METHODS AND SYSTEMS OF BEAM STEERING SYSTEM FOR LIDAR AND A FIELD PROGRAMMABLE PHASE CONTROLLER
20220390563 · 2022-12-08
Inventors
Cpc classification
International classification
G01S7/481
PHYSICS
Abstract
A metal-oxide semiconductor (MOS) structure to achieve a LIDAR beam steering, comprising: a n-number of waveguides, wherein the n-number of waveguides are connected to a laser transmitter and a receiver; a n-number phase shifters; wherein the MOS structure comprises a doping concentration of an N-drift region that is varied and a different drain-source current (IDS) to gate-source voltage (VGS) or drain-source voltage (VDS) characteristics are obtained, and wherein the IDS exists when the VGS is positive, and a magnitude of the IDS depends on a magnitude of the VGS and the VDS apart from the doping concentration of N− drift region, wherein the n-number of waveguides are connected to a laser transmitter and a receiver device, wherein the VGS is used as a control signal, wherein the VDS is set to a power supply voltage (VDD) based on at least one doping profile of the N-drift region of the MOS structure, wherein a plurality of different drain-to-source currents (IDS) are provided through the n-number of phase shifters, and wherein with a set of specified drain currents (IDS), a phase is shifted differently by the n-number of phase shifters and the beam is steered in a specified direction, and wherein only one control signal is used to achieve beam steering.
Claims
1. A metal-oxide semiconductor (MOS) structure to achieve a beam steering, comprising: a n-number of waveguides, wherein the n-number of waveguides are connected to a laser transmitter and a receiver; a n-number phase shifters; wherein the MOS structure comprises a doping concentration of an N-drift region that is varied and a different drain-source current (I.sub.DS) to gate-source voltage (V.sub.GS) or drain-source voltage (V.sub.DS) characteristics are obtained, and wherein the I.sub.DS exists when the V.sub.GS is positive, and a magnitude of the I.sub.DS depends on a magnitude of the V.sub.GS and the V.sub.DS apart from the doping concentration of N− drift region, wherein the n-number of waveguides are connected to a laser transmitter and a receiver device, wherein the V.sub.GS is used as a control signal, wherein the V.sub.DS is set to a power supply voltage (V.sub.DD) based on at least one doping profile of the N.sup.−drift region of the MOS structure, wherein a plurality of different drain-to-source currents (I.sub.DS) are provided through the n-number of phase shifters, and wherein with a set of specified drain currents (I.sub.DS), a phase is shifted differently by the n-number of phase shifters and the beam is steered in a specified direction, and wherein only one control signal is used to achieve beam steering.
2. The MOS structure of claim 1, wherein the n-number of waveguides comprises four waveguides.
3. The MOS structure of claim 1, wherein the n-number of phase shifters comprises four phase shifters.
4. The MOS structure of claim 1, wherein a P-diffusion region of the MOS structure below an N.sup.+ source is introduced so that a current flow is only along one or more trenches of the MOS structure.
5. The MOS structure of claim 1, wherein when the control signal is modified, the drain-to-source current also changes and with this change the phase shifted by the n-number phase shifters is modified and the beam steered in a specified direction.
6. The MOS structure of claim 1, wherein the MOS structure is used in a cascaded fashion to achieve a desired phase shifting.
7. The MOS structure of claim 6, wherein a doping level of the N− drift region forms one cascading unit which controls the phase.
8. The MOS structure of claim 7, wherein a set of doping levels are each identical.
9. The MOS structure of claim 7, wherein the set of doping levels are each different.
10. The MOS structure of claim 7, wherein the V.sub.GS is used as the control signal.
11. The MOS structure of claim 10, wherein the V.sub.DS is represented is set to a power supply voltage (V.sub.DD) of a cascading unit.
12. The MOS structure of claim 11, wherein the cascading unit comprises a combination of doping levels.
13. The MOS structure of claim 1 wherein Vis is used as the control signal.
14. The MOS structure of claim 13, wherein the V.sub.DS set to V.sub.DD and a ground terminal is provided.
15. The MOS structure of claim 14, a set of different doping profiles of the N− drift region of the MOS structure are also provided.
16. The MOS structure of claim 15, wherein set of different doping profiles comprises a 1*10.sup.15 cm.sup.−3 doping profile.
