Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
  • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
  • G01S5/14—Determining absolute distances from a plurality of spaced points of known location
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S11/00—Systems for determining distance or velocity not using reflection or reradiation
  • G01S11/02—Systems for determining distance or velocity not using reflection or reradiation using radio waves
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
  • G01S5/0009—Transmission of position information to remote stations
  • G01S5/0045—Transmission from base station to mobile station
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
  • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
  • G01S5/0205—Details
  • G01S5/0221—Receivers
  • G01S5/02213—Receivers arranged in a network for determining the position of a transmitter
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
  • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
  • G01S5/10—Position of receiver fixed by co-ordinating a plurality of position lines defined by path-difference measurements, e.g. omega or decca systems
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
  • G01D5/00—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable
  • G01D5/48—Mechanical means for transferring the output of a sensing member; Means for converting the output of a sensing member to another variable where the form or nature of the sensing member does not constrain the means for converting; Transducers not specially adapted for a specific variable using wave or particle radiation means

Definitions

• the method can include receiving a base guided surface wave launched from a ground station; identifying a wavelength and a phase of the base guided surface wave; receiving an overlaid guided surface wave launched from the ground station; identifying a range of the overlaid guided surface wave, wherein the range of the overlaid guided surface wave is measured as a number of wavelengths of the base guided surface wave; calculating a distance from the ground station based at least in part on the phase of the base guided surface wave and the range of the overlaid guided surface wave; and determining a current location based at least in part on the distance from the ground station.
• the overlaid guided surface wave has a higher frequency than the base guided surface wave.
• the method further includes identifying an approximate position based at least in part on inertial data. In some of these embodiments, determining the current location is further based at least in part on the approximate position. In one or more embodiments, the method further includes identifying an approximate position based at least in part on an identity of a cellular network tower. In some of these embodiments, determining the current location is further based at least in part on the approximate position. In one or more embodiments, the method further includes receiving a broadcast transmission and identifying an approximate position based at least in part on an identity of the broadcast transmission.
• the system can include a guided surface wave receive structure configured to obtain electrical energy from a guided surface wave traveling along a terrestrial medium; a processor; a memory; and an application stored in the memory that, when executed by the processor, causes the apparatus to at least: identify a wavelength and a phase of a base guided surface wave launched from a ground station and received by the guided surface wave receive structure; identify a range of an overlaid guided surface wave launched from the ground station and received by the guided surface wave receive structure, wherein the range of the overlaid guided surface wave is measured as a number of wavelengths of the base guided surface wave; calculate a distance of the guided surface wave receive structure from the ground station based at least in part on the phase of the base guided surface wave and the range of the overlaid guided surface wave; and determine a location of the guided surface wave receive structure based at least in part on the distance of the guided surface wave receive structure from the ground station.
• FIG. 2 is a drawing that illustrates a propagation interface with two regions employed for transmission of a guided surface wave according to various embodiments of the present disclosure.
• FIG. 6 is a graphical representation illustrating the effect of elevation of a charge terminal on the location where the electric field of FIG. 5A intersects with the lossy conducting medium at a Brewster angle according to various embodiments of the present disclosure.
• FIGS. 8A through 8C are graphical representations illustrating examples of equivalent image plane models of the guided surface waveguide probe of FIGS. 3 and 7 according to various embodiments of the present disclosure.
• FIGS. 9A and 9B are graphical representations illustrating examples of single- wire transmission line and classic transmission line models of the equivalent image plane models of FIGS. 8B and 8C according to various embodiments of the present disclosure.
• FIG. 12 is a drawing that illustrates an example of a guided surface waveguide probe according to various embodiments of the present disclosure.
• FIG. 13 is a graphical representation illustrating the incidence of a synthesized electric field at a complex Brewster angle to match the guided surface waveguide mode at the Hankel crossover distance according to various embodiments of the present disclosure.
• FIG. 18D is a flow chart illustrating an example of adjusting a receiving structure according to various embodiments of the present disclosure.
• FIG. 19 depicts an example of an additional receiving structure that can be employed to receive energy transmitted in the form of a guided surface wave launched by a guided surface waveguide probe according to the various embodiments of the present disclosure.
• FIGS. 20A-E depict various circuit symbols used in the discussion of the application of guided surface waves for geolocation according to various embodiments of the present disclosure.
• FIG. 22 illustrates the principles underlying the operation of the navigation unit, according to various embodiments of the present disclosure.
• FIG. 24 illustrates the principles underlying the operation of the navigation unit, according to various embodiments of the present disclosure.
• FIG. 25 is a flowchart depicting the operation of various components of the navigation unit according to various embodiments of the present disclosure.
• FIG. 1 shown is a graph 100 of field strength in decibels (dB) above an arbitrary reference in volts per meter as a function of distance in kilometers on a log-dB plot to further illustrate the distinction between radiated and guided electromagnetic fields.
• the graph 100 of FIG. 1 depicts a guided field strength curve 103 that shows the field strength of a guided electromagnetic field as a function of distance.
• This guided field strength curve 103 is essentially the same as a transmission line mode.
• the graph 100 of FIG. 1 depicts a radiated field strength curve 106 that shows the field strength of a radiated electromagnetic field as a function of distance.
• the radiated field strength curve 106 falls off geometrically (1/d, where d is distance), which is depicted as a straight line on the log-log scale.
• the guided field strength curve 103 has a characteristic exponential decay of e ⁇ ad / fd and exhibits a distinctive knee 109 on the log-log scale.
• the guided field strength curve 103 and the radiated field strength curve 106 intersect at point 112, which occurs at a crossing distance. At distances less than the crossing distance at intersection point 112, the field strength of a guided electromagnetic field is significantly greater at most locations than the field strength of a radiated electromagnetic field.
• the guided and radiated field strength curves 103 and 106 further illustrate the fundamental propagation difference between guided and radiated electromagnetic fields.
• Milligan T., Modern Antenna Design, McGraw-Hill, 1 st Edition, 1985, pp.8-9, which is incorporated herein by reference in its entirety.
• antennas excite the continuum eigenvalues of the wave equation, which is a radiation field, where the outwardly propagating RF energy with E z and ⁇ ⁇ in- phase is lost forever.
• waveguide probes excite discrete eigenvalues, which results in transmission line propagation. See Collin, R. E., Field Theory of Guided Waves, McGraw-Hill, 1960, pp. 453, 474-477. While such theoretical analyses have held out the hypothetical possibility of launching open surface guided waves over planar or spherical surfaces of lossy, homogeneous media, for more than a century no known structures in the engineering arts have existed for accomplishing this with any practical efficiency.
• Region 2 is a second medium that shares a boundary interface with Region 1 and has different constitutive parameters relative to Region 1.
• Region 2 can comprise, for example, any insulator such as the atmosphere or other medium.
• the reflection coefficient for such a boundary interface goes to zero only for incidence at a complex Brewster angle. See Stratton, J. A. , Electromagnetic Theory, McGraw-Hill, 1941 , p. 516.
• the present disclosure sets forth various guided surface waveguide probes that generate electromagnetic fields that are substantially mode-matched to a guided surface waveguide mode on the surface of the lossy conducting medium comprising Region 1 .
• such electromagnetic fields substantially synthesize a wave front incident at a complex Brewster angle of the lossy conducting medium that can result in zero reflection.
• z is the vertical coordinate normal to the surface of Region 1 and p is the radial coordinate, is a complex argument Hankel function of the second kind and order n
• u t is the propagation constant in the positive vertical (z) direction in Region 1
• u 2 is the propagation constant in the vertical (z) direction in Region 2
• ⁇ 1 is the conductivity of Region 1
• ⁇ is equal to 2nf, where is a frequency of excitation
• ⁇ 0 is the permittivity of free space
• ⁇ 1 is the permittivity of Region 1
• A is a source constant imposed by the source
• ⁇ is a surface wave radial propagation constant.
• FIG. 3 which shows an example of a guided surface waveguide probe 200a that includes a charge terminal Ti elevated above a lossy conducting medium 203 (e.g., the Earth) along a vertical axis z that is normal to a plane presented by the lossy conducting medium 203.
• the lossy conducting medium 203 makes up Region 1
• a second medium 206 makes up Region 2 and shares a boundary interface with the lossy conducting medium 203.
• the guided surface waveguide probe 200a includes a feed network 209 that couples an excitation source 212 to the charge terminal ⁇ via, e.g., a vertical feed line conductor.
• a charge Qi is imposed on the charge terminal ⁇ to synthesize an electric field based upon the voltage applied to terminal ⁇ at any given instant.
• ⁇ angle of incidence
• E electric field
• Equation (13) implies that the electric and magnetic fields specified in Equations (1)-(3) may result in a radial surface current density along the boundary interface, where the radial surface current density can be specified by
• the negative sign means that when source current (I 0 ) flows vertically upward as illustrated in FIG. 3, the "close-in” ground current flows radially inward.
• Equation (14) the radial surface current density of Equation (14) can be restated as
• Equations (1)-(6) and (17) have the nature of a transmission line mode bound to a lossy interface, not radiation fields that are associated with groundwave propagation. See Barlow, H. M. and Brown, J., Radio Surface Waves, Oxford University Press, 1962, pp. 1-5.
• Equations (20b) and (21) differ in phase by Jj, which corresponds to an extra phase advance or "phase boost" of 45° or, equivalently, ⁇ /8.
• the "far out" representation predominates over the "close-in” representation of the Hankel function.
• the distance to the Hankel crossover point (or Hankel crossover distance) can be found by equating Equations (20b) and (21) for -y ' yp, and solving for R x .
• x ⁇ / ⁇ 0
• the Hankel function asymptotes may also vary as the conductivity ( ⁇ ) of the lossy conducting medium changes. For example, the conductivity of the soil can vary with changes in weather conditions.
• the advantage of an increased capacitive elevation for the charge terminal Ti is that the charge on the elevated charge terminal Ti is further removed from the ground plane, resulting in an increased amount of free charge q free to couple energy into the guided surface waveguide mode. As the charge terminal ⁇ is moved away from the ground plane, the charge distribution becomes more uniformly distributed about the surface of the terminal. The amount of free charge is related to the self-capacitance of the charge terminal Ti .
• the charge terminal Ti can include any shape such as a sphere, a disk, a cylinder, a cone, a torus, a hood, one or more rings, or any other randomized shape or combination of shapes.
• An equivalent spherical diameter can be determined and used for positioning of the charge terminal Ti .
