Sensor for identifying the position of the interface, liquid level gauge

Abstract

Disclosed is an interface sensor having a well-balanced configuration in which the total number of conductive wires drawn from the interface sensor is less than the total number of observation points. 【Solution means】The interface sensor 1 is an interface sensor having a configuration determined by a symbol system and its specific symbol words. a) Regarding the number e(k) of electrode pairs included in the k-th (k ∈ [K]) sensor block included in the interface sensor 1, the maximum value max on the set [K] of the number e(k) k∈[K] e(k) and the minimum value min k∈[K] The difference between e(k) is smaller than that value of the prior art, or b) Regarding the number t(j) of electrode pairs connected to the j-th (j ∈ [J] = [Σ k∈[K] c(k)], c(k) is the number of conductive wires included in the k-th (k ∈ [K]) sensor block), the maximum value max on the set [J] of the number t(j) j∈[J] t(j) and the minimum value min j∈[J] The difference between t(j) is smaller than that value of the prior art, holds.

Description

Technical Field

[0001] The present disclosure relates to a sensor for specifying the position of an interface between two substances (hereinafter referred to as an interface sensor), and a liquid level gauge including the interface sensor.

Background Art

[0002] The applicant of the present application is the applicant of Patent Document 1 (International Publication No. WO2023 / 203912A1), Patent Document 2 (International Publication No. WO2023 / 218744A1), Patent Document 3 (International Publication No. WO2023 / 248947A1), and Patent Document 4 (International Publication No. WO2024 / 024325A1).

[0003] FIG. 1 is a copy of FIG. 9 of Patent Document 1. FIG. 2 is a copy of FIG. 13 of Patent Document 2. FIG. 3 is a copy of FIG. 10 of Patent Document 3. FIG. 4 is a copy of FIG. 16 of Patent Document 4.

[0004] The interface sensor having the configuration shown in FIG. 1 is An interface sensor 2 for specifying the position of an interface between a first substance and a second substance, including K sensor blocks 3, where K is a predetermined integer satisfying 2 ≤ K, the k-th sensor block 3 among the K sensor blocks 3 includes M(k) electrode pairs 5 and n(k)+1 conductors 7, where k ∈ {x ∈ N: 1 ≤ x ≤ K}, N is the set of all positive integers, n(k) is a predetermined integer satisfying 2 ≤ n(k), M(1) ≥ 8, and for each k ∈ {x ∈ N: 1 ≤ x ≤ K},

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[0005] The interface sensor having the configuration shown in FIG. 2 is 'an interface sensor 2 for specifying the position of the interface between the first substance and the second substance, comprising a first electrical conductor 5a and K sensor blocks 3, where K is a predetermined integer satisfying 2 ≤ K, the k-th sensor block 3 among the K sensor blocks 3 comprises M(k) second electrical conductors 5b and n(k) conductors 7, where k ∈ {x ∈ N : 1 ≤ x ≤ K}, N is the set of all positive integers, n(k) is a predetermined integer satisfying 2 ≤ n(k), M(1) = 4 or M(1) = 6 or M(1) ≥ 8, and for each k ∈ {x ∈ N : 1 ≤ x ≤ K},

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[0006] The interface sensor having the configuration shown in FIG. 3 is 'A sensor 200 for specifying the position of the interface between the first substance and the second substance, including E electrode pairs 500, L conductors 700, and a conductor selector 800, where

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[0007] The interface sensor having the configuration shown in FIG. 4 is 'A sensor 200 for specifying the position of the interface between the first substance and the second substance, including a first electrical conductor 500a, E second electrical conductors 500b, L conductors 700, and a conductor selector 800, provided that

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Prior Art Documents

Patent Documents

[0008]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Summary of the Invention

Problems to be Solved by the Invention

[0009] All of the interface sensors disclosed in Patent Documents 1 to 4 have an unbalanced configuration. The meaning of unbalance will be mentioned in [Analysis of the Prior Art] described later.

[0010] We disclose an interface sensor having a balanced configuration with the total number of conducting wires drawn from the interface sensor being less than the total number of observation points, and a liquid level gauge including the interface sensor.

Means for Solving the Problem

[0011] The technical matters described herein are not for explicitly or implicitly limiting the invention described in the claims, nor for enabling persons other than those who benefit from the present invention (e.g., the applicant and the patentee) to limit the invention described in the claims. Instead, they are merely provided for facilitating the understanding of the gist of the present invention. The overview of the present invention from other viewpoints can be understood, for example, from the claims of this patent application at the time of filing.