17. The MOS structure of claim 15, wherein set of different doping profiles comprises a 5*10.sup.15 cm.sup.−3 doping profile.
18. The MOS structure of claim 15, wherein set of different doping profiles comprises a 1*10.sup.16 cm.sup.−3 doping profile.
19. The MOS structure of claim 15, wherein set of different doping profiles comprises a 5*10.sup.16 cm.sup.−3 doping profile.
20. The MOS structure of claim 15, wherein with a set of different voltages applied to the phase shifters the phase is shifted differently by the n-number phase shifters and the beam steered in a specified direction, when the control signal changes, one or more voltages applied to the n-number phase shifters is changed and the phase shifted by the n-number of phase shifters such that the beam steered in a specified direction, and wherein the beam comprises a LIDAR or a RADAR beam.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
[0019] The present application can be best understood by reference to the following description taken in conjunction with the accompanying figures, in which like parts may be referred to by like numerals.
[0020]
[0021]
[0022]
[0023]
[0024] The flat-band condition energy diagram of N.sup.+P MOS Capacitor is shown in
[0025]
[0026]
[0027]
[0028] The flat-band condition energy diagram of P.sup.+N MOS Capacitor is shown in
[0029]
[0030]
[0031]
[0032]
[0033]
[0034]
[0035]
[0036]
[0037]
[0038]
[0039]
[0040]
[0041] The Figures described above are a representative set and are not exhaustive with respect to embodying the invention.
DESCRIPTION
[0042] Disclosed are a system, method, and article of manufacture for beam steering system for lidar and a field programmable phase controller. The following description is presented to enable a person of ordinary skill in the art to make and use the various embodiments. Descriptions of specific devices, techniques, and applications are provided only as examples. Various modifications to the examples described herein will be readily apparent to those of ordinary skill in the art, and the general principles defined herein may be applied to other examples and applications without departing from the spirit and scope of the various embodiments.
[0043] Reference throughout this specification to “one embodiment,” “an embodiment,” “one example,” or similar language means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, appearances of the phrases “in one embodiment,” “in an embodiment,” and similar language throughout this specification may, but do not necessarily, all refer to the same embodiment.
[0044] Furthermore, the described features, structures, or characteristics of the invention may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided, such as examples of programming, software modules, user selections, network transactions, database queries, database structures, hardware modules, hardware circuits, hardware chips, etc., to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art can recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, components, materials, and so forth. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the invention.
[0045] The schematic flow chart diagrams included herein are generally set forth as logical flow chart diagrams. As such, the depicted order and labeled steps are indicative of one embodiment of the presented method. Other steps and methods may be conceived that are equivalent in function, logic, or effect to one or more steps, or portions thereof, of the illustrated method. Additionally, the format and symbols employed are provided to explain the logical steps of the method and are understood not to limit the scope of the method. Although various arrow types and line types may be employed in the flow chart diagrams, and they are understood not to limit the scope of the corresponding method. Indeed, some arrows or other connectors may be used to indicate only the logical flow of the method. For instance, an arrow may indicate a waiting or monitoring period of unspecified duration between enumerated steps of the depicted method. Additionally, the order in which a particular method occurs may or may not strictly adhere to the order of the corresponding steps shown.
Definitions
[0046] Complementary metal-oxide-semiconductor (CMOS) is a technology used to manufacture integrated circuits. Electronic components such as microprocessors, microcontrollers, memory chips, digital sensors etc. make use of CMOS technology to achieve the stated functionality of the components. CMOS technology uses both NMOS and PMOS to achieve logic functions.
[0047] NMOS may be a N-channel metal-oxide-semiconductor. The channel refers to mode of current and N-channel means channel of electrons.
[0048] PMOS may be a P-channel metal-oxide-semiconductor. The channel refers to mode of current and P-channel means channel of holes.
[0049] Field-programmable gate array (FPGA) is an integrated circuit designed to be configured by a customer or a designer after manufacturing.
[0050] Lidar is a method for determining ranges (e.g., as a variable distance) by targeting an object with a laser and measuring the time for the reflected light to return to the receiver. Lidar can utilize visible, and/or near infrared light to image objects. A narrow laser beam can map physical features.
