Embedded Files
A presentation of classical antenna theory (by interface VAC) and celestial mechanics ( by interface Galileo ) on the computer screen by dsbirkett Address all correspondence to coolvariant@gmail.com
Use of interface VAC to demonstrate universality of Ampere's law.
As in the virtual anechoic chamber the target dA can be made any size and positioned easily with respect to any radiator, it is an ideal vehicle for illustration of Ampere's law, which relates the time rate of change of magnetic flux through the target dA and the line integral of the electric field around the perimeter of dA
A radiating dipole aligned along the y axis and about 1 m from the target produces electric flux through the target. The time derivative of the flux equals the line integral of magnetic field around dA.
Use of interface VAC to demonstrate universality of Faraday's law.
As in the virtual anechoic chamber the target dA can be made any size and positioned easily with respect to any radiator, it is an ideal vehicle for illustration of Faraday's law, which relates the time rate of change of electric flux through the target dA and the line integral of the magnetic field around the perimeter of dA .
Use of interface Galileo to demonstrate principle of least action.
The principle of least action can be illustrated using the Galileo interface developed in App Designer. The interface shows graphically that the action of any elliptical path is indeed a minimum for the actual path. If a deviation is of any kind is imposed upon the path, the Action of the motion is shown to increase. As the actual action is a minimum, its linear dependance on disturbance is shown to be 0 and it is of quadratic dependence at the minimum.
in MATLAB App Designer
Celestial Mechanics by interface Galileo
Classical Antenna Theory by interface VAC
Virtual Anechoic Chamber
The virtual anechoic chamber presents at the origin along the x axis in three dimensions one of many tuned radiators and their corresponding ideal detector configurations to show the predicted behavior of the radiator in a real anechoic chamber in which reflections off walls and auxiliary hardware are successfully rendered negligible.
1 Virtual Anechoic Chamber- Half Wave Dipole
The half wave dipole is tuned by length for resonance and deployed at the origin along the x axis in three dimensions for any operating frequency. The interface displays numerically the instantaneous current anywhere along the radiating element. The interface displays graphically the peak current along the radiating element. Target dA of arbitrary size can be placed anywhere with respect to the radiator to show graphically the polarization in that direction.
2 Virtual Anechoic Chamber- Poynting Vector
The Poynting vector in the three principal planes is displayed in blue for any deployment of radiator. The total power radiated by the element is shown in agreement with theory for peak element current amplitude and distribution.
3 Virtual Anechoic Chamber- Gauss Law
A sphere of radius r_o encompasses the origin. The flow of power through this sphere is calculated, along with the total power detected at infinity.
Following Gauss law the total power flux depends critically on the location of the radiator inside or outside the sphere. If the radiator is inside the sphere the total power through the sphere is equal to the total power detected at infinity, and is equal to the theoretical power, for both
half wave dipole and short dipole.
4 Virtual Anechoic Chamber- Faraday/Ampere Law
Faraday's law and Ampere's law relate the time derivatives of certain area defined fluxes to line integrals around the perimeter of these areas. The virtual anechoic chamber can position an arbitrary area dA almost without restriction with respect to a radiator, and can thus demonstrate these laws directly, continuously in operation of the interface.
5 Virtual Anechoic Chamber- Directivity
As the differential target dA can be made arbitrarily small, so the directivity of the radiator as defined in the references in the direction of dA can be estimated continuously. The maximum directivity of the half wave dipole at any frequency is 1.64. That of the short dipole is 1.5.
6 Virtual Anechoic Chamber- Quadrupole
The virtual anechoic chamber shows the phase relations between the currents on the elements
of the quadrupole and the Poynting field.
7 Virtual Anechoic Chamber- Multi element Yagi
The virtual anechoic chamber shows the phase relations between the currents on the elements of the quadrupole and the Poynting field.
8 Virtual Anechoic Chamber- Four turn helix
The half wave dipole is tuned by length for resonance and deployed at the origin in three dimensions for any operating frequency. The interface displays numerically the instantaneous current anywhere along the radiating element. Target dA of arbitrary size can be placed anywhere with respect to the radiator to show graphically the polarization in that direction.
9 Virtual Anechoic Chamber- Low Frequency Non Resonant Loop
The directional properties of the low frequency loop radiator are shown.
The structure of the electric field within the loop and its relation to the loop current are shown.
