Ultrasonic sensor

Abstract

A piezoelectric element includes a piezoelectric body (121), a first electrode, and a second electrode (123). The piezoelectric body (121) has a first surface positioned on a bottom plate side and a second surface (P2) positioned on the opposite side of the first surface. The first electrode is provided on the first surface. The second electrode (123) is provided on the second surface (P2). The second electrode (123) faces the first electrode via the piezoelectric body (121). When viewed from a direction perpendicular to a bottom plate, the piezoelectric body (121) has a rectangular shape including two sides (S1) extending in the longitudinal direction and another two sides (S2) extending in the lateral direction. When viewed from the direction perpendicular to the bottom plate, the second electrode (123) is formed so as to avoid the four corners (C) of the rectangular shape.

Description

Ultrasonic sensor

[0001] The present invention relates to an ultrasonic sensor.

[0002] As a prior art document that discloses an ultrasonic transmitting sensor, there is International Publication No. 2013 / 047544 (Patent Document 1). The ultrasonic sensor described in Patent Document 1 includes a bottomed cylindrical case and a piezoelectric element. The case has a bottom surface which is a vibration region. The piezoelectric element has a piezoelectric substrate, a first electrode, a second electrode, and a third electrode. The piezoelectric substrate has a first surface and a second surface facing the first surface. The first electrode is provided on the first surface. The second electrode is provided on a part of the second surface. The third electrode is provided on a part of the second surface separated from the second electrode and is connected to the first electrode. The first electrode is joined to the bottom surface, and the center of the piezoelectric element is arranged at a position different from the center of the vibration region when viewed in a plan view of the bottom surface.

[0003] International Publication No. 2013 / 047544

[0004] For ultrasonic sensors, it is required to improve efficiency. The present invention has been made in view of the above problems, and an object thereof is to provide an ultrasonic sensor with improved efficiency.

[0005] The ultrasonic sensor according to the present invention includes a case and a piezoelectric element. The case has a bottom plate and a peripheral wall and is cylindrical. The piezoelectric element is mounted on the bottom plate within a recess surrounded by the bottom plate and the peripheral wall. When viewed from a direction perpendicular to the bottom plate, the recess extends in a longitudinal direction parallel to the bottom plate and in a short direction orthogonal to the longitudinal direction, and the maximum dimension of the recess in the longitudinal direction is larger than the maximum dimension of the recess in the short direction. The piezoelectric element includes a piezoelectric body, a first electrode, and a second electrode. The piezoelectric body has a first surface located on the bottom plate side and a second surface located on the opposite side of the first surface. The first electrode is provided on the first surface. The second electrode is provided on the second surface. The second electrode faces the first electrode through the piezoelectric body. When viewed from a direction perpendicular to the bottom plate, the piezoelectric body has a rectangular shape formed by two sides extending in the longitudinal direction and the other two sides extending in the short direction. When viewed from a direction perpendicular to the bottom plate, the second electrode is formed avoiding the four corners of the rectangular shape.

[0006] According to the present invention, the efficiency of ultrasonic sensors can be improved.

[0007] This is a perspective view of the ultrasonic sensor according to Embodiment 1 of the present invention, viewed from the bottom plate side. This is a perspective view of the ultrasonic sensor according to Embodiment 1 of the present invention, viewed from the side opposite to the bottom plate side. This is a cross-sectional view of the ultrasonic sensor in Figure 2, viewed from the direction of the arrow III-III. This is a plan view showing the dimensional relationship of the case and piezoelectric element of the ultrasonic sensor according to Embodiment 1 of the present invention. This is an equivalent circuit diagram of the ultrasonic sensor according to Embodiment 1 of the present invention. This is a contour diagram showing the stress distribution acting in the longitudinal direction (X-axis direction) of the recess. This is a contour diagram showing the stress distribution acting in the short direction (Y-axis direction) of the recess. This is a plan view showing the arrangement of the second electrode in the piezoelectric element of the ultrasonic sensor according to Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Modification 1 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Modification 2 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Modification 3 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Modification 4 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Modification 5 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Modification 6 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 7 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 8 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 9 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 10 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 11 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 12 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 13 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 14 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 15 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 16 of Embodiment 1 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 17 of Embodiment 1 of the present invention.This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 18 of Embodiment 1 of the present invention. This is a cross-sectional view of an ultrasonic sensor according to Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 2 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 1 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 2 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 3 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 4 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 5 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 6 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 7 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 8 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 9 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 10 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 11 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 12 of Embodiment 2 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a comparative example. This is a graph showing the rate of change of the force coefficient and electromechanical coupling coefficient of ultrasonic sensors according to Modification 1 and Modification 8 of Embodiment 2 compared to the comparative example. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Embodiment 3 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 1 of Embodiment 3 of the present invention. This is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 2 of Embodiment 3 of the present invention. This is an equivalent circuit diagram of an ultrasonic sensor according to Embodiment 4 of the present invention. This is a graph showing the relationship between the frequency characteristics of impedance in a series circuit of piezoelectric elements and the force coefficient and electromechanical coupling coefficient. This is a graph showing the frequency characteristics of impedance in a parallel circuit and a series circuit of piezoelectric elements of an ultrasonic sensor according to Embodiment 4 of the present invention. This is a graph showing the frequency characteristics of the overall sensitivity of ultrasonic sensors according to Embodiment 1 and Embodiment 4.This graph shows the frequency characteristics of impedance in a parallel circuit and a series circuit of piezoelectric elements of an ultrasonic sensor according to Embodiment 5 of the present invention. This graph shows the frequency characteristics of the overall sensitivity of ultrasonic sensors according to Embodiments 1 and 5. This figure is for explaining the detection frequency range. This graph shows the frequency characteristics of impedance in a parallel circuit and a series circuit of piezoelectric elements of an ultrasonic sensor according to Embodiment 5 of the present invention, when the inductance of the secondary winding Lp is increased while the total capacitance of capacitance Cp and equivalent parallel capacitance Cd is decreased.

[0008] The ultrasonic sensors according to each embodiment of the present invention will be described below with reference to the figures. In the following description of the embodiments, the same or corresponding parts in the figures will be denoted by the same reference numerals, and their descriptions will not be repeated.

[0009] (Embodiment 1) Figure 1 is a perspective view of the ultrasonic sensor according to Embodiment 1 of the present invention, viewed from the bottom plate side. Figure 2 is a perspective view of the ultrasonic sensor according to Embodiment 1 of the present invention, viewed from the side opposite to the bottom plate side. Figure 3 is a cross-sectional view of the ultrasonic sensor of Figure 2, viewed from the direction of the arrow III-III. Figure 4 is a plan view showing the dimensional relationship between the case and the piezoelectric element of the ultrasonic sensor according to Embodiment 1 of the present invention.

[0010] As shown in Figures 1 to 4, the ultrasonic sensor 100 according to Embodiment 1 of the present invention comprises a case 110 and a piezoelectric element 120. The ultrasonic sensor 100 further comprises a first terminal 131, a second terminal 132, a first wiring 141, a second wiring 142, a filler material 150, and a lid 160.

[0011] The case 110 is cylindrical and has a bottom plate 111 and a peripheral wall 112. The bottom plate 111 has a disc shape with a diameter of D1. The peripheral wall 112 extends upward from the periphery of the bottom plate 111. The case 110 has a recess 113 surrounded by the bottom plate 111 and the peripheral wall 112.

[0012] As shown in Figure 4, when viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the recess 113 extends in the longitudinal direction (X-axis direction) parallel to the base plate 111 and in the short direction (Y-axis direction) perpendicular to the longitudinal direction (X-axis direction). The maximum dimension L1 of the recess 113 in the longitudinal direction (X-axis direction) is greater than the maximum dimension W1 of the recess 113 in the short direction (Y-axis direction). When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the recess 113 has a roughly rectangular shape with rounded corners.

[0013] The case 110 is made of a conductive material. In this embodiment, the case 110 is made of, for example, an aluminum alloy. The case 110 is formed, for example, by forging or cutting.

[0014] As shown in Figures 3 and 4, the piezoelectric element 120 is mounted on the base plate 111 within the recess 113. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the piezoelectric element 120 is positioned such that its center lies on the center of the base plate 111. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the piezoelectric element 120 extends along the longitudinal direction (X-axis direction). The maximum dimension L2 of the piezoelectric element 120 in the longitudinal direction (X-axis direction) is greater than the maximum dimension W2 of the piezoelectric element 120 in the short direction (Y-axis direction). In this embodiment, when viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the piezoelectric element 120 is a rectangle with a longer side extending in the longitudinal direction (X-axis direction). However, the piezoelectric element 120 may be a square when viewed from a direction perpendicular to the base plate 111 (Z-axis direction).

