Golf ball locating nonlinear radar system employing a snowflake nonlinear passive tag and associated method(s)

Abstract

A nonlinear radar system includes a handheld unit including a display screen, a first antenna configured to generate and emit an incident signal having a first frequency, and a second antenna configured to receive a reflected return harmonic signal having a second frequency, as well as a transponder tag is attached to an existing golf ball. Such a transponder tag is in communication with and responsive to the handheld unit, and includes an electromagnetic nonlinear element configured to be detected by the incident signal without the need for a line of sight. Upon being detected by the incident signal, the transponder tag is configured to transmit the reflected return harmonic signal having the second frequency different from the first frequency. The transponder tag is passive and does not require a power source other than incident radiation.

Claims

1. A radar system comprising: a handheld unit including a display screen, a first antenna configured to generate and emit an incident signal having a first frequency, and a second antenna configured to receive a reflected return harmonic signal having a second frequency; and a transponder tag attached to an existing golf ball, said transponder tag being in communication with and responsive to said handheld unit, said transponder tag including an electromagnetic nonlinear element being configured to be detected by said incident signal, and wherein upon being detected by said incident signal, said transponder tag being configured to transmit said reflected return harmonic signal having said second frequency different from said first frequency; wherein said transponder tag is passive and does not require a power source other than incident radiation; wherein said handheld unit further includes a transmitting block in communication with said electromagnetic nonlinear element for generating and transmitting said incident signal within civilian-use-permitted frequency bands and at a power of about one watt, a receiving block in communication with said electromagnetic nonlinear element for receiving and processing said reflected return harmonic signal, and a processing block configured to determine a signal strength of said reflected return harmonic signal and illustrate on said display screen a distance from the existing golf ball to said handheld unit; wherein transponder tag includes a plurality of stems radially extended outwardly from a center of said transponder tag, and a plurality of lobes coupled to a distal end of said stems, respectively; wherein a quantity of said stems equals a quantity of said lobes and have a 1:1 ratio.

2. The radar system of claim 1, wherein said handheld unit comprises: a graphical user interface illustrated on said display screen; wherein said graphical user interface is configured to graphically display said distance from the existing golf ball to said handheld unit as well as said signal strength of said reflected return harmonic signal.

3. The radar system of claim 1, wherein said electromagnetic nonlinear element is a Schottky diode.

4. The radar system of claim 1, wherein said handheld unit is configured to radiate at two or more unique frequencies and further configured to receive at least one of said reflected return harmonic signal generated by said electromagnetic nonlinear element.

5. The radar system of claim 1, wherein said transponder tag is disposed at the existing golf ball.

6. The radar system of claim 1, wherein said transponder tag is disposed on a surface of the existing golf ball.

7. The radar system of claim 1, wherein said transponder tag is integral and congruous with the existing golf ball.

8. The radar system of claim 1, wherein said transponder tag is painted on the surface of the existing ball with metallic or conductive paint.

9. The radar system of claim 1, wherein each of said first antenna and said second antenna is a fractal antenna.

10. The radar system of claim 1, wherein said handheld unit is configured to generate and emit at least one audible signal associated with said distance from the existing golf ball to said handheld unit to indicate said signal strength of said reflected return harmonic signal as well as a direction from said handheld unit to the existing golf ball.

11. The radar system of claim 1, wherein said handheld unit further comprises: a power source selected from a group including a rechargeable battery and a solar array.

12. The radar system of claim 1, wherein said electromagnetic nonlinear element comprises: at least one of a metal-metal contact and a metal-metal oxide contact.

13. The radar system of claim 1, wherein said first antenna is solely a transmitting antenna.

14. The radar system of claim 1, wherein said second antenna is solely a receiving antenna.

15. The radar system of claim 1, wherein said transponder tag comprises: a conductive paint layer in electrical communication with said electromagnetic nonlinear element; wherein said electromagnetic nonlinear element includes a Schottky diode.

16. The radar system of claim 1, wherein said transponder tag comprises: a snowflake shape having a center and a plurality of stems radially extended from said center; wherein each of said stems includes said electromagnetic nonlinear element spaced apart along an outer perimeter of said snowflake shape.

17. The radar system of claim 16, wherein each of said lobes comprises: a conductive paint layer in electrical communication with said electromagnetic nonlinear element, respectively.

18. The radar system of claim 17, wherein each of said lobes emits a unique one of said reflected return harmonic signal.

19. The radar system of claim 18, wherein each said reflected return harmonic signal is configured to be detected by said receiving block and analyzed by said processing block to determine said distance and a direction from the existing golf ball to said handheld unit.

Description

BRIEF DESCRIPTION OF THE NON-LIMITING EXEMPLARY DRAWINGS

(1) The novel features believed to be characteristic of non-limiting exemplary embodiment(s) of the present disclosure are set forth with particularity in the appended claims. The non-limiting exemplary embodiment(s) of the present disclosure itself, however, both as to its organization and method of operation, together with further objects and advantages thereof, may best be understood by reference to the following description taken in connection with the accompanying drawings in which:

(2) FIG. 1 is a schematic diagram of a harmonic system for testing the functions of the non-linear radar system, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(3) FIG. 2 is a single-element antenna structural configuration of the non-linear radar system, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(4) FIG. 3 is a perspective view of a laser cut antenna snowflake tag pattern, employed by the non-linear radar system, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(5) FIG. 4A is a top plan view of a multi-element snowflake nonlinear passive tag, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(6) FIG. 4B is a side elevational view of a single-element snowflake nonlinear passive tag positioned next to a U.S. coin (quarter), in accordance with a non-limiting exemplary embodiment of the present disclosure;

(7) FIG. 4C is a top plan view of a modified multi-element snowflake nonlinear passive tag, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(8) FIG. 5 is a perspective view of a spectrum analyzer and a signal generator used to verify the functions of the transmission and receiving antennas employed by the present system, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(9) FIG. 6A is a graph illustrating the measurement peak of 97.42 dBm on the spectrum analyzer at the center frequency of the modified multi-element tag at a distance of 2.7 ft, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(10) FIG. 6B is a graph illustrating the nonlinearity of instruments after averaging, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(11) FIG. 7 is a graph illustrating the signal-to-noise ratio (SNR) versus distance plot comparison between single-element, multi-element, and modified multi-element configurations; in accordance with a non-limiting exemplary embodiment of the present disclosure;

