ULTRASONIC TRANSDUCER

[0001] The present disclosure relates, in general, to ultrasonic surgical instruments and more particularly to ultrasonic transducers to drive ultrasonic blades. Ultrasonic instruments, including both hollow core and solid core instruments, are used for the safe and effective treatment of many medical conditions. Ultrasonic instruments, and particularly solid core ultrasonic instruments, are advantageous because they may be used to cut and/or coagulate organic tissue using energy in the form of mechanical vibrations transmitted to a surgical end effector at ultrasonic frequencies. Ultrasonic vibrations, when transmitted to organic tissue at suitable energy levels and using a suitable end effector, may be used to cut, dissect, elevate or cauterize tissue or to separate muscle tissue from bone. Ultrasonic instruments utilizing solid core technology are particularly advantageous because of the amount of ultrasonic energy that may be transmitted from the ultrasonic transducer, through a waveguide, and to the surgical end effector. Such instruments may be used for open procedures or minimally invasive procedures, such as endoscopic or laparoscopic procedures, wherein the end effector is passed through a trocar to reach the surgical site.

[0002] Activating or exciting the end effector (e.g., cutting blade) of such instruments at ultrasonic frequencies induces longitudinal vibratory movement that generates localized heat within adjacent tissue. Because of the nature of ultrasonic instruments, a particular ultrasonically actuated end effector may be designed to perform numerous functions, including, for example, cutting and coagulation. Ultrasonic vibration is induced in the surgical end effector by electrically exciting a transducer, for example. The transducer may be constructed of one or more piezoelectric or magnetostrictive elements in the instrument hand piece. Vibrations generated by the transducer are transmitted to the surgical end effector via an ultrasonic waveguide extending from the transducer to the surgical end effector. The waveguide and end effector are designed to resonate at the same frequency as the transducer. Therefore, when an end effector is attached to a transducer, the overall system frequency is the same frequency as the transducer itself.

[0003] The amplitude of the longitudinal ultrasonic vibration at the tip, d, of the end effector behaves as a simple sinusoid at the resonant frequency as given by:

d=A sin(ωt)

where:

[0004] ω=the radian frequency which equals 2π times the cyclic frequency, f; and

[0005] A=the zero-to-peak amplitude.

The longitudinal excursion of the end effector tip is defined as the peak-to-peak (p-t-p) amplitude, which is just twice the amplitude of the sine wave or 2 A. Often, the end effector can comprise a blade which, owing to the longitudinal excursion, can cut and/or coagulate tissue. U.S. Pat. No. 6,283,981, which issued on Sep. 4, 2001 and is entitled METHOD OF BALANCING ASYMMETRIC ULTRASONIC SURGICAL BLADES; U.S. Pat. No. 6,309,400, which issued on Oct. 30, 2001 and is entitled CURVED ULTRASONIC BLADE HAVING A TRAPEZOIDAL CROSS SECTION; and U.S. Pat. No. 6,436,115, which issued on Aug. 20, 2002 and is entitled BALANCED ULTRASONIC BLADE INCLUDING A PLURALITY OF BALANCE ASYMMETRIES, the entire disclosures of which are hereby incorporated by reference herein, disclose various ultrasonic surgical instruments.

[0006] It may be recognized that the effectiveness of an ultrasonic surgical instrument may be related in part to the amount of the longitudinal excursion of the end effector tip. An ultrasonic surgical instrument having an end effector tip capable of a large longitudinal excursion can accomplish more work during a surgical procedure. Consequently, it may be useful to design components of the ultrasonic surgical instrument to maximize the potential excursion of the end effector tip. Further, because there may be some error in the driving frequency produced by the energy source used to power the ultrasonic surgical instrument transducer, it may further be useful to design components of the ultrasonic surgical instrument that may increase the tolerance of the device to such frequency errors.

[0007] In one general aspect, various aspects are directed to an ultrasonic surgical instrument that comprises a transducer configured to produce vibrations along a longitudinal axis of a surgical tool at a predetermined frequency. In various aspects, the surgical tool may include an ultrasonic blade extends along the longitudinal axis and is coupled to the transducer. In various aspects, the surgical tool includes a body having a proximal end and a distal end, wherein the distal end is movable relative to the longitudinal axis by the vibrations produced by the transducer, and the proximal end is mechanically coupled to the transducer.

[0008] In one general aspect, an ultrasonic surgical instrument may comprise an ultrasonic horn comprising: a proximal flange; a first cylindrical portion having a first diameter and positioned distal to the proximal flange; a second cylindrical portion comprising a second diameter and a distal end, wherein the second cylindrical portion is at a position located distal to the first cylindrical portion and wherein the second diameter is smaller than the first diameter; a tapered portion disposed between the first cylindrical portion and the second cylindrical portion; and a cylindrical mass disposed about the horn at a position located between the flange and the distal end of the second cylindrical portion.

[0009] In one general aspect, an ultrasonic system may comprise: an end-bell; an ultrasonic horn, wherein the ultrasonic horn comprises: a proximal flange; a first cylindrical portion having a first diameter and positioned distal to the proximal flange; a second cylindrical portion comprising a second diameter and a distal end, wherein the second cylindrical portion is at a position located distal to the first cylindrical portion and wherein the second diameter is smaller than the first diameter; a tapered portion disposed between the first cylindrical portion and the second cylindrical portion; and a cylindrical mass disposed about the horn at a position located between the flange and the distal end of the second cylindrical portion; a transducer portion disposed between the end-bell and the ultrasonic horn; and an ultrasonic power source configured to supply an electrical signal having a predetermined frequency component to actuate the transducer portion.

[0021] Before explaining various aspects in detail, it should be noted that such aspects are not limited in their application or use to the details of construction and arrangement of parts illustrated in the accompanying drawings and description. The illustrative aspects may be implemented or incorporated in other aspects, variations and modifications, and may be practiced or carried out in various ways. For example, the surgical instruments disclosed below are illustrative only and not meant to limit the scope or application thereof. Furthermore, unless otherwise indicated, the terms and expressions employed herein have been chosen for the purpose of describing the illustrative aspects for the convenience of the reader and are not to limit the scope thereof.

[0022] Certain exemplary aspects will now be described to provide an overall understanding of the principles of the structure, function, manufacture, and use of the devices and methods disclosed herein. One or more examples of these aspects are illustrated in the accompanying drawings. Those of ordinary skill in the art will understand that the devices and methods specifically described herein and illustrated in the accompanying drawings are non-limiting exemplary aspects and that the scope of the various aspects is defined solely by the claims. The features illustrated or described in connection with one exemplary aspect may be combined with the features of other aspects. Such modifications and variations are intended to be included within the scope of the claims.

[0023] Various aspects described herein relate, in general, to ultrasonic surgical instruments and blades for use therewith. Examples of ultrasonic surgical instruments and blades are disclosed in U.S. Pat. Nos. 5,322,055; 5,954,736; 6,309,400; 6,278,218; 6,283,981; 6,325,811; and 8,319,400, wherein the entire disclosures of which are incorporated by reference herein.

[0024] The term “phase margin” (PM), as used herein, is the difference in frequency between the anti-resonant frequency (f_a) and a resonant frequency (f_r) of a piezoelectric transducer. In one non-limiting example, f_r may be determined as the frequency at a trough of an impedance vs. frequency graph of the piezoelectric transducer. Similarly, f_a may be determined as the frequency at a peak of the impedance vs. frequency graph of the piezoelectric transducer. Therefore, PM equals f_a−f_r of the piezoelectric transducer.

[0025] The abbreviation “OD” as used herein is the outer diameter of a component of the ultrasonic transducer. More specifically, OD may refer to the outer diameter of a ring or cylindrical mass associated with an ultrasonic horn of the ultrasonic transducer.

[0026] According to various aspects, an ultrasonic instrument comprising a surgical tool having an end effector such as a blade can be of particular benefit, among others, in orthopedic procedures where it is desirable to remove cortical bone and/or tissue while controlling bleeding. Due to its cutting and coagulation characteristics, a blade of an ultrasonic surgical instrument may be useful for general soft tissue cutting and coagulation. In certain circumstances, a blade according to various aspects may be useful to simultaneously cut and hemostatically seal or cauterize tissue. A blade may be straight or curved, and useful for either open or laparoscopic applications. A blade according to various aspects may be useful in spine surgery, especially to assist in posterior access in removing muscle from bone.

[0027] FIG. 1 illustrates one aspect of an ultrasonic system 10. One aspect of the ultrasonic system 10 comprises an ultrasonic signal generator 12 coupled to an ultrasonic transducer 14, a hand piece assembly 60 comprising a hand piece housing 16, and an end effector 50. The ultrasonic transducer 14, which is known as a “Langevin stack”, generally includes a transduction portion 18, a first resonator or end-bell 20, and a second resonator or fore-bell 22, and ancillary components. In various aspects, the ultrasonic transducer 14 is preferably an integral number of one-half system wavelengths (nλ/2) in length as will be described in more detail below. An acoustic assembly 24 can include the ultrasonic transducer 14, a mount 26, a velocity transformer 28, and a surface 30.

[0028] It will be appreciated that the terms “proximal” and “distal” are used herein with reference to a clinician gripping the hand piece assembly 60. Thus, the end effector 50 is distal with respect to the more proximal hand piece assembly 60. It will be further appreciated that, for convenience and clarity, spatial terms such as “top” and “bottom” also are used herein with respect to the clinician gripping the hand piece assembly 60. However, surgical instruments are used in many orientations and positions, and these terms are not intended to be limiting and absolute.

[0029] The distal end of the end-bell 20 is connected to the proximal end of the transduction portion 18, and the proximal end of the fore-bell 22 is connected to the distal end of the transduction portion 18. The fore-bell 22 and the end-bell 20 have a length determined by a number of variables, including the thickness of the transduction portion 18, the density and modulus of elasticity of the material used to manufacture the end-bell 20 and the fore-bell 22, and the resonant frequency of the ultrasonic transducer 14. The fore-bell 22 may be tapered inwardly from its proximal end to its distal end to amplify the ultrasonic vibration amplitude of the velocity transformer 28, or, alternately, fore-bell 22 may have no amplification.