[0012] The disclosed interface sensor is an interface sensor having a configuration determined by the adopted symbol system and its specific symbol language, a) Regarding the number e(k) of electrode pairs or electrical conductors included in the k-th (k ∈ [K]) sensor block included in the interface sensor, the difference between the maximum value max k∈[K] e(k) and the minimum value min k∈[K] e(k) on the set [K] of that number is smaller than that value in the prior art, or b) Regarding the number t(j) of electrode pairs or electrical conductors connected to the j-th (j ∈ [J] = [Σ k∈[K] c(k)], where c(k) is the number of conducting wires (excluding the conducting wires connected to the e(k) electrode pairs or electrical conductors included in the k-th (k ∈ [K]) sensor block) included in the k-th (k ∈ [K]) sensor block) of the conducting wires (excluding the conducting wires connected to the e(k) electrode pairs or electrical conductors included in the k-th (k ∈ [K]) sensor block), the difference between the maximum value max j∈[J] t(j) and the minimum value min j∈[J] t(j) on the set [J] of that number is smaller than that value in the prior art, holds.

Advantages of the Invention

[0013] The interface sensor of the present disclosure has a well-balanced configuration with the total number of conducting wires drawn from the interface sensor being less than the total number of observation points.

Brief Description of the Drawings

[0014]

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Modes for Carrying Out the Invention

[0015] Hereinafter, unless otherwise specified, \(N\) is the set of all positive integers. The symbol \(N\) is represented in boldface on the blackboard in mathematical formulas.

[0016] [Analysis of the prior art] According to the prior art interface sensor, \(M\) planes \(P(1),\cdots,P(M)\) that do not coincide with each other and are parallel to each other are predetermined, and the position of the interface is specified as one of \(M + 1\) intervals \(I(1),\cdots,I(M + 1)\) determined by the \(M\) planes \(P(1),\cdots,P(M)\). Interval \(I(1)\) is one of the two half-spaces obtained by dividing the space by plane \(P(1)\) and does not contain planes \(P(2),\cdots,P(M)\). Interval \(I(m)\) (\(m\in\{x\in N:2\leq x\leq M\}\)) is the space region between adjacent planes \(P(m - 1)\) and \(P(m)\). Interval \(I(M + 1)\) is one of the two half-spaces obtained by dividing the space by plane \(P(M)\) and does not contain planes \(P(2),\cdots,P(M)\). The fact that the position of the interface can be specified by the interface sensor means that a distinguishable codeword can be assigned to each of the \(M + 1\) intervals \(I(1),\cdots,I(M + 1)\). Although there is no limitation on the codeword, for the sake of facilitating the discussion, hereinafter, the codeword is represented by the concatenation of \(K\) non-negative integers. \(K\) is the total number of sensor blocks included in the interface sensor and satisfies \(2\leq K\).

[0017] In the configuration of the interface sensor disclosed in Patent Document 1 or Patent Document 2, as follows, \(M + 1\) codewords are systematically assigned to the \(M + 1\) intervals \(I(1),\cdots,I(M + 1)\). When \(M\) is represented as the product of \(K\) factors \(n(k)\) (see Equation (1)), the \(k\)th sensor block is located on \(\Pi\) different planes among the \(M\) planes \(P(1),\cdots,P(M)\) i=k K \(n(i)\) planes i=k KSince it includes n(i) electrode pairs (or electrical conductors), one of the n(k) types of non - negative integers determined by the number of conducting wires n(k) is systematically assigned to each of the spatial regions distinguished by these boundaries, with these planes where the electrode pairs (or electrical conductors) are located as the boundaries. Specifically, for the M + 1 intervals I(1),..., I(M + 1) in the k - th sensor block (k ∈ {x ∈ N: 2 ≤ x ≤ K - 1}), M + 1 non - negative integers are assigned according to Equation (2). Equation (2) represents an arrangement of non - negative integers and is not a matrix. In Equation (2), the lower - right exponent Π i=1 k-1 n(i) represents the number of repetitions of each non - negative integer, and the upper - right exponent Π i=k+1 K n(i) represents the number of repetitions of the arrangement of non - negative integers. The lower - right exponent is defined as 1 for the first sensor block, and the upper - right exponent is defined as 1 for the K - th sensor block. Therefore, the set of M + 1 codewords assigned to the M + 1 intervals I(1),..., I(M + 1) is represented by Equation (3). As is clear from Equation (3), the codeword for interval I(1) and the codeword for interval I(M + 1) are the same as each other. However, by measuring the capacitance of any one electrode pair (or electrical conductor) included in the K - th sensor block, the codeword for interval I(1) and the codeword for interval I(M + 1) can be distinguished.