(12) FIG. 8 is a block diagram illustrating the interrelationship between the major electronic components of the present disclosure, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(13) FIG. 9 is another block diagram illustrating the interrelationship between the major electronic components of the present disclosure with operating parameters, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(14) FIG. 10 is a flowchart illustrating the control logic algorithm of the software employed by the present disclosure, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(15) FIG. 11 is a top plan view of the snowflake nonlinear passive tag employed by the present disclosure, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(16) FIG. 12 is a top plan of a group of alternate snowflake nonlinear passive tag employed by the present disclosure, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(17) FIG. 13 is a high level schematic block diagram illustrating the interrelationship between the major electronic components of the present disclosure, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(18) FIG. 13A is a high level schematic block diagram illustrating the interrelationship between selected major electronic components of a transponder tag, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(19) FIG. 14 is a top plan view identifying element (stem) lengths of a snowflake transponder tag structure, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(20) FIG. 15 is another top plan view identifying a quantity of elements (stems) of the snowflake transponder tag structure shown in FIG. 14, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(21) FIG. 16 is another top plan view identifying a DC-Short position of the snowflake transponder tag structure shown in FIG. 14, in accordance with a non-limiting exemplary embodiment of the present disclosure;

(22) FIG. 17 is another top plan view identifying separation angles between the elements (stems) of the snowflake transponder tag structure shown in FIG. 14, in accordance with a non-limiting exemplary embodiment of the present disclosure; and

(23) FIG. 18 is another top plan view identifying shapes and sizes of the lobes (pebbles) of the snowflake transponder tag structure shown in FIG. 14, in accordance with a non-limiting exemplary embodiment of the present disclosure.

(24) Those skilled in the art will appreciate that the figures are not intended to be drawn to any particular scale; nor are the figures intended to illustrate every non-limiting exemplary embodiment(s) of the present disclosure. The present disclosure is not limited to any particular non-limiting exemplary embodiment(s) depicted in the figures nor the shapes, relative sizes or proportions shown in the figures.

DETAILED DESCRIPTION OF NON-LIMITING EXEMPLARY EMBODIMENT(S) OF THE PRESENT DISCLOSURE

(25) The present disclosure will now be described more fully hereinafter with reference to the accompanying drawings, in which non-limiting exemplary embodiment(s) of the present disclosure is shown. The present disclosure may, however, be embodied in many different forms and should not be construed as limited to the non-limiting exemplary embodiment(s) set forth herein. Rather, such non-limiting exemplary embodiment(s) are provided so that this application will be thorough and complete, and will fully convey the true spirit and scope of the present disclosure to those skilled in the relevant art(s). Like numbers refer to like elements throughout the figures.

(26) The illustrations of the non-limiting exemplary embodiment(s) described herein are intended to provide a general understanding of the structure of the present disclosure. The illustrations are not intended to serve as a complete description of all of the elements and features of the structures, systems and/or methods described herein. Other non-limiting exemplary embodiment(s) may be apparent to those of ordinary skill in the relevant art(s) upon reviewing the disclosure. Other non-limiting exemplary embodiment(s) may be utilized and derived from the disclosure such that structural, logical substitutions and changes may be made without departing from the true spirit and scope of the present disclosure. Additionally, the illustrations are merely representational and are to be regarded as illustrative rather than restrictive.

(27) One or more embodiment(s) of the disclosure may be referred to herein, individually and/or collectively, by the term non-limiting exemplary embodiment(s) merely for convenience and without intending to voluntarily limit the true spirit and scope of this application to any particular non-limiting exemplary embodiment(s) or inventive concept. Moreover, although specific embodiment(s) have been illustrated and described herein, it should be appreciated that any subsequent arrangement designed to achieve the same or similar purpose may be substituted for the specific embodiment(s) shown. This disclosure is intended to cover any and all subsequent adaptations or variations of other embodiment(s). Combinations of the above embodiment(s), and other embodiment(s) not specifically described herein, will be apparent to those of skill in the relevant art(s) upon reviewing the description.

(28) References in the specification to one embodiment(s), an embodiment(s), a preferred embodiment(s), an alternative embodiment(s) and similar phrases mean that a particular feature, structure, or characteristic described in connection with the embodiment(s) is included in at least an embodiment(s) of the non-limiting exemplary embodiment(s). The appearances of the phrase non-limiting exemplary embodiment in various places in the specification are not necessarily all meant to refer to the same embodiment(s).

(29) Directional and/or relationary terms such as, but not limited to, left, right, nadir, apex, top, bottom, vertical, horizontal, back, front and lateral are relative to each other and are dependent on the specific orientation of an applicable element or article, and are used accordingly to aid in the description of the various embodiment(s) and are not necessarily intended to be construed as limiting.

(30) If used herein, about, generally, and approximately mean nearly and in the context of a numerical value or range set forth means?15% of the numerical.

(31) If used herein, substantially means largely if not wholly that which is specified, but so close that the difference is insignificant.

(32) The terms stem, element, and variations thereof are interchangeably used throughout the present disclosure.

(33) The terms lobe, pebbles, and variations thereof are interchangeably used throughout the present disclosure.

(34) The terms transmitting antenna, TX antenna, first antenna, and variations thereof are interchangeably used throughout the present disclosure.

(35) The terms receiving antenna, RX antenna, second antenna, and variations thereof are interchangeably used throughout the present disclosure.

(36) The term element includes at least one stem and at least one lobe/pebble.

(37) Non-limiting exemplary embodiment(s) of the present disclosure is referred to generally in FIGS. 1-18, and is intended to provide a specially configured golf ball locating nonlinear radar system 20 that is able to detect and locate a golf ball 26 that is not within a user's line of sight. It should be understood that the exemplary embodiment(s) may be used to locate a variety of objects (archery arrows, tennis balls, etc.) and should not be limited to any particular object described herein.

(38) Advantageously, the present disclosure includes use of nonlinear passive tags 25 for location detection using harmonic radar for objection detection. The nonlinear passive tags 25 provide a second-order harmonic system 20 with various antenna configurations. The tag's antennas 23, 24 were fabricated with laser-cut pattern masks and conductive materials, and their performance was greatly enhanced by the multi-element 28 design and Schottky diode 35 nonlinearity. The detective distance of up to 6.7 ft of the tags 25 was tested using a benchtop setup having a 7.9 GHz transmitter and a 15.8 GHz receiver antenna without any signal amplification. The lightweight and miniature tags 25 have great potential for extensive applications in locating objects.

(39) In a non-limiting exemplary embodiment, the nonlinear radar system 20 for finding a golf ball 26 employs lightweight miniature multi-element snowflake-shaped nonlinear passive tags 25 for wireless tracking. A hand held unit 21 is in communication with a transponder tag 25 (snowflake 40 nonlinear passive tag 25) for object location. In particular, the present disclosure provides a passive nonlinear tag 25 structural configuration with a novel snowflake 40 pattern and fabrication method. The snowflake tag 25 is very light weight and cost effective. It can be used as a battery-less tracker to be tracked by a harmonic radar. The tag antennas 23, 24 were fabricated with laser-cut pattern masks and conductive materials, and their performance was greatly enhanced by the multi-element 28 snowflake 40 patterned design. The detective distance of up to 6.7 ft of tag 25 was tested using a benchtop setup of a 7.9 GHz transmitter and a 15.8 GHz receiver antenna without any battery or signal amplification on the tag 25 side. The lightweight and miniature tags 25 have great potential for extensive applications in locating objects.