Calculus of Variations
Celestial Mechanics
Kepler's Laws
Introduction
Introduction
Precise measurement of the directional properties of a microwave antenna takes place in an anechoic chamber in which interfering radiation reflecting off walls and test equipment is reduced using absorbent materials. If these are effective at the test frequency, the anechoic chamber measures the directional properties of a radiator in empty space by incremental rotation of the radiator relative to a distant field detector in a noise environment of little or no coherent interference or environmental noise.
Precise measurement of the directional properties of a microwave antenna takes place in an anechoic chamber in which interfering radiation reflecting off walls and test equipment is reduced using absorbent materials. If these are effective at the test frequency, the anechoic chamber measures the directional properties of a radiator in empty space by incremental rotation of the radiator relative to a distant field detector in a noise environment of little or no coherent interference or environmental noise.
Such measurements and many more are much easier in a virtual anechoic chamber in which the chamber elements, radiator and detector, are replaced by three dimensional models subject to translation and rotation using interactive graphical software. The virtual anechoic chamber here developed in MATLAB App Designer will serve as a versatile graphing calculator for the myriad quantities and fields and concepts which comprise antenna theory.
Such measurements and many more are much easier in a virtual anechoic chamber in which the chamber elements, radiator and detector, are replaced by three dimensional models subject to translation and rotation using interactive graphical software. The virtual anechoic chamber here developed in MATLAB App Designer will serve as a versatile graphing calculator for the myriad quantities and fields and concepts which comprise antenna theory.
Main screen of the virtual anechoic chamber
Main screen of the virtual anechoic chamber
The main screen of the virtual chamber presents two projections and a variety of tables and graphics for essential characterization of a radiator. Here a half wave dipole in magenta resonant at 60 MHz, length 2.5 m, is positioned at the origin along the x axis and rotated 18 degrees around the z axis. The square target in white is at zenith 0 and range 5 m. The scale of length indicated at the origin is 5 m.
The main screen of the virtual chamber presents two projections and a variety of tables and graphics for essential characterization of a radiator. Here a half wave dipole in magenta resonant at 60 MHz, length 2.5 m, is positioned at the origin along the x axis and rotated 18 degrees around the z axis. The square target in white is at zenith 0 and range 5 m. The scale of length indicated at the origin is 5 m.
In the upper right the differentials of length and angle are set, and a radiator is selected and subject to translation and rotation by these quantities. In the lower left the range, azimuth, and zenith of the target are set. At the top two of a variety of graphics and projections are selected. At the bottom a table of quantities of interest computed from data is configured. This table indicates that the target of area dA=25 m^2 intercepts power dP of 93.8 uW. In the lower right the target position and real time field strengths at the target are presented. On the right variables subject to differential control are presented. Here the peak element current is set to provide for 1 mW total power emitted.
In the upper right the differentials of length and angle are set, and a radiator is selected and subject to translation and rotation by these quantities. In the lower left the range, azimuth, and zenith of the target are set. At the top two of a variety of graphics and projections are selected. At the bottom a table of quantities of interest computed from data is configured. This table indicates that the target of area dA=25 m^2 intercepts power dP of 93.8 uW. In the lower right the target position and real time field strengths at the target are presented. On the right variables subject to differential control are presented. Here the peak element current is set to provide for 1 mW total power emitted.
Elements of the chamber
Elements of the chamber
In the virtual chamber there are no problematic reflections and no confining walls, and the tedium of incrementally moving a clumsy detector relative to an unstable radiator is eliminated in favor of a large number of ideal field detectors and a model radiator, everything easily positioned and moved mathematically. Ideal detectors are transparent to one another, with perfect real time three axis calibration. The number of detectors employed and their configuration as a target is set by the operator. The main target dA is a square array of detectors. Importantly, dA is a true differential of arbitrary size which can be placed anywhere in the chamber, pointing at the origin.
In the virtual chamber there are no problematic reflections and no confining walls, and the tedium of incrementally moving a clumsy detector relative to an unstable radiator is eliminated in favor of a large number of ideal field detectors and a model radiator, everything easily positioned and moved mathematically. Ideal detectors are transparent to one another, with perfect real time three axis calibration. The number of detectors employed and their configuration as a target is set by the operator. The main target dA is a square array of detectors. Importantly, dA is a true differential of arbitrary size which can be placed anywhere in the chamber, pointing at the origin.