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[0018] Figure 5 shows a specific example of the assignment of M + 1 codewords to the M + 1 intervals I(1),..., I(M + 1) in the configuration of the interface sensor disclosed in Patent Document 1. In this example, M = 30, K = 3, n(1)=3, n(2)=5, n(3)=2. For example, when k = 2, since the value of the upper - right exponent in Equation (2) is 2 and the value of the lower - right exponent is 3, the arrangement of non - negative integers according to Equation (2) is as follows. 0 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 4 4 4 3 3 3 2 2 2 1 1 1 0 0 0 Therefore, the code words for each interval according to Equation (3) are as follows. I(31): 000 I(30): 142 I(29): 141 I(28): 140 I(27): 132 I(26): 131 I(25): 130 I(24): 122 I(23): 121 I(22): 120 I(21): 112 I(20): 111 I(19): 110 I(18): 102 I(17): 101 I(16): 100 I(15): 042 I(14): 041 I(13): 040 I(12): 032 I(11): 031 I(10): 030 I(9): 022 I(8): 021 I(7): 020 I(6): 012 I(5): 011 I(4): 010 I(3):002 I(2):001 I(1):000

[0019] The configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4 is based on the configuration of the interface sensor disclosed in Patent Document 1 or Patent Document 2. Therefore, the set of M + 1 codewords assigned to the M + 1 intervals I(1),..., I(M + 1) in the configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4 is obtained by changing the set of codewords represented by Equation (3). Specifically, in the configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4, when M is represented as the product of K factors n(k) (see Equation (1)), the set of codewords assigned to each of the M + 1 intervals I(1),..., I(M + 1) is represented by Equation (4). G k R represents the upside-down of the sequence G of non-negative integers k of the k-th (k ∈ {x ∈ N: 1 ≤ x ≤ K - 1}) sensor block. The total number of G k and G k R appearing alternately is Π i=k+1 K n(i).

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[0020] Fig. 6 shows a specific example of the assignment of M + 1 codewords to the M + 1 intervals I(1),..., I(M + 1) in the configuration of the interface sensor disclosed in Patent Document 3. In this example, M = 24, K = 3, n(1) = 3, n(2) = 4, and n(3) = 2. The configuration of the interface sensor considered from the disclosure of Patent Document 3 is shown on the left side of Fig. 6, and this configuration is equivalent to the circuit configuration shown on the right side of Fig. 6. For example, when k = 2, the sequence of non-negative integers in the second sensor block is as follows. 0 0 0 0 1 1 1 2 2 2 3 3 3 3 3 3 2 2 2 1 1 1 0 0 0 Therefore, the code words for each section according to formula (4) are as follows. I(25): 000 I(24): 100 I(23): 101 I(22): 102 I(21): 112 I(20): 111 I(19): 110 I(18): 120 I(17): 121 I(16): 122 I(15): 132 I(14): 131 I(13): 130 I(12): 030 I(11): 031 I(10): 032 I(9): 022 I(8): 021 I(7): 020 I(6): 010 I(5): 011 I(4): 012 I(3): 002 I(2): 001 I(1): 000

[0021] From the above description, it can be seen that the set of M + 1 code words assigned to the M + 1 sections I(1),..., I(M + 1) in the configuration of the interface sensor disclosed in Patent Document 1 or Patent Document 2 is a code based on the place-value notation.

[0022] From the above description, it can be seen that the set of M + 1 codewords assigned to the M + 1 intervals I(1),..., I(M + 1) in the configuration of the interface sensor disclosed in Patent Document 3 or Patent Document 4 is the reflected Gray code when n(K) is even, and is the reflected Gray code except for the interval I(M + 1) when n(K) is odd.

[0023] This suggests that the configuration of the interface sensor is determined by the adopted code system and its specific codewords.