• the charge terminal Ti can be positioned at a physical height that is at least four times the spherical diameter (or equivalent spherical diameter) of the charge terminal Ti to reduce the bounded charge effects.
• FIG. 5A shown is a ray optics interpretation of the electric field produced by the elevated charge Qi on charge terminal Ti of FIG. 3.
• minimizing the reflection of the incident electric field can improve and/or maximize the energy coupled into the guided surface waveguide mode of the lossy conducting medium 203.
• the amount of reflection of the incident electric field may be determined using the Fresnel reflection coefficient, which can be expressed as where ⁇ ⁇ is the conventional angle of incidence measured with respect to the surface normal.
• the ray optic interpretation shows the incident field polarized parallel to the plane of incidence having an angle of incidence of 6 which is measured with respect to the surface normal (z).
• (0 ⁇ ) 0 and thus the incident electric field will be completely coupled into a guided surface waveguide mode along the surface of the lossy conducting medium 203.
• the numerator of Equation (25) goes to zero when the angle of incidence is
• the electric field vector E can be depicted as an incoming non-uniform plane wave, polarized parallel to the plane of incidence.
• the electric field vector E can be created from independent horizontal and vertical components as
• a generalized parameter W is noted herein as the ratio of the horizontal electric field component to the vertical electric field component given by
• Equation (30b) [0073]
• the concept of an electrical effective height can provide further insight into synthesizing an electric field with a complex angle of incidence with a guided surface waveguide probe 200.
• the electrical effective height ⁇ h eff has been defined as
• the integration of the distributed current 7(z) of the structure is performed over the physical height of the structure (h p ), and normalized to the ground current (I 0 ) flowing upward through the base (or input) of the structure.
• the distributed current along the structure can be expressed by
• ⁇ 0 is the propagation factor for current propagating on the structure.
• I c is the current that is distributed along the vertical structure of the guided surface waveguide probe 200a.
• a feed network 209 that includes a low loss coil (e.g., a helical coil) at the bottom of the structure and a vertical feed line conductor connected between the coil and the charge terminal T ⁇
• V f the velocity factor on the structure
• ⁇ 0 the wavelength at the supplied frequency
• ⁇ ⁇ the propagation wavelength resulting from the velocity factor V f .
• the phase delay is measured relative to the ground (stake) current I 0 .
• the current fed to the top of the coil from the bottom of the physical structure is
• the geometric parameters are related by the electrical effective height (h efr ) of the charge terminal ⁇ by
• FIG. 5A a right triangle is depicted having an adjacent side of length R x along the lossy conducting medium surface and a complex Brewster angle ⁇ ⁇ ⁇ measured between a ray 124 extending between the Hankel crossover point 121 at R x and the center of the charge terminal ⁇ , and the lossy conducting medium surface 127 between the Hankel crossover point 121 and the charge terminal TV
• the charge terminal ⁇ positioned at physical height h p and excited with a charge having the appropriate phase delay ⁇
• the resulting electric field is incident with the lossy conducting medium boundary interface at the Hankel crossover distance R x , and at the Brewster angle. Under these conditions, the guided surface waveguide mode can be excited without reflection or substantially negligible reflection.
• FIG. 6 graphically illustrates the effect of decreasing the physical height of the charge terminal ⁇ on the distance where the electric field is incident at the Brewster angle.
• the height is decreased from h 3 through h 2 to hi , the point where the electric field intersects with the lossy conducting medium (e.g. , the Earth) at the Brewster angle moves closer to the charge terminal position.
• Equation (39) indicates, the height Hi (FIG.
• the height of the charge terminal ⁇ should be at or higher than the physical height (h p ) in order to excite the far-out component of the Hankel function.
• the height should be at least four times the spherical diameter (or equivalent spherical diameter) of the charge terminal ⁇ as mentioned above.
• a guided surface waveguide probe 200 can be configured to establish an electric field having a wave tilt that corresponds to a wave illuminating the surface of the lossy conducting medium 203 at a complex Brewster angle, thereby exciting radial surface currents by substantially mode-matching to a guided surface wave mode at (or beyond) the Hankel crossover point 121 at R x .
• FIG. 7 shown is a graphical representation of an example of a guided surface waveguide probe 200b that includes a charge terminal ⁇ .
• An AC source 212 acts as the excitation source for the charge terminal T which is coupled to the guided surface waveguide probe 200b through a feed network 209 (FIG. 3) comprising a coil 215 such as, e.g. , a helical coil.
• the AC source 212 can be inductively coupled to the coil 215 through a primary coil.
• an impedance matching network may be included to improve and/or maximize coupling of the AC source 212 to the coil 215.
• the coil 215 is coupled to a ground stake 218 at a first end and to the charge terminal ⁇ via a vertical feed line conductor 221 .
• the coil connection to the charge terminal ⁇ can be adjusted using a tap 224 of the coil 215 as shown in FIG. 7.
• the coil 215 can be energized at an operating frequency by the AC source 212 through a tap 227 at a lower portion of the coil 215.
• the AC source 212 can be inductively coupled to the coil 215 through a primary coil.
• the conductivity ⁇ and relative permittivity e r can be determined through test measurements of the lossy conducting medium 203.
• the complex Brewster angle ( ⁇ ⁇ ⁇ ) measured from the surface normal can also be determined from Equation (26) as
• 6 B arctan(J£ r - jx) , (42) or measured from the surface as shown in FIG. 5A as
• Equation (40) The wave tilt at the Hankel crossover distance (W Rx ) can also be found using Equation (40).
• the complex effective height (h efr ) includes a magnitude that is associated with the physical height (h p ) of the charge terminal ⁇ and a phase delay ( ⁇ ) that is to be associated with the angle ( ⁇ ) of the wave tilt at the Hankel crossover distance (R x ).
• phase delay 0 C of a helically-wound coil can be determined from Maxwell's equations as has been discussed by Corum, K.L. and J.F. Corum, "RF Coils, Helical Resonators and Voltage Magnification by Coherent Spatial Modes," Microwave Review, Vol. 7, No. 2, September 2001 , pp. 36-45., which is incorporated herein by reference in its entirety.
• H/D > 1 the ratio of the velocity of propagation ( ⁇ ) of a wave along the coil's longitudinal axis to the speed of light (c), or the "velocity factor," is given by
• H H is the axial length of the solenoidal helix
• D is the coil diameter
• N is the number of turns of the coil
• ⁇ 0 is the free-space wavelength.
• the principle is the same if the helix is wound spirally or is short and fat, but V f and 6 C are easier to obtain by experimental measurement.
• the expression for the characteristic (wave) impedance of a helical transmission lin also been derived as [0088]
• the spatial phase delay Q y of the structure can be determined using the traveling wave phase delay of the vertical feed line conductor 221 (FIG. 7).
• the capacitance of a cylindrical vertical conductor above a prefect ground plane can be expressed as
• the velocity factor is a constant with V w ⁇ 0.94, or in a range from about 0.93 to about 0.98. If the mast is considered to be a uniform transmission line, its average characteristic impedance can be approximated by
• Equation (51) implies that Z w for a single-wire feeder varies with frequency.
• the phase delay can be determined based upon the capacitance and characteristic impedance.
• the electric field produced by the charge oscillating Qi on the charge terminal Ti is coupled into a guided surface waveguide mode traveling along the surface of a lossy conducting medium 203. For example, if the Brewster angle ( ⁇ ⁇ ⁇ ), the phase delay (0 y ) associated with the vertical feed line conductor 221 (FIG. 7), and the configuration of the coil 215 (FIG.
• the position of the tap 224 may be adjusted to maximize coupling the traveling surface waves into the guided surface waveguide mode. Excess coil length beyond the position of the tap 224 can be removed to reduce the capacitive effects.
• the vertical wire height and/or the geometrical parameters of the helical coil may also be varied.
• the coupling to the guided surface waveguide mode on the surface of the lossy conducting medium 203 can be improved and/or optimized by tuning the guided surface waveguide probe 200 for standing wave resonance with respect to a complex image plane associated with the charge Qi on the charge terminal Ti. By doing this, the performance of the guided surface waveguide probe 200 can be adjusted for increased and/or maximum voltage (and thus charge Qi) on the charge terminal Ti .
• the effect of the lossy conducting medium 203 in Region 1 can be examined using image theory analysis.
• This analysis may also be used with respect to a lossy conducting medium 203 by assuming the presence of an effective image charge Q beneath the guided surface waveguide probe 200.
• the effective image charge Q coincides with the charge on the charge terminal about a conducting image ground plane 130, as illustrated in FIG. 3.
• the image charge Q is not merely located at some real depth and 180° out of phase with the primary source charge on the charge terminal T ⁇ as they would be in the case of a perfect conductor.
• the lossy conducting medium 203 e.g., a terrestrial medium
• Equation (12) The complex spacing of the image charge, in turn, implies that the external field will experience extra phase shifts not encountered when the interface is either a dielectric or a perfect conductor.
• the lossy conducting medium 203 is a finitely conducting Earth 133 with a physical boundary 136.
• the finitely conducting Earth 133 may be replaced by a perfectly conducting image ground plane 139 as shown in FIG.8B, which is located at a complex depth z 1 below the physical boundary 136.
• This equivalent representation exhibits the same impedance when looking down into the interface at the physical boundary 136.
• the equivalent representation of FIG. 8B can be modeled as an equivalent transmission line, as shown in FIG. 8C.
• the depth z t can be determined by equating the TEM wave impedance looking down at the Earth to an image ground plane impedance z in seen looking into the transmission line of FIG. 8C.
• the equivalent representation of FIG. 8B is equivalent to a TEM transmission line whose characteristic impedance is that of air (z 0 ), with propagation constant of ⁇ 0 , and whose length is z x .
• the image ground plane impedance Z in seen at the interface for the shorted transmission line of FIG. 8C is given by
• Z w is the characteristic impedance of the elevated vertical feed line conductor 221 in ohms
• Z c is the characteristic impedance of the coil 215 in ohms
• Z 0 is the characteristic impedance of free space.
• the equivalent image plane models of FIGS. 9A and 9B can be tuned to resonance with respect to the image ground plane 139.
• the impedance of the equivalent complex image plane model is purely resistive, which maintains a superposed standing wave on the probe structure that maximizes the voltage and elevated charge on terminal , and by equations (1)-(3) and (16) maximizes the propagating surface wave.