As the detectors are ideal, the potential accuracy of the virtual chamber as an emulator of the real thing is contingent upon a satisfactory model of the radiator. Following classical treatments, the calculator applies linearity and superposition to the well known field of the infinitesimal dipole to find the radiation field in three dimensions of the wide variety of familiar radiator geometries. The operator can set the dimensions, wavelength and resolution of the source at the origin, and then rotate and translate the source into a position relative to the target required for evaluation of the device. As in a real chamber, only the relative position of the radiator with respect to the detectors has physical significance. It is instructive to show this in operation. In a well designed real chamber it is easy to swap out and in different radiators for direct comparison without disturbing a configuration of detectors. This is of course also true of the virtual chamber.
As the detectors are ideal, the potential accuracy of the virtual chamber as an emulator of the real thing is contingent upon a satisfactory model of the radiator. Following classical treatments, the calculator applies linearity and superposition to the well known field of the infinitesimal dipole to find the radiation field in three dimensions of the wide variety of familiar radiator geometries. The operator can set the dimensions, wavelength and resolution of the source at the origin, and then rotate and translate the source into a position relative to the target required for evaluation of the device. As in a real chamber, only the relative position of the radiator with respect to the detectors has physical significance. It is instructive to show this in operation. In a well designed real chamber it is easy to swap out and in different radiators for direct comparison without disturbing a configuration of detectors. This is of course also true of the virtual chamber.
Differential control
Differential control
A single differential of angle is used to control rotation of the radiator and target, as well as the phase of the fields and currents within the chamber. A single differential of length is used for translation of the radiator and target, and to modify linear dimensions. Related physical quantities within the chamber such as current magnitude, power, field strength are also subject to incremental control. The length of the infinitesimal dipoles of which the radiator models are composed can be made as small as necessary, within processing limits, to satisfy resolution requirements.
A single differential of angle is used to control rotation of the radiator and target, as well as the phase of the fields and currents within the chamber. A single differential of length is used for translation of the radiator and target, and to modify linear dimensions. Related physical quantities within the chamber such as current magnitude, power, field strength are also subject to incremental control. The length of the infinitesimal dipoles of which the radiator models are composed can be made as small as necessary, within processing limits, to satisfy resolution requirements.
The differential target dA
The differential target dA
Two graphics, dA and dr, are used to show the polarization and amplitudes in real time of the electric and magnetic fields near target dA. Red indicates electric field and green indicates magnetic field. dA shows the electric and magnetic field polarization and amplitude and phase at each detector across dA. dr, a radius extending from dA, is used to show these transverse fields also. The fields at the center of dA are shown by the asterisks in dA, at the left extreme abscissa of dr, and numerically in the lower right corner. Importantly, these quantities are always in agreement. The phase and polarization of the field at dA can also be read from the comet diagrams in dA. The transverse fields shown in dA and dr are presented in the local spherical coordinates at dA. Yellow represents the phi component and cyan represents theta. This color code helps the operator to orient spatially with one another the many graphics and projections which present the fields at target dA , here for example projections XY, dA , and dr_transverse shown above.
Two graphics, dA and dr, are used to show the polarization and amplitudes in real time of the electric and magnetic fields near target dA. Red indicates electric field and green indicates magnetic field. dA shows the electric and magnetic field polarization and amplitude and phase at each detector across dA. dr, a radius extending from dA, is used to show these transverse fields also. The fields at the center of dA are shown by the asterisks in dA, at the left extreme abscissa of dr, and numerically in the lower right corner. Importantly, these quantities are always in agreement. The phase and polarization of the field at dA can also be read from the comet diagrams in dA. The transverse fields shown in dA and dr are presented in the local spherical coordinates at dA. Yellow represents the phi component and cyan represents theta. This color code helps the operator to orient spatially with one another the many graphics and projections which present the fields at target dA , here for example projections XY, dA , and dr_transverse shown above.
Presentation of data
Presentation of data
Data in real time from the detectors will suffice to find all dependent magnitudes of interest in the chamber, including average power flux, field intensity, current density, polarization, directivity, beam width. A variety of graphics and tables is employed to encompass all quantities and fields. Typically two graphics and a table of selected quantities will essentially describe a radiator in three dimensions. Importantly, data developed on any graphic or table is always consistent at any instant with that on any other, for any set of quantities under consideration, any configuration of source and target. This makes the virtual chamber a versatile graphing calculator for the innumerable functional, temporal, and spatial relationships found in antenna theory. Many quantities within the chamber are linearly or quadratically dependent on peak element current Io. These quantities can be manipulated under differential control as virtual independent variables by the calculator.