[0024] Incidentally, in any of the interface sensors disclosed in Patent Documents 1 to 4, the number of electrode pairs (or electrical conductors) is the largest in the first sensor block and the smallest in the K-th sensor block, and the difference between the number of electrode pairs (or electrical conductors) included in the K-th sensor block and the number of electrode pairs (or electrical conductors) included in the k-th sensor block (k ∈ {x ∈ N: 1 ≤ x ≤ K - 1}) expands multiplicatively as k decreases. That is, any of the interface sensors disclosed in Patent Documents 1 to 4 has an unbalanced configuration in this regard. Considering that the factorization of M by Equation (1) is not always uniquely determined, in the interface sensor disclosed in Patent Document 1 or Patent Document 2, the minimum value of the difference between the number of electrode pairs (or electrical conductors) included in the first sensor block and the number of electrode pairs (or electrical conductors) included in the K-th sensor block is given by Equation (5), and in the interface sensor disclosed in Patent Document 3 or Patent Document 4, the minimum value of the difference between the number of electrode pairs (or electrical conductors) included in the first sensor block and the number of electrode pairs (or electrical conductors) included in the K-th sensor block is given by Equation (6). Hereinafter, unless otherwise specified, max represents the maximum element of a set, and min represents the minimum element of a set. Hereinafter, unless otherwise specified, the symbol [X] represents the set {x ∈ N: 1 ≤ x ≤ X} determined by the positive integer X. Therefore, [K] is the set {x ∈ N: 1 ≤ x ≤ K}. Hereinafter, unless otherwise specified, the symbol sandwiching M / 2 is the floor function. Hereinafter, unless otherwise specified, the symbol similar to a backslash represents the difference set. For example, when M = 24 and K = 3, the factorization of M is M = 2 × 2 × 6 or M = 2 × 4 × 3 (note that the order of the factors is not considered). Thus, F(M, K) = {{2, 6}, {2, 3, 4}}. Therefore, the value of Equation (5) is 18, and the value of Equation (6) is 6.

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[0025] As is clear from equations (5) and (6), the value of equation (6) is always smaller than the value of equation (5). Therefore, regarding the number e(k) of electrode pairs (or electrical conductors) included in the k-th (k ∈ [K]) sensor block included in the interface sensor, the maximum value max on the set [K] of that number e(k) k∈[K] e(k) = max{e(1),..., e(K)} and the minimum value min k∈[K] If the difference between e(k) = min{e(1),..., e(K)} is smaller than the value of equation (6), it can be said that the interface sensor has a well-balanced configuration compared to the prior art interface sensors.

[0026] From another perspective, in any of the interface sensors disclosed in Patent Documents 1 to 4, the number of electrode pairs (or electrical conductors) connected to one conductor (excluding the conductor connected to all electrode pairs or electrical conductors included in the sensor block to which this conductor belongs) is the largest in the first sensor block and the smallest in the K-th sensor block. The number of electrode pairs (or electrical conductors) connected to one conductor (excluding the conductor connected to all electrode pairs or electrical conductors included in the first sensor block) in the first sensor block and the number of electrode pairs (or electrical conductors) connected to one conductor (excluding the conductor connected to all electrode pairs or electrical conductors included in the k-th sensor block) in the k-th sensor block (k ∈ {x ∈ N: 1 ≤ x ≤ K - 1}) differ multiplicatively as k decreases. That is, any of the interface sensors disclosed in Patent Documents 1 to 4 has an unbalanced configuration in this regard. Considering that the factorization of M according to Equation (1) is not always uniquely determined, in the interface sensor disclosed in any of Patent Documents 1 to 4, the minimum value of the difference between the number of electrode pairs (or electrical conductors) connected to one conductor (excluding the conductor connected to all electrode pairs or electrical conductors included in the first sensor block) in the first sensor block and the number of electrode pairs (or electrical conductors) connected to one conductor (excluding the conductor connected to all electrode pairs or electrical conductors included in the K-th sensor block) in the K-th sensor block is given by Equation (7). For example, when M = 24 and K = 3, the factorization of M is M = 2 × 2 × 6 or M = 2 × 4 × 3 (note that the order of the factors is not considered). Therefore, F(M, K) = {{2, 6}, {2, 3, 4}}. Thus, the value of Equation (7) is 3.

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[0027] Therefore, for the j-th (j ∈ [J] = [Σ k∈[K]c(k)], c(k) is the maximum value max of the number t(j) of electrode pairs (or electrical conductors) connected to the conductors (excluding the e(k) electrode pairs or electrical conductors connected to the kth (k∈[K]) sensor block) in the set [J] of t(j) j∈[J] t(j)=max{e(1),...,e(J)} and the minimum value min j∈[J] If the difference between t(j)=min{e(1),...,e(J)} is smaller than the value of equation (7), the interface sensor can be said to have a well-balanced configuration compared to prior art interface sensors.

