The invention relates to antenna arrangements having a plurality of frequency modes in the VHF, UHF, S, C, X or higher frequency bands. More precisely, an antenna arrangement of a compact form factor may be designed according to the invention to match a specification and built from a library of basic elements such as primary of secondary trunks, branches and leaves. Thanks to the invention, a designer of such antenna arrangements may be provided with tools and libraries that greatly improve his/her efficiency in the development of antennas.
There is a need for terminals or smartphones on-board aircraft, ships, trains, trucks, cars, or carried by pedestrians to be connected while on the move. All kinds of objects on-board vehicles or located in a manufacturing plant, an office, a warehouse, a storage facility, retail establishments, hospitals, sporting venues, or a home are connected to the Internet of Things (loT): tags to locate and identify objects in an inventory or to keep people in or out of a restricted area; devices to monitor physical activity or health parameters of their users; sensors to capture environmental parameters (concentration of pollutants, hygrometry, wind speed, etc.); actuators to remotely control and command all kinds of appliances, or more generally, any type of electronic device that could be part of a command, control, communication and intelligence system, the system being for instance programmed to capture/process signals/data, transmit the same to another electronic device, or a server, process the data using processing logic implementing artificial intelligence or knowledge based reasoning and return information or activate commands to be implemented by actuators.
RF communications are more versatile than fixed-line communications for connecting these types of objects or platforms. As a consequence, radiofrequency T/R modules are and will be more and more pervasive in professional and consumer applications. A plurality of T/R modules may be implemented on the same device. By way of example, a smartphone typically includes a cellular communications T/R module, a Wi-Fi/Bluetooth T/R module, a receiver of satellite positioning signals (from a Global Navigation Satellite System or GNSS). Wi-Fi™, Bluetooth™ and 3 or 4G cellular communications are in the 2,5 GHz frequency band (S-band). GNSS receivers typically operate in the 1,5 GHz frequency band (L-band). RadioFrequency IDentification (RFID) tags operate in the 900 MHz frequency band (UHF) or lower. Near Field Communication (NFC) tags operate in the 13 MHz frequency band (HF) at a very short distance (about 10 cm).
It seems that a good compromise for loT connections lies in VHF or UHF bands (30 to 300 MHz and 300 MHz to 3 GHz) to get sufficient available bandwidth and range, a good resilience to multipath reflections as well as a low-power budget.
A problem to be solved for the design of T/R modules at these frequency bands is to have antennas which are compact enough to fit in the form factor of a connected object. A traditional omnidirectional antenna of a monopole type, adapted for VHF bands, has a length between 25 cm and 2,5 m (λ/4). A solution to this problem is notably provided by PCT application published under n° WO2015007746, which has the same inventor and is co-assigned to the applicant of this application. This application discloses an antenna arrangement of a bung type, where a plurality of antenna elements are combined so that the ratio between the largest dimension of the arrangement and the wavelength may be much lower than a tenth of a wavelength, even lower than a twentieth or, in some embodiments than a fiftieth of a wavelength. To achieve such a result, the antenna element which controls the fundamental mode of the antenna is wound up in a 3D form factor, such as, for example, a helicoid, so that its outside dimensions are reduced relative to its length.
But there is also a need for the connected devices to be compatible with terminals which communicate using Wi-Fi or Bluetooth frequency bands and protocols. In this use case, some stages of the T/R module have to be compatible with both VHF and S bands. If a GNSS receiver is added, a T/R capacity in the L band is also needed. This means that the antenna arrangements of such devices should be able to communicate simultaneously or successively in different frequency bands. Adding as many antennas as frequency bands is costly in terms of form factor, power budget and materials. This creates another challenging problem for the design of the antenna. Some solutions are disclosed for base station antennas by PCT applications published under n° WO2001/22528 and WO2003/34544. But these solutions do not operate in VHF bands and do not provide arrangements which would be compact enough in these bands.
The applicant of this application has filed a European patent application published under n° EP3285333 that has the same inventor as this application. This application discloses a “bonsai” antenna arrangement, i.e. an antenna arrangement comprising: a first conductive element configured to radiate above a defined frequency of electromagnetic radiation; one or more additional (or secondary) conductive elements located at or near one or more positions defined as a function of positions of nodes of current (i.e. zero current or Open Circuit—OC—positions) of harmonics of the electromagnetic radiation.
The bonsai antenna arrangement disclosed by the said patent application provides a certain flexibility to adjust the radiating frequencies of the antenna around the higher order modes of the “trunk” antenna, thanks to “leaves” that are placed by the designer of the antenna arrangement at selected spots on the trunk. But this flexibility is constrained in certain limits. Notably, the number of frequencies that may be adjusted on a same trunk should in practice be limited to four (fundamental mode plus the three first higher order modes), to avoid electromagnetic coupling between the leaves added to the trunk. Also, the length of the leaves should remain a fraction of the length of the trunk to avoid perturbating the other modes, so that the shift in frequency is limited to a fraction of the value of the radiating frequency of each mode. Therefore, it is not possible to implement any kind of selected frequencies on an antenna arrangement of the type disclosed by this first patent application.
Some limitations of this prior art have been overcome to a certain extent by providing an addition of secondary trunks and/or branches to a primary trunk to increase the number of resonating frequencies of the antenna arrangement and enlarge its frequency domain of use, as disclosed by European patent application filed under n° EP2017/306929.5 with the same inventor and the same applicant as the instant application.
Also, this first application does not disclose how to control bandwidth around a resonating frequency. This drawback has been overcome to a certain extent by providing an addition of other resonating elements to a primary trunk at controlled positions to form a resonating structure of an order higher than one at a frequency of one of the selected harmonics of the electromagnetic radiation of the primary trunk, as disclosed by European patent application filed under n° EP2016/306768.9 with the same inventor and the same applicant as the instant application.
These three patent applications disclose design methods associated to the antenna arrangements that they disclose. But there is still a need for an antenna arrangement of a bonsai type that could be designed easily and rapidly to match a typical specification and then built to this design from a library of elementary components using design tools that are accessible to a person of ordinary skill in the design of antennas.
The instant patent application overcomes these limitations to a significant extent.
The invention fulfills this need by providing an antenna arrangement that is built from primary and secondary elements that can be drawn from a library of trunks, branches and/or leaves that are configurable and can be assembled according to a set of design rules based on a number of design parameters, such as their electromagnetic susceptance to match a desired specification in terms of resonating frequencies, bandwidths and form factors.
More specifically, the invention discloses antenna arrangement comprising: a primary conductive element having defined geometric parameters, the primary conductive element having a proximal end and a distal end, the proximal end being connected at a feed line (210), the distal end being an open circuit position, the primary conductive element defining a first plurality of resonating frequencies; one or more secondary conductive elements, each having defined geometric parameters, a proximal end and a distal end, the proximal end being connected at a feed connection on the primary conductive element, the distal end being an open circuit position and defining an orientation relative to the primary conductive element, the one or more secondary conductive elements generating a second plurality of resonating frequencies; wherein the frequencies in the second plurality of resonating frequencies each satisfy a condition of resonance at the feed line, the condition of resonance being determined by a sequence of combinations of input susceptances of a segment of the primary conductive element and of one of the one or more secondary conductive elements, each combination being generated at the feed connection of the said one of the one or more secondary conductive elements on the primary conductive element, a segment of the primary conductive element connecting one of its distal end or a feed connection of another of the one or more secondary conductive elements to the one of the one or more secondary elements, the sequence starting from the distal end of the primary conductive element and ending at its proximal end.