(40) Referring again to FIGS. 1-18, the nonlinear radar system 20 includes a handheld unit 21 including a display screen 22, a first antenna 23 configured to generate and emit an incident signal having a first frequency, and a second antenna 24 configured to receive a reflected return harmonic signal having a second frequency. A transponder tag 25 is attached to an existing golf ball 26. Such a transponder tag 25 is in communication with and responsive to the handheld unit 21, and includes an electromagnetic nonlinear element 28 configured to be detected by the incident signal transmitted from the hand held unit 21. Advantageously, upon being detected by the incident signal, the transponder tag 25 is configured to transmit the reflected return harmonic signal having the second frequency different from the first frequency. Advantageously, the transponder tag 25 is passive and does not require a power source 36 other than incident radiation;

(41) Advantageously, the handheld unit 21 further includes a transmitting block 30 in communication with the electromagnetic nonlinear element 28 and configured for generating and transmitting the incident signal within civilian-use-permitted frequency bands and at a power of about one watt, a receiving block 31 in communication with the electromagnetic nonlinear element 28 and configured for receiving and processing the reflected return harmonic signal, and a processing block 32 configured to determine a signal strength of the reflected return harmonic signal and illustrate on the display screen 22 a distance from the existing golf ball 26 to the handheld unit 21.

(42) In a non-limiting exemplary embodiment, the handheld unit 21 includes a graphical user interface 33 illustrated on display screen 22. Such a graphical user interface 33 is configured to graphically display the distance and a direction from the existing golf ball 26 to the handheld unit 21 as well as the signal strength of the reflected return harmonic signal.

(43) In a non-limiting exemplary embodiment, the electromagnetic nonlinear element 28 is a Schottky diode 35.

(44) In a non-limiting exemplary embodiment, the handheld unit 21 is configured to radiate at two or more unique frequencies and further configured to receive at least one of the reflected return harmonic signal generated by the electromagnetic nonlinear element 28.

(45) In a non-limiting exemplary embodiment, the transponder tag 25 is disposed at the existing golf ball 26.

(46) In a non-limiting exemplary embodiment, the transponder tag 25 is disposed on a surface of the existing golf ball 26.

(47) In a non-limiting exemplary embodiment, the transponder tag 25 is integral and congruous with the existing golf ball 26.

(48) In a non-limiting exemplary embodiment, the transponder tag 25 is painted on the surface of the existing ball 26 with metallic and/or conductive paint.

(49) In a non-limiting exemplary embodiment, the transponder tag 25 may be placed on an inner sphere (under an outer sphere cover) of the golf ball 26. The harmonic signal penetrates the outer sphere cover effectively.

(50) In a non-limiting exemplary embodiment, each of the first antenna 23 and the second antenna 24 is a fractal antenna.

(51) In a non-limiting exemplary embodiment, the handheld unit 21 is configured to generate and emit at least one audible signal associated with the distance and/or direction from the existing golf ball 26 to the handheld unit 21 to indicate the signal strength of the reflected return harmonic signal as well as a direction from the handheld unit 21 to the existing golf ball 26.

(52) In a non-limiting exemplary embodiment, the handheld unit 21 further includes a power source 36 selected from a group including a rechargeable battery and a solar array.

(53) In a non-limiting exemplary embodiment, the electromagnetic nonlinear element 28 includes at least one of a metal-metal contact 45 and a metal-metal oxide contact 46.

(54) In a non-limiting exemplary embodiment, the transponder tag 25 includes one of a metal foil 47 and a metallic wire 48.

(55) In a non-limiting exemplary embodiment, the first antenna 23 is solely a transmitting antenna.

(56) In a non-limiting exemplary embodiment, the second antenna 24 is solely a receiving antenna.

(57) In a non-limiting exemplary embodiment, the transponder tag 25 includes a conductive paint layer 39 in electrical communication with the electromagnetic nonlinear element 28. Advantageously, the electromagnetic nonlinear element 28 includes a Schottky diode 35.

(58) In a non-limiting exemplary embodiment, transponder tag 25 includes a snowflake 40 shape having a center 40a and a plurality of stems 38a radially extended from the center 40a. Advantageously, a plurality of lobes (pebbles) 38b are attached to distal ends of the stems 38a and may include the electromagnetic nonlinear element 28 spaced apart along an outer perimeter of the snowflake 40 shape. The shapes and sizes of the pebbles 38b, length and quantity of the stems 38a, and angles of the stems 38a relative to each other from the center 40a of the snowflake 40 shape help determine the effectiveness of transponder tag 25.

(59) In a non-limiting exemplary embodiment, each of the lobes 38b includes a conductive paint layer 39 in electrical communication with the electromagnetic nonlinear element 28, respectively.

(60) In a non-limiting exemplary embodiment, each of the lobes 38b emits a unique one of the reflected return harmonic signal.

(61) In a non-limiting exemplary embodiment, each the reflected return harmonic signal is configured to be detected by the receiving block 31 and analyzed by the processing block 32 to determine the distance and a direction (angle) from the existing golf ball 26 to the handheld unit 21.

(62) In a non-limiting exemplary embodiment, the small and lightweight tag 25 could be easily applied to various subjects for location detection and finding tagged objects concealed/blocked by clutters. The tag 25 does not require any power supply, complex integrated chip, or battery. It is completely passive and very cost effective.

(63) In a non-limiting exemplary embodiment, the present disclosure describes a novel design and fabrication of nonlinear tags 25 with liquid conductive paint and a Schottky diode 35. The tag antennas 23, 24 were designed to cover the frequencies 7.9 GHz and 15.8 GHz at transmitter 23 and receiver 24 antennas. Various configurations with multiple antenna elements and parameters were developed, fabricated, and tested. The test bench setup did not use any amplifiers; the transmitting and receiving antennas 23, 24 were directly connected to the lab measuring equipment, shown in FIG. 5.

(64) In a non-limiting exemplary embodiment, in harmonic configurations, a fundamental frequency ?.sub.1 is transmitted by the transmitting antenna 23, and the receiving antenna 24 collects an integer-order harmonic frequency ?.sub.2 of the fundamental frequency. For instance, a second-order harmonic would have a fundamental frequency at ?.sub.1, and receiving frequency of ?.sub.2=2??.sub.1. At the n.sup.th order harmonics, the receiving frequency ?.sub.2 will be n??.sub.1, where n is an integer.