[0015] As shown in Figure 3, the piezoelectric element 120 includes a piezoelectric body 121, a first electrode 122, and a second electrode 123. The piezoelectric body 121 has a first surface P1 located on the bottom plate 111 side, and a second surface P2 located on the opposite side of the first surface P1. The first electrode 122 is provided on the entire first surface P1. The second electrode 123 is provided on a part of the second surface P2. The second electrode 123 faces the first electrode 122 via the piezoelectric body 121. The piezoelectric body 121 is made of piezoelectric ceramics. In this embodiment, the piezoelectric body 121 is made of PZT (lead zirconate titanate) ceramics. However, the piezoelectric body 121 is not limited to PZT ceramics, and may be made of other piezoelectric materials.

[0016] A unimorph type piezoelectric vibrator is formed by attaching a piezoelectric element 120 to the base plate 111. Alternatively, a bimorph type piezoelectric vibrator or a multimorph type piezoelectric vibrator may be used instead of the unimorph type piezoelectric vibrator.

[0017] The first electrode 122 is connected to the base plate 111 by adhesive. The peripheral wall 112 is electrically connected to the first terminal 131 through the first wiring 141. As a result, the first terminal 131 and the first electrode 122 are electrically connected. The second electrode 123 is electrically connected to the second terminal 132 through the second wiring 142. Each of the first electrode 122 and the second electrode 123 is made of a conductive film of substantially uniform thickness.

[0018] When a voltage is applied between the first electrode 122 and the second electrode 123, the piezoelectric element 120 is driven to vibrate. As the piezoelectric element 120 vibrates, the bottom plate 111 vibrates.

[0019] Furthermore, when the bottom plate 111 of the case 110 vibrates due to external ultrasonic waves, the piezoelectric element 120 also vibrates in conjunction with this vibration. The vibration of the piezoelectric element 120 generates an electric charge, which converts the ultrasonic waves into an electrical signal in the piezoelectric element 120. This electrical signal is output from a pair of electrodes consisting of a first electrode 122 and a second electrode 123.

[0020] As shown in Figure 3, the recess 113 is filled with a filler material 150. The filler material 150 is, for example, silicone resin. The filler material 150 may be composed of two or more types of resin. The recess 113 is closed by a lid 160. The lid 160 is made of, for example, an insulator. The first terminal 131 and the second terminal 132 pass through the lid 160. The filler material 150 and the lid 160 prevent water and foreign matter from entering the case 110. The lid 160 is not necessarily required.

[0021] Figure 5 is an equivalent circuit diagram of an ultrasonic sensor according to Embodiment 1 of the present invention. As shown in Figure 5, the equivalent circuit 12 of the piezoelectric element 120 of the ultrasonic sensor 100 has an equivalent series inductance Ls, an equivalent series capacitance Cs, an equivalent series resistance Rs, an equivalent parallel capacitance Cd, and an equivalent parallel resistance Rd. The equivalent series inductance Ls, equivalent series capacitance Cs, and equivalent series resistance Rs are connected in series with each other to form a series circuit 13. The series circuit 13, the equivalent parallel capacitance Cd, and the equivalent parallel resistance Rd are connected in parallel between the first terminal T1 and the second terminal T2.

[0022] Here, we will explain the results of a simulation analysis of the stress distribution generated in the vibrating part of the bottom plate 111 when the ultrasonic sensor 100 is in operation. Figure 6 is a contour plot showing the stress distribution acting in the longitudinal direction (X-axis direction) of the recess. Figure 7 is a contour plot showing the stress distribution acting in the short direction (Y-axis direction) of the recess.

[0023] As shown in Figure 6, tensile stress occurs in the longitudinal direction (X-axis direction) of the recess outside the virtual ellipse n, and compressive stress occurs in the longitudinal direction (X-axis direction) of the recess inside the virtual ellipse n. As shown in Figure 7, tensile stress occurs in the short direction (Y-axis direction) of the recess outside the virtual ellipse n, and compressive stress occurs in the short direction (Y-axis direction) of the recess inside the virtual ellipse n. Note that in Figures 6 and 7, the darker the color outside the virtual ellipse n, the higher the tensile stress, and the darker the color inside the virtual ellipse n, the higher the compressive stress.

[0024] In other words, in the vibrating portion of the base plate 111, the outer part of the virtual ellipse n vibrates in opposite phase to the inner part of the virtual ellipse n, and the position of the virtual ellipse n is a node in the vibration of the base plate 111.

[0025] In an ultrasonic sensor 100 having such a vibration pattern, the sound pressure generated from the vibrating part inside the virtual ellipse n is weakened by the sound pressure generated from the vibrating part outside the virtual ellipse n. Therefore, by reducing the size of the vibrating part outside the virtual ellipse n, the efficiency of the ultrasonic sensor 100 can be improved. Accordingly, in the piezoelectric element 120 of the ultrasonic sensor 100 according to Embodiment 1 of the present invention, the efficiency of the ultrasonic sensor 100 is improved by reducing the size of the vibrating part outside the virtual ellipse n, as viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction).

[0026] Figure 8 is a plan view showing the arrangement of the second electrode in the piezoelectric element of the ultrasonic sensor according to Embodiment 1 of the present invention. As shown in Figure 8, when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the piezoelectric body 121 has a rectangular shape consisting of two sides S1 extending in the longitudinal direction (X-axis direction) and the other two sides S2 extending in the short direction (Y-axis direction).

[0027] As a result of performing the above simulation analysis by changing the maximum dimension L1 in the longitudinal direction (X-axis direction) and the maximum dimension W1 in the short direction (Y-axis direction) of the recess 113 in various ways, when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the dimension of the major axis L3 of the virtual ellipse n shown in Figure 8 was within the range of 65% to 70% of the maximum dimension L1 in the longitudinal direction (X-axis direction) of the recess 113 shown in Figure 4, and the dimension of the minor axis W3 of the virtual ellipse n shown in Figure 8 was within the range of 55% to 60% of the maximum dimension W1 in the short direction (Y-axis direction) of the recess 113 shown in Figure 4.

[0028] In this embodiment, the maximum dimension W2 of the piezoelectric element 120 in the shorter direction (Y-axis direction) shown in Figure 4 is greater than the dimension of the minor axis W3 of the virtual ellipse n shown in Figure 8. However, within the range where the four corners of the rectangular shape of the piezoelectric body 121 are located outside the virtual ellipse n, the maximum dimension W2 of the piezoelectric element 120 in the shorter direction (Y-axis direction) may be less than or equal to the dimension of the minor axis W3 of the virtual ellipse n. That is, the maximum dimension W2 of the piezoelectric element 120 in the shorter direction (Y-axis direction) may be more than 60% but less than 100% of the maximum dimension W1 of the recess 113 in the shorter direction (Y-axis direction). Furthermore, the maximum dimension W2 of the piezoelectric element 120 in the shorter direction (Y-axis direction) may be more than 60% but 80% or less of the maximum dimension W1 of the recess 113 in the shorter direction (Y-axis direction).

[0029] In this embodiment, the maximum dimension L2 of the piezoelectric element 120 in the longitudinal direction (X-axis direction) shown in Figure 4 is smaller than the dimension of the major axis L3 of the virtual ellipse n shown in Figure 8. However, the maximum dimension L2 of the piezoelectric element 120 in the longitudinal direction (X-axis direction) may be greater than or equal to the dimension of the major axis L3 of the virtual ellipse n. For example, the maximum dimension L2 of the piezoelectric element 120 in the longitudinal direction (X-axis direction) is 40% to 90% of the maximum dimension L1 of the recess 113 in the longitudinal direction (X-axis direction). Note that the maximum dimension L2 of the piezoelectric element 120 in the longitudinal direction (X-axis direction) may be 50% to 85% of the maximum dimension L1 of the recess 113 in the longitudinal direction (X-axis direction), or 60% to 80% of the maximum dimension L1 of the recess 113 in the longitudinal direction (X-axis direction).

[0030] As shown in Figure 8, when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the second electrode 123 is formed avoiding the four corners C of the rectangular shape. In other words, the second electrode 123 is not formed at the four corners C of the rectangular shape. This reduces the number of second electrodes 123 located outside the virtual ellipse n, thereby improving the efficiency of the ultrasonic sensor 100.

[0031] The four corners of the rectangular shape of the piezoelectric element 121 are four square-shaped regions enclosed by either side S1 of the two sides S1 and either side S2 of the other two sides S2. In this specification, each of the four corners of the rectangular shape of the piezoelectric element 121 is a square-shaped region enclosed by four sides having a length of 10% of the length of side S2 at the corner position of the rectangular shape.