• the load impedance Z L of the charge terminal is adjusted to bring the probe structure into standing wave resonance with respect to the image ground plane (130 of FIG. 3 or 139 of FIG. 8), which is at a complex depth of - d/2. In that case, the impedance seen from the image ground plane has zero reactance and the charge on the charge terminal Ti is maximized.
• two relatively short transmission line sections of widely differing characteristic impedance may be used to provide a very large phase shift.
• a probe structure composed of two sections of transmission line, one of low impedance and one of high impedance, together totaling a physical length of, say, 0.05 ⁇ , may be fabricated to provide a phase shift of 90° which is equivalent to a 0.25 ⁇ resonance. This is due to the large jump in characteristic impedances.
• a physically short probe structure can be electrically longer than the two physical lengths combined. This is illustrated in FIGS. 9A and 9B, where the discontinuities in the impedance ratios provide large jumps in phase. The impedance discontinuity provides a substantial phase shift where the sections are joined together.
• FIG. 10 shown is a flow chart 150 illustrating an example of adjusting a guided surface waveguide probe 200 (FIGS. 3 and 7) to substantially mode- match to a guided surface waveguide mode on the surface of the lossy conducting medium, which launches a guided surface traveling wave along the surface of a lossy conducting medium 203 (FIG. 3).
• the charge terminal ⁇ of the guided surface waveguide probe 200 is positioned at a defined height above a lossy conducting medium 203.
• the Hankel crossover distance can also be found by equating the magnitudes of Equations (20b) and (21) for -y ' yp, and solving for R x as illustrated by FIG. 4.
• the complex index of refraction (n) can be determined using Equation (41), and the complex Brewster angle ( ⁇ ⁇ ⁇ ) can then be determined from Equation (42).
• the physical height (h p ) of the charge terminal Ti can then be determined from Equation (44).
• the charge terminal Ti should be at or higher than the physical height (h p ) in order to excite the far-out component of the Hankel function. This height relationship is initially considered when launching surface waves.
• the height should be at least four times the spherical diameter (or equivalent spherical diameter) of the charge terminal T ⁇
• the electrical phase delay ⁇ of the elevated charge on the charge terminal Ti is matched to the complex wave tilt angle ⁇ .
• the phase delay (0 C ) of the helical coil and/or the phase delay (0 y ) of the vertical feed line conductor can be adjusted to make ⁇ equal to the angle ( ⁇ ) of the wave tilt (W). Based on Equation (31), the angle ( ⁇ ) of the wave tilt can be determined from:
• the load impedance of the charge terminal Ti is tuned to resonate the equivalent image plane model of the guided surface waveguide probe 200.
• the depth (d/2) of the conducting image ground plane 139 of FIG. 9A and 9B (or 130 of FIG. 3) can be determined using Equations (52), (53) and (54) and the values of the lossy conducting medium 203 (e.g., the Earth), which can be measured.
• the impedance (Z in ) as seen "looking down" into the lossy conducting medium 203 can then be determined using Equation (65). This resonance relationship can be considered to maximize the launched surface waves.
• the impedance at the physical boundary 136 "looking up" into the guided surface waveguide probe 200 is the conjugate of the impedance at the physical boundary 136 "looking down" into the lossy conducting medium 203.
• An iterative approach may be taken to tune the load impedance Z L for resonance of the equivalent image plane model with respect to the conducting image ground plane 139 (or 130). In this way, the coupling of the electric field to a guided surface waveguide mode along the surface of the lossy conducting medium 203 (e.g., Earth) can be improved and/or maximized.
• the lossy conducting medium 203 e.g., Earth
• the wave length can be determined as
• the velocity factor of the vertical feed line conductor (approximated as a uniform cylindrical conductor with a diameter of 0.27 inches) can be given as 0.93. Since h p « A 0 , the propagation phase constant for the vertical feed line conductor can be approximated as:
• FIG. 11 shows a plot of both over a range of frequencies. As both ⁇ and ⁇ are frequency dependent, it can be seen that their respective curves cross over each other at approximately 1.85 MHz.
• Equation (45) For a helical coil having a conductor diameter of 0.0881 inches, a coil diameter (D) of 30 inches and a turn-to-turn spacing (s) of 4 inches, the velocity factor for the coil can be determined using Equation (45) as:
• Equation (35) the propagation factor from Equation (35) is:
• Equation (46) the axial length of the solenoidal helix (H) can be determined using Equation (46) such that:
• Equation (65) the impedance seen "looking down" into the lossy conducting medium 203 (i.e., Earth) can be determined as:
• the coupling into the guided surface waveguide mode may be maximized. This can be accomplished by adjusting the capacitance of the charge terminal ⁇ without changing the traveling wave phase delays of the coil and vertical feed line conductor. For example, by adjusting the charge terminal capacitance (C T ) to 61.8126 pF, the load impedance from Equation (62) is:
• Equation (51) the impedance of the vertical feed line conductor (having a diameter (2a) of 0.27 inches) is given as
• Equation (63) the impedance seen "looking up" into the vertical feed line conductor is given by Equation (63) as:
• Equation (47) the characteristic impedance of the helical coil is given as
• the guided field strength curve 103 of the guided electromagnetic field has a characteristic exponential decay of e ⁇ ad / fd and exhibits a distinctive knee 109 on the log-log scale.
• the surface waveguide may be considered to be "mode- matched".
• the charge terminal ⁇ is of sufficient height Hi of FIG. 3 (h ⁇ R x tan if i B ) so that electromagnetic waves incident onto the lossy conducting medium 203 at the complex Brewster angle do so out at a distance (> R x ) where the 1/Vr term is predominant.
• Receive circuits can be utilized with one or more guided surface waveguide probes to facilitate wireless transmission and/or power delivery systems.
• operation of a guided surface waveguide probe 200 may be controlled to adjust for variations in operational conditions associated with the guided surface waveguide probe 200.
• an adaptive probe control system 230 can be used to control the feed network 209 and/or the charge terminal ⁇ to control the operation of the guided surface waveguide probe 200.
• Operational conditions can include, but are not limited to, variations in the characteristics of the lossy conducting medium 203 (e.g., conductivity ⁇ and relative permittivity e r ), variations in field strength and/or variations in loading of the guided surface waveguide probe 200.
• ⁇ ; ⁇ ) can be affected by changes in soil conductivity and permittivity resulting from, e.g. , weather conditions.
• Field or field strength (FS) meters may also be distributed about the guided surface waveguide probe 200 to measure field strength of fields associated with the guided surface wave.
• the field or FS meters can be configured to detect the field strength and/or changes in the field strength (e.g., electric field strength) and communicate that information to the probe control system 230.
• the information may be communicated to the probe control system 230 through a network such as, but not limited to, a LAN, WLAN, cellular network, or other appropriate communication network.
• the guided surface waveguide probe 200 may be adjusted to maintain specified field strength(s) at the FS meter locations to ensure appropriate power transmission to the receivers and the loads they supply.
• the complex angle trigonometry is shown for the ray optic interpretation of the incident electric field (E) of the charge terminal Ti with a complex Brewster angle ( ⁇ ⁇ ⁇ ) at the Hankel crossover distance (R x ).
• the Brewster angle is complex and specified by equation (38).
• the geometric parameters are related by the electrical effective height (Kff) °f the charge terminal ⁇ by equation (39).
• the angle of the desired guided surface wave tilt at the Hankel crossover distance (W Rx ) is equal to the phase ( ⁇ ) of the complex effective height (h efr ).
• Equation (39) means that the physical height of the guided surface waveguide probe 200 can be relatively small. While this will excite the guided surface waveguide mode, this can result in an unduly large bound charge with little free charge.
• the charge terminal ⁇ can be raised to an appropriate elevation to increase the amount of free charge. As one example rule of thumb, the charge terminal ⁇ can be positioned at an elevation of about 4-5 times (or more) the effective diameter of the charge terminal ⁇ .
• FIG. 6 illustrates the effect of raising the charge terminal ⁇ above the physical height (h p ) shown in FIG. 5A. The increased elevation causes the distance at which the wave tilt is incident with the lossy conductive medium to move beyond the Hankel crossover point 121 (FIG. 5A).
• a lower compensation terminal T 2 can be used to adjust the total effective height (h TE ) of the charge terminal Ti such that the wave tilt at the Hankel crossover distance is at the Brewster angle.
• the charge terminal ⁇ is positioned over the lossy conducting medium 203 at a physical height Hi
• the compensation terminal T 2 is positioned directly below ⁇ along the vertical axis z at a physical height H 2 , where H 2 is less than Hi.
• the charge terminal Ti has an isolated (or self) capacitance Ci
• the compensation terminal T 2 has an isolated (or self) capacitance C 2 .
• a mutual capacitance C M can also exist between the terminals Ti and T 2 depending on the distance there between.
• charges Qi and Q 2 are imposed on the charge terminal Ti and the compensation terminal T 2 , respectively, depending on the voltages applied to the charge terminal Ti and the compensation terminal T 2 at any given instant.
• the total effective height can be written as the superposition of an upper effective height (h UE ) associated with the charge terminal Ti and a lower effective height (h LE ) associated with the compensation terminal T 2 such that
• O l the phase delay applied to the lower compensation terminal T 2
• h p the physical height of the charge terminal
• h d the physical height of the compensation terminal T 2 .
• the lower effective height can be used to adjust the total effective height (h TE ) to equal the complex effective height (h eff ) of FIG. 5A.
• Equations (85) or (86) can be used to determine the physical height of the lower disk of the compensation terminal T 2 and the phase angles to feed the terminals in order to obtain the desired wave tilt at the Hankel crossover distance.
• Equation (86) can be rewritten as the phase shift applied to the charge terminal ⁇ as a function of the compensation terminal height (h d ) to give
• the total effective height (h TE ) is the superposition of the complex effective height (h UE ) of the upper charge terminal and the complex effective height (h LE ) of the lower compensation terminal T 2 as expressed in Equation (86).
• the tangent of the angle of incidence can be expressed geometrically as
• the h TE can be adjusted to make the wave tilt of the incident ray match the complex Brewster angle at the Hankel crossover point 121. This can be accomplished by adjusting h p , ⁇ , and/or h d .
• FIG. 14 shown is a graphical representation of an example of a guided surface waveguide probe 200d including an upper charge terminal Ti (e.g. , a sphere at height h T ) and a lower compensation terminal T 2 (e.g. , a disk at height h d ) that are positioned along a vertical axis z that is substantially normal to the plane presented by the lossy conducting medium 203.