(65) In a non-limiting exemplary embodiment, the present disclosure focuses on the second-order harmonic tag 25 design with a fundamental frequency of 7.9 GHz and receiving frequency of 15.8 GHz.

(66) In a non-limiting exemplary embodiment, the design parameters of the tag antennas 23, 24 are based on the fundamental frequencies. Therefore, the lengths of the antennas 23, 24 are designed based on the wavelength of the transmitting and receiving frequencies: the wavelengths ? can be calculated with ?=c/?, where c is the speed of light, and ? is the frequency. In some cases, the wavelength design parameters were determined by the ratio of the fundamental frequency ?.sub.1, and the common ratios are l=0.5?.sub.1, and l=0.6?.sub.1, where l is the total length of the antenna. The corresponding antenna lengths have 2l.sub.1=l.sub.2 relationship. The two-element antenna design is shown in FIGS. 1, 8, and 9.

(67) In a non-limiting exemplary embodiment, the experiment was conducted with different design parameters of the antenna lengths l with 0.4?.sub.1, 0.45?.sub.1, 0.5?.sub.1, 0.55?.sub.1, and 0.6?.sub.1, accounting for the gap 50 length of the diode of 0.4 to 0.5 mm, along with varying widths from 0.1 mm to 0.4 mm at 0.1 mm increments. With all the parameter variations tested, it was found that strictly following the transmitting and receiving frequencies at their quarter wavelengths gave the best results for this application. While experimenting with different antenna parameter designs, it was found that tags 25 with more extended elements, i.e., 0.7?.sub.1 to 2?.sub.1 would still provide a decent signal-to-noise ratio (SNR), the extended element tags 25 could not match the performance of the tags 25 designed based on the quarter-wave lengths.

(68) In a non-limiting exemplary embodiment, a multi-element 28 (multiple stems 38a and lobes 38b) configuration was developed to enhance the reflected signal strength at the same distance while significantly increasing the detection range of a single-element 28 design. And further modulations on the multi-element 28 structure considerably boosted the reflected signal strength and the detectable distance.

(69) In a non-limiting exemplary embodiment, the tag 25 patterns were designed on a computer drawing board and used a laser cuter with 0.1 mm precision to cut a paintable mask, and the conductive material was then applied through the mask to form the shape of the tag 25 on a paper substrate. The thickness h of the painted conductive layer was estimated to be less than 0.1 mm. Finally, using the adhesive nature of the conductive material, the Schottky diode 35 adhered to the gap 50 (as shown in FIG. 2). The tag's 25 measured weight, including the paper substrate, was less than 0.1 grams for a single-element 28 configuration and less than 0.2 grams for multi-element 28 structures. And the total weight of the conductive paint and Schottky diode 35 is less than 0.004 grams. The tag 25 size compared with a 25-cent coin is illustrated in FIG. 4B. The Schottky diode 35 with 0402 packing has a length of 0.6 mm and a width w of 0.3 mm. All testing tags 25 were fabricated manually, resulting in the painted antennas having up to 1 mm deviation in length and 0.5 mm deviation in width compared to the design parameters.

(70) In a non-limiting exemplary embodiment, experimental tests focused on the nonlinear tag's 25 distance performance with respect to the (SNR) ratio reflected on the R&S FSU spectrum analyzer 52 shown at graph 58 in FIG. 6A. The transmitting antenna 23 was directly connected to an HP 83630A signal generator 53 with a 7.9 GHz supplied frequency and power level at 19 dBm, and the receiving antenna 24 was directly connected to the spectrum analyzer with a center frequency of 15.8 GHz. FIG. 6A shows the measurement peak of 97.42 dBm on the spectrum analyzer at the center frequency of the modified multi-element tag 25 at a distance of 2.7 ft. Graph 59 in FIG. 6B shows the nonlinearity of instruments after averaging. The noise floor (NF) was determined using the spectrum analyzer's 52 averaging function. And it also shows the second harmonic NF peak at the center frequency of 15.8 GHz at ?128.7 dBm, while the NF at the sideband frequencies stays relatively constant, averaging at ?131 dBm. The instruments' nonlinearities may present different values at different times, depending on the placements of the transmitting and receiving antennas 23, 24 and the power supplied by the signal generator. Thus, an averaging was conducted before each measurement. To have a clear view of the peak at the center frequency on the spectrum analyzer 52, reduce any access noise, and create an observable sweep time of 1 second, the resolution bandwidth and video bandwidth were set at 100 Hz, and the frequency span was set at 5 kHz. Two sets of 10-minute averaging were conducted for the experimental results shown in FIG. 7, with NF of ?124.55 dBm and ?125.98 dBm, respectively. And the average NF of ?125.27 dBm was used to calculate the SNR.

(71) In a non-limiting exemplary embodiment, FIG. 7 is a graph 60 shows the SNR versus distance plot comparison between single-element 28, multi-element 28, and modified multi-element 28 configurations. The term element 28 means an electromagnetic nonlinear element 28 (i.e., Schottky diode 35 which has a stem 38a and a lobe/pebble 38b). The SNR values were obtained by taking the absolute difference between the NF and the peak value at the center frequency from the spectrum analyzer 52. The results of the single-element 28 tag 25 presented successful results for the intended purpose of the present disclosure based on the Schottky diode's 35 nonlinearity. With the appropriate antenna parameters, there exists a second-order harmonic response. Integrating multiple elements onto tag 25 significantly improved the SNR at the same distance as the single-element 28 configuration and increased the detectable distance by 50% from 2.6 ft to 3.9 ft. The distance test was conducted by using a hand-held tag 25 moving away from the transmitting and receiving antennas 23, 24, observing, and recording the peak response from the spectrum analyzer 52. Location experiments were performed by sticking tag 25 on top of a chair and affixing the transmitting and receiving antenna 23, 24 on a mobile platform. Then rotating the platform scans across the space to find the direction of the tagged objects, and the reflected signal strength presented a relative distance between the platform and the tag 25.

(72) In a non-limiting exemplary embodiment, multiple modifications were made to the single-element 28 and multi-element 28 configurations. And the best-performing modification is shown in FIG. 3. From the SNR versus distance plot, the modified multi-element 28 gained significant SNR compared to the unmodified version and further increased the detectable distance by 67% from 3.9 ft to 6.6 ft. Data points were recorded by reading the peak response values from the spectrum analyzer 52. And it should be noted that all recorded data must have shown the measurement's sustainability and repeatability of the peak because of the sensitive nature of the antennas and instruments.

(73) In a non-limiting exemplary embodiment, with reference to Table 1 below, system 20 of the present disclosure includes three main blocks: a transmitting block 30, a receiving block 31, and a processing block 32.