[0030] Referring again to FIG. 1, end-bell 20 can include a threaded member extending therefrom which can be configured to be threadably engaged with a threaded aperture in fore-bell 22. In various aspects, piezoelectric elements, such as piezoelectric elements 32, for example, can be compressed between end-bell 20 and fore-bell 22 when end-bell 20 and fore-bell 22 are assembled together. It may be recognized that proper compression of the piezoelectric elements 32 between end-bell 20 and fore-bell 22 may be useful to assure good mechanical coupling between the piezoelectric elements 32 and fore-bell 22. Good mechanical coupling may optimize the transmission of the motion induced in the piezoelectric elements 32 by an electrical field into the distal components of the ultrasonic system 10. In some aspects, proper compression may be accomplished through the use of a torqueing tool (such as a torque wrench) applied to fore-bell 22 during the fabrication of the transduction portion 18. Piezoelectric elements 32 may be fabricated from any suitable material, such as, for example, lead zirconate-titanate, lead meta-niobate, lead titanate, and/or any suitable piezoelectric crystal or ceramic material, for example.

[0031] In various aspects, as discussed in greater detail below, transducer 14 can further comprise electrodes, such as positive electrodes 34 and negative electrodes 36, for example, which can be configured to create a voltage potential across one or more piezoelectric elements 32. Each of the positive electrodes 34, negative electrodes 36, and the piezoelectric elements 32 can comprise a bore extending through the center which can be configured to receive the threaded member of end-bell 20. In various aspects, the positive and negative electrodes 34 and 36 are electrically coupled to wires 38 and 40, respectively, wherein the wires 38 and 40 can be encased within a cable 42 and electrically connectable to the ultrasonic signal generator 12 of the ultrasonic system 10.

[0032] In various aspects, the ultrasonic transducer 14 of the acoustic assembly 24 converts the electrical signal from the ultrasonic signal generator 12 into mechanical energy that results in primarily longitudinal vibratory motion of the ultrasonic transducer 24 and the end effector 50 at ultrasonic frequencies. A suitable generator is available as model number GEN11, from Ethicon Endo-Surgery, Inc., Cincinnati, Ohio. When the acoustic assembly 24 is energized, a vibratory motion standing wave is generated through the acoustic assembly 24. A suitable vibrational frequency range may be about 20 Hz to 120 kHz and a well-suited vibrational frequency range may be about 30-70 kHz and one example operational vibrational frequency may be approximately 50 kHz.

[0033] The amplitude of the vibratory motion at any point along the acoustic assembly 24 may depend upon the location along the acoustic assembly 24 at which the vibratory motion is measured. A minimum or zero crossing in the vibratory motion standing wave is generally referred to as a node (i.e., where motion is usually minimal), and an absolute value maximum or peak in the standing wave is generally referred to as an anti-node (i.e., where motion is usually maximal). The distance between an anti-node and its nearest node is one-quarter wavelength (λ/4).

[0034] As outlined above, the wires 38 and 40 transmit an electrical signal from the ultrasonic signal generator 12 to the positive electrodes 34 and the negative electrodes 36. The piezoelectric elements 32 are energized by the electrical signal supplied from the ultrasonic signal generator 12 in response to a foot switch 44, for example, to produce an acoustic standing wave in the acoustic assembly 24. The electrical signal causes disturbances in the piezoelectric elements 32 in the form of repeated small displacements resulting in large compression forces within the material. The repeated small displacements cause the piezoelectric elements 32 to expand and contract in a continuous manner along the axis of the voltage gradient, producing longitudinal waves of ultrasonic energy.

[0035] In various aspects, the ultrasonic energy produced by transducer 14 can be transmitted through the acoustic assembly 24 to the end effector 50 via an ultrasonic transmission waveguide 46. In order for the acoustic assembly 24 to deliver energy to the end effector 50, the components of the acoustic assembly 24 are acoustically coupled to the end effector 50. For example, the distal end of the ultrasonic transducer 14 may be acoustically coupled at the surface 30 to the proximal end of the ultrasonic transmission waveguide 46 by a threaded connection such as a stud 48.

[0036] The components of the acoustic assembly 24 can be acoustically tuned such that the length of any assembly is an integral number of one-half wavelengths (nλ/2), where the wavelength λ is the wavelength of a pre-selected or operating longitudinal vibration drive frequency f_d of the acoustic assembly 24, and where n is any positive integer. It is also contemplated that the acoustic assembly 24 may incorporate any suitable arrangement of acoustic elements.

[0037] The ultrasonic end effector 50 may have a length substantially equal to an integral multiple of one-half system wavelengths (λ/2). A distal end 52 of the ultrasonic end effector 50 may be disposed at, or at least near, an antinode in order to provide the maximum, or at least nearly maximum, longitudinal excursion of the distal end. When the transducer assembly is energized, in various aspects, the distal end 52 of the ultrasonic end effector 50 may be configured to move in the range of, for example, approximately 10 to 500 microns peak-to-peak and preferably in the range of approximately 30 to 150 microns at a predetermined vibrational frequency.

[0038] As outlined above, the ultrasonic end effector 50 may be coupled to the ultrasonic transmission waveguide 46. In various aspects, the ultrasonic end effector 50 and the ultrasonic transmission guide 46 as illustrated are formed as a single unit construction from a material suitable for transmission of ultrasonic energy such as, for example, Ti6Al4V (an alloy of titanium including aluminum and vanadium), aluminum, stainless steel, and/or any other suitable material. Alternately, the ultrasonic end effector 50 may be separable (and of differing composition) from the ultrasonic transmission waveguide 46, and coupled by, for example, a stud, weld, glue, quick connect, or other suitable known methods. The ultrasonic transmission waveguide 46 may have a length substantially equal to an integral number of one-half system wavelengths (λ/2), for example. The ultrasonic transmission waveguide 46 may be preferably fabricated from a solid core shaft constructed out of material that propagates ultrasonic energy efficiently, such as titanium alloy (i.e., Ti6Al4V) or an aluminum alloy, for example.

[0039] In the aspect illustrated in FIG. 1, the ultrasonic transmission waveguide 46 comprises a plurality of stabilizing silicone rings or compliant supports 56 positioned at, or at least near, a plurality of nodes. The silicone rings 56 can dampen undesirable vibration and isolate the ultrasonic energy from a sheath 58 at least partially surrounding waveguide 46, thereby assuring the flow of ultrasonic energy in a longitudinal direction to the distal end 52 of the end effector 50 with maximum efficiency.

[0040] As shown in FIG. 1, the sheath 58 can be coupled to the distal end of the handpiece assembly 60. The sheath 58 generally includes an adapter or nose cone 62 and an elongated tubular member 64. The tubular member 64 is attached to and/or extends from the adapter 62 and has an opening extending longitudinally therethrough. In various aspects, the sheath 58 may be threaded or snapped onto the distal end of the housing 16. In at least one aspect, the ultrasonic transmission waveguide 46 extends through the opening of the tubular member 64 and the silicone rings 56 can contact the sidewalls of the opening and isolate the ultrasonic transmission waveguide 46 therein. In various aspects, the adapter 62 of the sheath 58 is preferably constructed from Ultem®, for example, and the tubular member 64 is fabricated from stainless steel, for example. In at least one aspect, the ultrasonic transmission waveguide 46 may have polymeric material, for example, surrounding it in order to isolate it from outside contact.

[0041] As described above, a voltage, or power, source can be operably coupled with one or more of the piezoelectric elements of a transducer, wherein a voltage potential applied to each of the piezoelectric elements can cause the piezoelectric elements to expand and contract, or vibrate, in a longitudinal direction. As also described above, the voltage potential can be cyclical and, in various aspects, the voltage potential can be cycled at a frequency which is the same as, or nearly the same as, the resonant frequency of the system of components comprising transducer 14, wave guide 46, and end effector 50, for example. In various aspects, however, certain of the piezoelectric elements within the transducer may contribute more to the standing wave of longitudinal vibrations than other piezoelectric elements within the transducer. More particularly, a longitudinal strain profile may develop within a transducer wherein the strain profile may control, or limit, the longitudinal displacements that some of the piezoelectric elements can contribute to the standing wave of vibrations, especially when the system is being vibrated at or near its resonant frequency.

[0042] As described above, a voltage, or power, source can be operably coupled with one or more of the piezoelectric elements of a transducer, wherein a voltage potential applied to each of the piezoelectric elements can cause the piezoelectric elements to expand and contract, or vibrate, in a longitudinal direction. As also described above, the voltage potential can be cyclical and, in various aspects, the voltage potential can be cycled at a frequency which is the same as, or nearly the same as, the resonant frequency of the system of components comprising transducer 14, wave guide 46, and end effector 50, for example. In various aspects, however, certain of the piezoelectric elements within the transducer may contribute more to the standing wave of longitudinal vibrations than other piezoelectric elements within the transducer. More particularly, a longitudinal strain profile may develop within a transducer wherein the strain profile may control, or limit, the longitudinal displacements that some of the piezoelectric elements can contribute to the standing wave of vibrations, especially when the system is being vibrated at or near its resonant frequency.

[0043] It may be recognized, in reference to the ultrasonic surgical instrument system 10 of FIG. 1, that multiple components may be required to couple the mechanical vibrations from the piezoelectric elements 32 through the wave guide 46 to the end effector 50. The additional elements comprising the acoustic assembly 24 may add additional manufacturing costs, fabrication steps, and complexity to the system. Disclosed below are aspects of an ultrasonic medical device that may require fewer components, manufacturing steps, and costs than the equivalent device illustrated in FIG. 1 and as disclosed above.

[0044] Again, referring to FIG. 1, the piezoelectric elements 32 are configured into a “Langevin” stack, in which the piezoelectric elements 32 and their activating electrodes 34 and 36 (together, transducer 14) are interleaved. The mechanical vibrations of the activated piezoelectric elements 32 propagate along the longitudinal axis of the transducer 14, and are coupled via the acoustic assembly 24 to the end of the waveguide 46. Examples of piezoelectric elements 32 that may be used in the ultrasonic surgical instrument system 10 may include, without limitation, ceramic piezoelectric elements comprising, for example, lead zirconate-titanate, lead meta-niobate, or lead titanate.