• charges and Q 2 are imposed on the charge and compensation terminals and T 2 , respectively, depending on the voltages applied to the terminals and T 2 at any given instant.
• An AC source 212 acts as the excitation source for the charge terminal T ⁇ which is coupled to the guided surface waveguide probe 200d through a feed network 209 comprising a coil 215 such as, e.g., a helical coil.
• the AC source 212 can be connected across a lower portion of the coil 215 through a tap 227, as shown in FIG. 14, or can be inductively coupled to the coil 215 by way of a primary coil.
• the coil 215 can be coupled to a ground stake 218 at a first end and the charge terminal ⁇ at a second end. In some implementations, the connection to the charge terminal ⁇ can be adjusted using a tap 224 at the second end of the coil 215.
• the compensation terminal T 2 is positioned above and substantially parallel with the lossy conducting medium 203 (e.g., the ground or Earth), and energized through a tap 233 coupled to the coil 215.
• An ammeter 236 located between the coil 215 and ground stake 218 can be used to provide an indication of the magnitude of the current flow (I 0 ) at the base of the guided surface waveguide probe.
• a current clamp may be used around the conductor coupled to the ground stake 218 to obtain an indication of the magnitude of the current flow (I 0 ).
• An ammeter 236 located between the coil 215 and ground stake 218 can be used to provide an indication of the magnitude of the current flow at the base of the guided surface waveguide probe 200d.
• a current clamp may be used around the conductor coupled to the ground stake 218 to obtain an indication of the magnitude of the current flow.
• the compensation terminal T 2 is positioned above and substantially parallel with the lossy conducting medium 203 (e.g. , the ground).
• connection to the charge terminal located on the coil 215 above the connection point of tap 233 for the compensation terminal T 2 allows an increased voltage (and thus a higher charge Qi) to be applied to the upper charge terminal Ti .
• the connection points for the charge terminal Ti and the compensation terminal T 2 can be reversed. It is possible to adjust the total effective height (h TE ) of the guided surface waveguide probe 200d to excite an electric field having a guided surface wave tilt at the Hankel crossover distance R x .
• the Hankel crossover distance can also be found by equating the magnitudes of equations (20b) and (21) for -jyp, and solving for R x as illustrated by FIG. 4.
• a spherical diameter (or the effective spherical diameter) can be determined.
• the terminal configuration may be modeled as a spherical capacitance having an effective spherical diameter.
• the size of the charge terminal can be chosen to provide a sufficiently large surface for the charge imposed on the terminals. In general, it is desirable to make the charge terminal Ti as large as practical. The size of the charge terminal Ti should be large enough to avoid ionization of the surrounding air, which can result in electrical discharge or sparking around the charge terminal.
• the desired elevation to provide free charge on the charge terminal Ti for launching a guided surface wave should be at least 4-5 times the effective spherical diameter above the lossy conductive medium (e.g., the Earth).
• the compensation terminal T 2 can be used to adjust the total effective height (h TE ) of the guided surface waveguide probe 200d to excite an electric field having a guided surface wave tilt at R x .
• the coil phase can be determined from Re ⁇ Oy ⁇ , as graphically illustrated in plot 175.
• FIG. 15B shows a schematic diagram of the general electrical hookup of FIG. 14 in which Vi is the voltage applied to the lower portion of the coil 215 from the AC source 212 through tap 227, V 2 is the voltage at tap 224 that is supplied to the upper charge terminal Ti, and V 3 is the voltage applied to the lower compensation terminal T 2 through tap 233.
• the resistances R p and R d represent the ground return resistances of the charge terminal and compensation terminal T 2 , respectively.
• the charge and compensation terminals and T 2 may be configured as spheres, cylinders, toroids, rings, hoods, or any other combination of capacitive structures.
• the size of the charge and compensation terminals and T 2 can be chosen to provide a sufficiently large surface for the charges and Q 2 imposed on the terminals. In general, it is desirable to make the charge terminal ⁇ as large as practical. The size of the charge terminal ⁇ should be large enough to avoid ionization of the surrounding air, which can result in electrical discharge or sparking around the charge terminal.
• the self- capacitance C p and C d of the charge and compensation terminals Ti and T 2 respectively, can be determined using, for example, equation (24).
• a resonant circuit is formed by at least a portion of the inductance of the coil 215, the self-capacitance C d of the compensation terminal T 2 , and the ground return resistance R d associated with the compensation terminal T 2 .
• the parallel resonance can be established by adjusting the voltage V 3 applied to the compensation terminal T 2 (e.g., by adjusting a tap 233 position on the coil 215) or by adjusting the height and/or size of the compensation terminal T 2 to adjust C d .
• the position of the coil tap 233 can be adjusted for parallel resonance, which will result in the ground current through the ground stake 218 and through the ammeter 236 reaching a maximum point.
• the position of the tap 227 for the AC source 212 can be adjusted to the 50 ⁇ point on the coil 215.
• Voltage V 2 from the coil 215 can be applied to the charge terminal Ti , and the position of tap 224 can be adjusted such that the phase ( ⁇ ) of the total effective height (h TE ) approximately equals the angle of the guided surface wave tilt (W Rx ) at the Hankel crossover distance (R x ).
• the position of the coil tap 224 can be adjusted until this operating point is reached, which results in the ground current through the ammeter 236 increasing to a maximum.
• the resultant fields excited by the guided surface waveguide probe 200d are substantially mode-matched to a guided surface waveguide mode on the surface of the lossy conducting medium 203, resulting in the launching of a guided surface wave along the surface of the lossy conducting medium 203. This can be verified by measuring field strength along a radial extending from the guided surface waveguide probe 200.
• Resonance of the circuit including the compensation terminal T 2 may change with the attachment of the charge terminal Ti and/or with adjustment of the voltage applied to the charge terminal Ti through tap 224. While adjusting the compensation terminal circuit for resonance aids the subsequent adjustment of the charge terminal connection, it is not necessary to establish the guided surface wave tilt (W Rx ) at the Hankel crossover distance (R x ).
• the system may be further adjusted to improve coupling by iteratively adjusting the position of the tap 227 for the AC source 212 to be at the 50 ⁇ point on the coil 215 and adjusting the position of tap 233 to maximize the ground current through the ammeter 236.
• Resonance of the circuit including the compensation terminal T 2 may drift as the positions of taps 227 and 233 are adjusted, or when other components are attached to the coil 215.
• the voltage V 2 from the coil 215 can be applied to the charge terminal ⁇ , and the position of tap 233 can be adjusted such that the phase ( ⁇ ) of the total effective height (h TE ) approximately equals the angle ( ⁇ ) of the guided surface wave tilt at R x .
• the position of the coil tap 224 can be adjusted until the operating point is reached, resulting in the ground current through the ammeter 236 substantially reaching a maximum.
• the resultant fields are substantially mode-matched to a guided surface waveguide mode on the surface of the lossy conducting medium 203, and a guided surface wave is launched along the surface of the lossy conducting medium 203. This can be verified by measuring field strength along a radial extending from the guided surface waveguide probe 200.
• the system may be further adjusted to improve coupling by iteratively adjusting the position of the tap 227 for the AC source 212 to be at the 50 ⁇ point on the coil 215 and adjusting the position of tap 224 and/or 233 to maximize the ground current through the ammeter 236.
• operation of a guided surface waveguide probe 200 may be controlled to adjust for variations in operational conditions associated with the guided surface waveguide probe 200.
• a probe control system 230 can be used to control the feed network 209 and/or positioning of the charge terminal Ti and/or compensation terminal T 2 to control the operation of the guided surface waveguide probe 200.
• Operational conditions can include, but are not limited to, variations in the characteristics of the lossy conducting medium 203 (e.g. , conductivity ⁇ and relative permittivity e r ), variations in field strength and/or variations in loading of the guided surface waveguide probe 200.
• Equipment such as, e.g. , conductivity measurement probes, permittivity sensors, ground parameter meters, field meters, current monitors and/or load receivers can be used to monitor for changes in the operational conditions and provide information about current operational conditions to the probe control system 230.
• the probe control system 230 can then make one or more adjustments to the guided surface waveguide probe 200 to maintain specified operational conditions for the guided surface waveguide probe 200. For instance, as the moisture and temperature vary, the conductivity of the soil will also vary.
• Conductivity measurement probes and/or permittivity sensors may be located at multiple locations around the guided surface waveguide probe 200. Generally, it would be desirable to monitor the conductivity and/or permittivity at or about the Hankel crossover distance R x for the operational frequency.
• Conductivity measurement probes and/or permittivity sensors may be located at multiple locations ⁇ e.g., in each quadrant) around the guided surface waveguide probe 200.
• a guided surface waveguide probe 200e that includes a charge terminal ⁇ and a charge terminal T 2 that are arranged along a vertical axis z.
• the guided surface waveguide probe 200e is disposed above a lossy conducting medium 203, which makes up Region 1.
• a second medium 206 shares a boundary interface with the lossy conducting medium 203 and makes up Region 2.
• the charge terminals Ti and T 2 are positioned over the lossy conducting medium 203.
• the charge terminal is positioned at height and the charge terminal T 2 is positioned directly below along the vertical axis z at height H 2 , where H 2 is less than
• the guided surface waveguide probe 200e includes a feed network 209 that couples an excitation source 212 to the charge terminals and T 2 .
• the charge terminals and/or T 2 include a conductive mass that can hold an electrical charge, which may be sized to hold as much charge as practically possible.
• the charge terminal Ti has a self-capacitance Ci
• the charge terminal T 2 has a self- capacitance C 2 , which can be determined using, for example, equation (24).
• a mutual capacitance C M is created between the charge terminals Ti and T 2 .
• the charge terminals Ti and T 2 need not be identical, but each can have a separate size and shape, and can include different conducting materials.
• the field strength of a guided surface wave launched by a guided surface waveguide probe 200e is directly proportional to the quantity of charge on the terminal Ti .
• the guided surface waveguide probe 200e When properly adjusted to operate at a predefined operating frequency, the guided surface waveguide probe 200e generates a guided surface wave along the surface of the lossy conducting medium 203.
• the excitation source 212 can generate electrical energy at the predefined frequency that is applied to the guided surface waveguide probe 200e to excite the structure.