Advantageously, the second plurality of resonating frequencies is deduced from the first plurality of resonating frequencies by one or more of shifting one or more frequency values, enlarging a bandwidth of one or more frequencies in the plurality of resonating frequencies, or adding one or more new resonating frequencies.
Advantageously, the input susceptance of a segment of the primary conductive element is determined by the defined geometric parameters of the said primary conductive element.
Advantageously, the input susceptance of each one of the one or more secondary conductive elements depends on the defined geometric parameters of the said each one of the one or more secondary conductive elements, and on its orientation relative to the primary conductive element.
Advantageously, the defined geometric parameters of the primary conductive element and of each one of the one or more secondary elements comprise a geometry, a form factor and a main dimension.
Advantageously, one of the one or more secondary conductive elements has a main dimension that is lower than a quarter of a wavelength corresponding to a highest value in the second plurality of resonating frequencies of the antenna arrangement, the addition of the one or more secondary conductive elements having an effect of shifting one or more of the first plurality of resonating frequencies of the antenna arrangement.
Advantageously, one of the one or more secondary conductive elements has a main dimension that is higher than a quarter of a wavelength corresponding to a highest value in the second plurality of resonating frequencies of the antenna arrangement and lower than a quarter of a wavelength corresponding to the lowest value in the second plurality of resonating frequencies of the antenna arrangement.
Advantageously, the addition of the one or more secondary conductive elements has an effect of adding one or more potential new resonating frequencies to the first plurality of resonating frequencies of the antenna arrangement, the new resonating frequencies having values in between a value corresponding to a wavelength equal to a quarter of the main dimension of the said one of the one or more secondary conductive elements and the highest value in the second plurality of resonating frequencies.
Advantageously, one or more of the potential new resonating frequencies are new resonating frequencies if they are sufficiently separated from the all frequency values in the first plurality of resonating frequencies.
Advantageously, the addition of the one of the one or more secondary conductive elements has an effect of shifting one or more resonating frequencies in the first plurality of resonating frequencies of the antenna arrangement having values in between the lowest value in the second plurality of resonating frequencies and a frequency value corresponding to a wavelength equal to a quarter of the main dimension of the said one of the one or more secondary conductive elements , when the one of the one or more secondary conductive elements has a feed connection that is not located at the feed line.
Advantageously, one of the one or more secondary conductive elements has an input susceptance that equals a characteristic admittance of an equivalent monopole antenna multiplied by a tangent of a coefficient multiplied by an equivalent length of the one of the one or more secondary conductive elements, the coefficient being equal to 2πf/c where f is one of the plurality of resonating frequencies and c is the speed of light.
Advantageously, the one of the one or more secondary conductive elements has a feed connection at a distance ′ of the distal end of the primary conductive element and at a distance
″ of the proximal end of the primary conductive element, its input susceptance equaling a characteristic admittance of an equivalent monopole antenna multiplied by a difference between a cotangent of a coefficient multiplied by
and a tangent of a coefficient multiplied by
′, the coefficient being equal to 2πf/c where f is one of the plurality of resonating frequencies and c is the speed of light.
Advantageously, the one of the one or more secondary conductive elements has a feed connection at a distance ′ of the distal end of the primary conductive element and at a distance
″+
″ of the proximal end of the primary conductive element, the antenna arrangement further comprising another secondary conductive element having a feed connection at a distance
from the feed connection of the one of the one or more secondary conductive elements and at a distance
″ from the feed line, the input susceptance of the another secondary conductive element equaling a characteristic admittance of an equivalent monopole antenna multiplied by a difference between a cotangent of a coefficient multiplied by
″ and a tangent of a coefficient multiplied by a sum of
″ and a length equivalent to the one of the one or more secondary conductive element in parallel with the segment connecting the distal end of the primary conductive element to the feed connection of the one of the one or more secondary conductive element, the coefficient being equal to 2πf/c where f is one of the plurality of resonating frequencies and c is the speed of light.
Advantageously, the antenna arrangement of the invention further comprises one or more ternary conductive, each having defined geometric parameters, a proximal end and a distal end, the proximal end being connected at a feed connection on one of the one or more secondary conductive elements, the distal end being an open circuit position and defining an orientation relative to the one of the one or more secondary conductive elements.
Advantageously, the antenna arrangement of the invention further comprises one or more quaternary conductive elements each having defined geometric parameters, a proximal end and a distal end, the proximal end being connected at a feed connection on one of the one or more ternary conductive elements, the distal end being an open circuit position and defining an orientation relative to the one of the one or more ternary conductive elements.
Advantageously, the antenna arrangement of the invention is tuned to radiate in two or more frequency bands, comprising one or more of an ISM band, a Wi-Fi band, a Bluetooth band, a 3G band, a LTE band and a 5G band.
The invention further discloses a method of designing an antenna arrangement comprising: defining a primary conductive element with determined geometric parameters, the primary conductive element having a proximal end and a distal end, the proximal end being connected at a feed line, the distal end being an open circuit position, the primary conductive element defining a first plurality of resonating frequencies; defining one or more secondary conductive elements, each having determined geometric parameters, a proximal end and a distal end, the proximal end being connected at a feed connection on the primary conductive element, the distal end being an open circuit position and defining an orientation relative to the primary conductive element, the one or more secondary conductive elements generating a second plurality of resonating frequencies; wherein the geometric parameters of the primary conductive element and of the one or more secondary conductive elements are determined in such a way that the frequencies in the second plurality of resonating frequencies each satisfy a condition of resonance at the feed line, the condition of resonance being determined by a sequence of combinations of input susceptances of a segment of the primary conductive element and of one of the one or more secondary conductive elements, each combination being generated at the feed connection of the said one of the one or more secondary conductive elements on the primary conductive element, a segment of the primary conductive element connecting one of its distal end or a feed connection of another of the one or more secondary conductive elements to the one of the one or more secondary elements, the sequence starting from the distal end of the primary conductive element and ending at its proximal end.
Advantageously, the one or more secondary conductive elements are iteratively added at defined locations to the primary conductive element so as to match a specification of the antenna arrangement comprising the second plurality of predefined frequencies.
Advantageously, the one or more secondary conductive elements that are added to match the specification of the antenna arrangement are further defined to match a specified bandwidth for at least one or more frequencies in the second plurality of predefined frequencies.
Advantageously, the one or more secondary conductive elements that are added to match a specification are further defined to match a form factor of the antenna arrangement.
Advantageously, the one or more secondary elements are drawn from a database of predefined elements.
Advantageously, the predefined elements have been generated by using one or more of a graphical calculation based on Smith Charts, an analytical computation, a simulation tool or a model.
Advantageously, the matching the specification is performed by using one or more of a graphical calculation based on Smith Charts, an analytical computation, a simulation tool or a model.