[0045] Efficiency of the ultrasonic transducer 14 may be associated with maximizing the amount of power used to drive the piezoelectric elements 32 at a defined frequency and maximizing the amount of physical displacement of the piezoelectric elements 32 for a given amount of power at the defined frequency of actuation.

[0046] Power may be maximized by operating the piezoelectric elements 32 at a frequency at or near a node or resonant frequency (f_r) in which the impedance of the ultrasonic transducer 14 is at a minimum. A minimum amount of power may be required to operate the piezoelectric elements 32 at a frequency at or near an anti-node or anti-resonant frequency (f_a) in which the impedance of the ultrasonic transducer 14 is at a maximum. In some ultrasonic transducers, the phase margin (f_a−f_r) may be very small with respect to the node resonant frequency, for example about 0.6%. It may be recognized that some error or deviation may occur in the frequency of the signal sourced by an ultrasonic signal generator 12. Such a frequency error may result in the ultrasonic signal departing from the resonant frequency (minimum impedance) and approaching the anti-resonant frequency (maximum impedance). Therefore, an optimized ultrasonic transducer 14 may be designed to have a maximum phase margin in order to minimize the possible effects of frequency error in the ultrasonic signal generator 12.

[0047] It is also recognized that the amplitude of piezoelectric induced ultrasonic vibrations may be amplified by the shape, geometry, and material density of an ultrasonic transducer. Therefore, by altering the shape and/or geometry of an ultrasonic transducer, the transducer may be fabricated to maximize the displacement of an end effector attached thereto.

[0048] Disclosed, below, are examples of a fore-bell or horn of an ultrasonic transducer that may optimize the impedance characteristics and maximize the displacement of the ultrasonic transducer.

[0049] FIG. 2A illustrates a general aspect of an ultrasound transducer 14. As disclosed above with respect to FIG. 1, the ultrasound transducer 14 comprises an end-bell 20, a fore-bell or horn 22, and a transduction portion 18 therebetween. The transduction portion 18 may comprise one or more piezoelectric elements 32. The ultrasound transducer 14 may be assembled, for example, by placing the piezoelectric elements 32 on a threaded shaft portion of the end-bell 20 and threading the threaded shaft portion of the end-bell 20 into a mating threaded portion of the fore-bell or horn 22.

[0050] The fore-bell or horn 22 may comprise a number of components. A proximal flange 210 may be used to secure the piezoelectric elements 32. A first cylindrical portion 220 may have a first diameter and may be positioned distal to the proximal flange 210. A second cylindrical portion 230 may have a second diameter and a distal end. The second cylindrical portion 230 may be located at a position located distal to the first cylindrical portion 210. In some non-limiting examples, the second diameter may be smaller than the first diameter. The fore-bell or horn 22 may also include a tapered portion 240 disposed between the first cylindrical portion 220 and the second cylindrical portion 230. In some non-limiting examples, the tapered portion 240 may include multiple tapered sections 242,244. Each of the multiple tapered sections 242,244 may have a radius of curvature. In some non-limiting examples, the radius of curvature of each of the multiple tapered sections 242,244 may be the same. In other non-limiting examples, the radius of curvature of one of the multiple tapered sections 242,244 may differ from a radius of curvature of a different tapered section. Although only two tapered sections 242, 244 are illustrated in FIG. 2, it may be recognized that the tapered portion 240 may include three, four, or more individual tapered sections. In some non-limiting examples, the tapered portion may further comprise a flat disposed at a position located between two successive tapered sections, for example between a first tapered section 242 and a second tapered section 244.

[0051] Further, the fore-bell or horn 22 may include a cylindrical mass 260 disposed about the horn 22 at a position located between the flange 210 and the distal end of the second cylindrical portion 230. The cylindrical mass 260 may take the form of a ring or a cylinder. It may be understood that a ring shape may be a circular ring or a polyhedral ring with multiple flat or curved edges. In some non-limiting examples, the cylindrical mass 260 may be disposed about the horn at the first cylindrical portion 220. For example, the cylindrical mass 260 may be disposed about the horn 22 at a distal section of the first cylindrical portion 220. In another non-limiting example, the cylindrical mass 260 may be disposed about the horn 22 at the tapered portion 240. For a horn 22 comprising multiple tapered sections 242,244, the cylindrical mass 260 may be disposed at a position located between successive tapered sections, for example between a first tapered section 242 and a second tapered section 244. In some non-limiting examples, the cylindrical mass 260 may be disposed about the horn 22 at the second cylindrical portion 230. For example, the cylindrical mass 260 may be disposed about the horn 22 at a proximal section of the second cylindrical portion 230. Although only a single cylindrical mass 260 is disclosed above and illustrated, for example, in FIG. 2, it may be understood that any number of cylindrical masses, such as a second cylindrical mass, may be disposed about the horn 22 between the flange 210 and the distal end of the second cylindrical portion 230.

[0052] FIGS. 2B-2D illustrate different examples of the horn, especially depicting differences in the first tapered section 242a-c. FIG. 2A illustrates a number of configurations of the first tapered section 242 depicted as overlays. FIGS. 2B-2D present separate illustrations of each of the configurations illustrated in FIG. 2A.

[0053] As disclosed above, the shape/size and geometry of an ultrasonic horn may induce a gain in the displacement of an ultrasonic transducer as well as any end effector attached thereto. FIGS. 3-7 illustrate a variety of ultrasonic horn examples overlaid on graphs depicting simulations of axial displacement (magnitude and phase) of the components of the ultrasonic transducer to which they are attached. Table 1, below, discloses descriptions of the ultrasonic horn examples in addition to the simulation conditions and some exemplary results as depicted in FIGS. 3-7.

TABLE 1
Figure Number	FIG. 3	FIG. 4	FIG. 5	FIG. 6	FIG. 7
Ring	No	Large	Shift	Shift	Shift
Configuration	rings	Ring 2	Ring 1	Ring 1	Ring 2
Ring Width	—	2	2	2	2
(mm)
Ring OD (mm)	—	20	8	12	25
Ring Distance	—	18	7.6	7.6	30.4
to Distal End
(mm)
PM (Hz)	336	704	454	477	384
Displacement	17.1	30.64	20.9	22.3	18.7
(mm)
Impedance	54.1	18.3	36	33.4	45.5
(ohm)
Vp-p (Volts)	27	27	27	27	27
Current (mA)	175.8	517.5	258.8	285.6	209.8
Power (W)	1.68	4.94	2.47	2.72	2.0
Qm Factor	3033	4399	3268	3488	3112
Resonant	50678	48656	50510	49694	50618
Frequency (Hz)

[0054] As disclosed above, PM (phase margin) is defined as the difference in frequency between the anti-resonant frequency (f_a) and the resonant frequency (f_r). The piezoelectric coupling factor (K_p) for a piezoelectric disc expresses a coupling between an electric field parallel to the direction in which the ceramic element is polarized and mechanical effects that produce radial vibrations, relative to the direction of polarization. As an approximation, K_p for a piezoelectric disc may be described by:

$K_p\approx \sqrt{2.51\left(\frac{f_a-f_r}{f_a}\right)-{\left(\frac{f_a-f_r}{f_a}\right)}^2}$

where f_a is the anti-resonant frequency and f_r is the resonant frequency. If the phase margin (PM=f_a−f_r) is small with respect to the anti-resonant frequency, then the second term in the radical becomes small with respect to the first term, and the relationship between the phase margin and the coupling factor may be expressed as:

PM∝f_ak_p²

[0055] The displacement in Table 1 corresponds to the axial displacement at the end of the ultrasonic transducer. The impedance in Table 1 is that of the ultrasonic transducer when the simulations are run at the resonant frequency, V_p-p, and current as indicated. The mechanical quality factor Q_m may be calculated from an impedance vs. frequency graph as:

$Q_m=\frac{f_r}{2\Delta f}$

in which 2Δf is the full width at √{square root over (2)} times the minimum impedance value at f_r. Exemplary impedance vs. frequency graphs are depicted in FIGS. 17-19.

[0056] FIG. 3 depicts a physical representation of an ultrasonic transducer 500 overlaid on a displacement magnitude graph 300, presenting the magnitude of the axial displacement of a portion of the ultrasonic transducer 500, and a displacement phase graph 400, presenting the phase of the axial displacement of a portion of the ultrasonic transducer 500. The abscissa of the graph presented in FIG. 3 (distance in mm from the tail 517 of the transducer) applies equally to the representation of the ultrasonic transducer 500, the displacement magnitude graph 300, and the displacement phase graph 400. The left ordinate of the graph relates to the magnitude of the axial displacement in μm and the right ordinate of the graph relates to the phase of the axial displacement in degrees. The displacement magnitude graph 300 and displacement phase graph 400 were derived from simulations of the geometry of ultrasonic transducer 500 having input parameters of V_p-p (27 V) and current (175.8 mA) at the resonant frequency of 50,678 Hz, as shown in Table 1.

[0057] The ultrasonic transducer 500 comprises a tail 517, a transduction portion 518, and an ultrasonic horn. For the purposes of the simulations depicted in the displacement magnitude graph 300 and the displacement phase graph 400, a test load 550 portion is attached to the ultrasonic horn at the distal end 535 of the ultrasonic horn. The test load 550 may be used to simulate the effects on the waveguide and the end effector of the behavior of the ultrasonic transducer 500 during activation of the piezoelectric transducers. The transduction portion 518 may include one or more piezoelectric transducers to mechanically actuate components attached thereto. The ultrasonic horn comprises a flange 510, a first cylindrical portion 520, a tapered portion 540 and a second cylindrical portion 530. The ultrasonic horn extends from the flange 510 to the distal end 535. The tapered portion 540 further comprises a first tapered section 542, a second tapered section 544, and a flat 546 disposed between the first tapered section 542 and the second tapered section 544.