(74) In a non-limiting exemplary embodiment, referring to FIGS. 8-10, the transmitting block 30 generates and transmits the fundamental frequency to detect the tagged target (golf ball). The circuit contains a voltage-controlled oscillator generating the fundamental frequency at 4 GHz. The transmit frequency may vary from 1 to 8 GHz. The signal then goes through a series of filters and amplifiers to ensure only the desired frequency is being transmitted and amplified at the transmitting antenna 23. The transmitting frequency is split into two paths: one goes to the transmitting antenna 23, and another goes through a frequency doubler and sent to the mixer for down-conversion.

(75) In a non-limiting exemplary embodiment, the receiving antenna 24 detects the 2nd-order harmonic frequency bounced back by the nonlinear tag 25, sending the signal through the receiving chain with a series of low-noise amplifiers and a bandpass filter. As a result, the received 2nd-order harmonic signal is weak and will be amplified and filtered at the desired receiving frequency of 8 GHz. The receive frequency may vary from 2 to 16 GHz.

(76) In a non-limiting exemplary embodiment, the processing block 32 first down-converts the doubled transmitting frequency and the received 2nd harmonic frequency with a mixer and sends a direct current (DC) signal to a baseband analog to digital converter (ADC) for sampling. The sampled data is then sent to a microcontroller which controls the output to either a set of speakers and display or to a BLUETOOTH? (a short-range wireless technology standard that is used for exchanging data between fixed and mobile devices over short distances and building personal area networks) device for smartphone connection.

(77) TABLE-US-00001 TABLE 1 System Components And Their Parameters VCO (? 1) 4 GHz Pout +5 dBm Frequency 3.9-4.45 GHz BPF 4 GHz 50 ? (? 1) Pass band 3.7-4.5 GHz Insertion Loss 1.4 dB (4.1 GHz typical) VSWR 1.5 dB BPF 8 GHz (? 1) 50 ? Pass band 7.9-8.1 GHz Insertion Loss 2 dB (8 GHz typical) VSWR 1.6 dB LPF 4 GHz (? 1) 50 ? Cut-Off Frequency 5.2 GHz Insertion Loss 0.9 dB (@ 4 GHz) Return Loss 16.31 dB LNA (? 2) 50 ? 8 GHz Receiver Gain 23.1 dB (typical) Input Return Loss 20 dB Output Return Loss 16 dB P1dB 19.8 dB OIP3 28.7 dB NF 1.2 dB Circulator 50 ? (? 1) Frequency Range 3.8-4.0 GHz Isolation 9 dB (3.9 GHz) Insertion Loss 1.1 dB VSWR 1.8 dB Splitter 50 ? (? 1) Frequency 2.8-7.2 GHz Total Loss 3.5 dB @ 4 GHz Mixer Bandwidth 3.7-10 GHz (? 1) Conversion Loss ~6 dB (8 GHz) IP3 ~14 dBm (LO +7 dBm) Multiplier 50 ? (? 1) Output Bandwidth 5.4-9.6 GHz Conversion Loss 12.09 dB (4 GHz input) 21.89 dB (8 GHz output) Monolithic Amplifier 50 ? Gain 14.9 dB @ 4 GHz OIP3 35 dB @ 1 GHz TX (first) Antenna Frequency: 7.42 dB 2 ? 2 @ 4 GHz 3.94 GHz RX (second) Antenna Frequency: 9.8~10.07 dB 2 ? 2 @ 8 GHz 7.88 GHz

(78) Advantageously, the present disclosure provides a series of passive nonlinear miniature tag 25 designs, via laser-assisted fabrication, and successful range tests up to 6.7 ft. The tags 25 are light-weight, inexpensive, and can be fabricated manually. In addition, the strong signal reflection from the tags 25 has excellent potential for locating subjects of various types and sizes.

(79) In a non-limiting exemplary embodiment, a hand held unit 21 contains a radio frequency transmitter, a receiver, processing and display electronics, and a power source 36. The transmitter transmits a low power signal (<1 watt) at a radio frequency, f1, allowed for civilian, commercial use.

(80) In a non-limiting exemplary embodiment, the transponder tag 25 is attached to or imbedded in the object (golf ball) to be located and includes an electromagnetically nonlinear element 28 and two antennas 23, 24. One antenna is designed for the primary signal, f1. By virtue of the nonlinear device, a second RF signal, f2, an integer multiple of the primary frequency, is generated and transmitted by the second antenna 24. Generally, f2 is twice f1. The transponder tag 25 is passive, requiring no power source 36 other than the received, primary signal.

(81) In a non-limiting exemplary embodiment, the receiver includes an antenna designed for the frequency of the transponder output, f2, signal processing electronics, involving a microprocessor, which converts the received signal to distance and signal strength information. That information is supplied to the display electronics, visual and/or audio, for the user. The user determines the direction to the tag 25 as that provides the maximum signal when slewing the hand held unit 21 from side to side.

(82) In a non-limiting exemplary embodiment, a cell phone with the appropriate software application(s) could provide power to the hand held unit 21 and display audio and visual signals, which are output from unit 21.

(83) In a non-limiting exemplary embodiment, the present disclosure refers to a type of nonlinear radar called harmonic radar system 20 in which a signal primary frequency is transmitted by a hand held unit 21, and a second frequency (an integer multiple of the primary frequency) is returned by the tag 25.

(84) In a non-limiting exemplary embodiment, another type of nonlinear radar is intermodal radar system, in which two or more primary signals could be transmitted and several frequencies returned. The returned signals are linear combinations of the two primary signals. This system would also use a passive tag 25 as described above, but the transmitter/receiver would be more complex.

(85) Advantageously, this present disclosure combines a compact, lightweight, and uncomplicated transceiver and tag 25 with adequate range to be practical and useful for the golfer. Tag 25 may be built into the center of the ball 26, just under the ball 26 cover, or on the ball 26 surface. This present disclosure includes a light weight, pocket sized transceiver similar to a cell phone and a very small, lightweight tag 25 so as not to affect flight characteristics of the ball 26.

(86) Referring to FIGS. 1-18, in a non-limiting exemplary embodiment(s), the present disclosure provides a nonlinear radar system 20 for finding a golf ball 26 which is not observable or easily located by an observer's line of sight. The nonlinear radar system 20 includes a hand held unit 21, which generates and emits a radar signal and receives the reflected signal. Transponder tag 25 contains an electromagnetically nonlinear element 28 attached to a golf ball 26. Whenever the radar signal encounters a nonlinear element 28, a series of reflected return signals are generated at harmonic frequencies, integer multiples of the illuminating frequency (harmonic radar). If the radar set (hand held unit 21) generates two signals at different frequencies, multiple combinations of those two frequencies are generated by the transponder tag 25 (intermodal radar). In either case, the radar set receiver (hand held unit 21) would be turned to a harmonic frequency or an intermodal frequency. Notably, most objects on a golf course, such as grass, leaves, brush, or an ordinary golf ball 26 will reflect the illuminating radiation so monitoring the return at the illuminating frequency would detect return from all objects making it impossible to detect a golf ball 26. Monitoring a harmonic of the illuminating frequency would enable the nonlinear radar system 20 to see an object equipped with a nonlinear element 28 but not grass, leaves and other materials on the course since they would not return a signal at a harmonic frequency.