Data in real time from the detectors will suffice to find all dependent magnitudes of interest in the chamber, including average power flux, field intensity, current density, polarization, directivity, beam width. A variety of graphics and tables is employed to encompass all quantities and fields. Typically two graphics and a table of selected quantities will essentially describe a radiator in three dimensions. Importantly, data developed on any graphic or table is always consistent at any instant with that on any other, for any set of quantities under consideration, any configuration of source and target. This makes the virtual chamber a versatile graphing calculator for the innumerable functional, temporal, and spatial relationships found in antenna theory. Many quantities within the chamber are linearly or quadratically dependent on peak element current Io. These quantities can be manipulated under differential control as virtual independent variables by the calculator.
In operation of this interface, great use is made of the notation and concepts of differential and integral calculus in the spherical coordinate system. Antenna theory is classically developed in this setting, so the interface will serve not only as a graphing calculator for evaluation of specific radiators, but as an interface for presentation of the fundamentals of antenna theory and more generally electromagnetic field theory. The virtual chamber is effective in presenting the invisible three dimensional properties of the fields launched around a radiator in free space on the two dimensional computer screen
In operation of this interface, great use is made of the notation and concepts of differential and integral calculus in the spherical coordinate system. Antenna theory is classically developed in this setting, so the interface will serve not only as a graphing calculator for evaluation of specific radiators, but as an interface for presentation of the fundamentals of antenna theory and more generally electromagnetic field theory. The virtual chamber is effective in presenting the invisible three dimensional properties of the fields launched around a radiator in free space on the two dimensional computer screen
In the following paragraphs the properties of the half wave dipole in the virtual chamber are presented. Because of its importance this dipole is thoroughly analyzed in most antenna theory texts. The chamber shows numerically the well known independence of radiation resistance on frequency, and the maximum directivity 1.637 for the radiator. The chamber shows graphically the important dependence of the polarization of the launched field on element orientation. The chamber also shows graphically the phase relation between current within the radiating element and fields at the target.
In the following paragraphs the properties of the half wave dipole in the virtual chamber are presented. Because of its importance this dipole is thoroughly analyzed in most antenna theory texts. The chamber shows numerically the well known independence of radiation resistance on frequency, and the maximum directivity 1.637 for the radiator. The chamber shows graphically the important dependence of the polarization of the launched field on element orientation. The chamber also shows graphically the phase relation between current within the radiating element and fields at the target.
Half Wave Dipole at 1.5 GHz in the Virtual Chamber
Half Wave Dipole at 1.5 GHz in the Virtual Chamber
The fields and currents and their three dimensional relationships in and around a 1.5 GHz dipole are comprehensively displayed in real time graphically and numerically in the virtual chamber. The dipole element is of length 10 cm, one half wavelength, aligned at the origin along the x axis. Target dA is at range 20 cm along the z axis to show phase relationships. The peak current at the center of the resonant element is 1 A, yielding 36.95 W radiated power. The target dA = .04 m^2 intercepts 3.48 W of average power.
The fields and currents and their three dimensional relationships in and around a 1.5 GHz dipole are comprehensively displayed in real time graphically and numerically in the virtual chamber. The dipole element is of length 10 cm, one half wavelength, aligned at the origin along the x axis. Target dA is at range 20 cm along the z axis to show phase relationships. The peak current at the center of the resonant element is 1 A, yielding 36.95 W radiated power. The target dA = .04 m^2 intercepts 3.48 W of average power.
The Poynting vector in three planes is shown around the radiator in blue. The unit of length .2 m is indicated at the origin by the yellow + . The Poynting vector at the target is 120 W/m^2 in the z direction. The distribution of current along the resonant element is shown in green, maximum peak current Io = 1 A. The well known theoretical power out of a half wave, which depends quadratically only on peak current, is computed as 36.6 W, showing close agreement with the integrated value. This accuracy of about 1 part in 100 may be expected of estimates of this kind, due to various discrete integrations.
The Poynting vector in three planes is shown around the radiator in blue. The unit of length .2 m is indicated at the origin by the yellow + . The Poynting vector at the target is 120 W/m^2 in the z direction. The distribution of current along the resonant element is shown in green, maximum peak current Io = 1 A. The well known theoretical power out of a half wave, which depends quadratically only on peak current, is computed as 36.6 W, showing close agreement with the integrated value. This accuracy of about 1 part in 100 may be expected of estimates of this kind, due to various discrete integrations.
The element is represented by 20 short dipole radiators. Dipole 10 along the element is shown by coordinate and instantaneous current. The electric and magnetic fields at this instant at the target are shown lower right. Note that the cross product of the electric and magnetic field intensities at the target, the Poynting vector, points away from the source, in the positive z direction.