[0058] The ultrasonic horn depicted in FIG. 3 includes no rings or other cylindrical masses disposed about the horn, and may be taken as a baseline configuration against which alternative geometries for an ultrasonic horn may be functionally compared. In some aspects, the ultrasonic horn depicted in FIG. 3 may include torque features 525 associated with the first cylindrical portion 520. Such torque features 525 may be used to releasably engage a torqueing tool, such as a torque wrench, to enable the horn to be assembled together with the transduction portion 518 and the tail 517. As disclosed above, the use of such a torqueing tool during fabrication may induce a compression of the transduction portion 518 thereby improving the mechanical coupling of the transduction portion 518 to the rest of the ultrasonic device. As will become clear as disclosed below, such torque features 525 may be included on or incorporated in any one or more components of the ultrasonic horn, including, but not limited to, the flange 510, the first cylindrical portion 520, the second cylindrical portion 530, and any additional rings or cylindrical masses.

[0059] The displacement phase graph 400 presents the phase of the axial displacement along the length of the ultrasonic transducer 500 including the test load 550. The phase may have a positive value along the length of the transduction portion 518 including the flange 510 (from the tail 517 to a position at about 20 mm from the tail 517) and along the length of a distal segment of the test load 550 (from about 82 mm from the tail 517 to the distal end of the test load 550 at about 105 mm from the tail 517). The phase may also have a negative value along the length of the ultrasonic horn (from the flange 510 at about 20 mm from the tail 517 to the distal end 535 of the ultrasonic horn) and also along at least a portion of the test load 550 (from about 60 mm from the tail 517 to a position at about 82 mm from the tail 517).

[0060] The displacement magnitude graph 300 presents the absolute value of the magnitude of the axial displacement along the length of the ultrasonic transducer 500 including the test load 550. The displacement magnitude graph 300 depicts an amount of mechanical gain in the magnitude of the axial displacement of the ultrasonic transducer 500 that may be due, in part, to the geometry of the horn. Thus, while the maximum displacement magnitude of the transduction portion 518 may be about 2.5 μm, the maximum displacement magnitude at the second cylindrical portion 530 may be about 16 μm, and the maximum displacement magnitude 360 at the distal end of the test load 550 may be about 17.1 μm. In this manner, a gain in the magnitude of the axial displacement of about 6.8 from the transduction portion 518 to the end of the test load 550 may be realized.

[0061] FIGS. 4-7 present examples of alternative ultrasonic transducers and their related simulated axial displacement magnitude and axial displacement phase graphs. Many of the alternative transducers comprise identical components as those disclosed above for the ultrasonic transducer 500 depicted in FIG. 3. Examples of such identical components may include, without limitation, the tail 517, the transduction portion 518, the first cylindrical portion 520, the second cylindrical portion 530, the tapered portion 540, the first tapered section 542, the second tapered section 544, the distal end 535 of the second tapered section, and the test load 550. To reduce the complexity of FIGS. 4-7, identical components are numbered with identical reference numbers. Further, components of the ultrasonic transducers depicted in FIGS. 4-7 that are not otherwise characterized by reference numbers may be understood to refer to the similarly named components and reference numbers depicted in FIG. 3.

[0062] FIG. 4 depicts a physical representation of an ultrasonic transducer 501 overlaid on a displacement magnitude graph 301, presenting the magnitude of the axial displacement of a portion of the ultrasonic transducer 501, and a displacement phase graph (equivalent to displacement phase graph 400 of FIG. 3), presenting the phase of the axial displacement of a portion of the ultrasonic transducer 501. The abscissa of the graph presented in FIG. 4 (distance in mm from the tail (517 of the transducer) applies equally to the representation of the ultrasonic transducer 501, the displacement magnitude graph 301, and the displacement phase graph. The left ordinate of the graph relates to the magnitude of the axial displacement in μm and the right ordinate of the graph relates to the phase of the axial displacement in degrees. The displacement magnitude graph 301 and displacement phase graph were derived from simulations of the geometry of ultrasonic transducer 501 having input parameters of V_p-p (27 V) and current (517.5 mA) at the resonant frequency of 48,656 Hz, as shown in Table 1.

[0063] The ultrasonic transducer 501 comprises a tail, a transduction portion, and an ultrasonic horn. The ultrasonic horn comprises a flange 510, a first cylindrical portion 520, a tapered portion, and a second cylindrical portion. The tapered portion further comprises a first tapered section 542 and a second tapered section 544. The ultrasonic horn depicted in FIG. 4 includes torque features 525 located at the distal end of the first cylindrical portion 520 (at about 10 mm distal from the flange 510). Unlike similar functional features included in ultrasonic transducer 500 (FIG. 3), the torque features 525 in ultrasonic transducer 501 are not incorporated in the body of the first cylindrical portion 520, but constitute an additional radially extended portion located at a distal end of the first cylindrical portion 520. Ultrasonic transducer 501 further comprises a ring or cylindrical mass 548 disposed between the first tapered section 542 and the second tapered section 544 (at about 18 mm proximal to the distal end 535 of the second cylindrical portion). The cylindrical mass 548 has an outer diameter of about 27 mm and a width of about 2 mm.

[0064] The displacement phase graph (equivalent to displacement phase graph 400 of FIG. 3) presents the phase of the axial displacement along the length of the ultrasonic transducer 501 including the test load. The phase may have a positive value along the length of the transduction portion including the flange 510 (from the tail to a position at about 20 mm from the tail) and along the length of a distal segment of the test load from about 82 mm from the tail to the distal end of the test load at about 105 mm from the tail). The phase may also have a negative value along the length of the ultrasonic horn (from the flange 510 at about 20 mm from the tail to the distal end 535 of the ultrasonic horn) and also along at least a portion of the test load (from about 60 mm from the tail to a position at about 82 mm from the tail).

[0065] The displacement magnitude graph 301 presents the absolute value of the magnitude of the axial displacement along the length of the ultrasonic transducer 501 including the test load. The displacement magnitude graph 301 depicts an amount of mechanical gain in the magnitude of the axial displacement of the ultrasonic transducer 501 that may be due, in part, to the geometry of the horn. Thus, while the maximum displacement magnitude of the transduction portion may be about 7.5 μm, the maximum displacement magnitude of the horn at the second cylindrical portion may be about 28 μm, and the maximum displacement magnitude 361 at the distal end of the test load may be about 30.6 μm. In this manner, a gain in the magnitude of the axial displacement of about 4.1 from the transduction portion to the end of the test load may be realized. Although the displacement gain of the ultrasonic horn depicted in FIG. 4 is less than that of the ultrasonic horn depicted in FIG. 3, the maximum displacement magnitude 361 of the horn depicted in FIG. 4 (30.6 μm) is greater than the maximum displacement magnitude 360 of the horn depicted in FIG. 3 (17.1 μm) by about 14 μm (or by a factor of 82%). It is therefore apparent that the addition of rings or cylindrical masses to the ultrasonic horn may be used to increase the displacement of an end effector attached to the ultrasonic transducer.

[0066] The geometry of ultrasonic transducer 501 depicted in FIG. 4 may result in an increased maximum displacement magnitude 361 over ultrasonic transducer 500 depicted in FIG. 3. Further, the entries in Table I show that the horn geometry depicted in FIG. 4 requires increased current, and therefore power, used to operate ultrasonic transducer 501 with respect to ultrasonic transducer 500. Specifically, ultrasonic transducer 501 uses nearly twice the power as that of ultrasonic transducer 500. Without being bound by theory, the power increase to operate ultrasonic transducer 501 may result from the additional current used by ultrasonic transducer 501 due, in part, to the reduced impedance of the transduction portion 514.

[0067] FIG. 5 depicts a physical representation of an ultrasonic transducer 502 overlaid on a displacement magnitude graph 302, presenting the magnitude of the axial displacement of a portion of the ultrasonic transducer 502, and a displacement phase graph (equivalent to displacement phase graph 400 of FIG. 3), presenting the phase of the axial displacement of a portion of the ultrasonic transducer 502. The abscissa of the graph presented in FIG. 5 (distance in mm from the tail of the transducer) applies equally to the representation of the ultrasonic transducer 502, the displacement magnitude graph 302, and the displacement phase graph. The left ordinate of the graph relates to the magnitude of the axial displacement in μm and the right ordinate of the graph relates to the phase of the axial displacement in degrees. The displacement magnitude graph 302 and displacement phase graph were derived from simulations of the geometry of ultrasonic transducer 502 having input parameters of V_p-p (27 V) and current (258.8 mA) at the resonant frequency of 50,510 Hz, as shown in Table 1.

[0068] The ultrasonic transducer 502 comprises a tail, a transduction portion, and an ultrasonic horn. The ultrasonic horn comprises a flange 510, a first cylindrical portion 520, a tapered portion 540 and a second cylindrical portion 530. The tapered portion 540 further comprises a first tapered section 542, a second tapered section 544 and a flat 546 therebetween. The ultrasonic horn depicted in FIG. 5 includes torque features 525 located at the distal end of the first cylindrical portion 520 (at about 10 mm distal from the flange 510). Unlike similar functional features included in ultrasonic transducer 500 (FIG. 3), the torque features 525 in ultrasonic transducer 502 are not incorporated in the body of the first cylindrical portion 520, but constitute an additional radially extended portion located at a distal end of the first cylindrical portion 520. The ultrasonic horn depicted in FIG. 5 includes a ring or cylindrical mass 532 disposed at a distal portion of the second tapered section 544 and proximal to the second cylindrical portion 530 (at about 7.6 mm proximal to the distal end 535 of the second cylindrical portion). The cylindrical mass 532 has an outer diameter of about 8 mm and a width of about 2 mm.

[0069] The displacement phase graph presents the phase of the axial displacement along the length of the ultrasonic transducer 502 including the test load. The phase may have a positive value along the length of the transduction portion including the flange 510 (from the tail to a position at about 20 mm from the tail) and along the length of a distal segment of the test load from about 82 mm from the tail to the distal end of the test load at about 105 mm from the tail). The phase may also have a negative value along the length of the ultrasonic horn (from the flange 510 at about 20 mm from the tail to the distal end 535 of the ultrasonic horn) and also along at least a portion of the test load (from about 60 mm from the tail to a position at about 82 mm from the tail).