Advantageously, the matching the specification if further performed by optimizing a cost function.
The antenna arrangement of the invention offers the advantage of providing a plurality of resonating frequencies on a very wide frequency domain, with controlled values and controlled bandwidths.
The antenna arrangement of the invention may be compact, allowing its integration in small volumes or reduced surfaces.
The antenna arrangement of the invention is advantageously simple to design, notably when tuning at least two radiating frequencies, but possibly more, to desired values, taking into account the impact of the environment of the antenna arrangement, notably the ground plane, the relative positioning of the first and second main conductive elements and of secondary conductive elements (or “leaves”) that have an electromagnetic impact on its electrical performance.
The antenna arrangement of the invention is easy to manufacture and thus has a very low cost.
Also, the antenna arrangement of the invention is very easy to connect either in an orthogonal configuration or in a coplanar configuration to a RF Printed Circuit Board (PCB).
In some optional embodiments, the bandwidths of a fundamental radiating frequency or of higher order modes may be controlled, taking into account a target matching level, so as to guarantee a minimum quality of service at these controlled frequencies to transmit video or other content that need a high throughput.
According to the invention, a plurality of design tools is provided that allow to find graphically, analytically or numerically (or using a combination of the three) the possible design parameters that match the specification.
The invention and its advantages will be better understood upon reading the following detailed description of a particular embodiment, given purely by way of non-limiting example, this description being made with reference to the accompanying drawings in which:
The problem to be solved by a designer of an antenna arrangement is to define the various elements of the antenna arrangement that allow matching the performance criteria of the technical specification. Typically, the performance criteria will comprise:
the values of the specified bandwidths around these centre frequencies, {Δfi, i ∈{1, . . . ,n}}.
There will generally be a plurality of solutions that will fulfil the specified requirements, so that other constraints may be added.
For instance, the specification of an antenna may be defined by radiating frequencies with defined bandwidths at a specified matching level and their radiation patterns at these frequencies. The radiation patterns define the gain that the antenna should achieve in each direction of space and corresponding Signal to Noise Ratio (SNR) for a radio link using the antenna.
Some constraints may also be defined in terms of number of elements in the antenna arrangement, in terms of dimensions and/or weight.
Thanks to the invention, it is possible to offer to the designer of an antenna, arrangement tools that allow designing the arrangement by assembling pre-defined elements that have predefined resonating modes and whose behaviour when assembled is known.
Therefore, according to the invention, a set of rules are defined to efficiently assemble the elements to match the specification.
The antenna arrangement 200 has a main trunk, MT, 211, that is connected at the feed line, 210, of the arrangement. A number of secondary trunks {STk}, may also be provisioned. The trunks have a fundamental mode that is defined by their length. They may have different form factors, as explained below. In the case illustrated on the figure, there is only one Secondary Trunk, ST1, 212. By definition, all Secondary Trunks are connected to the feed line, 210. The main advantage of an ST is that its resonating modes may be added to the antenna arrangement without impacting the resonating modes of the other antenna elements in the antenna arrangement. It should be noted that the number of STs that may be connected to an MT is limited, the limitation being contingent upon the form factor of the main trunk and the type, number, form factor and connection points of other elements borne by the said main trunk, MT.
An MT or an ST may bear a number of branches {Bj}. A branch allows adding new resonating modes, but this addition modifies some of the resonating modes of the other antenna elements in the antenna arrangement, unless the connection of the added element is at the feed line 210 of the antenna. In the exemplary antenna arrangement of
Then, leaves {Li} may be added to a trunk (main or secondary) or to a branch to adjust one or more of the centre frequencies of the resonating modes (fundamental or higher orders). In the example illustrated on
A person of ordinary skill in the art of antenna design will therefore be in a position to use various kinds of elements defined according to the invention. The invention also provides this person with a set of rules to select the adequate elements and position them in the structure of the antenna arrangement to be designed.
An antenna arrangement according to the invention comprises antenna elements that are of a type exemplified on one of
equal to λ/4 where λ is the wavelength of the fundamental mode of this antenna element with λ=c/f where f is the radiating frequency at the fundamental mode and c the speed of light in vacuum.
The Main Trunk, MT, is the basic radiating element of the antenna arrangement. It generates within the range of frequencies [fmin, fmax] a number nMT of radiating modes (fundamental and higher orders) at defined frequencies, each of the radiating modes defining a transmit/receive communication channel. Preferably, the fundamental mode of MT will be associated with the frequency that is the closest to fmin, which is the lowest frequency of interest. But some other embodiments are also possible.
′ defining another resonating frequency f′ of the antenna arrangement, with
′=λ′/4 and λ′=f′. As explained in more details below, the Secondary Trunk adds a number of new resonating frequencies to the antenna arrangement within the range of frequencies [fmin, fmax], without impacting the resonating frequencies defined by the Main Trunk (provided that the elements remain in a relative position to one another that does not create electromagnetic interference at this frequency).
Secondary Trunks are therefore advantageously used to add new transmit/receive communication channels to the antenna arrangement.
of about 6.3 cm that has a fundamental resonating mode at the E5 frequency:
This Trunk has two higher order resonating modes at frequencies f(1)=3×f(0)=3575,385 MHz and f(2)=5×f(0)=5958,975 MHz. It is possible to add to the Trunk a first Leaf that will be designed and positioned so as to shift the first higher order resonating mode of the antenna arrangement from 3575,385 MHz down to 2472 MHz. It is also possible to add to the Trunk a second Leaf that will be designed and positioned so as to shift the second higher order resonating mode of the antenna arrangement from 5958,975 MHz down to 5700 MHz. In this example, the maximum length of the Leaf is defined by the second higher order resonating mode and is equal to 1.26 cm (max=c/4×f(2))
A Leaf is a non-resonating element that is mostly used to control the frequencies of the radiating modes of a Main Trunk, a Secondary Trunk or a Branch, to which it is attached.
Each of the antenna elements MT, ST, B and L as defined above, are further defined by intrinsic parameters and extrinsic parameters.
The intrinsic parameters comprise:
The extrinsic parameters comprise:
According to the invention, an antenna element of the type depicted on one of
If the antenna element has a dimension D that is lower than λmin/4 (Region 1 on
If the antenna element has a dimension D that is greater than λmin/4 and lower than λmax/4 (Region 2 on
The figures illustrate some of the possible embodiments of the invention in relation to the intrinsic parameters of a Main Trunk or a Secondary Trunk.
On
On
On
On
On
On
On
The antenna elements depicted on
The same geometries and form factors may also be applied to variants of Branches or Leaves.
On
According to the invention, the value of the susceptance B (in Siemens, S) seen at the input of this antenna element is calculated to be used in further calculations of the impact of the antenna element on the frequencies and bandwidths of a resonating element that incorporates this antenna element.