The element is represented by 20 short dipole radiators. Dipole 10 along the element is shown by coordinate and instantaneous current. The electric and magnetic fields at this instant at the target are shown lower right. Note that the cross product of the electric and magnetic field intensities at the target, the Poynting vector, points away from the source, in the positive z direction.
The transverse electric and magnetic fields along the radius dr = .4 m (two wavelengths) are shown at time 0 ns. The maximum values of electric and magnetic field at lower right are shown graphically at the origin of dr_transverse.
The transverse electric and magnetic fields along the radius dr = .4 m (two wavelengths) are shown at time 0 ns. The maximum values of electric and magnetic field at lower right are shown graphically at the origin of dr_transverse.
The period at 1.5 GHz is .666 ns. The chamber at time .666 ns is shown. The location of dipole 10 along the element is indicated by asterisk in the ZX projection. The coordinates and current at this point are shown on the right.
The period at 1.5 GHz is .666 ns. The chamber at time .666 ns is shown. The location of dipole 10 along the element is indicated by asterisk in the ZX projection. The coordinates and current at this point are shown on the right.
The differential of angle is set to 2pi/8, one eighth period, and the chamber is advanced to 75 ns. All fields and currents advance together.
The differential of angle is set to 2pi/8, one eighth period, and the chamber is advanced to 75 ns. All fields and currents advance together.
The differential of angle is set to 2pi/8, one eighth period, and the chamber is advanced to 83.3 ns. The real time current magnitude at dipole 10 is displayed. The field magnitude at the target is displayed. The Poynting field at the target on the z axis is 120 W/m^2.
The differential of angle is set to 2pi/8, one eighth period, and the chamber is advanced to 83.3 ns. The real time current magnitude at dipole 10 is displayed. The field magnitude at the target is displayed. The Poynting field at the target on the z axis is 120 W/m^2.
The collective current along an element is shown in real time by projection Source. Above at t = 0 ns the current at element center is maximum Io = 1 A . The target magnetic field at range 20 cm, one wavelength, is maximum .79 A/m
The collective current along an element is shown in real time by projection Source. Above at t = 0 ns the current at element center is maximum Io = 1 A . The target magnetic field at range 20 cm, one wavelength, is maximum .79 A/m
The collective current along the element at 16.6 ns, one quarter wavelength, momentarily vanishes, including at dipole 10.The familiar density of charge along the element at this instant is apparent graphically. The important phase relation between elements in a multi-element source is well displayed by projection Source.
The collective current along the element at 16.6 ns, one quarter wavelength, momentarily vanishes, including at dipole 10.The familiar density of charge along the element at this instant is apparent graphically. The important phase relation between elements in a multi-element source is well displayed by projection Source.
The element is rotated about the z axis by 2pi/20 radian. The transverse field around dr is rotated. Element dipole 10 is rotated. Note that the total power emitted, and the Poynting vector in the z direction, are unchanged.
The element is rotated about the z axis by 2pi/20 radian. The transverse field around dr is rotated. Element dipole 10 is rotated. Note that the total power emitted, and the Poynting vector in the z direction, are unchanged.
The instantaneous current 1 A at dipole 10 along the element is shown in I dl_element. Maximum current is indicated graphically when the asterisk-point charge is as shown, centered. The comet tail indicates polarization in the x direction. The comet tail is essential to showing the phase relationships which may be displayed, for example circular polarization.
The instantaneous current 1 A at dipole 10 along the element is shown in I dl_element. Maximum current is indicated graphically when the asterisk-point charge is as shown, centered. The comet tail indicates polarization in the x direction. The comet tail is essential to showing the phase relationships which may be displayed, for example circular polarization.
The instantaneous current 0 A at dipole 10 along the element is shown. The comet tail indicates polarization in the x direction. 0 current at this dipole is also indicated on the right.
The instantaneous current 0 A at dipole 10 along the element is shown. The comet tail indicates polarization in the x direction. 0 current at this dipole is also indicated on the right.
The transverse fields across the target are shown in projection dA. Maximum field obtains at the center of dA. Polarization across dA is almost constant. Comet diagrams indicate field polarized in x direction at target center.
The transverse fields across the target are shown in projection dA. Maximum field obtains at the center of dA. Polarization across dA is almost constant. Comet diagrams indicate field polarized in x direction at target center.