[0070] The displacement magnitude graph 302 presents the absolute value of the magnitude of the axial displacement along the length of the ultrasonic transducer 502 including the test load. The displacement magnitude graph 302 depicts an amount of mechanical gain in the magnitude of the axial displacement of the ultrasonic transducer 502 that may be due, in part, to the geometry of the horn. Thus, while the maximum displacement magnitude of the transduction portion may be about 3.5 μm, the maximum displacement magnitude of the horn at the second cylindrical portion 530 may be about 19.5 μm, and the maximum displacement magnitude 362 at the distal end of the test load may be about 20.9 μm. In this manner, a gain in the magnitude of the axial displacement of about 6 from the transduction portion to the end of the test load may be realized. The displacement gain of the ultrasonic horn depicted in FIG. 5 is less than that of the ultrasonic horn depicted in FIG. 3, but it is significantly greater than the displacement gain of the ultrasonic horn depicted in FIG. 4. The maximum displacement magnitude 362 of the horn depicted in FIG. 5 (21 μm) is somewhat greater than the maximum displacement magnitude 360 of the horn depicted in FIG. 3 (17.1 μm) by almost 4 μm (or by a factor of 23%). A comparison of the maximum displacement magnitude 362 for the horn depicted in FIG. 5 to the maximum displacement magnitude 361 for the horn depicted in FIG. 4 suggests that moving the cylindrical mass further along the length of the horn from the flange 510 and reducing the outer diameter of the cylindrical mass may lessen the effect of the cylindrical mass on the maximum displacement.

[0071] Although the geometry of ultrasonic transducer 502 depicted in FIG. 5 may result in a modest increase in maximum displacement magnitude 362 over ultrasonic transducer 500 depicted in FIG. 3, the entries in Table I show that the horn geometry depicted in FIG. 5 also provides only a modest increase in power consumption over that of ultrasonic transducer 500. Specifically, ultrasonic transducer 502 requires less than 50% more power compared to that of ultrasonic transducer 500. Further, the resonant frequency of ultrasonic transducer 502 is shifted only about 0.3% (lower) from that of ultrasonic transducer 500 (compared to a shift of about 4% for ultrasonic transducer 501). It may be useful to assure that the resonant frequency of an ultrasonic transducer does not deviate excessively from an operating frequency of the ultrasonic power source if the power source has a tuned (and potentially fixed) operating frequency.

[0072] FIG. 6 depicts a physical representation of an ultrasonic transducer 503 overlaid on a displacement magnitude graph 303, presenting the magnitude of the axial displacement of a portion of the ultrasonic transducer 503, and a displacement phase graph (equivalent to displacement phase graph 400 of FIG. 3), presenting the phase of the axial displacement of a portion of the ultrasonic transducer 503. The abscissa of the graph presented in FIG. 6 (distance in mm from the tail of the transducer) applies equally to the representation of the ultrasonic transducer 503, the displacement magnitude graph 303, and the displacement phase graph. The left ordinate of the graph relates to the magnitude of the axial displacement in μm and the right ordinate of the graph relates to the phase of the axial displacement in degrees. The displacement magnitude graph 303 and displacement phase graph were derived from simulations of the geometry of ultrasonic transducer 503 having input parameters of V_p-p (27 V) and current (285.6 mA) at the resonant frequency of 49,694 Hz, as shown in Table 1.

[0073] The ultrasonic transducer 503 comprises a tail, a transduction portion, and an ultrasonic horn. The ultrasonic horn comprises a flange 510, a first cylindrical portion 520, a tapered portion 540 and a second cylindrical portion 530. The tapered portion 540 further comprises a first tapered section 542, a second tapered section 544 and a flat 546 therebetween. The ultrasonic horn depicted in FIG. 6 includes torque features 525 located at the distal end of the first cylindrical portion 520 (at about 10 mm distal from the flange 510). Unlike similar functional features included in ultrasonic transducer 500 (FIG. 3), the torque features 525 in ultrasonic transducer 503 are not incorporated in the body of the first cylindrical portion 520, but constitute an additional radially extended portion located at a distal end of the first cylindrical portion 520. and a ring or cylindrical mass 534 disposed at a distal portion of the second tapered section 544 and proximal to the second cylindrical portion 530 (at about 7.6 mm proximal to the distal end 535 of the second cylindrical portion). The cylindrical mass 534 has an outer diameter of about 12 mm and a width of about 2 mm. It may be observed that the only difference between ultrasonic transducer 502 and ultrasonic transducer 503 is the outer diameter of the cylindrical mass (cylindrical mass 534 has an outer diameter about 50% larger than the equivalent cylindrical mass 532).

[0074] The displacement phase graph presents the phase of the axial displacement along the length of the ultrasonic transducer 503 including the test load. The phase may have a positive value along the length of the transduction portion including the flange 510 (from the tail to a position at about 20 mm from the tail) and along the length of a distal segment of the test load from about 82 mm from the tail to the distal end of the test load at about 105 mm from the tail). The phase may also have a negative value along the length of the ultrasonic horn (from the flange 510 at about 20 mm from the tail to the distal end 535 of the ultrasonic horn) and also along at least a portion of the test load (from about 60 mm from the tail to a position at about 82 mm from the tail).

[0075] The displacement magnitude graph 303 presents the absolute value of the magnitude of the axial displacement along the length of the ultrasonic transducer 503 including the test load. The displacement magnitude graph 303 depicts an amount of mechanical gain in the magnitude of the axial displacement of the ultrasonic transducer 503 that may be due, in part, to the geometry of the horn. Thus, while the maximum displacement magnitude of the transduction portion may be about 4 μm, the maximum displacement magnitude of the horn at the second cylindrical portion 530 may be about 21 μm, and the maximum displacement magnitude 363 at the distal end of the test load may be about 22.3 μm. In this manner, a gain in the magnitude of the axial displacement of about 5.6 from the transduction portion to the end of the test load may be realized. The displacement gain of the ultrasonic horn depicted in FIG. 6 is slightly less than that of the ultrasonic horn depicted in FIG. 5 (by about 7%), and the maximum displacement magnitude 363 of the horn depicted in FIG. 6 (22.5 μm) is a bit greater than the maximum displacement magnitude 362 of the horn depicted in FIG. 5 (21 μm) by about a 7%. A comparison of the maximum displacement magnitude 363 for the horn depicted in FIG. 6 to the maximum displacement magnitude 362 for the horn depicted in FIG. 5 suggests that increasing the outer diameter of the second cylindrical mass may somewhat increase the maximum displacement at the distal end of the ultrasonic transducer.

[0076] The geometry of ultrasonic transducer 503 depicted in FIG. 6 may result in a modest increase in maximum displacement magnitude 363 over that of ultrasonic transducer 502 depicted in FIG. 5. The entries in Table I also show that the horn geometry depicted in FIG. 6 results in a modest increase in power use over that of ultrasonic transducer 502. Specifically, ultrasonic transducer 503 uses about 10% more power to operate compared to that of ultrasonic transducer 502. Additionally, the resonant frequency of ultrasonic transducer 503 is shifted by about 2.0% (lower) from that of ultrasonic transducer 500 (compared to a shift of about 0.3% for ultrasonic transducer 502).

[0077] FIG. 7 depicts a physical representation of an ultrasonic transducer 504 overlaid on a displacement magnitude graph 304, presenting the magnitude of the axial displacement of a portion of the ultrasonic transducer 504, and a displacement phase graph (equivalent to displacement phase graph 400 of FIG. 3), presenting the phase of the axial displacement of a portion of the ultrasonic transducer 504. The abscissa of the graph presented in FIG. 7 (distance in mm from the tail of the transducer) applies equally to the representation of the ultrasonic transducer 504, the displacement magnitude graph 304, and the displacement phase graph. The left ordinate of the graph relates to the magnitude of the axial displacement in μm and the right ordinate of the graph relates to the phase of the axial displacement in degrees. The displacement magnitude graph 304 and displacement phase graph were derived from simulations of the geometry of ultrasonic transducer 504 having input parameters of V_p-p (27 V) and current (41.36 mA) at the resonant frequency of 48,524 Hz, as shown in Table 1.

[0078] The ultrasonic transducer 504 comprises a tail, a transduction portion, and an ultrasonic horn. The ultrasonic horn comprises a flange 510, a first cylindrical portion 520, a tapered portion 540 and a second cylindrical portion 530. The tapered portion 540 further comprises a first tapered section 542 and a second tapered section 544. Similar to the ultrasonic horn depicted in FIG. 3, the ultrasonic horn depicted in FIG. 7 may include torque features 525 fabricated as part of a distal portion of the first cylindrical portion 520. The ultrasonic horn of FIG. 7 also includes a ring or cylindrical mass 528 disposed on the first cylindrical portion 520 (at about 30.4 mm proximal to the distal end 535 of the second cylindrical portion). The cylindrical mass 528 has an outer diameter of about 25 mm and a width of about 2 mm. It may be observed that the primary difference between ultrasonic transducer 500 and ultrasonic transducer 504 is that the ultrasonic transducer 504 includes the cylindrical mass 528.

[0079] The displacement phase graph presents the phase of the axial displacement along the length of the ultrasonic transducer 504 including the test load. The phase may have a positive value along the length of the transduction portion including the flange 510 (from the tail to a position at about 20 mm from the tail) and along the length of a distal segment of the test load from about 82 mm from the tail to the distal end of the test load at about 105 mm from the tail). The phase may also have a negative value along the length of the ultrasonic horn (from the flange 510 at about 20 mm from the tail to the distal end 535 of the ultrasonic horn) and also along at least a portion of the test load (from about 60 mm from the tail a position at about 82 mm from the tail).

[0080] The displacement magnitude graph 304 presents the absolute value of the magnitude of the axial displacement along the length of the ultrasonic transducer 504 and the test load. The displacement magnitude graph 304 depicts an amount of mechanical gain in the magnitude of the axial displacement of the ultrasonic transducer 504 that may be due, in part, to the geometry of the horn. Thus, while the maximum displacement magnitude of the transduction portion may be about 3.5 μm, the maximum displacement magnitude of the horn at the second cylindrical portion 530 may be about 17.5 μm, and the maximum displacement magnitude 364 at the distal end of the test load may be about may be about 18.7 μm. In this manner, a gain in the magnitude of the axial displacement of about 5.3 from the transduction portion to the end of the test load may be realized. The displacement gain of the ultrasonic horn depicted in FIG. 7 is less than that of the ultrasonic horn depicted in FIG. 3 (by about 22%), but the maximum displacement magnitude 364 of the horn depicted in FIG. 7 (18.7 μm) is more than the maximum displacement magnitude 360 of the horn depicted in FIG. 3 (17.1 μm) by about 9%. A comparison of the maximum displacement magnitude 364 for the horn depicted in FIG. 7 to the maximum displacement magnitude 360 for the horn depicted in FIG. 3 suggests that the addition of the cylindrical mass 528 at the distal end of the first cylindrical portion 520 may result in a modest increase in maximum displacement magnitude.