[0032] In this embodiment, as shown in Figure 8, the second electrode 123 is elliptical in shape when viewed from a direction perpendicular to the base plate 111 (Z-axis direction). The second electrode 123 overlaps with a portion of each of the two sides S1 and a portion of each of the other two sides S2 when viewed from a direction perpendicular to the base plate 111 (Z-axis direction). When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the center of gravity of the second electrode 123 is located at approximately the same position as the center of the roughly rectangular recess 113.

[0033] In this embodiment, compared to the case where the second electrode 123 is provided across the entire second surface P2, reducing the number of second electrodes 123 located outside the virtual ellipse n reduces the vibration area outside the virtual ellipse n, thereby improving the efficiency of the ultrasonic sensor 100. Furthermore, compared to the case where the piezoelectric body 121 is formed in an elliptical shape, forming the piezoelectric body 121 in a rectangular shape improves the moldability and yield of the piezoelectric body 121.

[0034] Furthermore, by extending the vibration region of the bottom plate 111 in the longitudinal direction (X-axis direction), it is possible to narrow the directivity of the ultrasonic sensor 100 in the longitudinal direction (X-axis direction) while ensuring a wide directivity in the short direction (Y-axis direction). In other words, the ultrasonic sensor according to this embodiment is highly efficient while having the desired directivity.

[0035] Furthermore, by increasing the maximum dimension L2 of the piezoelectric element 120 in the longitudinal direction (X-axis direction), the force coefficient A can be increased, while by forming the second electrode 123 while avoiding the four corners C of the rectangular shape, the decrease in the electromechanical coupling coefficient kp due to the increase in equivalent parallel capacitance Cd can be suppressed.

[0036] The force coefficient A (N / V) is the value obtained by dividing the force applied to the bottom plate 111 by the voltage applied to the ultrasonic sensor 100. If the mode attenuation is D (N・s / m), the mode stiffness is K (N / m), and the mode mass is M (kg), then the equivalent series resistance Rs = D / A 2 The relationship satisfies, and the equivalent series capacitance Cs = A 2 The relationship / K is satisfied, and the equivalent series inductance Ls = M / A 2 It satisfies the relationship.

[0037] Hereinafter, modifications 1 to 18 of Embodiment 1 of the present invention will be described. In the following modifications 1 to 18 of Embodiment 1, only the shape and arrangement of the second electrode differ from the ultrasonic sensor 100 according to Embodiment 1, so the same configuration as the ultrasonic sensor 100 according to Embodiment 1 will not be repeated in the description.

[0038] Figure 9 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 1 of Embodiment 1 of the present invention. As shown in Figure 9, in the ultrasonic sensor 100a according to Modification 1 of Embodiment 1 of the present invention, when viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the second electrode 123a has a rectangular shape with chamfered corners, and the long side extending in the longitudinal direction (X-axis direction). Specifically, the second electrode 123a is octagonal. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the second electrode 123a overlaps with a part of each of the two sides S1 and a part of each of the other two sides S2. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the center of gravity of the second electrode 123a is located at approximately the same position as the center of the roughly rectangular recess 113.

[0039] In the ultrasonic sensor 100a according to the modified example 1 of Embodiment 1, the second electrode 123a has a shape in which the four corners of a rectangle with a long side extending in the longitudinal direction (X-axis direction) are beveled, thereby reducing vibrations outside the virtual ellipse n and improving the efficiency of the ultrasonic sensor 100a. Furthermore, because the second electrode 123a has a shape in which the four corners of a rectangle with a long side extending in the longitudinal direction (X-axis direction) are beveled, the equivalent parallel capacitance Cd can be reduced while the electromechanical coupling coefficient kp can be increased, thereby improving the efficiency of the ultrasonic sensor 100a.

[0040] Figure 10 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 2 of Embodiment 1 of the present invention. As shown in Figure 10, in the ultrasonic sensor 100b according to a modified example 2 of Embodiment 1 of the present invention, the second electrode 123b, when viewed from a direction perpendicular to the base plate 111 (Z-axis direction), has a rectangular shape with its four corners cut out, and the longer side extending in the longitudinal direction (X-axis direction). Specifically, the second electrode 123b is a dodecagon. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the second electrode 123b overlaps with a part of each of the two sides S1 and a part of each of the other two sides S2. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the center of gravity of the second electrode 123b is located at approximately the same position as the center of the roughly rectangular recess 113.

[0041] In the ultrasonic sensor 100b according to the modified example 2 of Embodiment 1, the second electrode 123b has a shape in which the four corners of a rectangle with a long side extending in the longitudinal direction (X-axis direction) are cut out, thereby reducing vibrations outside the virtual ellipse n and improving the efficiency of the ultrasonic sensor 100b. Furthermore, because the second electrode 123b has a shape in which the four corners of a rectangle with a long side extending in the longitudinal direction (X-axis direction) are cut out, the equivalent parallel capacitance Cd can be reduced while the electromechanical coupling coefficient kp can be increased, thereby improving the efficiency of the ultrasonic sensor 100b.

[0042] Figure 11 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 3 of Embodiment 1 of the present invention. As shown in Figure 11, in the ultrasonic sensor 100c according to Modification 3 of Embodiment 1 of the present invention, the second electrode 123c is elliptical when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). The second electrode 123c overlaps with a part of each of the two sides S1 and a part of one of the other two sides S2 when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123c is located at a position shifted in the longitudinal direction (X-axis direction) from the center of the substantially rectangular recess 113. In the ultrasonic sensor 100c according to Modification 3 of Embodiment 1, the efficiency of the ultrasonic sensor 100c can also be improved by reducing vibrations outside the virtual ellipse n.

[0043] Fig. 12 is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Modification 4 of Embodiment 1 of the present invention. As shown in Fig. 12, in the ultrasonic sensor 100d according to Modification 4 of Embodiment 1 of the present invention, when viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction), the second electrode 123d has an elliptical shape. The second electrode 123d overlaps a part of any one of the two sides S1 and a part of each of the other two sides S2 when viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123d is located at a position shifted in the short-side direction (Y-axis direction) from the center of the substantially rectangular shape of the recess 113. Also in the ultrasonic sensor 100d according to Modification 4 of Embodiment 1, the vibration outside the virtual ellipse n can be reduced to improve the efficiency of the ultrasonic sensor 100d.

[0044] Fig. 13 is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Modification 5 of Embodiment 1 of the present invention. As shown in Fig. 13, in the ultrasonic sensor 100e according to Modification 5 of Embodiment 1 of the present invention, when viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction), the second electrode 123e has an elliptical shape with one end in the longitudinal direction (X-axis direction) cut off. The second electrode 123e overlaps a part of each of the two sides S1 and a part of any one of the other two sides S2 when viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123e is located at a position shifted in the longitudinal direction (X-axis direction) from the center of the substantially rectangular shape of the recess 113. Also in the ultrasonic sensor 100e according to Modification 5 of Embodiment 1, the vibration outside the virtual ellipse n can be reduced to improve the efficiency of the ultrasonic sensor 100e.

[0045] FIG. 14 is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Modification 6 of Embodiment 1 of the present invention. As shown in FIG. 14, in the ultrasonic sensor 100f according to Modification 6 of Embodiment 1 of the present invention, when viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction), the second electrode 123f has an elliptical shape with one end in the short side direction (Y-axis direction) cut out. The second electrode 123f overlaps a part of one of the two sides S1 and a part of each of the other two sides S2 when viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123f is located at a position shifted in the short side direction (Y-axis direction) from the center of the substantially rectangular shape of the concave portion 113. Also in the ultrasonic sensor 100f according to Modification 6 of Embodiment 1, the vibration outside the virtual ellipse n can be reduced to improve the efficiency of the ultrasonic sensor 100f.

[0046] FIG. 15 is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Modification 7 of Embodiment 1 of the present invention. As shown in FIG. 15, in the ultrasonic sensor 100g according to Modification 7 of Embodiment 1 of the present invention, when viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction), the second electrode 123g has a shape in which a rectangle and a semi-ellipse arranged in the short side direction (Y-axis direction) are combined. The second electrode 123g overlaps a part of one of the two sides S1 and a part of each of the other two sides S2 when viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from the direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123g is located at a position shifted in the short side direction (Y-axis direction) from the center of the substantially rectangular shape of the concave portion 113. Also in the ultrasonic sensor 100g according to Modification 7 of Embodiment 1, the vibration outside the virtual ellipse n can be reduced to improve the efficiency of the ultrasonic sensor 100g.

[0047] Figure 16 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 8 of Embodiment 1 of the present invention. As shown in Figure 16, in the ultrasonic sensor 100h according to Modification 8 of Embodiment 1 of the present invention, the second electrode 123h is rectangular in shape when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the second electrode 123h overlaps with a part of each of the two sides S1 and is spaced apart from each of the other two sides S2. When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123h is located at approximately the same position as the center of the roughly rectangular recess 113. In the ultrasonic sensor 100h according to Modification 8 of Embodiment 1, the efficiency of the ultrasonic sensor 100h can also be improved by reducing vibrations outside the virtual ellipse n.