[0051] Metal-oxide-silicon transistor (MOS transistor) can be a type of insulated-gate field-effect transistor that is fabricated by the controlled oxidation of a semiconductor, typically silicon. The voltage of the gate terminal determines the electrical conductivity of the device; this ability to change conductivity with the amount of applied voltage can be used for amplifying or switching electronic signals.
[0052] Optical phased array (OPA) is the optical analog of a radio-wave phased array. By dynamically controlling the optical properties of a surface on a microscopic scale, it is possible to steer the direction of light beams (e.g. in an OPA transmitter), or the view direction of sensors (e.g. in an OPA receiver), without any moving parts.
[0053] Radar is a detection system that uses radio waves to determine the range, angle, or velocity of objects. A radar system consists of a transmitter producing electromagnetic waves in the radio or microwaves domain, a transmitting antenna, a receiving antenna (e.g. the same antenna is used for transmitting and receiving) and a receiver and processor to determine properties of the object(s). Radio waves (e.g. can be pulsed or continuous) from the transmitter reflect off the object and return to the receiver, giving information about the object's location and speed.
[0054] Waveguide is a structure that guides waves with minimal loss of energy by restricting the transmission of energy to one direction.
[0055] Example Beam Steering in Lidar and Radar Based on Differential Doping Using CMOS Technology
[0056] Example embodiments of a beam steering in Lidar and Radar based on differential doping using CMOS technology are now discussed. In one example, an optical phased array is used for beam steering from devices such as Lidar (e.g. Light Detection and Ranging) so that range and other auxiliary data can be obtained of the surroundings. The beam is steered by the control unit by controlling the phase of the signal through waveguides. The phase is controlled by varying the magnitude of the phase shifter attached to the waveguide. In the legacy system with N waveguides, the beam steering is achieved by controlling a similar number of control signals to the phase shifters. Keeping track of large number of control signals makes the system bulky and costly. A system is proposed that can achieve beam steering through only one control signal using complimentary metal-oxide-semiconductor (CMOS) process. The proposed system makes the beam steering process less complicated, less bulky and is cost effective when compared with the legacy system.
[0057] An example Beam Steering Mechanism is now discussed. Beam Steering is achieved by controlling the phase of each individual phase shifter. The spacing between each waveguide is λ/2 or less. So, when the light propagates in the air from the waveguide it gets superimposed by the light coming out from other waveguides. It can be thought of as light is being superimposed immediately in the air in the vicinity of the waveguides. The superimposition can be constructive or destructive. There can be propagation of light where there is constructive superimposition. There may not be any propagation of light where there is destructive superimposition. Whether the waveguide contributes to constructive superimposition or destructive superimposition is controlled by the phase of light in each individual waveguide. By varying the phase of the light in each individual waveguide, the direction where there would be constructive superimposition and where there would be destructive superimposition is controlled. Thus, the light beam coming out of waveguides can be steered by controlling the direction of constructive superimposition and destructive superimposition.
[0058] An example Phase Controller is now proposed and discussed. This phase controller eliminates the need of N separate control signals for N phase shifters to be controlled from the main processor. This in turn can eliminate the need for N separate digital to analog convertors (DAC's) and its associated auxiliary circuits. This phase controller can thus reduce the used computing resources as there may be no need to control and keep track of N control signals to the N phase shifters.
[0059] In some examples, a complimentary metal-oxide semiconductor (CMOS) fabrication process can be used to achieve phase control of N phase shifter.
[0060]
[0061]
[0062] This can be a MOS capacitor or a MOS transistor.
[0063]
[0064]
p.sub.S=N.sub.Ae.sup.−qϕ.sup.
[0065] Also, V.sub.G=V.sub.FB+ϕ.sub.S+V.sub.OX
[0066] Using Gauss's Law, E.sub.OX=Q.sub.acc/ε.sub.ox where E.sub.OX is the Electric Field in oxide and Q.sub.acc is the accumulation charge.
V.sub.OX=E.sub.OXT.sub.OX=−Q.sub.acc/C.sub.OX
[0067] where T.sub.ox and C.sub.ox are Thickness and Capacitance of oxide
Q.sub.acc=−C.sub.OXV.sub.OX
Q.sub.acc=C.sub.OX(V.sub.G−V.sub.FB−ϕ.sub.S)
[0068] Therefore the Q.sub.acc charge can depend on the surface voltage ϕ.sub.S and in turn the surface hole concentration ps which in turn depends on the doping concentration N.sub.A.