[0081] A comparison between the ultrasonic transducer 500 depicted in FIG. 3 and ultrasonic transducer 504 depicted in FIG. 7 may reveal additional effects of the addition of the cylindrical mass 528 to the transducer. For example, the phase margin (PM) of transducer 500 is smaller than that of transducer 504 by about 14%. As disclosed above, a larger phase margin may be useful to minimize the possible effects of frequency error in the ultrasonic signal generator. Thus, the addition of a cylindrical mass 528 may be useful in this regard. The entries in Table I also show that the horn geometry depicted in FIG. 7 uses about 20% more power to operate the transducer 504 than that of ultrasonic transducer 500. This is consistent with the 20% increased current draw of transducer 504 versus transducer 500 and the about 20% decrease in impedance of transducer 504 with respect to that of transducer 500.

[0082] It may be observed, based on the data in Table I and the graphs in FIGS. 3-7, that the width, size, and placement of one or more cylindrical masses along the length of an ultrasonic transducer may have a number of mutually interacting effects on the characteristics of the transducer. As disclosed above, it is desirable to produce a transducer having a geometry that can maximize the end displacement of the transducer, optimize the power used to drive the transducer, and maximize the phase margin (thereby minimizing the effect of possible power supply frequency drift from the resonant frequency of the transducer). FIGS. 8-16 depict simulation graphs of the effect of changes in ring geometry on the phase margin, end displacement, and impedance of a transducer powered at a fixed voltage and at the resonant frequency of the transducer. Such graphs may be useful to determine optimizing geometries of the transducer.

[0083] FIGS. 8-10 are graphs of phase margin (in Hz), end displacement (in μm), and impedance (in ohms), respectively, versus ring outer diameter (mm) for ultrasonic transducer 500. For these simulations, the “ring” comprises the flange 510 located at about 20 mm distal from the tail 511 of the transducer 500. It may be observed, for example in FIG. 3, that the flange 510 is located at a proximal node of the transducer 500 (a location where the axial displacement magnitude graph 300 is at a minimum). Thus, the response parameters of the transducer 500 due to changes in the geometry of the flange 510 may not be dependent on effects due to ring placement. In each of FIGS. 8-10, the flange 510 has a fixed width of 2 mm. It may be observed that both the graph of the phase margin (800 in FIG. 8) and graph of the end displacement (900 in FIG. 9) monotonically increase with ring outer diameter over the range in OD values. The graph of the transducer impedance (1000 in FIG. 10), however, monotonically decreases over the same range. Because the power required to operate the transducer is inversely proportional to the transducer impedance, a decrease in impedance may correspond to an increase in power to operate the transducer. It appears that the graphs of PM versus ring OD (800 in FIG. 8) and end displacement versus ring OD (900 in FIG. 9) may be modeled by a second order equation. Without being bound by theory, such graphs may suggest that both the PM and displacement are functions of the mass of the ring, which would be a function of the square of the radius (one half of the OD) of the ring.

[0084] FIGS. 11-13 are graphs of phase margin (in Hz), end displacement (in μm), and impedance (in ohms), respectively, versus ring width (in mm) for ultrasonic transducer 500. For these simulations, the “ring” comprises the flange 510 located at about 20 mm distal from the tail 511 of the transducer 500. It may be observed, for example in FIG. 3, that the flange 510 is located at a proximal node of the transducer 500 (a location where the axial displacement magnitude graph 300 is at a minimum). Thus, the response parameters of the transducer 500 due to changes in the geometry of the flange 510 may not be dependent on effects due to ring placement. In each of FIGS. 11-13, the flange 510 has a fixed outer diameter (OD) of 15 mm. It may be observed that both the graph of the phase margin (1100 in FIG. 11) and graph of the end displacement (1200 in FIG. 12) monotonically increase with ring width over the range in ring width values. The graph of the transducer impedance (1300 in FIG. 13), however, monotonically decreases over the same range. Because the power required to operate the transducer is inversely proportional to the transducer impedance, a decrease in impedance may correspond to an increase in power required to operate the transducer. A comparison of the graphs of PM versus ring OD or width (800 in FIG. 8 versus 1100 in FIG. 11) and end displacement versus ring OD or width (900 in FIG. 9 versus 1200 in FIG. 12) suggest that the effect due to ring width on both PM and end displacement may be greater than the effect of ring OD on the two measurements. Additionally, it appears that the slopes of the graphs of PM versus ring OD (800 in FIG. 8) and displacement versus ring OD (900 in FIG. 9) increase with increasing ring OD, while the slopes of the graphs of PM versus ring width (1100 in FIG. 11) and displacement versus ring width (1200 in FIG. 12) either decrease or remain constant with increasing ring width. These results may suggest that an increase in ring width may have a greater impact than ring OD on the PM and end displacement of the transducer, although the effect of ring width may decrease as the ring width becomes large. Without being bound by theory, the decrease in the effect of ring width on the on both PM and end displacement may be due to an increase in the local stiffness of the transducer 500 as the flange width increases along the axial dimension. Additionally, a comparison of the graphs of impedance versus ring OD or width (1000 in FIG. 10 versus 1300 FIG. 13) indicates that the effect due to ring OD on impedance is approximately linear with ring OD, while the effect due to ring width on impedance has a more complex dependency.

[0085] FIGS. 14-16 are graphs of phase margin (in Hz), end displacement (in μm), and impedance (in ohms), respectively, versus ring displacement along the longitudinal axis of the transducer (in percent of the distance between the proximal node and the proximal antinode) for ultrasonic transducer 500. Referencing FIG. 3 as an example, the proximal node may be found approximately at the location of flange 510 (about 20 mm from tail 517 where the axial displacement magnitude curve 300 is at a first minimum). Similarly, referencing FIG. 3 as an example, the proximal antinode may be found approximately at the distal end 535 of the ultrasonic horn at about 60 mm from the tail 517 where the axial displacement magnitude curve 300 has a first maximum in the ultrasonic horn. For these simulations, the “ring” has a fixed width of 2 mm. Unlike the graphs presented in FIGS. 8-13, the graphs presented in FIGS. 13-16 are not monotonic, but display maxima (1400 in FIGS. 14 and 1500 in FIG. 15) and a minimum (1600 in FIG. 16) throughout the range of values of percent distance between the node and antinode. It may also be noted that the maximum phase margin (1400 in FIG. 14) and displacement (1500 in FIG. 15) occur at the value of percent distance between the node and antinode that corresponds to the minimum in impedance as depicted in graph 1600 in FIG. 16. It may further be noted that the graphs depicted in FIGS. 14-16 do not appear to be symmetric. Without being bound by theory, the lack of symmetry in the graphs depicted in FIGS. 14-16 may result from the change in diameter of the ultrasonic horn from the first cylindrical portion 520 through the tapered portion 540, and to the second cylindrical portion 530. The peaks of the graphs depicted in graph 1400 in FIG. 14 and graph 1500 in FIG. 15 occur at approximately 50% of the node/antinode distance (approximately at 40 mm distal from tail 517) that may correspond to the location of flat 546. Similarly, the trough in graph 1600 in FIG. 16 occurs at approximately 50% of the node/antinode distance (approximately at 40 mm distal from tail 517) that may correspond to the location of flat 546.

[0086] It may be recognized, as disclosed above and in FIGS. 3-16, that a judicious selection of cylindrical masses or rings added to an ultrasonic transducer may help tune the response of the transducer when energized by an energy supply. FIGS. 17-22 depict the simulated results of selective placement and geometry of such rings on a transducer that may permit selective tuning of some response parameters of the transducer.

[0087] Table 2, below, relates some transducer response parameters to each of three different horn geometries. In Table 2, the entry under “Transducer” references the figure number corresponding to the transducer geometry, and the entry under “Response” references the figure number depicting the impedance graph associated with that transducer. In Table 2, F_r corresponds to the resonance frequency (in Hz) determined for the geometry shown in the corresponding transducer figure. F_r has a corresponding minimum impedance of Z_min (in ohms). As noted above, PM (phase margin) is the difference in Hz between the anti-resonance frequency (F_a) and the resonance frequency (F_r). The quality factor Qm is a unitless number calculated as the ratio of the resonance frequency to the width of the impedance graph at points corresponding to the full width at √{square root over (2)} times the minimum impedance value.

TABLE 2
		Fr	PM	Qm	Zmin
Transducer	Response	(Hz)	(Hz)	(Unitless)	(Ohms)
FIG. 17	FIG. 18	49760	270	3130	57.4
FIG. 19	FIG. 20	50219	309	7019	28.4
FIG. 21	FIG. 22	50209	344	6821	28.4

[0088] FIG. 17 depicts a first aspect of an ultrasonic horn 1722 characterized by a minimal flange 1710, a first cylindrical portion 1720 having no rings, a tapered portion 1740 having a flat, and a second cylindrical portion 1730. This may be taken as a base-line configuration against which the ultrasonic horns depicted in FIG. 19 (1922) and FIG. 21 (2122) may be compared. FIG. 18 depicts an impedance graph comprising an impedance amplitude graph 1800 and an impedance phase graph 1900 associated with the first ultrasonic horn 1722. The impedance amplitude graph 1800 shows a minimum impedance at the resonant frequency (F_r) 1820 and a maximum impedance at the anti-resonant frequency (F_a) 1830. The phase margin 1840 is the difference between F_a and F_r.