[0028] In short, a sufficient condition for the interface sensor disclosed herein to have a well-balanced configuration compared to prior art interface sensors is that, in an interface sensor having a configuration determined by the adopted code system and its specific code words, a) Regarding the number e(k) of electrode pairs (or electrical conductors) included in the kth (k∈[K]) sensor block included in the interface sensor, the maximum value max on the set [K] of the number e(k) k∈[K] e(k) and the minimum value min k∈[K] The difference in e(k) is smaller than the value of equation (6). or, b) The jth sensor included in the interface sensor (j∈[J]=[Σ k∈[K] c(k)], c(k) is the maximum value max of the number t(j) of electrode pairs (or electrical conductors) connected to the conductors (excluding the e(k) electrode pairs or electrical conductors connected to the kth (k∈[K]) sensor block) in the set [J] of t(j) j∈[J] t(j) and the minimum value min j∈[J] The difference of t(j) is smaller than the value of equation (7), is to be satisfied. Based on the analysis results of such prior art, embodiments of the interface sensor disclosed herein will be described.

[0029] [First Embodiment] The interface sensor 1 of the first embodiment is an interface sensor having a configuration determined by the adopted coding system and its specific code words. Regarding the number e(k) of electrode pairs included in the k-th (k ∈ [K]) sensor block included in the interface sensor, the maximum value max k∈[K] e(k) and the minimum value min k∈[K] The difference in e(k) is smaller than the value of Equation (6), and it has a configuration that is satisfied.

[0030] The interface sensor 1 of the first embodiment is a sensor for specifying the position of the interface between two types of substances (that is, a first substance and a second substance different from each other). The "interface" is the contact boundary between the first substance as a uniform phase and the second substance as a uniform phase. The "uniform phase" is an entity of a material system which is uniform in chemical composition and physical state. In other words, if the physical properties and chemical properties of any part V s of an entity of a certain material system are the same as those of any part W s which are different from the part V s of the entity of the material system, the entity of the material system is a "uniform phase". In order to accurately specify the position of the interface, the number of interfaces in the range from plane P(1) to plane P(M) to be described later must be 1 or 0. The interface sensor 1 includes Σ k∈[K] e(k) electrode pairs 5 and K + Σ k∈[K] c(k) conductors 7. Σ k∈[K]Each of the e(k) electrode pairs 5 is composed of two electrodes 5a and 5b. The identification of the position of the interface between the first substance and the second substance is achieved by utilizing the physical quantity generated in the electrode pair 5 according to the properties of the first substance or the second substance existing between the two electrodes 5a and 5b that constitute the electrode pair 5. Let the capacitance between two conductors with equal amounts of positive and negative charges be C, the electrical resistance between the two conductors be R, the permittivity of the medium between the two conductors be ε, and the electrical resistivity of the medium between the two conductors be ρ. Then, since the relationship RC = ερ holds, in the first embodiment, capacitance is adopted as the physical quantity generated in the electrode pair 5, and the description of the example in which electrical resistance is adopted as the physical quantity is omitted. A typical example of the interface sensor 1 is a sensor for identifying the position of the interface between a liquid (for example, water) as the first substance and a gas (for example, air) as the second substance.

[0031] The interface sensor 1 is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or having a configuration equivalent thereto. First, the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9" and its specific example will be described, and then the "equivalent configuration" and its specific example will be described.

[0032] <Condition 1> The interface sensor 1 includes K sensor blocks {B k : k ∈ [K]}. K is a predetermined integer satisfying 2 ≤ K < M. K preferably satisfies formula (8). Hereinafter, unless otherwise specified, the symbol sandwiching log2M represents the ceiling function. M is a predetermined integer satisfying 8 ≤ M except when K = 2, and is a predetermined odd number satisfying 9 ≤ M when K = 2. M determines the resolution of the interface sensor 1. That is, M coincides with the total number of the aforementioned "observation points".

Equation

[0033] The K sensor blocks {B k{B: k ∈ [K]} are formed on Q substrates 9 each having a flat plate shape without being limited to the following examples. Q is a predetermined integer satisfying 1 ≤ Q ≤ K. When Q < K, there are substrates 9 having two or more sensor blocks. In each example shown later, Q = 1. When Q ≥ 2, the Q substrates 9 may be arranged on one plane, may be arranged like angle steel or channel steel, or may be arranged like triangular pipes or square pipes without being limited to the following examples.