The calculation uses the following canonical definitions:
The equations to calculate the susceptance are then the following:
Then, resolving the equations above for the values of the parameters of the antenna element of
Alternatively, it is possible to obtain experimentally or by simulation the table below for a range of frequencies f:
On
The table below displays the measurements of the parameters above for various frequencies; alternatively, these parameters can be obtained by direct calculation using Equations 1 to 4:
On
The table below displays the measurements of the parameters above for various frequencies; alternatively, these parameters can be obtained by direct calculation using Equations 1 to 4:
On
The table below displays the measurements of the parameters above for various frequencies; alternatively, these parameters can be obtained by direct calculation using Equations 1 to 4:
It is to be noted that at the higher frequencies (5,5/6 GHz), D cannot be considered to be much smaller than λ/4 since at 6 GHz, λfreespace=5 cm and λ/=1.25 cm, while D=0.75 cm. Thus, the leaf begins having a resonant behavior that may generate new radiating frequencies of the antenna arrangement.
The tables above can be easily computed for other dimensions, using the formulas of equations 1 to 4 for the same form factors. These tables may be associated with the antenna elements in a library of antenna elements generated to implement the invention. Also, an electromagnetic simulation tool may be associated with the library to calculate “on-the fly”, the input susceptance of the antenna elements in the library for any geometry, form factor, values of dimensions and frequencies. Alternatively, tables can be used in combination with interpolation algorithms, to calculate the values of the input susceptance for various form factors and for dimensions and frequencies that are not tabulated.
The 2D form factors with drop or rectangle form factor allow for a better control of the bandwidths around target resonating frequency values.
A person of ordinary skill in the art would be able to generate tables similar to those commented upon in relation to
An antenna element of a ST, B or L type is assembled on an antenna element of a MT, ST or B type by a direct connection, through soldering for instance.
The combinations of antenna elements according to the invention are listed below:
ST on MT;
B on MT, on ST or on B;
L on MT, on ST or on B.
An MT is designated as a primary conductive element of the antenna arrangement. An ST is a secondary conductive element. A B may be a secondary conductive element when directly connected to the MT. It may also be a ternary conductive element when connected to an ST or to another B itself directly connected to the MT. It may also be a quaternary conductive element when connected to a B itself connected to a B connected to the MT, etc . . . Likewise for an L, that will be designated as a secondary conductive element when directed connected on an MT, a ternary conductive element when connected to a B connected directly to an MT or a quaternary conductive element when connected to a B itself to a B directly connected to the MT. The bonsai tree may be expanded iteratively by adding new levels of antenna elements (B or L) to better match the specification.
These elements may be stored in a database of discrete simple antenna elements (Trunks, Branches or Leaves). The database may also comprise assemblies of these discrete antenna elements ST with B(s) and/or L(s) directed connected thereto; B with other B(s) connected thereto, each B comprising L(s) or not, or any kind of assembly of these discrete elements with whatever number of levels in the architecture of the tree bonsai tree defined by the assembly. The susceptances of the elements and the assemblies may also be stored in the database, together with their geometric parameters.
We will then have:
When the new frequencies are sufficiently apart from the initial frequencies, new transmit/receive communication channels may be defined. Conversely, when one or more of them are close enough to a frequency of a pre-existing resonating mode, the bandwidth around this frequency is enlarged, provided however that the matching level at a specified value exceeds a predefined threshold.
In other embodiments, the Branch B may be positioned on a ST, in an antenna arrangement that is illustrated on
A Leaf L will be considered as such when having a main dimension D lower than or equal to λ(P)/4, where λ(P)=c/f(P), f(P) being the frequency of the Pth higher order mode of the antenna element where the Leaf L is attached and being the highest useful frequency generated by the combination of the L with an MT, an ST or a B, as explained above.
The intrinsic parameters of the Leaf (Geometry, Form Factor, Dimension) will define a first magnitude of the impact of the Leaf on the frequencies of the resonating modes of the antenna element to which the Leaf is attached. This impact will vary depending on the frequency of the resonating mode, a magnitude of the impact being defined by the input susceptance of the Leaf. Examples of this impact have been discussed above in relation to
Also, the extrinsic parameters (Orientation, Position) of the Leaf relative to the antenna element to which it is attached will modify the impact of the Leaf on the frequencies of the resonating modes of this antenna element.
All other things being equal, the shift in frequency imparted by a Leaf to a resonating mode of the antenna element to which it is attached will be maximum when the Leaf is positioned at a Hot Spot of the antenna element, i.e. a node of current of the antenna element or an Open Circuit. Conversely, the shift in frequency will be minimum when the Leaf is positioned at a Cold Spot of the antenna element, i.e. a maximum of current of the antenna element or a Short Circuit. Intermediate areas may easily be defined, that may be defined as “Tepid” Spots.
When the main electromagnetic parameters (input susceptance, input admittance for instance) of an antenna element have been defined as a function of the intrinsic parameters (G, F, D) and of the extrinsic parameter (Orientation), it is possible to define the impact on the resonating frequencies of the antenna arrangement by resolving either graphically, analytically or by simulation or modelling the equations that define the way in which admittances/susceptances of the combination of antenna elements are compounded. Conversely, finding the parameters (extrinsic and intrinsic) of a combination of antenna elements that will define an antenna arrangement that will comply with a specification is equivalent to solving the inverse problem. This can also be done graphically, analytically or by simulation or modelling, as will be explained further down in the description.
These figures represent various examples of assemblies comprising a first antenna element of an MT type and a second antenna element of an ST or a B type. Nevertheless, the second antenna element may very well be of a L type, the difference being in the dimension D relative to the frequency of the highest frequency useful mode of the first antenna element, useful meaning that they allow defining frequencies that are targeted according to the specification of the antenna.
Many other combinations are possible, allowing to match the specifications of the antenna arrangement.
A specification of an antenna arrangement comprises one or more of:
Some other specifications may be added, depending, at least partially, on the antenna arrangement, like the shape of the radiating beam, or depending mostly on other elements of the T/R processing chain, like power level or SNR. But these specifications are not dealt with here, while the invention applies to any kind of specification of antenna arrangement comprising such requirements.
For designing an antenna arrangement based on a main antenna element that is a monopole fulfilling the specification, the invention procures notably a method that comprises choosing a Main Trunk as a first element for the antenna arrangement, the Main Trunk having a length and a form factor ff and a geometry g (step 810).
At a first order, the length of the Main Trunk should be such as where λ=c/f, f being a resonating frequency of one of the resonating modes of the main antenna element. In an advantageous embodiment, f is selected to be the lowest frequency value in the list of frequency values and the resonating frequency of the fundamental mode.
The form factor and geometry of the trunk may be defined as a function of the compactness that has to be reached for a defined target frequency. If a maximum dimension of the antenna element is set to a value that is a number of times smaller than the length that is necessary to generate a specific resonating frequency, it is necessary to use specific form factors, generally of a 3D geometry, for instance of a helical type.
At a step 820, one models the electrical response of the antenna arrangement to determine the values of the frequencies of the resonating modes. Step 820 is implemented either after the first step 810 for a single antenna element (i.e. the main trunk, N being set at 1), described above or as part of the iterative steps (N=N+1) to be performed until all target frequencies and bandwidths of the specification are obtained (step 845). There, a number of antenna elements (secondary trunks, branches and/or leaves) have been picked up from a library of antenna elements and added to the antenna arrangement. The values of all frequencies associated to the resonating modes of the antenna arrangement may be determined by analytical calculation using an electrical model of the antenna arrangement. Models are available for simple structures, generally not for complex structures. In lieu of an analytical model, a graphical representation, for instance a Smith Chart, may be used to determine the values of the frequencies of the resonating modes. Electromagnetic simulation tools may be used to find proper solutions more rapidly. Examples of analytical models, graphical representations and simulation tools are discussed further down in the description of various embodiments of the invention.