• the electromagnetic fields generated by the guided surface waveguide probe 200e are substantially mode-matched with the lossy conducting medium 203, the electromagnetic fields substantially synthesize a wave front incident at a complex Brewster angle that results in little or no reflection.
• the surface waveguide probe 200e does not produce a radiated wave, but launches a guided surface traveling wave along the surface of a lossy conducting medium 203.
• the energy from the excitation source 212 can be transmitted as Zenneck surface currents to one or more receivers that are located within an effective transmission range of the guided surface waveguide probe 200e.
• far-out should differ from the phase of the surface current ⁇ J t ⁇ close-in by the propagation phase corresponding to ⁇ - ⁇ ⁇ ( ⁇ ⁇ - ⁇ p
• the properly adjusted synthetic radial surface current is
• an iterative approach may be used. Specifically, analysis may be performed of a given excitation and configuration of a guided surface waveguide probe 200e taking into account the feed currents to the terminals ⁇ and T 2 , the charges on the charge terminals ⁇ and T 2 , and their images in the lossy conducting medium 203 in order to determine the radial surface current density generated. This process may be performed iteratively until an optimal configuration and excitation for a given guided surface waveguide probe 200e is determined based on desired parameters.
• a guided field strength curve 103 may be generated using equations (1)-(12) based on values for the conductivity of Region 1 ( ⁇ ⁇ ) and the permittivity of Region 1 (s t ) at the location of the guided surface waveguide probe 200e.
• Such a guided field strength curve 103 can provide a benchmark for operation such that measured field strengths can be compared with the magnitudes indicated by the guided field strength curve 103 to determine if optimal transmission has been achieved.
• various parameters associated with the guided surface waveguide probe 200e may be adjusted.
• One parameter that may be varied to adjust the guided surface waveguide probe 200e is the height of one or both of the charge terminals Ti and/or T 2 relative to the surface of the lossy conducting medium 203.
• the distance or spacing between the charge terminals Ti and T 2 may also be adjusted. In doing so, one may minimize or otherwise alter the mutual capacitance C M or any bound capacitances between the charge terminals Ti and T 2 and the lossy conducting medium 203 as can be appreciated.
• the size of the respective charge terminals Ti and/or T 2 can also be adjusted. By changing the size of the charge terminals Ti and/or T 2 , one will alter the respective self-capacitances Ci and/or C 2 , and the mutual capacitance C M as can be appreciated.
• the feed network 209 associated with the guided surface waveguide probe 200e is another parameter that can be adjusted. This may be accomplished by adjusting the size of the inductive and/or capacitive reactances that make up the feed network 209. For example, where such inductive reactances comprise coils, the number of turns on such coils may be adjusted. Ultimately, the adjustments to the feed network 209 can be made to alter the electrical length of the feed network 209, thereby affecting the voltage magnitudes and phases on the charge terminals ⁇ and T 2 .
• operation of the guided surface waveguide probe 200e may be controlled to adjust for variations in operational conditions associated with the guided surface waveguide probe 200.
• a probe control system 230 shown in FIG. 12 can be used to control the feed network 209 and/or positioning and/or size of the charge terminals ⁇ and/or T 2 to control the operation of the guided surface waveguide probe 200e.
• Operational conditions can include, but are not limited to, variations in the characteristics of the lossy conducting medium 203 (e.g., conductivity ⁇ and relative permittivity e r ), variations in field strength and/or variations in loading of the guided surface waveguide probe 200e.
• the guided surface waveguide probe 200f includes the charge terminals ⁇ and T 2 that are positioned along a vertical axis z that is substantially normal to the plane presented by the lossy conducting medium 203 (e.g. , the Earth).
• the second medium 206 is above the lossy conducting medium 203.
• the charge terminal Ti has a self-capacitance Ci
• the charge terminal T 2 has a self-capacitance C 2 .
• charges and Q 2 are imposed on the charge terminals and T 2 , respectively, depending on the voltages applied to the charge terminals and T 2 at any given instant.
• a mutual capacitance C M may exist between the charge terminals and T 2 depending on the distance there between.
• bound capacitances may exist between the respective charge terminals and T 2 and the lossy conducting medium 203 depending on the heights of the respective charge terminals Ti and T 2 with respect to the lossy conducting medium 203.
• the guided surface waveguide probe 200f includes a feed network 209 that comprises an inductive impedance comprising a coil l_i a having a pair of leads that are coupled to respective ones of the charge terminals Ti and T 2 .
• the coil L a is specified to have an electrical length that is one-half (1 ⁇ 2) of the wavelength at the operating frequency of the guided surface waveguide probe 200f.
• the electrical length of the coil l_i a is specified as approximately one-half (1/2) the wavelength at the operating frequency, it is understood that the coil L a may be specified with an electrical length at other values. According to one embodiment, the fact that the coil l_i a has an electrical length of approximately one-half the wavelength at the operating frequency provides for an advantage in that a maximum voltage differential is created on the charge terminals ⁇ and T 2 . Nonetheless, the length or diameter of the coil l_i a may be increased or decreased when adjusting the guided surface waveguide probe 200f to obtain optimal excitation of a guided surface wave mode. Adjustment of the coil length may be provided by taps located at one or both ends of the coil. In other embodiments, it may be the case that the inductive impedance is specified to have an electrical length that is significantly less than or greater than 1 ⁇ 2 the wavelength at the operating frequency of the guided surface waveguide probe 200f.
• the excitation source 212 can be coupled to the feed network 209 by way of magnetic coupling. Specifically, the excitation source 212 is coupled to a coil L P that is inductively coupled to the coil l_i a . This may be done by link coupling, a tapped coil, a variable reactance, or other coupling approach as can be appreciated. To this end, the coil L P acts as a primary, and the coil l_i a acts as a secondary as can be appreciated.
• the heights of the respective charge terminals Ti and T 2 may be altered with respect to the lossy conducting medium 203 and with respect to each other. Also, the sizes of the charge terminals and T 2 may be altered. In addition, the size of the coil L a may be altered by adding or eliminating turns or by changing some other dimension of the coil L a .
• the coil L a can also include one or more taps for adjusting the electrical length as shown in FIG. 17. The position of a tap connected to either charge terminal Ti or T 2 can also be adjusted.
• FIGS. 18A, 18B, 18C and 19 shown are examples of generalized receive circuits for using the surface-guided waves in wireless power delivery systems.
• FIGS. 18A and 18B-18C include a linear probe 303 and a tuned resonator 306, respectively.
• FIG. 19 is a magnetic coil 309 according to various embodiments of the present disclosure.
• each one of the linear probe 303, the tuned resonator 306, and the magnetic coil 309 may be employed to receive power transmitted in the form of a guided surface wave on the surface of a lossy conducting medium 203 according to various embodiments.
• the lossy conducting medium 203 comprises a terrestrial medium (or Earth).
• the open-circuit terminal voltage at the output terminals 312 of the linear probe 303 depends upon the effective height of the linear probe 303. To this end, the terminal point voltage may be calculated as
• V T e Einc - dl, (96) where E inc is the strength of the incident electric field induced on the linear probe 303 in Volts per meter, dl is an element of integration along the direction of the linear probe 303, and h e is the effective height of the linear probe 303.
• An electrical load 315 is coupled to the output terminals 312 through an impedance matching network 318.
• the linear probe 303 When the linear probe 303 is subjected to a guided surface wave as described above, a voltage is developed across the output terminals 312 that may be applied to the electrical load 315 through a conjugate impedance matching network 318 as the case may be.
• the electrical load 315 In order to facilitate the flow of power to the electrical load 315, the electrical load 315 should be substantially impedance matched to the linear probe 303 as will be described below.
• the tuned resonator 306a also includes a receiver network comprising a coil L R having a phase shift ⁇ .
• One end of the coil L R is coupled to the charge terminal T R
• the other end of the coil L R is coupled to the lossy conducting medium 203.
• the receiver network can include a vertical supply line conductor that couples the coil L R to the charge terminal T R .
• the coil L R (which may also be referred to as tuned resonator L R -C R ) comprises a series-adjusted resonator as the charge terminal C R and the coil L R are situated in series.
• the phase delay of the coil L R can be adjusted by changing the size and/or height of the charge terminal T R , and/or adjusting the size of the coil L R so that the phase ⁇ of the structure is made substantially equal to the angle of the wave tilt ⁇ .
• the phase delay of the vertical supply line can also be adjusted by, e.g., changing length of the conductor.
• the reactance presented by the self-capacitance C R is calculated as l/ wC s .
• the total capacitance of the structure 306a may also include capacitance between the charge terminal T R and the lossy conducting medium 203, where the total capacitance of the structure 306a may be calculated from both the self-capacitance C R and any bound capacitance as can be appreciated.
• the charge terminal T R may be raised to a height so as to substantially reduce or eliminate any bound capacitance. The existence of a bound capacitance may be determined from capacitance measurements between the charge terminal T R and the lossy conducting medium 203 as previously discussed.
• the inductive reactance presented by a discrete-element coil L R may be calculated as / ⁇ , where L is the lumped-element inductance of the coil L R . If the coil L R is a distributed element, its equivalent terminal-point inductive reactance may be determined by conventional approaches.
• To tune the structure 306a one would make adjustments so that the phase delay is equal to the wave tilt for the purpose of mode-matching to the surface waveguide at the frequency of operation. Under this condition, the receiving structure may be considered to be "mode-matched" with the surface waveguide.
• a transformer link around the structure and/or an impedance matching network 324 may be inserted between the probe and the electrical load 327 in order to couple power to the load. Inserting the impedance matching network 324 between the probe terminals 321 and the electrical load 327 can effect a conjugate-match condition for maximum power transfer to the electrical load 327.
• an electrical load 327 may be coupled to the structure 306a by way of magnetic coupling, capacitive coupling, or conductive (direct tap) coupling.
• the elements of the coupling network may be lumped components or distributed elements as can be appreciated.
• magnetic coupling is employed where a coil l_s is positioned as a secondary relative to the coil L R that acts as a transformer primary.
• the coil L s may be link-coupled to the coil L R by geometrically winding it around the same core structure and adjusting the coupled magnetic flux as can be appreciated.
• the receiving structure 306a comprises a series-tuned resonator, a parallel-tuned resonator or even a distributed-element resonator of the appropriate phase delay may also be used.
• a receiving structure immersed in an electromagnetic field may couple energy from the field
• polarization-matched structures work best by maximizing the coupling, and conventional rules for probe-coupling to waveguide modes should be observed.