[0089] FIG. 19 depicts a second aspect of an ultrasonic horn 1922 characterized by an expanded flange 1910, a first cylindrical portion 1920 having torque features 1925 located at its distal end, a small ring 1934 located distal of the tapered portion, and a second cylindrical portion 1930. FIG. 20 depicts an impedance graph comprising an impedance amplitude graph 1801 and an impedance phase graph 1901 associated with the second ultrasonic horn 1922. The impedance amplitude graph 1801 shows a minimum impedance at the resonant frequency (F_r) 1821 and a maximum impedance at the anti-resonant frequency (F_a) 1831. The phase margin 1841 is the difference between F_a and F_r.

[0090] FIG. 21 depicts a third aspect of an ultrasonic horn 2122 characterized by an expanded flange 2110 having a greater width than the flange 1910 depicted in ultrasonic horn 1922, a first cylindrical portion 2120, a second cylindrical portion 2130, and a small ring 2134 located distal to the tapered portion and having an outer diameter and width comparable to that of the small ring 1934 of ultrasonic horn 1922. The small ring 2134 also includes torque features 2125. FIG. 22 depicts an impedance graph comprising an impedance amplitude graph 1802 and an impedance phase graph 1902 associated with the third ultrasonic horn 2122. The impedance amplitude graph 1802 shows a minimum impedance at the resonant frequency (F_r) 1822 and a maximum impedance at the anti-resonant frequency (F_a) 1832. The phase margin 1842 is the difference between F_a and F_r.

[0091] It may be observed that second ultrasonic horn 1922 and third ultrasonic horn 2122 appear to differ significantly from each other in their respective geometries. The flange of third ultrasonic horn 2122 is about twice as wide as that of second ultrasonic horn 1922. Further, the second ultrasonic horn 1922 includes additional torque features 1925 on the first cylindrical portion 1920 which are incorporated in the small ring 2134 of the third ultrasonic horn 2122. Of interest, however, is that the resonant frequency of the second ultrasonic horn 1922 is nearly identical to that of the third ultrasonic horn 2122, while F_r of both ultrasonic horns 1922 and 2122 are about 1% greater than that of the base-line horn 1722 (see Table 2). Further, as shown in Table 2, the impedance at the resonant frequency (Z_min) is also the same for both ultrasonic horns 1922 and 2122. The impedance at the resonant frequency (Z_min) of both ultrasonic horns 1922 and 2122 is also about half that of the base-line horn 1722. Table 2 further shows that the quality factor of the third horn 2122 is about 3% less than that of the second horn 1922, but both have a quality factor more than twice that of the base-line horn 1722. However, also referring to Table 2, the phase margin of the second ultrasonic horn 1922 is about 10% greater than that of base-line horn 1722, and the phase margin of the third horn 2122 is about 11% greater than that of the second horn 1922. Thus, it may be understood that geometric features may be added to an ultrasonic horn to tune one response feature (phase margin) while leaving other response features (F_r, Q_m, and Z_min) unchanged.

[0092] The examples of ultrasonic transducers and ultrasonic transducer horns disclosed above should not be taken as limiting. It may be understood that an ultrasonic transducer horn may comprise, for example, one or more cylindrical portions, one or more tapered sections, and one or more rings or cylindrical masses. The ultrasonic transducer horn may have a flange or may lack a flange.

[0093] The more than one cylindrical portions may have diameters and/or lengths that are the same or different. The cylindrical portions may have circular cross sections, elliptical cross sections, oval cross sections, or other smooth (non-angular) cross sections. The cross section of one cylindrical portion may be the same as or differ from the cross section of a second cylindrical portion.

[0094] The one or more tapered sections may have linear (conical) tapers or curved tapers. Curved tapers may be characterized as circular curves, elliptical curves, oval curves, parabolic curves, hyperbolic curves, or any other curve. The tapered sections of an ultrasonic horn having multiple tapered sections may have the same or different curvature (for a curved taper) or the same or different opening angle (for a conical taper). An ultrasonic horn may include multiple tapered sections in which all of the tapered sections have a linear taper, all of the tapered sections have a curved taper, or a combination or combinations of linear tapers and curved tapers. The one or more tapered sections may be distributed between any of the cylindrical portions. A first tapered section may be disposed proximate to a second tapered section. A flat may be disposed between a first tapered section and a second tapered section.

[0095] The rings or cylindrical masses may have a cylindrical outer surface wherein the cylinder may have a circular cross section, an elliptical cross section, an oval cross section, or any other closed curve cross section. The rings or cylindrical masses may have an outer surface that includes one or more flattened or partially flattened surfaces. An ultrasonic horn may comprise one or more of such rings. The geometries of the more than one ring may be the same or different. Thus, the outer diameter and/or width of a first ring may be the same as or differ from the respective outer diameter and/or width of a second ring. Similarly, the outer surfaces of the more than one ring may have the same geometry or may have different geometries.

[0096] An ultrasonic transducer horn may include torque features or may lack such torque features. Torque features may be incorporated in or added to any one or more of the components of the ultrasonic transducer horn, including a flange, one or more of the cylindrical portions, one or more of the tapered sections, one or more flats, and/or one or more rings or cylindrical masses. Torque features may include features that may be used to engage a torqueing tool. The torqueing tool may be used to assemble an ultrasonic transducer comprising the ultrasonic horn, transducer components (such as piezoelectric transducers), and an end or tail piece. The torqueing tool may be used to assure effective mechanical contact between the transducer components and the ultrasonic horn. In one non-limiting example, such torque features may include one or more surfaces on a component of an ultrasonic horn that are configured to engage appropriate mating surfaces of the torqueing tool.

[0097] While various details have been set forth in the foregoing description, it will be appreciated that the various aspects of the techniques for operating a generator for digitally generating electrical signal waveforms and surgical instruments may be practiced without these specific details. One skilled in the art will recognize that the herein described components (e.g., operations), devices, objects, and the discussion accompanying them are used as examples for the sake of conceptual clarity and that various configuration modifications are contemplated. Consequently, as used herein, the specific exemplars set forth and the accompanying discussion are intended to be representative of their more general classes. In general, use of any specific exemplar is intended to be representative of its class, and the non-inclusion of specific components (e.g., operations), devices, and objects should not be taken limiting.

[0098] Further, while several forms have been illustrated and described, it is not the intention of the applicant to restrict or limit the scope of the appended claims to such detail. Numerous modifications, variations, changes, substitutions, combinations, and equivalents to those forms may be implemented and will occur to those skilled in the art without departing from the scope of the present disclosure. Moreover, the structure of each element associated with the described forms can be alternatively described as a means for providing the function performed by the element. Also, where materials are disclosed for certain components, other materials may be used. It is therefore to be understood that the foregoing description and the appended claims are intended to cover all such modifications, combinations, and variations as falling within the scope of the disclosed forms. The appended claims are intended to cover all such modifications, variations, changes, substitutions, modifications, and equivalents.

[0099] For conciseness and clarity of disclosure, selected aspects of the foregoing disclosure have been shown in block diagram form rather than in detail. Some portions of the detailed descriptions provided herein may be presented in terms of instructions that operate on data that is stored in one or more computer memories or one or more data storage devices (e.g. floppy disk, hard disk drive, Compact Disc (CD), Digital Video Disk (DVD), or digital tape). Such descriptions and representations are used by those skilled in the art to describe and convey the substance of their work to others skilled in the art. In general, an algorithm refers to a self-consistent sequence of steps leading to a desired result, where a “step” refers to a manipulation of physical quantities and/or logic states which may, though need not necessarily, take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared, and otherwise manipulated. It is common usage to refer to these signals as bits, values, elements, symbols, characters, terms, numbers, or the like. These and similar terms may be associated with the appropriate physical quantities and are merely convenient labels applied to these quantities and/or states.

[0100] Unless specifically stated otherwise as apparent from the foregoing disclosure, it is appreciated that, throughout the foregoing disclosure, discussions using terms such as “processing” or “computing” or “calculating” or “determining” or “displaying” or the like, refer to the action and processes of a computer system, or similar electronic computing device, that manipulates and transforms data represented as physical (electronic) quantities within the computer system's registers and memories into other data similarly represented as physical quantities within the computer system memories or registers or other such information storage, transmission or display devices.

[0101] In a general sense, those skilled in the art will recognize that the various aspects described herein which can be implemented, individually and/or collectively, by a wide range of hardware, software, firmware, or any combination thereof can be viewed as being composed of various types of “electrical circuitry.” Consequently, as used herein “electrical circuitry” includes, but is not limited to, electrical circuitry having at least one discrete electrical circuit, electrical circuitry having at least one integrated circuit, electrical circuitry having at least one application specific integrated circuit, electrical circuitry forming a general purpose computing device configured by a computer program (e.g., a general purpose computer configured by a computer program which at least partially carries out processes and/or devices described herein, or a microprocessor configured by a computer program which at least partially carries out processes and/or devices described herein), electrical circuitry forming a memory device (e.g., forms of random access memory), and/or electrical circuitry forming a communications device (e.g., a modem, communications switch, or optical-electrical equipment). Those having skill in the art will recognize that the subject matter described herein may be implemented in an analog or digital fashion or some combination thereof.

[0102] The foregoing detailed description has set forth various forms of the devices and/or processes via the use of block diagrams, flowcharts, and/or examples. Insofar as such block diagrams, flowcharts, and/or examples contain one or more functions and/or operations, it will be understood by those within the art that each function and/or operation within such block diagrams, flowcharts, and/or examples can be implemented, individually and/or collectively, by a wide range of hardware, software, firmware, or virtually any combination thereof. In one form, several portions of the subject matter described herein may be implemented via an application specific integrated circuits (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), or other integrated formats. However, those skilled in the art will recognize that some aspects of the forms disclosed herein, in whole or in part, can be equivalently implemented in integrated circuits, as one or more computer programs running on one or more computers (e.g., as one or more programs running on one or more computer systems), as one or more programs running on one or more processors (e.g., as one or more programs running on one or more microprocessors), as firmware, or as virtually any combination thereof, and that designing the circuitry and/or writing the code for the software and or firmware would be well within the skill of one of skill in the art in light of this disclosure. In addition, those skilled in the art will appreciate that the mechanisms of the subject matter described herein are capable of being distributed as one or more program products in a variety of forms, and that an illustrative form of the subject matter described herein applies regardless of the particular type of signal bearing medium used to actually carry out the distribution. Examples of a signal bearing medium include, but are not limited to, the following: a recordable type medium such as a floppy disk, a hard disk drive, a Compact Disc (CD), a Digital Video Disk (DVD), a digital tape, a computer memory, etc.; and a transmission type medium such as a digital and/or an analog communication medium (e.g., a fiber optic cable, a waveguide, a wired communications link, a wireless communication link (e.g., transmitter, receiver, transmission logic, reception logic, etc.), etc.).