(87) In a non-limiting exemplary embodiment, the nonlinear radar system 20 includes a small, handheld device 21 which transmits a low power radar signal and receives the signal at the harmonic frequency from a golf ball 26 to which an electromagnetic nonlinear element 28 has been affixed. The handheld device 21 will have a readout screen which will indicate the distance and direction to the ball 26. Similarly, monitoring an intermodal frequency of the illuminating frequencies would enable the nonlinear radar set (unit 21) to see the object of interest.

(88) In a non-limiting exemplary embodiment, a nonlinear radar has been shown to be capable of locating and ranging an object which contains an electromagnetic nonlinear element 28. Elements that are inherently electromagnetically nonlinear, such as metal-metal contacts, semiconductors, ferroelectrics, antennas, or filters, will return radar signals at harmonic frequencies that differ from the illuminating frequency (?.sub.0) by integer multiples of the illuminating frequency, fn=nf0 where n=2, 3, 4, . . . ) or, if two frequencies, f1 and f2, are transmitted, at intermodal frequencies (such as 2nd harmonics at 2f1 and 2f2, and intermodal signals 2f1-f2, 2f2 f1, and f1+f2). Intermodal signals can also be generated at 3rd and higher order harmonics and by three or more transmitted frequencies). Advantageously, the nonlinear radar (handheld unit 21) is configured to emit one frequency and monitor a harmonic return frequency or emit multiple frequencies and monitor an intermodal return frequency (to avoid detecting grass, debris, non-golf ball objects).

(89) In a non-limiting exemplary embodiment, a Schottky diode 35 may be used as the nonlinear element 28, but other nonlinear elements may be used. Objects which did not contain such elements, such as grass, leaves, brush, trees, or rocks will return signals at the illuminating frequency creating strong background or clutter which would obscure the return from a small object at the illuminating frequency. An object equipped with an electromagnetic nonlinear element 28 can be distinguished from the background clutter by monitoring the harmonic returns (frequency levels).

(90) In a non-limiting exemplary embodiment, any golf ball 26 can be modified to carry an electromagnetic nonlinear element 28. While there are several types of such elements, (metal-metal contact, various types of semiconductors, ferro electrics, antennas), a Schottky diode 35 is preferably used to produce harmonic frequencies. The Schottky diode 35 can be made on the order of 0.3 millimeter (0.02 inches). The weight of such a small diode is very small and could easily be counterbalanced at the golf ball 26. The Schottky diode 35 could be glued to the ball 26 in a dimple and have negligible effect on flight characteristics. Alternatively, diode 35 could be inserted into the cover of the golf ball 26 by means of a very small slit in the cover or a small hole drilled into the cover or pressed into one of the dimples and secured or covered with an adhesive glue. In either case, a small amount of glue could be used to hold the Schottky diode 35 in place. Diode 35 must be in contact with two antennas at the golf ballone tuned to the illuminating frequency and one to the desired harmonic frequency. The desired harmonic frequency would normally be twice the illuminating frequency, but other multiples of the illuminating frequency may also be used. The antennas may be made of thin wire, painted on with an electrically conductive paint, or a fractal antenna. Fractal antennas are designed to be very compact and could be applied as a small sticker or decal. The antenna may not need to be in physical contact with the diode.

(91) In a non-limiting exemplary embodiment, an air gap 50 between the antenna and a micro RFID tag 25 is acceptable and even beneficial.

(92) In a non-limiting exemplary embodiment, the harmonic radiation may not be isotropic, so a single nonlinear element 28 may not provide a sufficiently strong signal to be detected depending on the orientation of the golf ball 26 and the handheld unit 21 (radar set). Multiple transponder tags 25 can be installed to provide an adequate signal over greater space. The attachment of a diode 35 and antennas would add much less weight to the golf ball 26 than any active element 28 using a battery or circuitry for an on/off switch or recharging, so the total weight of multiple diodes 35 and antennas should not affect flight characteristics if they are positioned correctly. For example, two elements at 180 degrees, three elements located in the equatorial plane at 120 degrees apart, four elements located tetrahedrally, etc. The diodes 35 are quite rugged and should not be damaged in the normal course of play, nor should the nonlinear element 28 fall off or out of the ball 26 in normal play. If an element 28 is lost or damaged, additional elements 28 can still provide nonlinear radar system 20 capabilities.

(93) In a non-limiting exemplary embodiment, the nonlinear radar system 20 includes a small, handheld unit 21, approximately the size of a cell phone, which can easily be carried by the golfer. Unit 21 includes a transmitter and receiver (collectively the unit 21) powered by batteries. Alternatively, unit 21 could be powered by a rechargeable battery or even photovoltaic solar array. Unit 21 serves as a transmitter of low powered electromagnetic radiation and a receiver of the return signal. The signal frequencies will be in the bandwidths allowed by law for commercial use and will have a strength of approximately one watt. Additional circuitry will measure the distance to the golf ball 26 and the signal strength. Unit 21 is also equipped with a flat screen display 22, such as an LED or backlit LCD array which can be read on the golf course. Display 22 will indicate the distance to the ball 26 as well as an indication of signal strength. By sweeping the handheld unit 21 horizontally from side to side, the direction to the ball 26 will be indicated on display 22 as the direction of the maximum signal strength. Unit 21 could also produce a tone to indicate distance and direction to ball 26.

(94) In a non-limiting exemplary embodiment, the golf ball 26, which could be any ball 26 the golfer desires, would be fitted with a transponder tag 25. The transponder tag 25 includes an electromagnetic nonlinear element 28 such as, but not limited to a diode 35, metal-metal contact, or metal-metal oxide contact, an antenna, and be passive, requiring no power source 36 but the incoming radiation from the handheld unit 21. The antenna may be a small wire, a fractal antenna, conductive paint, or other material which would serve as an antenna. The nonlinear element 28 can be attached to the ball 26 surface, or inserted into covering through a small hole cut or drilled into the covering. The diode 35 or other nonlinear element 28 would be placed into the hole, or, alternatively, placed in a dimple of the ball 26. The antennas would be attached or applied to, or painted on the ball 26 surface. The antenna may be in contact with the nonlinear element 28 or communicate with the ball 26 over a small gap 50. Alternatively, the nonlinear element 28 and antenna may be combined on a small adhesive patch. A fractal pattern antenna patch would be ideal since the golfer could apply a replacement on the course should a patch fall off or become damaged in the course of play. The antenna radiation strength is not generally isotropic (uniform in all directions). The golf ball 26 may be equipped with multiple transponders tags 25 to insure a strong signal in any direction and at acceptable distance.