• a TE 20 (transverse electric mode) waveguide probe may be optimal for extracting energy from a conventional waveguide excited in the TE 20 mode.
• a mode-matched and phase-matched receiving structure can be optimized for coupling power from a surface-guided wave.
• the guided surface wave excited by a guided surface waveguide probe 200 on the surface of the lossy conducting medium 203 can be considered a waveguide mode of an open waveguide. Excluding waveguide losses, the source energy can be completely recovered.
• Useful receiving structures may be E-field coupled, H-field coupled, or surface-current excited.
• the receiving structure can be adjusted to increase or maximize coupling with the guided surface wave based upon the local characteristics of the lossy conducting medium 203 in the vicinity of the receiving structure.
• Equation (97) the wave tilt angle ( ⁇ ) can be determined from Equation (97).
• phase delays (0 C + 0 y ) can be adjusted to match the phase shift ⁇ to the angle ( ⁇ ) of the wave tilt.
• a portion of the coil can be bypassed by the tap connection as illustrated in FIG. 18B.
• the vertical supply line conductor can also be connected to the coil L R via a tap, whose position on the coil may be adjusted to match the total phase shift to the angle of the wave tilt.
• the coupling into the guided surface waveguide mode may be maximized.
• FIG. 18D shown is a flow chart 180 illustrating an example of adjusting a receiving structure to substantially mode-match to a guided surface waveguide mode on the surface of the lossy conducting medium 203.
• the receiving structure includes a charge terminal T R (e.g., of the tuned resonator 306a of FIG. 18B)
• the charge terminal T R is positioned at a defined height above a lossy conducting medium 203 at 184.
• the physical height (h p ) of the charge terminal T R may be below that of the effective height.
• the physical height may be selected to reduce or minimize the bound charge on the charge terminal T R (e.g., four times the spherical diameter of the charge terminal). If the receiving structure does not include a charge terminal T R (e.g., of the tuned resonator 306b of FIG. 18C), then the flow proceeds to 187.
• the electrical phase delay ⁇ of the receiving structure is matched to the complex wave tilt angle ⁇ defined by the local characteristics of the lossy conducting medium 203.
• the phase delay (0 C ) of the helical coil and/or the phase delay (0 y ) of the vertical supply line can be adjusted to make ⁇ equal to the angle ( ⁇ ) of the wave tilt (W).
• the angle ( ⁇ ) of the wave tilt can be determined from Equation (86).
• the electrical phase ⁇ can then be matched to the angle of the wave tilt.
• the load impedance of the charge terminal T R can be tuned to resonate the equivalent image plane model of the tuned resonator 306a.
• the depth (d/2) of the conducting image ground plane 139 (FIG. 9A) below the receiving structure can be determined using Equation (100) and the values of the lossy conducting medium 203 (e.g., the Earth) at the receiving structure, which can be locally measured.
• the impedance (Z in ) as seen "looking down" into the lossy conducting medium 203 can then be determined using Equation (99). This resonance relationship can be considered to maximize coupling with the guided surface waves.
• the impedance (Z base ) of the tuned resonator 306a as seen "looking up” into the coil L R can be determined using Equations (101), (102), and (103).
• the equivalent image plane model of FIG. 9A also applies to the tuned resonator 306a of FIG. 18B.
• the impedance at the physical boundary 136 (FIG. 9A) "looking up" into the coil of the tuned resonator 306a is the conjugate of the impedance at the physical boundary 136 "looking down" into the lossy conducting medium 203.
• An iterative approach may be taken to tune the load impedance Z R for resonance of the equivalent image plane model with respect to the conducting image ground plane 139. In this way, the coupling of the electric field to a guided surface waveguide mode along the surface of the lossy conducting medium 203 (e.g., Earth) can be improved and/or maximized.
• the magnetic coil 309 comprises a receive circuit that is coupled through an impedance matching network 333 to an electrical load 336.
• the magnetic coil 309 may be positioned so that the magnetic flux of the guided surface wave, ⁇ ⁇ , passes through the magnetic coil 309, thereby inducing a current in the magnetic coil 309 and producing a terminal point voltage at its output terminals 330.
• the magnetic flux of the guided surface wave coupled to a single turn coil is expressed by
• T ⁇ ⁇ ⁇ ⁇ 0 ⁇ - ⁇ (104)
• T is the coupled magnetic flux
• ⁇ ⁇ is the effective relative permeability of the core of the magnetic coil 309
• ⁇ 0 is the permeability of free space
• H is the incident magnetic field strength vector
• n is a unit vector normal to the cross-sectional area of the turns
• a cs is the area enclosed by each loop.
• the magnetic coil 309 may be tuned to the guided surface wave frequency either as a distributed resonator or with an external capacitor across its output terminals 330, as the case may be, and then impedance-matched to an external electrical load 336 through a conjugate impedance matching network 333.
• the current induced in the magnetic coil 309 may be employed to optimally power the electrical load 336.
• the receive circuit presented by the magnetic coil 309 provides an advantage in that it does not have to be physically connected to the ground.
• the receive circuits presented by the linear probe 303, the mode-matched structure 306, and the magnetic coil 309 each facilitate receiving electrical power transmitted from any one of the embodiments of guided surface waveguide probes 200 described above.
• the energy received may be used to supply power to an electrical load 315/327/336 via a conjugate matching network as can be appreciated.
• the receive circuits presented by the linear probe 303, the mode-matched structure 306, and the magnetic coil 309 will load the excitation source 212 (e.g., FIGS. 3, 12 and 16) that is applied to the guided surface waveguide probe 200, thereby generating the guided surface wave to which such receive circuits are subjected.
• the excitation source 212 e.g., FIGS. 3, 12 and 16
• the guided surface wave generated by a given guided surface waveguide probe 200 described above comprises a transmission line mode.
• a power source that drives a radiating antenna that generates a radiated electromagnetic wave is not loaded by the receivers, regardless of the number of receivers employed.
• one or more guided surface waveguide probes 200 and one or more receive circuits in the form of the linear probe 303, the tuned mode-matched structure 306, and/or the magnetic coil 309 can make up a wireless distribution system.
• the distance of transmission of a guided surface wave using a guided surface waveguide probe 200 as set forth above depends upon the frequency, it is possible that wireless power distribution can be achieved across wide areas and even globally.
• the conventional wireless-power transmission/distribution systems extensively investigated today include "energy harvesting" from radiation fields and also sensor coupling to inductive or reactive near-fields.
• the present wireless-power system does not waste power in the form of radiation which, if not intercepted, is lost forever.
• the presently disclosed wireless-power system limited to extremely short ranges as with conventional mutual-reactance coupled near-field systems.
• the wireless-power system disclosed herein probe-couples to the novel surface-guided transmission line mode, which is equivalent to delivering power to a load by a wave-guide or a load directly wired to the distant power generator.
• FIGS. 20A-E shown are examples of various schematic symbols that are used with reference to the discussion that follows.
• a depiction of this symbol will be referred to as a guided surface waveguide probe P.
• any reference to the guided surface waveguide probe P is a reference to any one of the guided surface waveguide probes 200a, 200b, 200c, 200e, 200d, or 200f; or variations thereof.
• a symbol that represents a guided surface wave receive structure that may comprise any one of the linear probe 303 (FIG. 18A), the tuned resonator 306 (FIGS. 18B-18C), or the magnetic coil 309 (FIG. 19).
• a depiction of this symbol will be referred to as a guided surface wave receive structure R.
• any reference to the guided surface wave receive structure R is a reference to any one of the linear probe 303, the tuned resonator 306, or the magnetic coil 309; or variations thereof.
• FIG. 20C shown is a symbol that specifically represents the linear probe 303 (FIG. 18A).
• a depiction of this symbol will be referred to as a guided surface wave receive structure R P .
• any reference to the guided surface wave receive structure R P is a reference to the linear probe 303 or variations thereof.
• FIG. 20D shown is a symbol that specifically represents the tuned resonator 306 (FIGS. 18B-18C).
• a depiction of this symbol will be referred to as a guided surface wave receive structure R R .
• any reference to the guided surface wave receive structure R R is a reference to the tuned resonator 306 or variations thereof.
• FIG. 20E shown is a symbol that specifically represents the magnetic coil 309 (FIG. 19).
• a depiction of this symbol will be referred to as a guided surface wave receive structure R M .
• any reference to the guided surface wave receive structure R M is a reference to the magnetic coil 309 or variations thereof.
• a navigation device detects multiple guided surface waves launched from multiple guided surface wave waveguide probes P. By analyzing the time difference on arrival of the guided surface waves, the time each of the guided surface waves spent traveling from the corresponding guided surface wave waveguide probe P to the location of the navigation device, the difference in the intensity of the guided surface waves at the location of the navigation device compared to the original intensity of the guided surface waves, the phase shift between the guided surface waves measured at the location of the navigation device, or some combination of these approaches, the location of the navigation device on the Earth may be determined. Further, in some embodiments, the navigation device may be powered by one or more of the guided surface waves. Moreover, the guide surface waves may be used for time synchronization to improve the accuracy of the navigation device and/or other devices.
• the range of the guided surface waves is dependent on the frequency of the guided surface waves.
• guided surface waves with a frequency of approximately 20kHz or less are capable of travelling around the earth.
• the various embodiments of the present disclosure may be used for global positioning and navigation. Higher frequencies will go shorter distances, such as hundreds or tens of miles, limiting the various embodiments to regional usage for position and navigation.
• the frequency of the guided surface wave may also determine whether the guided surface wave travels at a uniform speed around the entire Earth. Specifically, the lower the frequency, the more likely that the guided surface wave will be uniform around its circumference. However, at higher frequencies, local terrain or water may cause a difference in the speed of propagation. Such effects should be taken into account in the various embodiments described herein if they are significant.
• the navigation unit 400 includes a receiver 403, an antenna mount 406, and a computing device 409.
• the receiver 403 is connected to the antenna mount 406, which is in turn connected to the computing device 409.
• the navigation unit 400 may include a display.
• the display may comprise, for example, one or more devices such as liquid crystal display (LCD) displays, gas plasma- based flat panel displays, organic light emitting diode (OLED) displays, electrophoretic ink (E ink) displays, LCD projectors, or other types of display devices, etc.
• LCD liquid crystal display
• OLED organic light emitting diode
• E ink electrophoretic ink
• the navigation unit 400 may be enclosed in an external case that protects the various components of the navigation unit 400.