At a step 830, the values of the resonating frequencies, matching levels and bandwidths of the antenna arrangement are compared to the specification.
Steps 820 and 830 may be replayed a number of times if simple adjustments of the parameters of the same structure of antenna elements allows convergence to the values of the specification.
If all values (frequencies, matching levels, bandwidths) of the specification are tested (Step 840) and confirmed to be met, the process ends (Step 845). If not, the electrical state of the points of the antenna elements currently in the antenna arrangement where new antenna elements may be added are mapped (Step 850). Notably, the Hot Spots and Cold Spots should be marked for each resonating mode. At the spots of the first category, leaves may be added that will impart the largest shift (all other things being equal) on the frequencies of the resonating modes of the antenna arrangement. At the spots of the second category, Secondary Trunks or Branches may be added, that will impart the smallest shift on the resonating frequencies of the resonating modes of the antenna arrangement and add a number of new resonating frequencies to the antenna arrangement, if the specification is not entirely fulfilled.
Then, at a step 860, a new antenna element is selected in the library of antenna elements to be added at a relevant spot of a relevant pre-existing antenna element in the antenna arrangement. A guide to select the type of antenna element based on the type of adjustment to be made to the target specifications of the antenna arrangement is provided further down in the description. Before being added to the antenna arrangement at the adequate position, the antenna element should be configured, i.e. its adjustable parameters (dimension(s), form factor, etc . . . ) should be defined to obtain the adequate susceptance that will procure the required effects on the frequency values and the bandwidths that have to be adjusted.
Then the loop is iterated until the specification is fully met.
In such an embodiment of the invention, we can reformulate the specification as:
It may be possible to fulfil all the specifications with a single trunk. At a step 910, we define nMT that is the number of resonating modes of the Main Trunk that can be used to generate frequencies listed in the specification. The satisfaction of the specification in terms of number of frequency values (or channels) is tested at step 920. If the number is correct (step 930), the frequency values themselves have to be tested (step 940). If all frequency values match the specification, the bandwidths have to be tested (steps 99G and 99H). If they are OK, the specification is declared to be met (Step 99I). If not, new resonating modes have to be added to control the bandwidths by adding Secondary Trunks (ST) and/or Branches (B); the resonating frequency values can be controlled by adding Leaves (L) on Secondary Trunks (ST) or Branches (B), Step 99E. Then the result is tested (Step 99F). In case this is needed, a new antenna element is added by an iterative loop (Step 99E/Step 99F).
Coming back to step 940, if some frequency values are different from the specified frequency values, it is possible to shift the frequency values corresponding to each resonating mode of the Main Trunk by a predetermined amount (Step 950). The amount of shifting will depend on the parameters of the leaf (its geometry (1D, 2D, 3D), its form factor, its characteristic dimensions) and the position and orientation of the leaf on the trunk. Then the frequency values are tested against the specification in the new configuration (step 955). If the frequency values are all OK, the method then goes on to test the bandwidths (steps 960 and 99D). If this is OK, the specification is declared to be met (step 991). If this is KO, the method branches at step 99E. If, at the output of test 955, one of the frequency values is KO, new channels are generated, tested and followed by tests on resonating frequency values and on bandwidths (steps 970, 975, 980).
Coming back to step 920, if the number of frequencies generated on the Main Trunk is lower than the number required by the specification, it is possible to generate missing channels by adding Secondary Trunks (ST) and/or Branches (B), step 99A. The number of channels is then tested (step 99B) with a loop with step 99A. Then the list of resonating frequencies is established (step 99C) and the method branches to step 940.
As explained above, the intrinsic parameters of the antenna elements (MT, ST, B, L) that can be tuned to meet the specification are their geometry (1D, 2D, 3D), their form factor and their characteristic dimensions. Also, their impact on the resonating frequencies of the whole antenna arrangement will depend on their composition (single element or an element to which sub-elements—Branches or Leaves—are connected) and their position relative to the Hot Spots and Cold Spots of the MT, ST or B to which it is appended.
The calculation of the resonating frequencies and the corresponding bandwidths for definite matching levels for a composition of the antenna arrangement, sets of parameters of each of the antenna elements and their positions may be performed analytically, graphically or by simulation. Likewise, the resolution of the inverse problem (finding sets of antenna elements, their intrinsic parameters and their positions that generate a set of resonating frequencies with defined bandwidths for a matching level) can also be obtained by one of these methods. Also, some artificial intelligence or knowledge-based tools, such as neural networks, may be used with tools to simulate or model the solutions as a function of the parameters, to explore the space of solutions of the inverse problem more rapidly. Simulation tools known to a person of ordinary skill in antenna design are for example CST™, HFSS™, Feko™ or Comsol™. But any other proprietary software having similar functionalities may also be used.
According to the invention, the different types of antenna elements (Main Trunk, Secondary Trunk, Branch, Leaf) have the following uses for a designer who has to design an antenna arrangement according to a specification, and may be combined to meet the parameters (resonating frequencies and bandwidths for a defined matching level) of the specification:
Based on these design rules and using the iterative algorithms, the calculations and the tools described in this specification, it is possible to build a database of antenna elements that allow matching all kinds of specifications.
On
The Main Trunk 1010 is formed of a conductive material, metallic wire or ribbon, with a deployed physical length which is defined as a function of the desired radiating frequency of the fundamental mode as already explained above. At this frequency,
=λ/4. The trunk may be inscribed in a plane. In some embodiments, the plane in which the trunk is inscribed may be parallel to the ground plane, for instance when the antenna arrangement is produced using a micro strip technology, or may be inscribed in the ground plane in a solution where the antenna and the ground plane are designed as a coplanar arrangement. In such an arrangement, the antenna may be engraved on a face of the substrate and the ground plane may be engraved on the backplane of the substrate. In other embodiments, the plane in which the trunk is inscribed is perpendicular to the ground plane. The trunk may alternatively be inscribed in a non-planar surface or a volume structure. Such a form factor is advantageous to increase the compactness of an antenna arrangement of a given physical length
.
The ground plane 1030 is the metallic backplane of a PCB structure which comprises the excitation circuits which feed the RF signal to the trunk at their point of mechanical and electrical connection 1040.
At this step, it is useful to introduce the notion of “electrical length” of a radiating element. The electrical length e(λ) of an element of physical length
at a wavelength λ is defined by
e(λ)=
/λ. Then, if the radiation propagates in a media of electromagnetic permittivity ϵr, where λ=c/f√{square root over (r)}, we will have
e(λ)=
×f×√{square root over (ϵr)}/c. In air, where ϵhd r=1, we then have
e(λ)=
×f/c.
It is possible to express an electrical length in degrees or in radians. For instance, for e(λ)1/4 (in λ unit), we can express this value as
e(°)=90 (in degree unit) or
e(rad)=π/2 (in radian unit).