[0048] Figure 17 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 9 of Embodiment 1 of the present invention. As shown in Figure 17, in the ultrasonic sensor 100i according to Modification 9 of Embodiment 1 of the present invention, the second electrode 123i is elliptical in shape, with one end in the longitudinal direction (X-axis direction) and one end in the short direction (Y-axis direction) cut out, when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). The second electrode 123i overlaps with a part of one of the two sides S1 and a part of one of the other two sides S2 when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123i is located at a position offset from the center of the substantially rectangular recess 113 in the longitudinal direction (X-axis direction) and the short direction (Y-axis direction). In the ultrasonic sensor 100i according to the modified example 9 of Embodiment 1, the efficiency of the ultrasonic sensor 100i can be improved by reducing vibrations outside the virtual ellipse n.

[0049] Figure 18 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 10 of Embodiment 1 of the present invention. As shown in Figure 18, in the ultrasonic sensor 100j according to a modified example 10 of Embodiment 1 of the present invention, the second electrode 123j is elliptical when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). The second electrode 123j is spaced apart from each of the two sides S1 and each of the other two sides S2 when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). The second electrode 123j is located inside the virtual ellipse n. When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123j is located at approximately the same position as the center of the roughly rectangular recess 113. In the ultrasonic sensor 100j according to a modified example 10 of Embodiment 1, the efficiency of the ultrasonic sensor 100j can also be improved by reducing vibrations outside the virtual ellipse n.

[0050] Figure 19 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 11 of Embodiment 1 of the present invention. As shown in Figure 19, in the ultrasonic sensor 100k according to the modified example 11 of Embodiment 1 of the present invention, the second electrode 123k is rectangular in shape when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). The second electrode 123k is spaced apart from each of the two sides S1 and each of the other two sides S2 when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123k is located at approximately the same position as the center of the roughly rectangular recess 113. In the ultrasonic sensor 100k according to the modified example 11 of Embodiment 1, the efficiency of the ultrasonic sensor 100k can also be improved by reducing vibrations outside the virtual ellipse n.

[0051] Figure 20 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 12 of Embodiment 1 of the present invention. As shown in Figure 20, in the ultrasonic sensor 100m according to the modified example 12 of Embodiment 1 of the present invention, the second electrode 123m, when viewed from a direction perpendicular to the base plate 111 (Z-axis direction), has a rectangular shape with chamfered corners and a long side extending in the longitudinal direction (X-axis direction). Specifically, the second electrode 123m is octagonal. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the second electrode 123m is spaced apart from each of the two sides S1 and each of the other two sides S2. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the center of gravity of the second electrode 123m is located at approximately the same position as the center of the roughly rectangular recess 113. In the ultrasonic sensor 100m according to the modified example 12 of Embodiment 1, the vibration outside the virtual ellipse n can be reduced and the efficiency of the ultrasonic sensor 100m can be improved.

[0052] Figure 21 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 13 of Embodiment 1 of the present invention. As shown in Figure 21, in the ultrasonic sensor 100n according to a modified example 13 of Embodiment 1 of the present invention, the second electrode 123n is elliptical in shape, with a notch N formed at the center of the longitudinal direction (X-axis direction) and at one end of the short-side direction (Y-axis direction) when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). The second electrode 123n overlaps with a part of each of the two sides S1 and a part of each of the other two sides S2 when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123n is located at a position shifted in the short-side direction (Y-axis direction) from the center of the substantially rectangular recess 113. In the ultrasonic sensor 100n according to a modified example 13 of Embodiment 1, the efficiency of the ultrasonic sensor 100n can also be improved by reducing vibrations outside the virtual ellipse n.

[0053] Figure 22 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modification 14 of Embodiment 1 of the present invention. As shown in Figure 22, in the ultrasonic sensor 100o according to a modification 14 of Embodiment 1 of the present invention, the second electrode 123o has an elliptical shape with a notch N formed at one end in the longitudinal direction (X-axis direction) and one end in the short direction (Y-axis direction) when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). The second electrode 123o overlaps with a part of each of the two sides S1 and a part of each of the other two sides S2 when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123o is located at a position offset from the center of the substantially rectangular recess 113 in the longitudinal direction (X-axis direction) and the short direction (Y-axis direction). In the ultrasonic sensor 100o according to the modified example 14 of Embodiment 1, the vibration outside the virtual ellipse n can be reduced to improve the efficiency of the ultrasonic sensor 100o.

[0054] Figure 23 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to modification 15 of Embodiment 1 of the present invention. As shown in Figure 23, in the ultrasonic sensor 100p according to modification 15 of Embodiment 1 of the present invention, when viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the second electrode 123p has the shape of a rectangle with chamfered corners, where the longer side extends in the longitudinal direction (X-axis direction). Specifically, the second electrode 123p is an octagon with a notch N formed at the center in the longitudinal direction (X-axis direction) and at one end in the short direction (Y-axis direction). When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the second electrode 123p overlaps with a part of each of the two sides S1 and a part of each of the other two sides S2. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the center of gravity of the second electrode 123p is located at a position shifted in the short direction (Y-axis direction) from the substantially rectangular center of the recess 113. In the ultrasonic sensor 100p according to the modified example 15 of Embodiment 1, the vibration outside the virtual ellipse n can be reduced to improve the efficiency of the ultrasonic sensor 100p.

[0055] Figure 24 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 16 of Embodiment 1 of the present invention. As shown in Figure 24, in the ultrasonic sensor 100q according to the modified example 16 of Embodiment 1 of the present invention, the second electrode 123q is elliptical in shape, with a notch N formed at one end in the longitudinal direction (X-axis direction) and in the center in the short direction (Y-axis direction) when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). The second electrode 123q overlaps with a part of one of the two sides S1 and a part of each of the other two sides S2 when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123q is located at a position shifted in the longitudinal direction (X-axis direction) from the center of the substantially rectangular recess 113. In the ultrasonic sensor 100q according to the modified example 16 of Embodiment 1, the efficiency of the ultrasonic sensor 100q can also be improved by reducing vibrations outside the virtual ellipse n.

[0056] Figure 25 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 17 of Embodiment 1 of the present invention. As shown in Figure 25, in the ultrasonic sensor 100r according to a modified example 17 of Embodiment 1 of the present invention, when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the second electrode 123r has an elliptical shape in which one end in the short-side direction (Y-axis direction) is cut off, and a notch N is formed at the center of the long-side direction (X-axis direction) and at one end in the short-side direction (Y-axis direction). When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the second electrode 123r overlaps with a part of one of the two sides S1 and a part of each of the other two sides S2. When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123r is located at a position shifted in the short-side direction (Y-axis direction) from the substantially rectangular center of the recess 113. In the ultrasonic sensor 100r according to the modified example 17 of Embodiment 1, the vibration outside the virtual ellipse n can be reduced to improve the efficiency of the ultrasonic sensor 100r.

[0057] Figure 26 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 18 of Embodiment 1 of the present invention. As shown in Figure 26, in the ultrasonic sensor 100s according to a modified example 18 of Embodiment 1 of the present invention, the second electrode 123s has a rectangular shape with a notch N formed at the center of the longitudinal direction (X-axis direction) and at one end of the short direction (Y-axis direction) when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the second electrode 123s overlaps with a part of each of the two sides S1 and is spaced apart from each of the other two sides S2. When viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the center of gravity of the second electrode 123s is located at a position shifted in the short direction (Y-axis direction) from the substantially rectangular center of the recess 113. In the ultrasonic sensor 100s according to the modified example 18 of Embodiment 1, the vibration outside the virtual ellipse n can be reduced to improve the efficiency of the ultrasonic sensor 100s.

[0058] (Embodiment 2) Hereinafter, an ultrasonic sensor according to Embodiment 2 of the present invention will be described with reference to the figures. The ultrasonic sensor according to Embodiment 2 of the present invention differs from the ultrasonic sensor according to Embodiment 1 of the present invention in that it is equipped with a third electrode, so the same configuration as the ultrasonic sensor according to Embodiment 1 of the present invention will not be described again.

[0059] Figure 27 is a cross-sectional view of an ultrasonic sensor according to Embodiment 2 of the present invention. Figure 28 is a plan view showing the shape of the piezoelectric element of the ultrasonic sensor according to Embodiment 2 of the present invention. In Figure 27, the cross-sectional view is the same as in Figure 3. As shown in Figures 27 and 28, in the ultrasonic sensor 200 according to Embodiment 2 of the present invention, the piezoelectric element 220 further includes a third electrode 223 provided on the second surface P2. The third electrode 223 is electrically connected to the first electrode 122. Specifically, as shown in Figure 27, the third electrode 223 is electrically connected to the first electrode 122 via a connecting electrode 222 formed on the side surface of the piezoelectric body 121. The third electrode 223 is made of a conductive film with substantially the same thickness as the second electrode 123.