(95) In a non-limiting exemplary embodiment, although the use of very small, surface mounted transponder tag 25 will allow the golfer to use the nonlinear radar system 20 with any golf ball 26 and to equip or even replace a transponder tag 25 in the field, the transponder tag 25 could be placed within the ball 26 during manufacture. Since the nonlinear radar system 20 does not require a battery or additional circuits to turn the power on or off or to recharge the battery, the golf ball 26 so equipped should be less expensive to produce and last much longer than a ball 26 using an active, battery powered transponder tag 25 nonlinear radar system 20.

(96) In a non-limiting exemplary embodiment, the nonlinear radar nonlinear radar system 20 may be used for locating many different types of objects beyond golf balls. For instance, a transponder tag 25 could be applied to eyeglasses, electronics remote units, keys, cell phones, computers or electronic tablets, or any other objects commonly misplaced in the home, car, or elsewhere. A transponder tag 25 could also be applied to archery arrows or other outside equipment that might be difficult to find in normal use.

(97) Referring to FIGS. 13-13A, in a non-limiting exemplary embodiment, the nonlinear radar system 20 includes a handheld unit 21 configured to generate and emit an incident signal frequency and a transponder tag 25 attached to an existing golf ball 26. Such a transponder tag 25 is in communication with and responsive to handheld unit 21. Transponder tag 25 includes an electromagnetic nonlinear element 28 and at least one antenna in communication with the electromagnetic nonlinear element 28. Advantageously, upon detecting the incident signal frequency, the antenna (part of snowflake 40 shape) is configured to transmit a return harmonic signal having a frequency different from the incident signal frequency. Notably, transponder tag 25 is passive and does not require a power source 36 other than incident radiation. Advantageously, the handheld unit 21 includes a first circuit in communication with the electromagnetic nonlinear element 28 for generating and transmitting the incident signal frequency within civilian-use-permitted frequency bands and at a power of about one watt, and a second circuit in communication with the electromagnetic nonlinear element 28 for receiving and processing the return harmonic signal configured to determine a distance and direction from the existing golf ball 26 to the handheld unit 21 as well as to determine a signal strength of the return harmonic signal.

(98) In a non-limiting exemplary embodiment, handheld unit 21 includes a display screen 22 and a graphical user interface 33 illustrated on the display screen 22. Such a graphical user interface 33 is configured to display the distance from the existing golf ball 26 to the handheld unit 21 as well as the signal strength of the return harmonic signal.

(99) In a non-limiting exemplary embodiment, the electromagnetic nonlinear element 28 is a Schottky diode 35.

(100) In a non-limiting exemplary embodiment, the handheld unit 21 is configured to radiate at two or more unique frequencies and further configured to receive at least one of the return harmonic intermodal signals generated by the electromagnetic nonlinear element 28.

(101) In a non-limiting exemplary embodiment, the transponder tag 25 is disposed inside the existing golf ball 26.

(102) In a non-limiting exemplary embodiment, the transponder tag 25 is disposed on a surface of the existing golf ball 26.

(103) In a non-limiting exemplary embodiment, the transponder tag 25 is placed within a small cavity of a cover of the existing golf ball 26.

(104) In a non-limiting exemplary embodiment, the antenna (part of snowflake 40 transponder tag 25) is painted on the surface of the existing ball 26 with metallic or conductive paint.

(105) In a non-limiting exemplary embodiment, the transponder tag 25 may be placed on an inner sphere (under an outer sphere cover) of the golf ball 26. The harmonic signal penetrates the outer sphere cover effectively.

(106) In a non-limiting exemplary embodiment, the transponder tag 25 antenna is a fractal antenna.

(107) In a non-limiting exemplary embodiment, the handheld unit 21 is configured to generate and emit at least one audible signal associated with the distance from the existing golf ball 26 to the handheld unit 21 as well as the signal strength of the return harmonic signal as well as a direction from the handheld unit 21 to the existing golf ball 26.

(108) In a non-limiting exemplary embodiment, the handheld transponder tag 25 further includes a power source 36 selected from a group including a rechargeable battery and a solar array.

(109) In a non-limiting exemplary embodiment, the electromagnetic nonlinear element 28 includes at least one of a metal-metal contact and a metal-metal oxide contact.

(110) In a non-limiting exemplary embodiment, the antenna includes one of a metal foil and a metallic wire.

(111) In a non-limiting exemplary embodiment, referring to FIG. 14, principles of the transponder tag 25 include varying the non-linear element 28 (stem 38a) lengths for the snowflake 40 structure. In particular, the structure of the snowflake 40 transponder tag 25 of non-linear element 28 lengths depend on the harmonic frequencies from the transceiver (from tag 25) and are calculated to be a quarter-wavelength of the transmit and receive frequencies (from handheld unit 21). Because there are two frequencies used in the present disclosure's harmonic system 20, the elements need to be in different lengths. For example, if the harmonic frequencies are 8 GHz and 16 GHz, the corresponding element 28 lengths are:

(112) ${\mathrm{Length}}_1=\frac{Wavelengt{h}_{8\mathrm{GHz}}}{4},\mathrm{where}$$\mathrm{Wavelength}=\left(\mathrm{Speed}\mathrm{of}\mathrm{Light}\right)/\mathrm{Frequency\_}\left(8\mathrm{GHz}\right)$$\mathrm{Length}2=\mathrm{Wavelength\_}\left(16\mathrm{GHz}\right)/4,\mathrm{where}$$\mathrm{Wavelength}=\left(\mathrm{Speed}\mathrm{of}\mathrm{Light}\right)/\mathrm{Frequency\_}\left(16\mathrm{GHz}\right)$

(113) In a non-limiting exemplary embodiment, referring to FIG. 15, the number of stems 38a were determined based on experimentation. For example, we started with a single set of stems: a longer stem and a shorter stem, based on the calculated lengths from the equation above. Then, gradually increased the number of elements (stem 38a) to test and see if there is a stronger returned signal. We discovered that the number of stems 38a/elements may operably range from two to eighteen total elements on a single transponder tag 25. The best results are preferably provided with transponder tags 25 having approximately ten stems 38a/elements, with each stem 38a having a lobe/pebble at the end of it. Thus, the number of lobes 38b/pebbles depends on the number of stems 38a/elements.

(114) In a non-limiting exemplary embodiment, referring to FIG. 16, the DC-Short 56 position and length were determined based on experimentation. The DC-Short 56 provides a conducting bridge for two sides of the diode on the transponder tag 25. It provides stability and boost in capturing and returning the signal. The DC-short 56 position may range between 0.5 to 3 mm from the diode, and the length of the DC-short 56 is +/?1 mm between the shorter elements of the transponder tag 25.