The different radiating modes are basically defined by the electrical length of the radiating pole element:
The resonating frequency f of the fundamental mode and the resonating frequencies of the first and the second higher modes, f1 and f2, are represented on graphical representations of the frequency response of the radiating element (
The antenna arrangement 1000c of
These dependencies are disclosed in European patent application filed under n° EP2016/306059.3, this antenna arrangement being analogous to a compact tree structure that in some aspects resembles the structure of a bonsai.
It is also possible to define an equivalent electrical length e(λ)eq. For instance, if a leaf of defined geometry, form factor and dimension is added on a trunk at a defined position with a defined orientation, the combination of the trunk and the leaf will have an equivalent electrical length defined by
e(λ)eq=
×f/c+Δ
e(λ)(f), where Δ
e(λ)(f), being a function of frequency f, is a variation of the electrical length of the trunk that is a consequence of the addition of the leaf.
There may be a plurality of leaves. The leaves may be seen as structures extending the length of the antenna of a defined amount in defined directions. They may be inscribed together in a same plane or different surfaces or not. They may be coplanar with the trunk or not.
It can be seen that the shift in frequency is the largest for the first higher order mode: the difference between the positions 1011b and 1011d being larger than the difference between the positions 1010b and 1010d and the difference between the positions 1012b and 1012d. This is determined by the position of the leaf on the Main Trunk. It can also be seen that the resonating frequencies are shifted to lower values because the total electrical length of the antenna arrangement is increased.
The antenna arrangement 1000e of
As already discussed, the ST 1050 may have different geometries, form factors, dimensions and orientations.
Since it is connected to the unique point that is a Cold Spot for all resonating modes of the Main Trunk 1010, there is no impact on the frequencies of these resonating modes that remain unchanged as illustrated on
If mandated by the specification, new radiating frequencies are created by the addition of the ST 1050:
The antenna arrangement 1000g of
As illustrated on
between the connection to the feed line 1140 (or Short Circuit point) and the Open Circuit point 1130, that is the top extremity of the monopole. The resonating frequency of the fundamental mode f0(0) is defined by: f0(0)=c/4
.
The electrical length of the antenna at the fundamental mode e(λ)(f0(0)) is represented by curve 1110b on
The normalized input admittance of the antenna is defined as: Yant
where Yc is the characteristic admittance of the monopole antenna.
At the fundamental mode Yant
Y
ant
(f0(0))=j×∞
Likewise, between the connection to the feed line 1140 (or Short Circuit point) and the Open Circuit point 1130, that is the free extremity of the monopole. The resonating frequency of the first higher order mode) f1(0) is defined by f1(0)=3c/4
.
One also has f1(0)=3f0(0).
The electrical length of the antenna at the first higher order mode e(λ)(f1(0)) is represented by curve 1110d on
The normalized input admittance of the antenna at the first higher order mode Yant
Likewise, between the connection to the feed line 1140 (or Short Circuit point) and the Open Circuit point 1130, that is the free extremity of the monopole. The resonating frequency of the first higher order mode f2(0) is defined by f2(0)=5c/4
.
One also has f2(0)=5f0(0).
The electrical length of the antenna at the second higher order mode)) e(λ)(f2(0)) is represented by curve 1110f on
The normalized input admittance of the antenna at the second higher order mode Yant
Y
ant
(f2(0))=j×∞.
It is of course possible to generalize the representations and calculations of
Using Smith Charts allows combining the admittances/susceptances of various antenna elements at their points of connections as explained below.
′ and 1212 of length
″ such that
=
′+
″.
We define the equivalent physical length at frequency f of the Leaf as the length eq.Leaf(f) (with
ea.Leaf(f) ∈ [0,λ/4[) of a rectilinear antenna element that would have the same input admittance YIN(f) as the Leaf; one must then solve: YIN(f)=YLeaf(f).
YLf (f) is a function of the intrinsic and extrinsic parameters of the Leaf 1220 (geometry, form factor, dimension and orientation).
If the equivalent rectilinear antenna element is presented with an input admittance YIN (f) at the connection P, 12201 with the Main Trunk, 1210, and has an admittance YL at its distal end OC, 12202, one has the following relationship between the admittances defined on the Leaf:
When the propagation media is the ambient air, we have β=2π/λ or β=2π×f/c. Then, Equation 5 can be solved graphically or analytically.
The graphical resolution is illustrated on the Smith Chart of
If we define e(λ)eq.Leaf(f) as the equivalent electrical length of Leaf 1220 (
e(λ)eq.Leaf(f)=
eq.Leaf(f)/λ, with
e(λ)eq.Leaf(f) ∈ [0,1/4[), the normalized input admittance YIN
e(λ)eq.Leaf(f).
The analytical resolution of Equation 5 uses the fact that YL=YOC=0. Thus:
Y
Leaf(f)=j×YC×tg(βeq.Leaf(f)) (Eq. 6)
Under the assumption that Leaf 1220 is lossless, we are in a position to assume that YLeaf(f)=j×BLeaf(f). We thus have:
B
Leaf(f)=YC×tg(βeq.Leaf(f)) (Eq. 7)
with BLeaf(f) ∈ [0,±∞[ and βeq.Leaf(f) ∈ └0,π/2└
that converts into:
Equations 7 and 8 define a relationship between the susceptance at the feed point 12201 of the Leaf 1220 and the equivalent length of this Leaf at frequency f.
In this embodiment we have as an example only: ′=0.1×λf
″=0.15×λf
=
′+
″=λf
The parameters (geometry, form factor, dimensions) of the Leaf 1220 are such that YLeaf
On the Smith Chart of ′e(λ)(f0(0))=0.1 of the antenna segment, starting with one segment the distal end of which is the OC.
The first segment 1211 of electrical length ′e(λ)(f0(0))°0.1 at frequency f0(0) that is the frequency of the fundamental mode of the antenna arrangement generates a normalized input admittance Yl′
The normalized admittance at point P, 12201, at the frequency f0(0) of the fundamental mode of the antenna arrangement, YP
We then have a total normalized input admittance at point P, YP
YP
Thus, the Leaf adds a rotation of 0,046 at f0(0).
We then add the electrical length ″e(λ)(f0(0))=0.15 of the second segment 1212 of the Main Trunk 1210, that determines a rotation 1240d that leads to point 1250d On the Smith Chart that determines a total rotation RotAnt where the normalized input admittance of the antenna arrangement, Y122
RotAnt=′e(λ))+RotLeaf1220+
″e(λ)(fo(0)) (Eq. 10)
where RotLeaf1220=0.046 (arc 1230d).
In the example illustrated on
We thus have an equivalent length of the antenna element 12001200(f0(0)) that is higher than a quarter wavelength at f0(0). The new fundamental mode of the antenna arrangement is therefore at a frequency f0(1) that is such that
1200(f0(1))=λf0(1)/4. The Leaf 1220 has thus decreased the frequency of the fundamental mode of the antenna arrangement 1200.