[0060] As shown in Figures 27 and 28, the third electrode 223 is positioned at a distance from the second electrode 123. As shown in Figure 28, when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the third electrode 223 overlaps with at least a portion of at least one of the two sides S1 and the other two sides S2. In this embodiment, the third electrode 223 overlaps with a portion of either side S1 of the two sides S1 and a portion of either side S2 of the other two sides S2.

[0061] As shown in Figure 28, when viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the third electrode 223 overlaps with at least a portion of the four corners C. In this embodiment, the third electrode 223 overlaps with one of the four corners C.

[0062] As shown in Figure 27, the first terminal 131 and the third electrode 223 are connected through the first wiring 141, thereby electrically connecting the first terminal 131 and the first electrode 122. In other words, the first terminal 131 and the first electrode 122 are electrically connected to each other without going through the case 110.

[0063] In the ultrasonic sensor 200 according to Embodiment 2 of the present invention, the third electrode 223 overlaps with at least a portion of at least one of the two sides S1 and the other two sides S2 when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), thereby allowing easy connection between the third electrode 223 and the first electrode 122 via a connecting electrode 222 formed on the side surface of the piezoelectric body 121. Furthermore, the third electrode 223 overlaps with at least a portion of the four corners C when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), thereby suppressing the reduction of the vibration region inside the virtual ellipse n by arranging the third electrode 223. In the ultrasonic sensor 200 according to Embodiment 2 of the present invention, the efficiency of the ultrasonic sensor 200 can also be improved by reducing vibrations outside the virtual ellipse n.

[0064] Hereinafter, modifications 1 to 12 of Embodiment 2 of the present invention will be described. In the following modifications 1 to 12 of Embodiment 2, only the shape and arrangement of the second electrode and the third electrode differ from the ultrasonic sensor 200 according to Embodiment 2; therefore, the same configuration as the ultrasonic sensor 200 according to Embodiment 2 will not be repeated in the description.

[0065] Figure 29 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 1 of Embodiment 2 of the present invention. As shown in Figure 29, in the ultrasonic sensor 200a according to Modification 1 of Embodiment 2 of the present invention, the third electrode 223 is positioned at a distance from the second electrode 123o. A part of the third electrode 223 is located within the notch N of the second electrode 123o when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). In the ultrasonic sensor 200a according to Modification 1 of Embodiment 2, the efficiency of the ultrasonic sensor 200a can also be improved by reducing vibrations outside the virtual ellipse n.

[0066] Figure 30 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 2 of Embodiment 2 of the present invention. As shown in Figure 30, in the ultrasonic sensor 200b according to a modified example 2 of Embodiment 2 of the present invention, the third electrode 223a is positioned at a distance from the second electrode 123c. The third electrode 223a overlaps with a part of each of the two sides S1 and with the entirety of one of the other two sides S2. The third electrode 223 overlaps with two of the four corners C. In the ultrasonic sensor 200b according to a modified example 2 of Embodiment 2, the vibration outside the virtual ellipse n can be reduced to improve the efficiency of the ultrasonic sensor 200b.

[0067] Figure 31 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modification 3 of Embodiment 2 of the present invention. As shown in Figure 31, in the ultrasonic sensor 200c according to modification 3 of Embodiment 2 of the present invention, the third electrode 223a is positioned at a distance from the second electrode 123e. In the ultrasonic sensor 200c according to modification 3 of Embodiment 2, the efficiency of the ultrasonic sensor 200c can also be improved by reducing vibrations outside the virtual ellipse n.

[0068] Figure 32 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modification 4 of Embodiment 2 of the present invention. As shown in Figure 32, in the ultrasonic sensor 200d according to modification 4 of Embodiment 2 of the present invention, the third electrode 223b is positioned at a distance from the second electrode 123d. The third electrode 223b overlaps with the entirety of one of the two sides S1 and with a portion of each of the other two sides S2. The third electrode 223b overlaps with two of the four corners C. In the ultrasonic sensor 200d according to modification 4 of Embodiment 2, the vibration outside the virtual ellipse n can be reduced and the efficiency of the ultrasonic sensor 200d can be improved.

[0069] Figure 33 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modification 5 of Embodiment 2 of the present invention. As shown in Figure 33, in the ultrasonic sensor 200e according to modification 5 of Embodiment 2 of the present invention, the third electrode 223b is positioned at a distance from the second electrode 123f. A part of the third electrode 223b is positioned at the cutout of the second electrode 123f when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). In the ultrasonic sensor 200e according to modification 5 of Embodiment 2, the vibration outside the virtual ellipse n can be reduced and the efficiency of the ultrasonic sensor 200e can be improved.

[0070] Figure 34 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modification 6 of Embodiment 2 of the present invention. As shown in Figure 34, in the ultrasonic sensor 200f according to modification 6 of Embodiment 2 of the present invention, the third electrode 223c is positioned at a distance from the second electrode 123r. The third electrode 223c overlaps with the entirety of one of the two sides S1 and with a portion of each of the other two sides S2. The third electrode 223c overlaps with two of the four corners C. A portion of the third electrode 223c is positioned in the cutout of the second electrode 123r and within the cutout N when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). In the ultrasonic sensor 200f according to modification 6 of Embodiment 2, the efficiency of the ultrasonic sensor 200f can also be improved by reducing vibrations outside the virtual ellipse n.

[0071] Figure 35 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 7 of Embodiment 2 of the present invention. As shown in Figure 35, in the ultrasonic sensor 200g according to Modification 7 of Embodiment 2 of the present invention, the third electrode 223d is positioned at a distance from the second electrode 123i. The third electrode 223d overlaps with the entirety of one of the two sides S1 and the entirety of one of the other two sides S2. The third electrode 223d overlaps with three of the four corners C. A part of the third electrode 223d is positioned at the cutout of the second electrode 123i when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). In the ultrasonic sensor 200g according to Modification 7 of Embodiment 2, the efficiency of the ultrasonic sensor 200g can also be improved by reducing vibrations outside the virtual ellipse n.

[0072] Figure 36 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 8 of Embodiment 2 of the present invention. As shown in Figure 36, in the ultrasonic sensor 200h according to Modification 8 of Embodiment 2 of the present invention, the third electrode 223e is positioned at a distance from the second electrode 123n. The third electrode 223e overlaps with a part of one of the two sides S1. The third electrode 223e does not overlap with the four corners C. A part of the third electrode 223e is positioned within the notch N of the second electrode 123n when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). In the ultrasonic sensor 200h according to Modification 8 of Embodiment 2, the efficiency of the ultrasonic sensor 200h can also be improved by reducing vibrations outside the virtual ellipse n.

[0073] Figure 37 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modification 9 of Embodiment 2 of the present invention. As shown in Figure 37, in the ultrasonic sensor 200i according to modification 9 of Embodiment 2 of the present invention, the third electrode 223e is positioned at a distance from the second electrode 123p. A part of the third electrode 223e is positioned within the notch N of the second electrode 123p when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). In the ultrasonic sensor 200i according to modification 9 of Embodiment 2, the efficiency of the ultrasonic sensor 200i can also be improved by reducing vibrations outside the virtual ellipse n.

[0074] Figure 38 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 10 of Embodiment 2 of the present invention. As shown in Figure 38, in the ultrasonic sensor 200j according to the modified example 10 of Embodiment 2 of the present invention, the third electrode 223e is positioned at a distance from the second electrode 123s. A part of the third electrode 223e is positioned within the notch N of the second electrode 123s when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). In the ultrasonic sensor 200j according to the modified example 10 of Embodiment 2, the vibration outside the virtual ellipse n can be reduced to improve the efficiency of the ultrasonic sensor 200j.

[0075] Figure 39 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 11 of Embodiment 2 of the present invention. As shown in Figure 39, in the ultrasonic sensor 200k according to the modified example 11 of Embodiment 2 of the present invention, the third electrode 223f is positioned at a distance from the second electrode 123q. The third electrode 223f overlaps with a part of one of the other two sides S2. The third electrode 223f does not overlap with the four corners C. A part of the third electrode 223f is positioned within the notch N of the second electrode 123q when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction). In the ultrasonic sensor 200k according to the modified example 11 of Embodiment 2, the vibration outside the virtual ellipse n can be reduced and the efficiency of the ultrasonic sensor 200k can be improved.