[0069] V.sub.G remaining same, changes in N.sub.A can give a different Q.sub.acc.
[0070]
[0071] This theory of different drain-source current (I.sub.DS) for different doping levels also applies to MOS structure with N-body and N.sub.D doping.
[0072] An example MOS structure with N-body and N.sub.D doping is discussed.
[0073]
[0074]
[0075]
n.sub.S=N.sub.De.sup.−qϕ.sup.
Q.sub.acc=−C.sub.ox(V.sub.G−V.sub.FB−ϕ.sub.S)
[0076] Therefore the Q.sub.acc charge can depend on the surface voltage ϕ.sub.S and in turn the surface electron concentration n.sub.S which in turn depends on the doping concentration N.sub.D.
[0077] V.sub.G remaining same, changes in N.sub.D can give a different Q.sub.acc.
[0078] Apart from the accumulation charge Q.sub.acc depending on doping concentration, the drift current density can also depend on the doping concentration or carrier concentration.
[0079] The drift current density, J.sub.n,drift can also depend on the carrier concentration. [0080] J.sub.n,drift=qμ.sub.nnE=qμ.sub.nN.sub.DE . . . where n is the carrier concentration, N.sub.D in this case; μ.sub.n is mobility of electrons, q is charge of an electron, E is the electric field.
[0081] The drift current can therefore be written as: [0082] I.sub.drift=qμ.sub.nN.sub.DE(W*L) . . . where W and L are the width and length of the drain current channel.
[0083] The drift current in the MOS capacitor in accumulation mode is same as the drain-source current (I.sub.DS). Therefore I.sub.DS=qμ.sub.nN.sub.DE(W*L)
[0084] From above, by varying the doping level N.sub.D, current I.sub.DS may be varied.
[0085] It is noted that varying the drain-source current (I.sub.DS) by varying the doping level N.sub.D, can work in conjunction with the MOS structure as in
[0086] An example MOS structure is provided in
[0087] It is noted that for MOS structure in
[0088] The current flow lines in the MOS structures are shown in
[0089] The output characteristics of the proposed structure are plotted in
Resistivity ρ=1/σ (Ω.Math.cm).
[0090] Drift Current Density according to Ohm's law form is given as J=σE=E/ρ.
[0091] Resistivity can vary with doping concentration.
[0092] A plot of resistivity of N type semiconductor and P type semiconductor with respect to doping concentration is shown in
[0093] Variation in drift drain-to-source current (I.sub.DS) density with different doping concentration for various gate-to-source voltage V.sub.GS is shown in
[0094] The fabrication of the MOS structure of
[0095] Fabrication of the MOS structure is not limited to the above method and in general the claim covers any other available fabrication technique that may be used to fabricate the MOS structure. The dimensions are provided by way of example and in general covers the cases, where the dimensions of the MOS structure may change and dimensions are not limited to the one listed above and may change as the fabrication techniques change and evolve.
[0096] The use of MOS structure of
R=(L*W)/(μ.sub.a*C.sub.OX*V.sub.GS)
[0097] Where R is the resistance,
[0098] L is channel length,
[0099] W is width of MOS structure,
[0100] μ.sub.a is accumulation layer mobility,
[0101] C.sub.OX is the oxide capacitance per square centimeter,
[0102] V.sub.GS is the gate-to-source voltage,
[0103] Therefore, with a channel length of 2 μm, width of 3 μm, C.sub.OX of 49.3 nF/cm.sup.2 for oxide thickness of 700° A, mobility μ.sub.a of 1000 cm.sup.2/V.Math.s and V.sub.GS of 15 V, resistance R=90 μΩ.Math.cm.sup.2 can be obtained. This specific “ON” resistance is extremely low when compared with conventional voltage divider, resistor, and capacitor circuits where resistance can be multifold times higher (.sup.˜10.sup.6 times). Therefore, many such MOS structures can be supported by a single control voltage and in turn control many phase shifters and achieve beam steering using just one control signal. The “ON” resistance of this trench MOS structure of
[0104]
[0105] In general, there may be a plural number of waveguides along with their phase shifters forming the phased array and the waveguides may be arranged to form a one-dimensional phased array or two-dimensional phased array. Also, the drain-to-source voltage V.sub.DS may be used as control signal instead of gate-to-source voltage Vis.