We have ′=0.3×λf
″=0.45×λf
=
′+
″=0.75×λf
The parameters (geometry, form factor, dimensions) of the Leaf 1220 are such that YLeaf
On the Smith Chart of
The first segment 1211 of electrical length ′e(λ)(f1(0))=0.3 at frequency f1(0) that is the frequency of the first higher order mode of the antenna arrangement generates a normalized input admittance Yl′
The normalized admittance at point P, 12201, at the frequency f1(0) of the first higher order mode of the antenna arrangement, YP
Starting from point P where the normalized input admittance is YP″e(λ)(f1(0)=0.45 of the second segment 1212 of the Main Trunk 1210 and then determine the normalized input admittance of the combined antenna arrangement 1200.
Equation 10 applies with replacing f0(0) by f1(0). We thus have Y1200
We thus have an equivalent length of the antenna element 12001200(f1(0)) that is higher than three quarter wavelength at f1(0). The new fundamental mode of the antenna arrangement is therefore at a frequency f1(1) that is such that
1200(f1(1))=3λf
We have ′=0.5×λf
″=0.75×λf
=
′+
″=1.25×λf
The parameters (geometry, form factor, dimensions) of the Leaf 1220 are such that YLeaf
On the Smith Chart of
The first segment 1211 of electrical length ′e(λ)(f2(0))=0.5 at frequency f2(0) that is the frequency of the second order higher mode of the antenna arrangement generates a normalized characteristic admittance Yl′
The normalized input admittance at point P, 12201, at the frequency f2(0) of the second higher order mode of the antenna arrangement, YP
Starting from point P where the normalized input admittance is YP
Equation 10 applies with replacing f0(0) by f2(0). We then have Y1200
We thus have an equivalent length of the antenna element 12001200 (f2(0)) that is higher than five quarter wavelength at f2(0). The new fundamental mode of the antenna arrangement is therefore at a frequency f2(1) that is such that
1200(f2(0))=5λf
In these embodiments where the Leaf 1220 that is added to the Main Trunk 1210 has a main dimension that is small in relation to the quarter of a wavelength of the radiating modes of the Main Trunk, the Leaf 1220 lengthens the Main Trunk that in turn advantageously generates a decrease of the values of the resonating frequencies of the proper modes of the antenna arrangement.
The Leaf is fully active (i.e. it generates a maximum additional rotation on the Smith Chart) for a given mode when it is located at a point P that is equivalent to an Open Circuit for this mode (or Hot Spot) and therefore imparts a shift on the resonating frequency that is maximum for this mode.
Conversely, the Leaf is “transparent” (i.e. it generates no additional rotation on the Smith Chart) when it is located at a point P that is equivalent to a Short Circuit for this mode (or Cold Spot) and therefore imparts no shift on the resonating frequency for this mode.
When the Leaf is located at a point P that is intermediate between a Hot Spot and a Cold Spot, the frequency shift that is imparted by the Leaf is increasing when one moves closer to an Hot Spot and is decreasing when one moves closer to a Cold Spot.
For a given mode, the position of a point P, where a Leaf is connected, defines its electrical state parameter that is a key parameter for controlling the amplitude of the shift in frequency imparted by the Leaf.
The top extremity of the Main Trunk 1210 is a Hot Spot for all modes, while its bottom extremity is a Cold Spot for all modes.
In some instances, the calculation of the resonating frequencies knowing the design parameters of the antenna arrangement (resolution of the direct problem) and the calculation of the design parameters for obtaining a set of defined resonating frequencies (resolution of the inverse problem) may also be carried out analytically using the relationships presented below.
One uses the definitions above. Also, a resonating frequency f is given. Some characteristics of the Main Trunk 1210 are fixed: the geometry is 1D and the form factor is rectilinear. The dimension (length) of the monopole may vary. The Leaf 1220 is 2D. Its form factor and dimension may vary and allow calculating its equivalent length EqLeaf(f) at frequency f (with
EqLeaf(f) ∈└0,λ/4└) and its input susceptance BLeaf (f) at frequency f (with BLeaf (f) ∈[0,+∞[).
Starting from the canonical equation of composition of the input admittances from segment 1211 and Leaf 1220 seen at point P of location of Leaf 1220 on Main Trunk 1210 and from the relationship between the susceptance and the admittance (the susceptance being the imaginary part of the admittance), one can write:
Compounding the admittance seen in P with segment 1212, one can write:
The antenna arrangement 1200 will resonate at a frequency fres that is such that the input admittance at the feed line point of the antenna has an infinite imaginary part (or susceptance), or its inverse is null. Starting from Equation 12, one finds the expression of the input susceptance of the Leaf 1220 at point P for the resonating frequency fres:
One notes that the member
is null at a Hot Spot, when
k ∈ N, and the impact of the input susceptance of the Leaf at this point P is maximum. Conversely, the impact of BLeafP (fres) is minimum at a Cold Spot. It is thus possible to define an efficiency factor (or conversely a coefficient of transparency) of the position of the Leaf on the Main Trunk that is a function of the impact of the Leaf on the combined input susceptance at point P as defined by Equation 11.
To solve the direct problem, all the design parameters are set first and the resonating frequencies of the antenna arrangement 1200 are the frequencies fi that solve Equation 13.
The resolution of the inverse problem starts from a list of frequencies defined by the specification of the antenna, for all frequencies fi, i ∈ {1,2, . . . n}. The designer or the design tools provided according to the invention will adjust the design parameters of the antenna so as to define a plurality of resonating modes, all the frequencies of which satisfy Equation 13.
In this embodiment with a rectilinear Main Trunk and a single Leaf, the design parameters that the designer may adjust to meet the specification in terms of frequencies are:
According to the invention, the input susceptance function at a point P located on an antenna element that is a 1D rectilinear monopole antenna (whether this antenna element is a Main Trunk, a Secondary Trunk or a Branch) to which the Leaf is connected may be deduced from Equation 13.
Thus, when the input susceptance function of the Leaf BLeaf(f) and its position P are known, the direct problem can be solved, i.e. the resonating frequencies of the antenna arrangement can be determined. There may be a plurality of solutions to the inverse problem (i.e. find a pair (P, Leaf) that allow generating resonating frequencies of a specification). This plurality of leaves that are solutions to the inverse problem have a susceptance that satisfies Equation 13 when positioned at point P. They can be selected in a database of antenna elements. The susceptance function can be expressed as depending upon the design parameters of the Leaf, the geometry, G, the form factor, F, a characteristic dimension, D, and the orientation relative to the antenna element to which it is connected, O. We therefore have:
B
Leaf(f)=B(f, GLeaf, FLeaf, DLeaf, OLeaf) (Eq. 14)
According to the invention, information about the susceptance function may be acquired and used according to different embodiments:
In some embodiments of the invention, the different approaches above may be combined. For instance, experimental measurements may be used in some parts of the domain of specification (geometries, form factors, dimensions, orientations), while simulations or models may be used in other parts of the domain of specification. Also, experimental measurements may be used to calibrate simulations or models. Simulations or models may also be used to interpolate or extrapolate values of the susceptance function in-between or beyond values that have been obtained experimentally.