(115) In a non-limiting exemplary embodiment, referring to FIG. 17, the element 28 separation angles were determined based on experimentation. We started by picking arbitrary angles, and varying the angles while keeping other parameters unchanged, and through experiments we found which angle configurations provide the strongest return signal. The element 28 separation angles also depend on the number of elements. ?: Angle between each element 28 on one side of the diode. ?: Angle between the closest elements on either side of the diode. For example, the angle between the elements 28 may range between 20 to 35 degrees for the elements/stems 38a which are placed on one side of the diode. Also, the angle between the elements/stems 38a may range between 60 to 90 degrees for the closest elements/stems 38a on opposite sides of the diode.

(116) In a non-limiting exemplary embodiment, referring to FIG. 18, the shapes and sizes of the lobes 38b/pebbles 38b were determined based on experimentation. Experiments with various shapes added to the tips of the elements/stems 38a include the following shapes: circle, oval, triangle, various polygons, and many other geometrical shapes. We compared the performances and determined that oval is the best shape for this configuration. The current best performing transponder tags 25 employed an oval shape, for both longer and shorter elements. The teardrop and heart shaped lobes 38b/pebbles 38b were effectively and operably suitable to a lesser extent. The sizes of the lobes 38b/pebbles 38b were arbitrarily chosen in the beginning, then we varied the lobe/pebble sizes and compared the returned signal strength to determine the optimal sizes of the lobes 38b/pebbles 38b.

(117) In a non-limiting exemplary embodiment, the number of pebbles 38b/lobes 38b are the same as the number of elements/stems 38a. Thus, there is a 1:1 ratio of the number of pebbles 38b/lobes 38b to the number of elements/stems 38a.

(118) In a non-limiting exemplary embodiment, transponder tag 25 includes a plurality of stems 38a radially extended outwardly from a center of the transponder tag 25, and a plurality of lobes 38b coupled to a distal end of the stems 38a, respectively. Advantageously, a quantity of stems 38a equals a quantity of the lobes 38b and have a 1:1 ratio.

(119) In a non-limiting exemplary embodiment, the number of transponder tags 25 applied onto the golf ball 26 was determined by experimentation. Such experimentation included starting with a single transponder tag 25, then gradually increasing the number of transponder tags 25 applied to the golf ball 26. Then, experiments were performed to determine if there are any interferences between transponder tags 25, and their relative positions and orientations. Next, experiments were conducted to determine if multiple transponder tags 25 can boost the returned signal, and their relative positions and orientations. Additionally, experiments were carried out to determine a minimal number of transponder tags 25 needed for the golf ball 26 to be effectively and operably detected with full coverage.

(120) In a non-limiting exemplary embodiment, experiments were conducted to determine a choice of optimal harmonic frequencies. The size of the transponder tag 25 for the application is highly restricted by the size of the golf ball 26. As frequencies get higher, the transponder tag 25 becomes smaller, but higher frequencies have shorter range. While lower frequencies provide longer detectable range, the transponder tag 25 sizes will increase. Golf balls have an average diameter of 42.67 mm, which limits the size of the transponder tag 25. Based on the experiments, when transponder tags 25 are bent and wrapped on the surface of the golf ball 26, their performance will change as well.

(121) In a non-limiting exemplary embodiment, experiments were conducted to determine antenna polarization of the transponder tags 25linear vs circular polarization. Linearly polarized antennas can only send out electromagnetic (EM) waves that are polarized in one linear direction. This means that if the transponder tags 25 are rotated to a certain angle such that their polarization is not consistent with the transceiver antenna, their ability to capture and reflect signals will be much weaker. And, if the transponder tags 25 polarization is perpendicular to the antennas' polarization orientation, then the transponder tags 25 will not reflect any signal. Circularly polarized antennas can send out the EM waves in a circularly polarized fashion, which means the instantaneous angle polarization keeps changing to cover the entire 360 degree surrounding the antenna. Therefore, transponder tag 25 orientations will no longer be an issue with circularly polarized antennas. This is critical for golf ball 26 localization since the golf ball 26 is round and can rotate to any orientation between 0-360 degrees.

(122) While various embodiments have been described, the description is intended to be exemplary, rather than limiting, and it is understood that many more embodiments and implementations are possible that are within the scope of the embodiments. Although many possible combinations of features are shown in the accompanying figures and discussed in this detailed description, many other combinations of the disclosed features are possible. Any feature of any embodiment may be used in combination with or substituted for any other feature or element in any other embodiment unless specifically restricted. Therefore, it will be understood that any of the features shown and/or discussed in the present disclosure may be implemented together in any suitable combination. Accordingly, the embodiments are not to be restricted except in light of the attached claims and their equivalents. Also, various modifications and changes may be made within the scope of the attached claims.

(123) While the foregoing has described what are considered to be the best mode and/or other examples, it is understood that various modifications may be made therein and that the subject matter disclosed herein may be implemented in various forms and examples, and that the teachings may be applied in numerous applications, only some of which have been described herein. It is intended by the following claims to claim any and all applications, modifications and variations that fall within the true scope of the present teachings.

(124) Unless otherwise stated, all measurements, values, ratings, positions, magnitudes, sizes, and other specifications that are set forth in this specification, including in the claims that follow, are approximate, not exact. They are intended to have a reasonable range that is consistent with the functions to which they relate and with what is customary in the art to which they pertain.

(125) The scope of protection is limited solely by the claims that now follow. That scope is intended and should be interpreted to be as broad as is consistent with the ordinary meaning of the language that is used in the claims when interpreted in light of this specification and the prosecution history that follows and to encompass all structural and functional equivalents. Notwithstanding, none of the claims are intended to embrace subject matter that fails to satisfy the requirement of Sections 101, 102, or 103 of the Patent Act, nor should they be interpreted in such a way. Any unintended embracement of such subject matter is hereby disclaimed.

(126) Except as stated immediately above, nothing that has been stated or illustrated is intended or should be interpreted to cause a dedication of any component, step, feature, object, benefit, advantage, or equivalent to the public, regardless of whether it is or is not recited in the claims.

(127) It will be understood that the terms and expressions used herein have the ordinary meaning as is accorded to such terms and expressions with respect to their corresponding respective areas of inquiry and study except where specific meanings have otherwise been set forth herein. Relational terms such as first and second and the like may be used solely to distinguish one entity or action from another without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms comprises, comprising, or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by a or an does not, without further constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element.

(128) The Abstract of the Disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, it can be seen that various features are grouped together in various examples for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claims require more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed example. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separately claimed subject matter.