l to 8 and configuration 19 and the related design equations (4) As claimed in claim(3) any antenna structure referred to in claim(3) with relative permeability above unity inside the coil (5) As claimed in claim(3) and claim(4) any antenna structure referred to in claim(3) with any material with relative permitivity above unity and- or relative permeability above unity in the region where the fields are mixed (6) Any antenna structure with conductor cross sections other than round conforming generally to the lay out of antennas referred to in claim(3) or claim(4) or claim(5) or any combination of these claims (7) The proof of the general mathematical technique of taking volumetric averages as described in section 1 (8) As claimed in claim(1) and claim(2) and claim(7) the antenna structures referred to as configurations 9 to 18 and related design equations (9) As claimed in claim(l) and claim(2) and claim(7) and claim(8) any antenna structure referred to in claim(8) with any material with relative permitivity above unity and-or relative permeability above unity in the region where the fields are mixed (10) Any antenna structure with a conductor cross section other than round conforming generally to the lay out of antennas referred to in claim(8) or claim(9) or both of these claims (11) Anything similar to any of the above claims is also claimed