• the navigation unit 400 may be a portable or handheld unit, with the receiver 403, the antenna mount 406, and the computing device 409 enclosed within a single shell.
• Such embodiments may include a mobile computing device, such as a tablet computer, a cellular phone, a smart phone, a personal digital assistant (PDA), and/or similar mobile computing device.
• PDA personal digital assistant
• Such embodiments may also include a dedicated navigation unit, such as personal navigation devices, handheld navigation devices, or navigation devices that can be mounted to the dashboard of a bus, automobile, motor boat, or similar vehicle.
• the receiver 403 may be remote or external to the computing device 409 and connected to the computing device via the antenna mount 406.
• vehicular navigation units 400 such as those found on ships or in airplanes.
• the receiver 403 may correspond to one or more structures capable of receiving a guided surface wave.
• the receiver 403 may include, for example, a linear probe, a tuned resonator, a magnetic coil, and/or similar structures for receiving a guided surface wave, as previously described above.
• the receiver 403 may represent a plurality of receivers 403, each of which is tuned to receive a guided surface wave on a different frequency from the other receivers 403.
• the receiver 403 may be configured to be tuned to receive multiple guided surface waves on different frequencies simultaneously.
• the receiver 403 may be configured to alternate frequencies in order to detect, receive, and/or measure a guided surface wave on a first frequency and then switch to a second frequency to detect a second guided surface wave on a second frequency.
• the antenna mount 406 may correspond to any physical structure capable of connecting the receiver 403 to the computing device 409.
• the computing device 409 can also include at least one processor circuit having a processor 413 and a memory 416, both of which are coupled to a local interface 419.
• the local interface 419 may comprise, for example, a data bus with an accompanying address/control bus or other bus structure as can be appreciated.
• Stored in the memory 416 are both data and several components that are executable by the processor 413.
• stored in the memory 416 and executable by the processor 413 is a multilateration application 423, and potentially other applications.
• Also stored in the memory 416 may be a data store 426, which may store map data 429, inertial data 431 , and/or potentially other data.
• an operating system may be stored in the memory 416 and executable by the processor 413.
• the map data 429 represents one or more geographies within which the navigation unit 400 may be navigating or in which geolocation may be occurring.
• Map data 429 may include global data, or data related to particular regions or locales, such as a hemisphere, continent, ocean, sea, lake, country, state/province, city, and/or portions thereof.
• Map data 429 may also include one or more coordinate systems for identifying a location on the globe, or within a particular region or locale. Such coordinate systems may include latitude and longitude lines, the Universal Transverse Mercator (UTM) coordinate system, the Universal Polar Stereographic (UPS) coordinate system, a grid system, and/or other coordinate systems.
• UDM Universal Transverse Mercator
• UPS Universal Polar Stereographic
• the map data 429 can include relevant data necessary to disambiguate between locations on the globe. This can include a list of cellular networks in various countries or regions. This can include a list of radio or television broadcast stations in various countries or regions. In some instances, this can include a list of media access control (MAC) addresses for wireless network access points at various locations. In various instances, this can also include data related to specific ground stations located around the globe. Such data can include the location of the ground station, a base frequency of a primary guided surface wave launched from a guided surface waveguide probe at the ground station, and the frequencies at which overlaid guided surface waves are launched from one or more other guided surface waveguide probes at the ground station. The data can also include the initial phase at which the various guided surface waves are launched from the ground station.
• MAC media access control
• the multilateration application 423 is executed to identify the location of the navigation unit 400 based on one or more guided surface waves received by the navigation unit 400. For example, the multilateration application 423 can determine which overlaid guided surface waves are reaching the navigation unit 400 in order to determine which wavelength of a base guided surface wave the navigation unit 400 is currently within. The multilateration application 423 can then determine the position of the navigation unit 400 within the wavelength from the phase of the base guided surface wave at the location of the navigation unit 400. Based on the position, the multilateration application 423 can calculate the distance from the ground station that includes the guided surface waveguide probe that launched the base guided surface wave.
• any one of a number of programming languages may be employed such as, for example, C, C++, C#, Objective C, Java ® , JavaScript ® , Perl, PHP, Visual Basic ® , Python ® , Ruby, Flash ® , or other programming languages.
• a number of software components are stored in the memory 416 and are executable by the processor 413.
• the term "executable” means a program file that is in a form that can ultimately be run by the processor 413.
• Examples of executable programs may be, for example, a compiled program that can be translated into machine code in a format that can be loaded into a random access portion of the memory 416 and run by the processor 413, source code that may be expressed in proper format such as object code that is capable of being loaded into a random access portion of the memory 416 and executed by the processor 413, or source code that may be interpreted by another executable program to generate instructions in a random access portion of the memory 416 to be executed by the processor 413, etc.
• An executable program may be stored in any portion or component of the memory 416 including, for example, random access memory (RAM), read-only memory (ROM), hard drive, solid-state drive, USB flash drive, memory card, optical disc such as compact disc (CD) or digital versatile disc (DVD), floppy disk, magnetic tape, or other memory components.
• RAM random access memory
• ROM read-only memory
• hard drive solid-state drive
• USB flash drive USB flash drive
• memory card such as compact disc (CD) or digital versatile disc (DVD), floppy disk, magnetic tape, or other memory components.
• CD compact disc
• DVD digital versatile disc
• the memory 416 is defined herein as including both volatile and nonvolatile memory and data storage components. Volatile components are those that do not retain data values upon loss of power. Nonvolatile components are those that retain data upon a loss of power.
• the memory 416 may comprise, for example, random access memory (RAM), read-only memory (ROM), hard disk drives, solid-state drives, USB flash drives, memory cards accessed via a memory card reader, floppy disks accessed via an associated floppy disk drive, optical discs accessed via an optical disc drive, magnetic tapes accessed via an appropriate tape drive, and/or other memory components, or a combination of any two or more of these memory components.
• the processor 413 may represent multiple processors 413 and/or multiple processor cores and the memory 416 may represent multiple memories 416 that operate in parallel processing circuits, respectively.
• the local interface 419 may be an appropriate network that facilitates communication between any two of the multiple processors 413, between any processor 413 and any of the memories 416, or between any two of the memories 416, etc.
• the local interface 419 may comprise additional systems designed to coordinate this communication, including, for example, performing load balancing.
• the processor 413 may be of electrical or of some other available construction.
• multilateration application 423 may be embodied in software or code executed by general purpose hardware as discussed above, as an alternative the same may also be embodied in dedicated hardware or a combination of software/general purpose hardware and dedicated hardware. If embodied in dedicated hardware, each can be implemented as a circuit or state machine that employs any one of or a combination of a number of technologies. These technologies may include, but are not limited to, discrete logic circuits having logic gates for implementing various logic functions upon an application of one or more data signals, application specific integrated circuits (ASICs) having appropriate logic gates, field- programmable gate arrays (FPGAs), or other components, etc. Such technologies are generally well known by those skilled in the art and, consequently, are not described in detail herein.
• a ground station 500 launches a base guided surface wave corresponding to a standing guided surface wave.
• the base guided surface wave traverses the Earth and reflects from the antipode of the ground station 500 to create a standing wave, the base guided surface wave is illustrated herein as having a range equal to that of the bas knee 503 for illustrative purposes.
• the ground station 500 also launches a number of overlaid guided surface waves at higher frequencies, which travel shorter distances before suddenly dissipating at the respective overlaid knees 506a, 506b, 506c, and 506d.
• the ground station 500 can include a single guided surface waveguide probe P.
• the single guided surface waveguide probe P can be configured to launch the base guided surface wave and each of the overlaid guided surface waves.
• the single guided surface waveguide probe P may first launch the based guided surface wave, then reconfigure itself (or be reconfigured) to launch a first overlaid guided surface wave at a first frequency at a later specified time.
• the single guided surface waveguide probe could then continue to launch additional overlaid guided surface waves before cycling back to relaunch the base guided surface wave, continuing the cycle.
• FIG. 23 shown is another illustration of some of the principals underlying geolocation using guided surface waves.
• the overlaid knees 506a, 506b, 506c, and 506d of the overlaid guided surface waves occur one wavelength of the base guided surface wave apart.
• Between the ground station 500 (FIG. 22) and the first overlaid knee 506a is a distance equal to a first wavelength 509a of the base guided surface wave of the base guided surface wave.
• the distance between the first overlaid knee 506a and the second overlaid knee 506b is a distance equal to a second wavelength 509b of the base guided surface wave.
• the distance between the second overlaid knee 506b and the third overlaid knee 506c is equal to a third wavelength 509c of the base guided surface wave.
• the distance between the third overlaid knee 506c and a fourth overlaid knee 506d is equal to a fourth wavelength 509d of the base guided surface wave.
• the navigation unit 400 can determine its location based on which of the overlaid guided surface waves it can receive. For example, if the navigation unit 400 determined that it could receive the overlaid guided surface waves corresponding to the third overlaid knee 506c, but not the guided surface wave corresponding to the second overlaid knee 506b, the navigation unit 400 could determine that its position is somewhere between the second overlaid knee 506b and the third overlaid knee 506c. By determining the phase of the base guided surface wave, the navigation unit 400 could determine where it was between the second overlaid knee 506b and the third overlaid knee 506c. [0214] Referring next to FIG.
• a first ground station 500a launches a first base guided surface wave and several overlaid guided surface waves.
• the navigation unit 400 receives the first base guided surface wave at a point along a first circumference of a first circle 513a.
• a second ground station 500b launches a second based guided surface wave and several overlaid guided surface waves.
• the navigation unit 400 receives the second based guided surface wave at a point somewhere along a second circumference of a second circle 513b.
• the navigation unit 400 also receives some of the overlaid guided surface waves launched from the first ground station 500a and some of the overlaid guided surface waves launched from the second ground station 500b.
• the navigation unit 400 can use the overlaid guided surface waves that are received to determine the distance of the navigation unit 400 from each ground station. For example, if the navigation unit 400 were to receive a second overlaid guided surface wave launched from the first ground station 500a with a second overlaid knee 506b, but not a first overlaid guided surface wave launched from the first ground station 500a, then the navigation unit 400 could determine how far it is from the first ground station 500a. This would correspond to a radius for the first circumference of the first circle 513a.