Artificial intelligence algorithms may also be applied to the databases/lookup tables/simulations/models defined above to solve the inverse problem, i.e. finding one or more sets of design parameters that satisfy a specification of an antenna arrangement comprising a plurality of frequencies. For instance, various kinds of neural networks may be used to explore the space of solutions much more rapidly than a pure brute force exploration.
and a bottom segment that is itself divided in two pieces, segment 1312 of length
and segment 1313 of length
′″ by a point Q where a second Leaf 1322 is connected. The lengths of the segments satisfy
=
′+
″+
′″.
(see
e(λ)(f0(0))=1/4 at frequency f0(0) of the fundamental mode is reproduced on the Smith Chart (see
In this embodiment, the lengths of segments 1311, 1312, 1313 (see
The definition of the parameters (geometry, form factor, dimensions) of the Leaf 1320 allow calculating the input admittance of the Leaf, YLeaf(f0(0)). The Leaf 1321 has in particular dimensions that are small enough for its equivalent length to be lower than λf
′e(λ)(f0(0))+
″e(λ)(f0(0))+
′″e(λ)(f0(0))=1/4.
On the Smith Chart of
The procedures that are carried out and the results are similar to the ones illustrated on
Equation 10 may be generalised and add the impact of the second Leaf 1322 and of the third segment 1313 on the compounded admittances.
On the Smith Chart that determines a total rotation RotAnt, the normalized input admittance of the antenna arrangement, Y1300
RotAnt satisfies Equation 15 below:
RotAnt=′e(λ)(f0(0))+RotLeaf1321+
″e(λ)(f0(0))+Rotleaf1322+
′″e(λ)(f0(0) (Eq. 15)
RotLeaf 1321 and RotLeaf 1322 are calculated as exemplified above in relation to Equation 10.
The increase of the equivalent electrical length of the antenna is higher with two Leaves than with only one Leaf. Therefore, the decrease in frequency of the fundamental mode is higher. We will have a new resonating frequency f0(2) for the fundamental mode that will be such that 1300(f0(2))=λf
The same procedures and conclusions apply for higher order modes.
The direct problem of defining the set of frequencies of the resonating modes of an antenna arrangement of the type of
For doing so, one replaces segment 1311 (that is electrically connected in parallel with Leaf 1321 at point P) by a segment of an equivalent length ′EqLeafP II
′ that is defined in such a way that Equation 16 below is satisfied:
When adding a second Leaf 1322 at point Q, one uses Equation 13 while replacing:
The solutions to the problem must then satisfy Equation 16 above and Equation 17 below:
The resolution of the inverse problem starts from a list of frequencies defined by the specification of the antenna, fi, i ∈{1,2, . . . n}. The designer will adjust the design parameters of the antenna so as to define a plurality of resonating modes the frequencies of which all satisfy Equations 16 and 17.
In this embodiment with a rectilinear Main Trunk and two Leaves, the design parameters that the designer may adjust to meet the specification in terms of frequencies are:
The comments made above about BLeaf (f) equally apply to this embodiment.
In this embodiment with a Main Trunk and two Leaves It is therefore possible to define eleven independent design parameters, three out of the four length parameters, ,
′,
″,
′″, the four length parameters being linked by
=
′+
″+
′″ and four parameters (geometry, form factor, dimension and orientation) for each Leaf:
The “wire” geometry/form factor is illustrated on
The characteristic dimension D must be lower than λf
The orientation may be defined by the angle between a characteristic axis of the Leaf and the Main Trunk.
As discussed above, the resolution of the inverse problem lies in finding the sets of design parameters that satisfy Equations 16 and 17 above for all frequencies of the specification. It may be that there is no exact solution for all frequencies. Then, it is possible to define a cost function as a sum of the squares of the difference between each actual susceptance and each target susceptance for each frequency of the specification. Possibly the squares of the differences may be weighted to favour one or more of the frequencies in the specification. The cost function can then be formulated as:
Of course, in a number of embodiments, the weights may be selected to be all equal to one.
Various algorithms may be used to solve this cost function, such as a gradient descent learning algorithm, possibly in combination with a neural network algorithm.
According to the invention, it is possible to generalize the solutions applied to the direct problem in the embodiment with two Leaves described above to embodiments with three or more Leaves. This can be done when the solution that is found after applying the resolution process described above is too far from an optimum solution. A threshold can be defined to automatically stop the process, or the process may be stopped when the designer decides to do so, because the gain in matching the specification would be less than the cost (both in non-recurrent expenses and in bill of materials) of adding a new antenna element.
As part of the design process of an antenna according to this invention, it may be beneficial to use electromagnetic simulation tools that use the theory of the characteristic modes in combination with the Method of Moments. See for instance: R. J. Garbacz and R. H. Turpin, “A generalized expansion for radiated and scattered fields”, IEEE Trans. Antennas Propagation, vol. AP-19, n°3, pp 348-358, May 1971; R. F. Harrington and J. R. Mautz, “Theory of characteristic modes for conducting bodies”, IEEE Trans. Antennas Propagation, vol. AP-19, n°5, pp 622-628, September 1971; R. F. Harrington and J. R. Mautz, “Computation of characteristic modes for conducting bodies”, IEEE Trans. Antennas Propagation, vol. AP-19, n°5, pp 629-639, September 1971; R. F. Harrington and J. R. Mautz, “Characteristic modes for dielectric and magnetic bodies”, IEEE Trans. Antennas Propagation, vol. AP-20, n°2, pp 194-198, March 1972.
Such tools are available in COTS (Commercial Off The Shelf) such as FE0KO™ and CST™ that implement the Method of Moments (MoM) . . . They allow designing electromagnetic devices and antennas from a description of their materials and geometries. They allow a representation of the distribution of current for each of the resonating modes of the antenna, without having to actually transmit or receive electromagnetic waves. The selectivity of each of the resonating modes may be assessed using a quality factor (in void), thus allowing a fair prediction of the bandwidth for matching level at a defined value. The process implemented in one of these tools may be applied at each step of the design method, allowing the calculation of the values of the different resonating frequencies of the antenna arrangement, or of some parts thereof, as well as the associated electrical performances of each element, to check compliance with the specification. The calculations may be performed at the level of the combined antenna arrangement. A person of ordinary skill of antenna design knows, once aware of the present disclosure how to chain the various steps of simulation to achieve a complete design matching the specification.
Using such tools, it is therefore possible to build a library of antenna elements with their characteristic parameters defined according to the invention, then computing the susceptances of each element and solving, either in an exact manner, in some instances, or in an approximated manner, with a known sub-optimality cost, the equations generalized from equations 16, 17 and 18 above.
The invention may also be applied to dipole antennas. A dipole antenna is a two poles antenna where the two poles are excited by a differential generator. The two poles of the dipole antenna each operate with stationary regimes which have the same behavior. The two pole antennas each have a structure with a trunk, one or more branches and one or more leaves. In some embodiments of the invention, the two structures are symmetrical.
The examples disclosed in this specification are therefore only illustrative of some embodiments of the invention. They do not in any manner limit the scope of said invention which is defined by the appended claims.
Number | Date | Country | Kind |
---|---|---|---|
18305898.1 | Jul 2018 | EP | regional |
Filing Document | Filing Date | Country | Kind |
---|---|---|---|
PCT/EP2019/067252 | 6/27/2019 | WO | 00 |