[0106] The MOS structures of
[0107]
[0108] Different doping profiles 1901-1904 of N.sup.− drift region of the MOS structure are also provided. For example, 1901 may be 1*10.sup.15 cm.sup.−3, 1902 may be 5*10.sup.15 cm.sup.−3, 1903 may be 1*10.sup.16 cm.sup.−3 and 1904 may be 5*10.sup.16 cm.sup.−3. The different voltages applied to the phase shifters 104 are represented by 1907, 1908, 1909 and 1910. With different voltages applied to the phase shifters 104, the phase can be shifted differently by the phase shifters 104 and the beam can be steered in the air in a specified direction 1911. When the control signal 1905 changes, the voltages 1907 to 1910 applied to the phase shifters 104 can also change and with this change the phase shifted by the phase shifters 104 can also change and thus the beam can be steered in some other direction say 1912.
[0109] The use of the MOS structure of
[0110] An alternative MOS structure to the MOS structure of
[0111] It is noted that the accumulation mode of the proposed structures can be used to achieve beam steering. One may in general also use inversion mode of the MOS structure to achieve beam steering. Example embodiments are not limited to doping concentration variation of the drift region alone. In some cases, the doping concentration of source and/or drain and/or substrate and/or diffusion region may be altered to achieve similar effect in various example embodiments. Example embodiments are not limited to doping concentration variation. In some cases, thickness and/or doping concentration of the drift region and/or substrate and/or diffusion region may be altered to achieve similar effect in various example embodiments.
[0112] In some examples, waveguides can carry the transmitted as well as received signal. This use of waveguides is shown only for the purpose of demonstration and is not limited to this specific case. Beam steering can be achieved using phase shifters. It is noted that example embodiments can be applied when phase shifters are used to achieve beam steering. Examples can be used when phase shifters are used to achieve beam steering. In some cases, an individual waveguide may carry signal in only one direction, either transmitted or received signal. In some examples, only a fraction of total number of waveguides may carry signal in both direction while the remaining waveguides may carry signal only in one direction.
[0113] Examples can be used to achieve the steering of electromagnetic optical signal. This can be used to steer any electromagnetic signal such as those used in Radar (Radio detection and ranging). The same principle as demonstrated over here may be used to shift phase in waveguides carrying radar signal.
[0114] Field Programmable Phase Controller Device
[0115] An example embodiment provides a field programmable device to control the beam steering of electromagnetic wave by a single control signal. The field programmable device contains MOS structures that control the phase of the electromagnetic signal traversing through the waveguides or antennas. The field programmable device contains multiple such MOS structures with various doping levels that in turn control the current through the phase shifter and thus the phase of the electromagnetic signal traversing through the waveguides or antennas to which the phase shifter is attached. In some other embodiments the waveguides or antennas themselves behave as phase shifters. The outputs from the field programmable device are given to the phase shifters to achieve phase control and beam steering. The connection from the various MOS structures to the output is field programmable. Also, the interconnection between the MOS structures is field programmable. Thus, the field programmable device can be programmed so that the various MOS structures can be arranged in some particular way and then connected to the output terminals so that when the output terminals are connected to the phase shifters of the waveguides or antennas, the beam gets steered by a single control signal.
[0116] Beam steering is a component of Lidar (light detection and ranging) and/or Radar (radio detection and ranging). If one intends to have chip-based Lidar or Radar, beam steering system can be utilized. One would then want a very compact, cost effective and less power consuming beam steering system and that too one that can be fabricated using the prevailing and matured complimentary metal-oxide-semiconductor CMOS fabrication process. Accordingly, a beam steering system can be tested before giving the design for fabrication. Example embodiments can have a capability to re-program the beam steering system in the eventuality of some problematic issue or for any other reason when the Lidar or Radar has already been deployed in the field.