• FIG. 25 shown is a flowchart that provides one example of the operation of a portion of the multilateration application 423 according to various embodiments. It is understood that the flowchart of FIG. 25 provides merely an example of the many different types of functional arrangements that may be employed to implement the operation of the portion of the multilateration application 423 as described herein. As an alternative, the flowchart of FIG. 25 may be viewed as depicting an example of elements of a method implemented in the computing device 409 (FIG. 21) according to one or more embodiments.
• the multilateration application 423 determines whether the navigation unit 400 is receiving guided surface waves from a minimum number of distinct ground stations and, therefore, a minimum number of distinct probes. For example, some embodiments of the invention may require that the navigation unit 400 receive guided surface waves launched from at least two different ground stations, while other embodiments may require that the navigation unit 400 receive guided surface waves launched from additional ground stations for increased accuracy. If the navigation unit 400 is receiving guided surface waves from the requisite number of ground stations, then execution proceeds to box 606. Otherwise, execution ends.
• the multilateration application 423 identifies each base guided surface wave it is receiving and the corresponding ground station 500 (FIG. 24) that launched it. For example, the multilateration application 423 may identify all of the guided surface waves that the navigation unit 400 is currently receiving and reference map data 429 (FIG. 21) to determine which of the guided surface waves are base guided surface waves and which ground station 500 corresponds to each base guided surface wave received.
• the multilateration application 423 identifies the overlaid guided surface waves it is receiving from each ground station 500 (FIG. 24). For example, the multilateration application 423 may identify all guided surface waves it is currently receiving and then reference map data 429 to determine which of the guided surface waves are overlaid guided surface waves and the corresponding ground station 500 that launched each one.
• the multilateration application 423 causes the navigation unit 400 to determine or otherwise measure the phase of each base guided surface wave that the navigation unit 400 is receiving at its current location.
• the multilateration application 423 calculates a distance from each ground station 500 to the navigation unit 400. For each ground station, the multilateration application 423 first determines the wavelength of the corresponding base guided surface wave on which the navigation unit 400 is located. The multilateration application 423 then uses the phase of the base guided surface wave to determine where on the wavelength the navigation unit 400 is located. The multilateration application 423 then can reference map data 429 to determine the distance of the navigation unit 400 from the ground station 500 or the multilateration application 423 can calculate the distance from the ground station 500 according to the following equation:
• the multilateration application 423 can determine the number of whole wavelengths between the navigation unit 400 and a ground station 500 based on which overlaid guided surface waves launched by the ground station 500 are received by the navigation unit 400.
• a ground station 500 can launch a number of overlaid guided surface waves, each of which has a range equal to a whole number of wavelengths of the based guided surface wave.
• the navigation unit 400 is more than two, but less than three, whole wavelengths of the base guided surface wave away from the ground station 500.
• the multilateration application 423 calculates, plots, or otherwise generates a circumference of a circle 503 (FIG. 22) around each of the ground stations 500 or antipodes of the ground stations 500 in order to identify the location 506 of the navigation unit 400.
• the circumference of the circle may, for example, be calculated by creating a circle with a center equivalent to the location of the ground station 500 with a radius equal to the calculated distance to the location of the ground station 500.
• the circle may not correspond to a perfect circle, but may instead represent a shape that is substantially circular.
• the location of the ground station 500 may be previously known and stored in the memory 416 (FIG. 21) of the navigation device 400 or may be determined using various approaches.
• the multilateration application 423 identifies each intersection 516 where each circumference of each circle intersects every other circumference of every other circle. This intersection 516 represents a possible location of the navigation unit 400 relative to each of the ground stations 500.
• any logic or application described herein, including the multilateration application 423, that comprises software or code can be embodied in any non-transitory computer-readable medium for use by or in connection with an instruction execution system such as, for example, a processor 413 in a computer system or other system.
• the logic may comprise, for example, statements including instructions and declarations that can be fetched from the computer-readable medium and executed by the instruction execution system.
• a "computer-readable medium" can be any medium that can contain, store, or maintain the logic or application described herein for use by or in connection with the instruction execution system.
• any logic or application described herein, including the multilateration application 423, may be implemented and structured in a variety of ways.
• one or more applications described may be implemented as modules or components of a single application.
• terms such as “application,” “service,” “system,” “engine,” “module,” and so on may be interchangeable and are not intended to be limiting.
• Example embodiments of the present disclosure are provided in the following clauses. These clauses provide several examples of various embodiments of the present disclosure. However, the description provided in these clauses does not exclude alternative implementations or embodiments. Rather, these clauses are intended to provide an illustration of potential embodiments of the present disclosure.
• An apparatus comprising: a charge terminal elevated over a lossy conducting medium; a receiver network coupled between the charge terminal and the lossy conducting medium, the receiver network having a phase delay ( ⁇ ) that matches a wave tilt angle ( ⁇ ) associated with the guided surface wave, the wave tilt angle ( ⁇ ) based at least in part upon characteristics of the lossy conducting medium in a vicinity of the receiving structure; a processor; a memory; and an application stored in the memory and executable by the processor, wherein the application causes the apparatus to perform at least the following actions when executed by the processor: identify a wavelength and a phase of a base guided surface wave launched from a ground station and received by the receiver network; identify a range of an overlaid guided surface wave launched from the ground station and received by the receiver network, wherein the range of the overlaid guided surface wave is measured as a number of wavelengths of the base guided surface wave; calculate a distance of the receiver network from the ground station based at least in part on the phase of the base guided surface wave and the range of the over
• Clause 3 The apparatus of clause 1 or 2, wherein the application, when executed by the processor, further causes the apparatus to at least identify an approximate position of the receiver network based at least in part on inertial data associated with the apparatus, wherein the inertial data is stored in the memory of the apparatus; and wherein causing the apparatus to determine the location of the receiver network is further based at least in part on the approximate position of the receiver network.
• Clause 4 The apparatus of clause 1 or 2, wherein the application, when executed by the processor, further causes the apparatus to at least identify an approximate position of the receiver network is based at least in part on an identity of a cellular network tower within range of the receiver network; and wherein causing the apparatus to determine the location of the receiver network is further based at least in part on the approximate position of the receiver network.
• Clause 5 The apparatus of clause 1 or 2, wherein the application, when executed by the processor, further causes the apparatus to at least identify an approximate position of the receiver network based at least in part on an identity of a radio transmission tower within range of the receiver network; and wherein causing the apparatus to determine the location of the receiver network is further based at least in part on the approximate position of the receiver network.
• Clause 7 The apparatus of clauses 1-6, wherein the overlaid guided surface wave has a higher frequency than the base guided surface wave.
• a method comprising: receiving a base guided surface wave launched from a ground station; identifying a wavelength and a phase of the base guided surface wave; receiving an overlaid guided surface wave launched from the ground station; identifying a range of the overlaid guided surface wave, wherein the range of the overlaid guided surface wave is measured as a number of wavelengths of the base guided surface wave; calculating a distance from the ground station based at least in part on the phase of the base guided surface wave and the range of the overlaid guided surface wave; and determining a current location based at least in part on the distance from the ground station.
• Clause 9 The method of clause 8, further comprising: receiving a second based guided surface wave launched from a second ground station; identifying a second wavelength and a second phase of the second base guided surface wave; receiving a second overlaid guided surface wave launched from a second ground station; identifying a second range of the second overlaid guided surface wave launched, wherein the second range of the second overlaid guided surface wave is measured as a second number of wavelengths of the second based guided surface wave; calculating a second distance from the second ground station based at least in part on the second phase of the second base guided surface wave and the second range of the second overlaid guided surface wave; and wherein determining the location is further based at least in part on the second distance from the second ground station.
• Clause 10 The method of clause 8 or 9, further comprising identifying an approximate position based at least in part on inertial data, wherein determining the current location is further based at least in part on the approximate position.
• Clause 11 The method of clause 8 or 9, further comprising identifying an approximate position based at least in part on an identity of a cellular network tower, wherein determining the current location is further based at least in part on the approximate position.
• Clause 12 The method of clause 8 or 9, further comprising: receiving a broadcast transmission; identifying an approximate position based at least in part on an identity of the broadcast transmission; and wherein determining the current location is further based at least in part on the approximate position.
• Clause 13 The method of clauses 8 or 9, further comprising: receiving a signal from a wireless network; identifying a media access control (MAC) address associated with an access point for the wireless network; identifying an approximate position based at least in part on the MAC address; and wherein determining the current location is further based at least in part on the approximate position.
• MAC media access control
• Clause 14 The method of clauses 8-13, wherein the overlaid guided surface wave has a higher frequency than the base guided surface wave.
• a system comprising: a guided surface wave receive structure configured to obtain electrical energy from a guided surface wave traveling along a terrestrial medium; a processor; a memory; and an application stored in the memory that, when executed by the processor, causes the apparatus to at least: identify a wavelength and a phase of a base guided surface wave launched from a ground station and received by the guided surface wave receive structure; identify a range of an overlaid guided surface wave launched from the ground station and received by the guided surface wave receive structure, wherein the range of the overlaid guided surface wave is measured as a number of wavelengths of the base guided surface wave; calculate a distance of the guided surface wave receive structure from the ground station based at least in part on the phase of the base guided surface wave and the range of the overlaid guided surface wave; and determine a location of the guided surface wave receive structure based at least in part on the distance of the guided surface wave receive structure from the ground station.
• Clause 16 The system of claim 15, wherein the application, when executed by the processor, further causes the system to at least: identify a second wavelength and a second phase of a second base guided surface wave launched from a second ground station and received by the guided surface wave receive structure; identify a second range of a second overlaid guided surface wave launched from the second ground station and received by the guided surface wave receive structure, wherein the second range of the second overlaid guided surface wave is measured as a second number of wavelengths of the second based guided surface wave; calculate a second distance of the guided surface wave receive structure from the second ground station based at least in part on the second phase of the second base guided surface wave and the second range of the second overlaid guided surface wave; and causing the apparatus to determine the location of the guided surface wave receive structure is further based at least in part on the second distance of the guided surface wave receive structure from the second ground station.
• Clause 17 The system of clause 15 or 16, wherein the application, when executed by the processor, further causes the system to at least identify an approximate position of guided surface wave receive structure based at least in part on inertial data associated with the system, wherein the inertial data is stored in the memory of the system; and wherein causing the system to determine the location of the guided surface wave receive structure is further based at least in part on the approximate position of the guided surface wave receive structure.
• Clause 20 The system of clauses 15-19, wherein the overlaid guided surface wave has a higher frequency than the base guided surface wave.

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