[0076] Figure 40 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a modified example 12 of Embodiment 2 of the present invention. As shown in Figure 40, in the ultrasonic sensor 200m according to a modified example 12 of Embodiment 2 of the present invention, the third electrode 223g is positioned at a distance from the second electrode 123. The third electrode 223g does not overlap with the two sides S1 and the other two sides S2. The third electrode 223g overlaps with one of the four corners C.

[0077] The first terminal 131 and the third electrode 223g are connected through the first wiring 141, and the first terminal 131 and the case 110 are connected through other wiring, thereby electrically connecting the third electrode 223g and the first electrode 122. In the ultrasonic sensor 200m according to the modified example 12 of Embodiment 2, the vibration outside the virtual ellipse n can be reduced, thereby improving the efficiency of the ultrasonic sensor 200m.

[0078] Here, we will describe the results of a simulation analysis of the rate of change of the force coefficient and electromechanical coupling coefficient of the ultrasonic sensors of modified examples 1 and 8 of Embodiment 2, compared to the ultrasonic sensor of the comparative example in which the third electrode is arranged in a notch formed inside the virtual ellipse n. The ultrasonic sensor of the comparative example differs from the ultrasonic sensor of Embodiment 2 only in the shape and arrangement of the electrodes in the piezoelectric element.

[0079] Figure 41 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to a comparative example. As shown in Figure 41, in the ultrasonic sensor 900 according to the comparative example, the third electrode 223z is positioned at a distance from the second electrode 123z. The second electrode 123z is elliptical in shape with a notch N formed at the center of the longitudinal direction (X-axis direction) and the center of the short direction (Y-axis direction). When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the second electrode 123z overlaps with a part of each of the two sides S1 and a part of each of the other two sides S2. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the center of gravity of the second electrode 123z is located at approximately the same position as the center of the roughly rectangular recess 113. The third electrode 223z does not overlap with the two sides S1 and the other two sides S2. The third electrode 223z overlaps with one of the four corners C. The entirety of the third electrode 223z is positioned within the notch N of the second electrode 123z when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction).

[0080] In the comparative example ultrasonic sensor 900, since a notch N is formed in the center of the virtual ellipse n, the vibration region inside the virtual ellipse n becomes narrower and the vibration intensity decreases, resulting in a lower efficiency for the ultrasonic sensor 900.

[0081] Figure 42 is a graph showing the rate of change of the force coefficient and electromechanical coupling coefficient of the ultrasonic sensors of modified examples 1 and 8 of Embodiment 2 compared to the comparative example. In Figure 42, the vertical axis shows the rate of change (%) of the force coefficient or electromechanical coupling coefficient, and the horizontal axis shows the sample name. The force coefficient data is shown as a solid line, and the electromechanical coupling coefficient data is shown as a dotted line.

[0082] As shown in Figure 42, compared to the ultrasonic sensor 900 according to the comparative example, the ultrasonic sensor 200a according to Modification 1 of Embodiment 2 showed an 8.5% improvement in force coefficient and a 6.9% improvement in electromechanical coupling coefficient, while the ultrasonic sensor 200h according to Modification 8 of Embodiment 2 showed a 6% improvement in force coefficient and a 6.8% improvement in electromechanical coupling coefficient. From the results of this simulation analysis, it was confirmed that the ultrasonic sensor 200a according to Modification 1 of Embodiment 2 and the ultrasonic sensor 200h according to Modification 8 of Embodiment 2 can broaden the bandwidth of the ultrasonic sensor by improving the force coefficient and electromechanical coupling coefficient compared to the ultrasonic sensor 900 according to the comparative example.

[0083] (Embodiment 3) Hereinafter, an ultrasonic sensor according to Embodiment 3 of the present invention will be described with reference to the figures. The ultrasonic sensor according to Embodiment 3 of the present invention differs from the ultrasonic sensor according to Embodiment 2 of the present invention in that it is equipped with a fourth electrode, so the same configuration as the ultrasonic sensor according to Embodiment 2 of the present invention will not be described again.

[0084] Figure 43 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Embodiment 3 of the present invention. As shown in Figure 43, in the ultrasonic sensor 300 according to Embodiment 3 of the present invention, the piezoelectric element further includes a fourth electrode 323 provided on the second surface P2. The fourth electrode 323 is electrically insulated from each of the first electrode 122, the second electrode 123, and the third electrode 223. Specifically, the fourth electrode 323 is formed on the second surface P2 with a gap between each of the second electrode 123 and the third electrode 223. Therefore, the potential of the fourth electrode 323 is floating. The fourth electrode 323 is made of a conductive film with approximately the same thickness as each of the second electrode 123 and the third electrode 223.

[0085] As shown in Figure 43, when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the fourth electrode 323 overlaps with at least a portion of at least one of the two sides S1 and the other two sides S2. In this embodiment, the fourth electrode 323 overlaps with a portion of either side S1 of the two sides S1 and a portion of either side S2 of the other two sides S2.

[0086] When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the fourth electrode 323 overlaps with at least a portion of the four corners C. In this embodiment, each of the three fourth electrodes 323 overlaps with one of the corresponding corners C. Note that the number of fourth electrodes 323 is not limited to three; one or more are acceptable.

[0087] In the ultrasonic sensor 300 according to Embodiment 3 of the present invention, by providing a fourth electrode 323 on the second surface P2, the piezoelectric element 121 can be polarized across the entire second surface P2. As a result, the piezoelectric effect of the piezoelectric element can be effectively utilized, improving the efficiency of the ultrasonic sensor 300. The same effect can be obtained by arranging a third electrode 223 instead of the fourth electrode 323.

[0088] In the ultrasonic sensor 300 according to Embodiment 3 of the present invention, when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the fourth electrode 323 overlaps with at least a part of at least one of the two sides S1 and the other two sides S2, thereby allowing the piezoelectric body 121 to be polarized overall up to the edge of the second surface P2. Furthermore, when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the fourth electrode 323 overlaps with at least a part of the four corners C, thereby suppressing the reduction of the vibration region inside the virtual ellipse n by arranging the fourth electrode 323. In the ultrasonic sensor 300 according to Embodiment 3 of the present invention, the vibration outside the virtual ellipse n can also be reduced, thereby improving the efficiency of the ultrasonic sensor 300.

[0089] The following describes a modified version of Embodiment 3 of the present invention. In the modified version of Embodiment 3 described below, only the shape and arrangement of the second electrode, third electrode, and fourth electrode differ from the ultrasonic sensor 300 according to Embodiment 3; therefore, the same configuration as the ultrasonic sensor 300 according to Embodiment 3 will not be repeated in the description.

[0090] Figure 44 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 1 of Embodiment 3 of the present invention. As shown in Figure 44, in the ultrasonic sensor 300a according to Modification 1 of Embodiment 3 of the present invention, the fourth electrode 323a is formed on the second surface P2 with a gap between each of the second electrode 123j and the third electrode 223a. The fourth electrode 323a overlaps with a part of each of the two sides S1 and the entirety of one of the other two sides S2. The fourth electrode 323a overlaps with two of the four corners C. In the ultrasonic sensor 300a according to Modification 1 of Embodiment 3, the vibration outside the virtual ellipse n can be reduced and the efficiency of the ultrasonic sensor 300a can be improved.

[0091] Figure 45 is a plan view showing the shape of the piezoelectric element of an ultrasonic sensor according to Modification 2 of Embodiment 3 of the present invention. As shown in Figure 45, in the ultrasonic sensor 300b according to Modification 2 of Embodiment 3 of the present invention, when viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the second electrode 123t has a shape in which the four corners C of a rectangle having a long side extending in the longitudinal direction (X-axis direction) are beveled. Specifically, the second electrode 123t has a nonagonal shape in which a notch N is formed at one end in the longitudinal direction (X-axis direction) and one end in the short direction (Y-axis direction) of a virtual octagon formed by beveling the four corners C of the rectangle. Note that the shape of the second electrode 123t is not limited to a nonagonal shape. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the second electrode 123t overlaps with a part of each of the two sides S1 and a part of each of the other two sides S2. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the center of gravity of the second electrode 123t is located at a position offset from the center of the roughly rectangular recess 113 in the longitudinal direction (X-axis direction) and the short direction (Y-axis direction).

[0092] In the ultrasonic sensor 300b, the third electrode 223 is positioned at a distance from the second electrode 123t. A portion of the third electrode 223 is located within the notch N of the second electrode 123t when viewed from a direction perpendicular to the base plate 111 (Z-axis direction). The third electrode 223 overlaps with one of the four corners C. When viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the third electrode 223 overlaps with a portion of one side S1 of the two sides S1 and a portion of one side S2 of the other two sides S2.