The element is rotated around the z axis by 2pi/20. Polarization at dA follows. The Poynting magnitude along z axis is unaltered.
The element is rotated around the z axis by 2pi/20. Polarization at dA follows. The Poynting magnitude along z axis is unaltered.
The line integrals of electric and magnetic field around the contour of dA are shown graphically. As dA may be positioned without restriction with respect to any source, it is an ideal vehicle for presentation of two laws, those of Ampere and Faraday. The magnetic and electric flux through dA can be calculated, and the time derivatives of these integrals compared to the respective line integrals to verify the validity of these fundamental equations.
The line integrals of electric and magnetic field around the contour of dA are shown graphically. As dA may be positioned without restriction with respect to any source, it is an ideal vehicle for presentation of two laws, those of Ampere and Faraday. The magnetic and electric flux through dA can be calculated, and the time derivatives of these integrals compared to the respective line integrals to verify the validity of these fundamental equations.
The target dA is a differential of arbitrarily small magnitude. dO is the solid angle subtended by dA. For any azimuth and zenith directivity of the half wave dipole in that direction can be estimated by finding the power density dP/dA of dP through dA in the limit dA small and r large. Following classical treatments dP/dA or dP/dO is normalized by the isotropic Poynting vector of the radiator, to form a quotient independent of power level. The isotropic Poynting vector of any radiator is calculated from the total power at infinity, which the chamber integrates with each step.
The target dA is a differential of arbitrarily small magnitude. dO is the solid angle subtended by dA. For any azimuth and zenith directivity of the half wave dipole in that direction can be estimated by finding the power density dP/dA of dP through dA in the limit dA small and r large. Following classical treatments dP/dA or dP/dO is normalized by the isotropic Poynting vector of the radiator, to form a quotient independent of power level. The isotropic Poynting vector of any radiator is calculated from the total power at infinity, which the chamber integrates with each step.
The directivity of the half wave dipole converges on the theoretical value for dA, dO small, r large. The accuracy of the integration of total power at infinity is typically set to about 1 part in 100.
The directivity of the half wave dipole converges on the theoretical value for dA, dO small, r large. The accuracy of the integration of total power at infinity is typically set to about 1 part in 100.
Several important features of the virtual anechoic chamber are used in the display the properties of the half wave dipole.
Several important features of the virtual anechoic chamber are used in the display the properties of the half wave dipole.
The familiar global directivity of this radiator in three planes is continuously displayed as the Poynting vector at infinity, in blue. This graphic of course moves with the radiator, just as in a real chamber.
The familiar global directivity of this radiator in three planes is continuously displayed as the Poynting vector at infinity, in blue. This graphic of course moves with the radiator, just as in a real chamber.
Source directivity is examined locally at any zenith and azimuth using the differentials dA and dP formed at the target dA. The quotient dP/dA is normalized by the total power emitted by the radiator, which is also integrated at infinity by the chamber. The quantities dA and dP are manipulated as true differentials of arbitrary magnitude in operation of the calculator.
Source directivity is examined locally at any zenith and azimuth using the differentials dA and dP formed at the target dA. The quotient dP/dA is normalized by the total power emitted by the radiator, which is also integrated at infinity by the chamber. The quantities dA and dP are manipulated as true differentials of arbitrary magnitude in operation of the calculator.
The fields around a radiator and the currents in its elements are invisible, yet their spatial and phase relationships are fundamental to the radiator's operation. The chamber can present graphically any current along an element, and the electromagnetic field at dA. These graphics are to be paired for comparison to show in three dimensions the relationship between element orientation and field polarization in real time. The chamber also presents graphically the collective current supported by a radiator as tuned, including the distinctive current of the resonant half wave dipole.
The fields around a radiator and the currents in its elements are invisible, yet their spatial and phase relationships are fundamental to the radiator's operation. The chamber can present graphically any current along an element, and the electromagnetic field at dA. These graphics are to be paired for comparison to show in three dimensions the relationship between element orientation and field polarization in real time. The chamber also presents graphically the collective current supported by a radiator as tuned, including the distinctive current of the resonant half wave dipole.
In the presentation of the anechoic chamber only the properties of sources of radiation have been considered. By the reciprocity theorem all directional estimates made by the calculator apply equally to structures of identical geometry employed as receive antennas.
In the presentation of the anechoic chamber only the properties of sources of radiation have been considered. By the reciprocity theorem all directional estimates made by the calculator apply equally to structures of identical geometry employed as receive antennas.
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DSBirkett Boston, June 2021
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