[0117] The field programmable phase controlling device includes an input terminal to which the beam steering control signal may be connected. This control signal may come from some external controller and it is used to steer the beam. The field programmable phase controlling device includes multiple MOS structures of
[0118] Each phase shifter is attached to a waveguide or to an antenna. The phase shifters are used to vary the phase of the electromagnetic signal in the waveguide or the antenna. The waveguides or the antennas are physically arranged to achieve beam steering of the signal propagating out of them and into the air. One such arrangement is to have a physical separation of half wavelength of the propagating signal between adjacent waveguides or antennas. In this arrangement, when the signal propagates in the air from the waveguide or the antenna, there is either constructive superimposition or destructive superimposition of the signal in the vicinity of the waveguides or the antennas. The phase of the signal in the waveguides or antennas decide where constructive superimposition or destructive superimposition will occur. The signal propagates where there is constructive superimposition. There will be no propagation of the signal where there is destructive superimposition. Thus, depending on the phase, the signal beam steering occurs.
[0119] The phase is controlled by the magnitude of current through the phase shifter or the voltage applied to the phase shifter. This magnitude depends on the MOS structures attached to the phase shifter. The control signal that may be connected to the input terminal may be used as gate-source voltage, Vis of MOS structures. The magnitude of the control signal gate-source voltage Vis is same across the field programmable phase controlling device. The doping concentration of the drift region of the MOS structures then decide the difference in magnitude of the current or voltage given to the phase shifters. Thus, the phase of the phase shifters is controlled by the doping concentration of the drift region of the MOS structures. When the magnitude of the control signal gate-source voltage V.sub.GS changes, the magnitude of the current or voltage given to the phase shifters also changes. Thus, the phase of the phase shifters is also controlled by the magnitude of the control signal gate-source voltage V.sub.GS.
[0120] The phase of the phase shifters is controlled by the doping concentration and the magnitude of the control signal gate-source voltage V.sub.GS.
[0121] Once the field programmable phase controlling device is programmed, when the magnitude of the control signal changes, the current or voltage given to the phase shifter changes and hence the phase of the signal also changes, and this leads to change in the direction of electromagnetic signal propagating out of waveguides or antennas and thus the beam gets steered in different direction.
[0122] The field programmable phase controlling device is capable of the following programming operations: [0123] programming the connection of the gate terminal of the MOS structure to a gate-source voltage V.sub.GS or a source terminal of some other MOS structure or a drain terminal of some other MOS structure or to leave the gate terminal floating. [0124] programming the connection of the drain terminal of the MOS structure to a drain-source voltage V.sub.DS or a gate terminal of some other MOS structure or a source terminal of some other MOS structure or an unoccupied output terminal or to leave the drain terminal floating. [0125] programming the connection of the source terminal of the MOS structure to a gate terminal of some other MOS structure or a drain terminal of some other MOS structure or an unoccupied output terminal or to leave the drain terminal floating.
[0126] If any of the terminal of the MOS structure is floating, then this MOS structure is not part of the final programmed circuit and does not contribute to any output.
[0127] The interconnections between the MOS structures are now discussed. The interconnections can be between MOS structures of same doping concentrations, or the interconnections can be between MOS structures different doping concentrations, or the interconnections can be between MOS structures of similar types, e.g. either interconnections between MOS structures of
[0128] The proposed field programmable phase controller (FPPC) device has similarity with the features of field programmable gated array (FPGA) device. Those with familiarity in the field can identify that the interconnections between various gates in the FPGA device are programmed to achieve a task. On similar lines, the interconnections between the MOS structures are programmable in the field programmable phase controller (FPPC) device.
[0129] An example embodiment programming of the field programmable phase controller (FPPC) device establishes the interconnections between the MOS structures and the connection between MOS structures and the output. The input to the device is the control signal from the Lidar or Radar control unit or some other external controller. This input control signal is used as gate-to-source voltage Vis in the device. When the example embodiment programming of the field programmable phase controller (FPPC) device is complete, changes in the magnitude of the control signal gate-source voltage Vis, changes the direction of electromagnetic signal propagating out of waveguides or antennas and thus beam steering is achieved.
CONCLUSION
[0130] Although the present embodiments have been described with reference to specific example embodiments, various modifications and changes can be made to these embodiments without departing from the broader spirit and scope of the various embodiments.