[0093] Each of the three fourth electrodes 323b is formed on the second surface P2, spaced apart from the second electrode 123t and the third electrode 223. Viewed from a direction perpendicular to the base plate 111 (Z-axis direction), each of the three fourth electrodes 323b overlaps with one of the corresponding corners C. Viewed from a direction perpendicular to the base plate 111 (Z-axis direction), each of the three fourth electrodes 323b overlaps with a portion of the corresponding side S1 of the two sides S1 and a portion of the corresponding side S2 of the other two sides S2. Viewed from a direction perpendicular to the base plate 111 (Z-axis direction), the fourth electrode 323b has a triangular shape along the chamfered edge, side S1, and side S2 of the second electrode 123t. Note that the number of fourth electrodes 323b is not limited to three; one or more are acceptable.

[0094] As described above, in the ultrasonic sensor 300b, when viewed from a direction perpendicular to the bottom plate 111 (Z-axis direction), the third electrode 223 and the three fourth electrodes 323b overlap with at least a portion of each of the four corners C. In the ultrasonic sensor 300b according to the modified example 2 of Embodiment 3, the vibration outside the virtual ellipse n can be reduced and the efficiency of the ultrasonic sensor 300b can be improved.

[0095] (Embodiment 4) Hereinafter, an ultrasonic sensor according to Embodiment 4 of the present invention will be described with reference to the figures. The ultrasonic sensor according to Embodiment 4 of the present invention differs from the ultrasonic sensor according to Embodiment 1 of the present invention in that it includes a circuit connected in parallel to the piezoelectric element, so the same configuration as the ultrasonic sensor according to Embodiment 1 of the present invention will not be described again.

[0096] Figure 46 is an equivalent circuit diagram of an ultrasonic sensor according to Embodiment 4 of the present invention. As shown in Figure 46, the ultrasonic sensor according to Embodiment 4 of the present invention includes a piezoelectric element 120, a secondary winding Lp of a transformer 20 for supplying a driving voltage to the piezoelectric element 120, a resistor Rp, and a capacitance Cp, all connected in parallel. The secondary winding Lp, resistor Rp, capacitance Cp, equivalent parallel capacitance Cd, and equivalent parallel resistor Rd are connected in parallel between a first terminal T1 and a second terminal T2, forming a parallel circuit 40. The electrical resonant frequency of the parallel circuit 40 and the electrical resonant frequency of the series circuit 13 of the piezoelectric element 120 are set to be the same as each other.

[0097] The transformer 20 consists of a primary winding Lo and a secondary winding Lp. The primary winding Lo is connected in series between the third terminal T3 and the fourth terminal T4. The voltage applied between the third terminal T3 and the fourth terminal T4 is boosted to a voltage obtained by multiplying the turns ratio of the primary winding Lo and the secondary winding Lp, and this voltage is applied from the secondary winding Lp between the first terminal T1 and the second terminal T2, and supplied to the piezoelectric element 120. The transformer 20, resistor Rp, and capacitance Cp are each composed of elements arranged on the circuit board 30 connected to the first terminal T1 (131) and the second terminal T2 (132).

[0098] Figure 47 is a graph showing the relationship between the frequency characteristics of impedance in a series circuit of piezoelectric elements, the force coefficient, and the electromechanical coupling coefficient. In Figure 47, the vertical axis represents the impedance in the series circuit 13 of piezoelectric elements 120, and the horizontal axis represents the frequency. The data for when the piezoelectric element 120 is square is shown by a dotted line, and the data for when the piezoelectric element 120 is rectangular with a longer side extending in the longitudinal direction (X-axis direction) is shown by a solid line. The length in the short direction (Y-axis direction) of the rectangular shape is the same as the length in the short direction (Y-axis direction) of the square shape.

[0099] As shown in Figure 47, when the piezoelectric element 120 is rectangular in shape, the impedance Zs in the series circuit 13 of the piezoelectric element 120 is lower compared to when the piezoelectric element 120 is square in shape. That is, the vibration area of ​​the piezoelectric element 120 is increased, and the force coefficient and electromechanical coupling coefficient increase, which lowers the impedance Zs in the series circuit 13 of the piezoelectric element 120. The decrease in impedance Zs in the series circuit 13 of the piezoelectric element 120 makes the ultrasonic sensor more efficient.

[0100] In the ultrasonic sensor according to Embodiment 4, the resistance value of resistor Rp is less than or equal to the resistance value of the equivalent series resistance Rs. Figure 48 is a graph showing the frequency characteristics of impedance in a parallel circuit of the ultrasonic sensor and a series circuit of piezoelectric elements according to Embodiment 4 of the present invention. In Figure 48, impedance is shown on the vertical axis and frequency on the horizontal axis.

[0101] As shown in Figure 48, in the ultrasonic sensor according to Embodiment 4, where the resistance value of resistor Rp is less than or equal to the resistance value of the equivalent series resistance Rs, the curve showing the frequency characteristics of the impedance Zs in the series circuit 13 of the piezoelectric element 120 and the curve showing the frequency characteristics of the impedance Zp in the parallel circuit 40 do not intersect. Therefore, the parallel circuit 40 functions to reduce the overall impedance of the ultrasonic sensor circuit.

[0102] Figure 49 is a graph showing the frequency characteristics of the overall sensitivity of the ultrasonic sensors according to Embodiment 1 and Embodiment 4. In Figure 49, the vertical axis represents the overall sensitivity of the ultrasonic sensor, and the horizontal axis represents frequency. The overall sensitivity of the ultrasonic sensor is the output value from the first terminal T1 and the second terminal T2. The data for the ultrasonic sensor according to Embodiment 1 is shown by a dotted line, and the data for the ultrasonic sensor according to Embodiment 4 is shown by a solid line.

[0103] As shown in Figure 49, the ultrasonic sensor according to Embodiment 4 has a lower overall impedance due to the parallel circuit 40, resulting in higher overall sensitivity compared to the ultrasonic sensor 100 according to Embodiment 1. Thus, in the ultrasonic sensor according to Embodiment 4, high sensitivity can be achieved by making the resistance value of resistor Rp less than or equal to the resistance value of the equivalent series resistance Rs.

[0104] (Embodiment 5) Hereinafter, an ultrasonic sensor according to Embodiment 5 of the present invention will be described with reference to the figures. The ultrasonic sensor according to Embodiment 5 of the present invention differs from the ultrasonic sensor according to Embodiment 4 of the present invention in that the resistance value of the resistor Rp is greater than the resistance value of the equivalent series resistor Rs. Therefore, the same configuration as that of the ultrasonic sensor according to Embodiment 4 of the present invention will not be repeated in the description.

[0105] Figure 50 is a graph showing the frequency characteristics of impedance in a parallel circuit of an ultrasonic sensor and a series circuit of a piezoelectric element according to Embodiment 5 of the present invention. In Figure 50, the vertical axis represents impedance and the horizontal axis represents frequency.

[0106] As shown in Figure 50, in the ultrasonic sensor according to Embodiment 5, where the resistance value of resistor Rp is greater than the resistance value of the equivalent series resistance Rs, the curve showing the frequency characteristics of the impedance Zs in the series circuit 13 of the piezoelectric element 120 intersects with the curve showing the frequency characteristics of the impedance Zp in the parallel circuit 40. Therefore, the parallel circuit 40 functions to broaden the frequency range of the impedance peak in the entire ultrasonic sensor circuit.

[0107] Figure 51 is a graph showing the frequency characteristics of the overall sensitivity of the ultrasonic sensors according to Embodiment 1 and Embodiment 5. In Figure 51, the vertical axis represents the overall sensitivity of the ultrasonic sensor, and the horizontal axis represents frequency. The data for the ultrasonic sensor according to Embodiment 1 is shown by a dotted line, and the data for the ultrasonic sensor according to Embodiment 5 is shown by a solid line.

[0108] As shown in Figure 51, the ultrasonic sensor according to Embodiment 5 has a wider frequency range of the peak impedance of the entire ultrasonic sensor circuit due to the parallel circuit 40. Therefore, compared to the ultrasonic sensor 100 according to Embodiment 1, the frequency band with high overall sensitivity is expanded. Thus, in the ultrasonic sensor according to Embodiment 5, the bandwidth can be broadened because the resistance value of resistor Rp is greater than the resistance value of the equivalent series resistance Rs.

[0109] Here, the detection frequency bandwidth is defined as the frequency band having a sensitivity of 6 dB or more lower than the maximum overall sensitivity of the ultrasonic sensor. Figure 52 is a diagram illustrating the detection frequency bandwidth. As shown in Figure 52, the detection frequency bandwidth Wd is the frequency band having a sensitivity of 6 dB or more lower than the maximum overall sensitivity (Max) of the ultrasonic sensor (Max-6).

[0110] In the ultrasonic sensor according to Embodiment 5, the maximum dimension L2 of the piezoelectric element 120 in the longitudinal direction (X-axis direction) is increased to reduce the impedance Zs in the series circuit 13 of the piezoelectric element 120, and the resistance value of the resistor Rp is made greater than the resistance value of the equivalent series resistance Rs, thereby ensuring a wide detection frequency width Wd and effectively broadening the bandwidth of the ultrasonic sensor.