[0103] In some instances, one or more elements may be described using the expression “coupled” and “connected” along with their derivatives. It should be understood that these terms are not intended as synonyms for each other. For example, some aspects may be described using the term “connected” to indicate that two or more elements are in direct physical or electrical contact with each other. In another example, some aspects may be described using the term “coupled” to indicate that two or more elements are in direct physical or electrical contact. The term “coupled,” however, also may mean that two or more elements are not in direct contact with each other, but yet still co-operate or interact with each other. It is to be understood that depicted architectures of different components contained within, or connected with, different other components are merely examples, and that in fact many other architectures may be implemented which achieve the same functionality. In a conceptual sense, any arrangement of components to achieve the same functionality is effectively “associated” such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as “associated with” each other such that the desired functionality is achieved, irrespective of architectures or intermedial components. Likewise, any two components so associated also can be viewed as being “operably connected,” or “operably coupled,” to each other to achieve the desired functionality, and any two components capable of being so associated also can be viewed as being “operably couplable,” to each other to achieve the desired functionality. Specific examples of operably couplable include but are not limited to physically mateable and/or physically interacting components, and/or wirelessly interactable, and/or wirelessly interacting components, and/or logically interacting, and/or logically interactable components, and/or electrically interacting components, and/or electrically interactable components, and/or optically interacting components, and/or optically interactable components.

[0104] In other instances, one or more components may be referred to herein as “configured to,” “configurable to,” “operable/operative to,” “adapted/adaptable,” “able to,” “conformable/conformed to,” etc. Those skilled in the art will recognize that “configured to” can generally encompass active-state components and/or inactive-state components and/or standby-state components, unless context requires otherwise.

[0105] While particular aspects of the present disclosure have been shown and described, it will be apparent to those skilled in the art that, based upon the teachings herein, changes and modifications may be made without departing from the subject matter described herein and its broader aspects and, therefore, the appended claims are to encompass within their scope all such changes and modifications as are within the true scope of the subject matter described herein. It will be understood by those within the art that, in general, terms used herein, and especially in the appended claims (e.g., bodies of the appended claims) are generally intended as “open” terms (e.g., the term “including” should be interpreted as “including but not limited to,” the term “having” should be interpreted as “having at least,” the term “includes” should be interpreted as “includes but is not limited to,” etc.). It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases “at least one” and “one or more” to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim recitation to claims containing only one such recitation, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an” (e.g., “a” and/or “an” should typically be interpreted to mean “at least one” or “one or more”); the same holds true for the use of definite articles used to introduce claim recitations.

[0106] In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should typically be interpreted to mean at least the recited number (e.g., the bare recitation of “two recitations,” without other modifiers, typically means at least two recitations, or two or more recitations). Furthermore, in those instances where a convention analogous to “at least one of A, B, and C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). In those instances where a convention analogous to “at least one of A, B, or C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, or C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). It will be further understood by those within the art that typically a disjunctive word and/or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms unless context dictates otherwise. For example, the phrase “A or B” will be typically understood to include the possibilities of “A” or “B” or “A and B.”

[0107] With respect to the appended claims, those skilled in the art will appreciate that recited operations therein may generally be performed in any order. Also, although various operational flows are presented in a sequence(s), it should be understood that the various operations may be performed in other orders than those which are illustrated, or may be performed concurrently. Examples of such alternate orderings may include overlapping, interleaved, interrupted, reordered, incremental, preparatory, supplemental, simultaneous, reverse, or other variant orderings, unless context dictates otherwise. Furthermore, terms like “responsive to,” “related to,” or other past-tense adjectives are generally not intended to exclude such variants, unless context dictates otherwise.

[0108] It is worthy to note that any reference to “one aspect,” “an aspect,” “one form,” or “a form” means that a particular feature, structure, or characteristic described in connection with the aspect is included in at least one aspect. Thus, appearances of the phrases “in one aspect,” “in an aspect,” “in one form,” or “in an form” in various places throughout the specification are not necessarily all referring to the same aspect. Furthermore, the particular features, structures or characteristics may be combined in any suitable manner in one or more aspects.

[0109] With respect to the use of substantially any plural and/or singular terms herein, those having skill in the art can translate from the plural to the singular and/or from the singular to the plural as is appropriate to the context and/or application. The various singular/plural permutations are not expressly set forth herein for sake of clarity.

[0110] In certain cases, use of a system or method may occur in a territory even if components are located outside the territory. For example, in a distributed computing context, use of a distributed computing system may occur in a territory even though parts of the system may be located outside of the territory (e.g., relay, server, processor, signal-bearing medium, transmitting computer, receiving computer, etc. located outside the territory).

[0111] A sale of a system or method may likewise occur in a territory even if components of the system or method are located and/or used outside the territory. Further, implementation of at least part of a system for performing a method in one territory does not preclude use of the system in another territory.

[0112] All of the above-mentioned U.S. patents, U.S. patent application publications, U.S. patent applications, foreign patents, foreign patent applications, non-patent publications referred to in this specification and/or listed in any Application Data Sheet, or any other disclosure material are incorporated herein by reference, to the extent not inconsistent herewith. As such, and to the extent necessary, the disclosure as explicitly set forth herein supersedes any conflicting material incorporated herein by reference. Any material, or portion thereof, that is said to be incorporated by reference herein, but which conflicts with existing definitions, statements, or other disclosure material set forth herein will only be incorporated to the extent that no conflict arises between that incorporated material and the existing disclosure material.

[0113] In summary, numerous benefits have been described which result from employing the concepts described herein. The foregoing description of the one or more forms has been presented for purposes of illustration and description. It is not intended to be exhaustive or limiting to the precise form disclosed. Modifications or variations are possible in light of the above teachings. The one or more forms were chosen and described in order to illustrate principles and practical application to thereby enable one of ordinary skill in the art to utilize the various forms and with various modifications as are suited to the particular use contemplated. It is intended that the claims submitted herewith define the overall scope.

[0114] Various aspects of the subject matter described herein are set out in the following numbered clauses:

[0115] An ultrasonic horn comprising: a proximal flange; a first cylindrical portion having a first diameter and positioned distal to the proximal flange; a second cylindrical portion comprising a second diameter and a distal end, wherein the second cylindrical portion is at a position located distal to the first cylindrical portion and wherein the second diameter is smaller than the first diameter; a tapered portion disposed between the first cylindrical portion and the second cylindrical portion; and a cylindrical mass disposed about the horn at a position located between the flange and the distal end of the second cylindrical portion.

[0116] The ultrasonic horn of example 1, wherein the cylindrical mass is disposed about the horn at the first cylindrical portion.

[0117] The ultrasonic horn of any of examples 1 or 2, wherein the cylindrical mass is disposed about the horn at a distal section of the first cylindrical portion.

[0118] The ultrasonic horn of any of examples 1 through 3, wherein the cylindrical mass is disposed about the horn at the tapered portion.

[0119] The ultrasonic horn of any of examples 1 through 4, wherein the cylindrical mass is disposed about the horn at the second cylindrical portion.

[0120] The ultrasonic horn of example 5, wherein the cylindrical mass is disposed about the horn at a proximal section of the second cylindrical portion.

[0121] The ultrasonic horn of any of examples 1 through 6, wherein the tapered portion comprises a first tapered section having a first radius of curvature and a second tapered section having a second radius of curvature.

[0122] The ultrasonic horn of example 7, wherein the first radius of curvature is equal to the second radius of curvature.

[0123] The ultrasonic horn of example 7, wherein the first radius of curvature is different than the second radius of curvature.

[0124] The ultrasonic horn of example 7, wherein the tapered portion further comprises a flat disposed at a position located between the first tapered section and the second tapered section.

[0125] The ultrasonic horn of example 7, wherein the cylindrical mass is disposed at a position located between the first tapered section and the second tapered section.

[0126] The ultrasonic horn of any of examples 1 through 11, further comprising a second cylindrical mass disposed about the horn at a position located between the flange and the distal end of the second cylindrical portion.

[0127] An ultrasonic system comprising: an end-bell; an ultrasonic horn, wherein the ultrasonic horn comprises: a proximal flange; a first cylindrical portion having a first diameter and positioned distal to the proximal flange; a second cylindrical portion comprising a second diameter and a distal end, wherein the second cylindrical portion is at a position located distal to the first cylindrical portion and wherein the second diameter is smaller than the first diameter; a tapered portion disposed between the first cylindrical portion and the second cylindrical portion; and a cylindrical mass disposed about the horn at a position located between the flange and the distal end of the second cylindrical portion; a transducer portion disposed between the end-bell and the ultrasonic horn; and an ultrasonic power source configured to supply an electrical signal having a predetermined frequency component to actuate the transducer portion.

[0128] The ultrasonic system of example 13, wherein the cylindrical mass is disposed about the horn at a position configured to optimize an electrical characteristic of the ultrasonic system.

[0129] The ultrasonic system of example 14, wherein the cylindrical mass is disposed about the horn at a position configured to minimize an impedance of the transducer portion with respect to the electrical signal.

[0130] The ultrasonic system of example 14, wherein the cylindrical mass is disposed about the horn at a position configured to maximize a phase margin of the transducer portion with respect to the electrical signal.

[0131] The ultrasonic system of any of examples 13 through 16, wherein the cylindrical mass is disposed about the horn at a position configured to optimize a mechanical characteristic of the ultrasonic system.

[0132] The ultrasonic system of example 17, wherein the cylindrical mass is disposed about the horn at a position configured to maximize a displacement of the distal end of the second cylindrical portion upon actuation of the transducer portion by the electrical signal.

[0133] The ultrasonic system of example 17, wherein the cylindrical mass is disposed about the horn at a position configured to maximize a ratio of a displacement of the distal end of the second cylindrical portion to a displacement of the transducer portion upon actuation of the transducer portion by the electrical signal.