[0111] The above method of broadening bandwidth uses the real part of the impedance, but it is also possible to broaden bandwidth using the imaginary part of the impedance. Specifically, by increasing the inductance of the secondary winding Lp while decreasing the total capacitance of the capacitance Cp and the equivalent parallel capacitance Cd, the ultrasonic sensor can be broadened. In this case, if the inductance of the secondary winding after increasing it is Lp2, it is set so that the relationship Lp2 = (Cp + Cd)Lp / Cd is satisfied. In order to decrease the total capacitance (Cp + Cd) of the capacitance Cp and the equivalent parallel capacitance Cd, the capacitance Cp is set to 300 pF or less.

[0112] Figure 53 is a graph showing the frequency characteristics of impedance in a parallel circuit and a series circuit of piezoelectric elements in an ultrasonic sensor according to Embodiment 5 of the present invention, when the inductance of the secondary winding Lp is increased while the total capacitance of the capacitance Cp and the equivalent parallel capacitance Cd is decreased. In Figure 53, the vertical axis represents impedance and the horizontal axis represents frequency. The solid line shows the impedance Zp when the inductance of the secondary winding Lp is increased while the total capacitance of the capacitance Cp and the equivalent parallel capacitance Cd is decreased, and the dotted line shows the impedance Zp before the total capacitance of the capacitance Cp and the equivalent parallel capacitance Cd and the inductance of the secondary winding Lp are changed.

[0113] As shown in Figure 53, by increasing the inductance of the secondary winding Lp, the slope of the portion of the curve showing the frequency characteristics of the impedance Zp of the parallel circuit 40 at lower frequencies below the peak can be made gentler. By decreasing the total capacitance (Cp + Cd) of capacitance Cp and equivalent parallel capacitance Cd, the slope of the portion of the curve showing the frequency characteristics of the impedance Zp of the parallel circuit 40 at higher frequencies above the peak can be made gentler. As a result, the frequency range Wc at the intersection of the curve showing the frequency characteristics of the impedance Zs in the series circuit 13 of the piezoelectric element 120 and the curve showing the frequency characteristics of the impedance Zp of the parallel circuit 40 is widened. This makes it possible to widen the bandwidth of the ultrasonic sensor.

[0114] As described above, from the perspective of broadening the bandwidth by using the imaginary part of the impedance, the capacitance Cp may be 50pF or more and 300pF or less. The capacitance Cp may be 100pF or more and 250pF or less. The capacitance Cp may be 150pF or more and 200pF or less. However, the capacitance Cp is not limited to 300pF or less.

[0115] In the description of the embodiments described above, the combinable configurations may be combined with each other.

[0116] The embodiments and examples disclosed herein should be considered in all respects to be illustrative and not restrictive. The scope of the invention is indicated by the claims rather than the foregoing description, and all modifications within the meaning and scope of the claims are intended to be included.

[0117] 12 Equivalent circuit, 13 Series circuit, 20 Transformer, 30 Circuit board, 40 Parallel circuit, 100, 100a, 100b, 100c, 100d, 100e, 100f, 100g, 100h, 100i, 100j, 100k, 100m, 100n, 100o, 100p, 100q, 100r, 100s, 200, 200a, 200b, 200c, 200d, 200e, 200f, 200g, 200h, 200i, 200j, 200k, 200m, 300, 300a, 300b, 900 Ultrasonic sensor, 110 Case, 111 Bottom plate, 112 Peripheral wall, 113 Recess, 120, 220 Piezoelectric element, 121 Piezoelectric body, 122 First electrode, 123, 123a, 123b, 123c, 123d, 123e, 123f, 123g, 123h, 123i, 123j, 123k, 123m, 123n, 123o, 123p, 123q, 123r, 123s, 123t, 123z Second electrode, 131, T1 First terminal, 132, T2 Second terminal, 141 First wiring, 142 Second wiring, 150 Filling material, 160 Lid, 222 Connecting electrode, 223, 223a, 223b, 223c, 223d, 223e, 223f, 223g, 223z Third electrode, 323, 323a, 323b Fourth electrode, C Four corners, Cd equivalent parallel capacitance, Cp capacitance, Cs equivalent series capacitance, L3 major axis, Lo primary winding, Lp secondary winding, Ls equivalent series inductance, N notch, P1 first face, P2 second face, Rd equivalent parallel resistance, Rp resistance, Rs equivalent series resistance, S1 two sides, S2 other two sides, T3 third terminal, T4 fourth terminal, W3 minor axis, Wc frequency range, Wd detection frequency width, Zp, Zs impedance, kp electromechanical coupling coefficient, n virtual ellipse.

Claims

1. An ultrasonic sensor comprising: a cylindrical case having a bottom plate and a peripheral wall; and a piezoelectric element mounted on the bottom plate within a recess surrounded by the bottom plate and the peripheral wall, wherein, viewed from a direction perpendicular to the bottom plate, the recess extends in a longitudinal direction parallel to the bottom plate and in a short direction perpendicular to the longitudinal direction, and the maximum dimension of the recess in the longitudinal direction is greater than the maximum dimension of the recess in the short direction; the piezoelectric element includes a piezoelectric body having a first surface located on the bottom plate side and a second surface located on the opposite side of the first surface, a first electrode provided on the first surface, and a second electrode provided on the second surface, the second electrode facing the first electrode via the piezoelectric body; viewed from a direction perpendicular to the bottom plate, the piezoelectric body has a rectangular shape consisting of two sides extending in the longitudinal direction and two other sides extending in the short direction; and viewed from a direction perpendicular to the bottom plate, the second electrode is formed avoiding the four corners of the rectangular shape.

2. The ultrasonic sensor according to claim 1, wherein the piezoelectric element further includes a third electrode provided on the second surface, and the third electrode is electrically connected to the first electrode.

3. The ultrasonic sensor according to claim 2, wherein, when viewed from a direction perpendicular to the bottom plate, the third electrode overlaps with at least a portion of at least one of the two sides and the other two sides.

4. The ultrasonic sensor according to claim 2 or 3, wherein, when viewed from a direction perpendicular to the base plate, the third electrode overlaps with at least a portion of the four corners.

5. The ultrasonic sensor according to any one of claims 2 to 4, wherein the piezoelectric element further includes a fourth electrode provided on the second surface, and the fourth electrode is electrically insulated from each of the first electrode, the second electrode, and the third electrode.

6. The ultrasonic sensor according to claim 5, wherein, when viewed from a direction perpendicular to the bottom plate, the fourth electrode overlaps with at least a portion of at least one of the two sides and the other two sides.

7. The ultrasonic sensor according to claim 5 or 6, wherein, when viewed from a direction perpendicular to the base plate, the fourth electrode overlaps with at least a portion of the four corners.

8. The ultrasonic sensor according to claim 7, as viewed from a direction perpendicular to the base plate, wherein the second electrode has a shape in which a notch is formed at one end in the longitudinal direction and one end in the short direction of a virtual octagon with chamfered corners of the rectangular shape, as viewed from a direction perpendicular to the base plate, a part of the third electrode is located within the notch of the second electrode, as viewed from a direction perpendicular to the base plate, the third electrode and the three fourth electrodes overlap with at least a part of each of the four corners, as viewed from a direction perpendicular to the base plate, the third electrode overlaps with a part of each of one of the two sides and one of the other two sides, as viewed from a direction perpendicular to the base plate, each of the three fourth electrodes overlaps with a part of each of the corresponding side of the two sides and one of the other two sides.

9. An ultrasonic sensor according to any one of claims 1 to 8, comprising a circuit in which the piezoelectric element, the secondary winding of a transformer for supplying a driving voltage to the piezoelectric element, a resistor, and a capacitance are connected in parallel to each other, wherein the piezoelectric element has an equivalent series inductance, an equivalent series capacitance, an equivalent series resistance, an equivalent parallel capacitance, and an equivalent parallel resistance, and the resistance value of the resistor is less than or equal to the resistance value of the equivalent series resistance.

10. An ultrasonic sensor according to any one of claims 1 to 8, comprising a circuit in which the piezoelectric element, the secondary winding of a transformer for supplying a driving voltage to the piezoelectric element, a resistor, and a capacitance are connected in parallel to each other, wherein the piezoelectric element has an equivalent series inductance, an equivalent series capacitance, an equivalent series resistance, an equivalent parallel capacitance, and an equivalent parallel resistance, and the resistance value of the resistor is greater than the resistance value of the equivalent series resistance.

11. The ultrasonic sensor according to claim 10, wherein the capacitance is 300 pF or less.

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