[0034] <Condition 2> For any k ∈ [K], among the K sensor blocks {B k : k ∈ [K]}, the k-th sensor block B k includes e(k) electrode pairs 5 and c(k) + 1 conducting wires 7. e(k) is a predetermined integer satisfying 1 ≤ e(k) < M. c(k) is a predetermined integer satisfying 2 ≤ c(k) ≤ e(k) except when e(k) = 1, and is 1 when e(k) = 1.

[0035] When e(k) ≠ 1, among the K sensor blocks {B k : k ∈ [K]}, the k-th sensor block B k The e(k) electrode pairs 5 included in have the same capacitance C with each other when the space between the electrodes 5a and 5b of each of the e(k) electrode pairs 5 is filled with, for example, a first substance. k The k-th sensor block B k The capacitance C of each of the e(k) electrode pairs 5 included in k may be the same as or different from the capacitance C of each of the e(j) electrode pairs 5 included in the j-th (j ≠ k) sensor block B j Each of the c(k) + 1 conducting wires 7 is a conducting wire drawn from any one of the K sensor blocks {B j : k ∈ [K]}, and as will be described later in relation to Condition 5, Σ that the interface sensor 1 has k k∈[K]It is connected to at least one of the e(k) electrode pairs 5. The c(k)+1 conducting wires 7 are connected to a measurement circuit described later. In the figure, for the sake of easy viewing of the figure, only some of the electrode pairs and some of the conducting wires are labeled.

[0036] <Condition 3> Σ that the interface sensor 1 has k∈[K] Each of the e(k) electrode pairs 5 is located on one of the M planes P(1),..., P(M) that do not coincide with each other and are parallel to each other. To each of the M planes P(1),..., P(M), Σ k∈[K] At least one of the e(k) electrode pairs 5 is located. That is, there is no plane among the M planes P(1),..., P(M) on which the electrode pair 5 is not located. The M planes P(1),..., P(M) are arranged in space in an order according to the order relation of the elements of the set [M] = {x ∈ N: 1 ≤ x ≤ M} (that is, the binary relation < on N (note that the binary relation < is a strict total order)). Specifically, between the first plane P(1) and the p-th plane P(p) (p ∈ {x ∈ N: 3 ≤ x ≤ M}), there exists a q-th plane P(q) (q ∈ {x ∈ N: 2 ≤ x ≤ p - 1}). More simply stated, when the normal direction of the M planes P(1),..., P(M) parallel to each other is called the first direction, the M planes P(1),..., P(M) are arranged in this order in the first direction. For any g ∈ {x ∈ N: 1 ≤ x ≤ M - 2} and any h ∈ {x ∈ N: g + 1 ≤ x ≤ M - 1}, the distance between the g-th plane P(g) and the g + 1-th plane P(g + 1) may be equal to the distance between the h-th plane P(h) and the h + 1-th plane P(h + 1), or may not be equal. For example, it is good to narrow the interval between adjacent planes in the measurement range where the position of the interface is to be specified more precisely. Note that when the first direction is the vertical direction, "plane" may be rephrased as, for example, "level".

[0037] <Condition 4> For any k ∈ [K], among the K sensor blocks {B k : k ∈ [K]}, the k-th sensor block B kWhen the i-th electrode pair 5 among the e(k) electrode pairs 5 included is located on the p-th plane P(p k,i ) of the M planes P(1),..., P(M), Equation (9) holds. Hereinafter, unless otherwise specified, the symbol "×" represents the direct product set, and A×B = {(a, b): a ∈ A ∧ b ∈ B}. k,i ) of the M planes P(1),..., P(M), Equation (9) holds. Hereinafter, unless otherwise specified, the symbol "×" represents the direct product set, and A×B = {(a, b): a ∈ A ∧ b ∈ B}.

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[0038] <Condition 5> For any (k, i) ∈ [K] × [e(k)], in the k-th sensor block B k : k ∈ [K]} of the K sensor blocks, one electrode 5a of the i-th electrode pair 5 among the e(k) electrode pairs 5 is connected to the s k -th conductor 7 among the c(k) + 1 conductors 7, and the other electrode 5b is connected to the (c(k) + 1)-th conductor 7 among the c(k) + 1 conductors 7. s k,i is represented by Equation (10). Hereinafter, unless otherwise specified, the symbol mod represents the remainder operation, and a mod b is the remainder obtained by dividing the dividend a by the divisor b in Euclidean division. In Equation (10), the dividend of the remainder operation is i - 1. In this example, one electrode 5a of the i-th (i ∈ [e(k)]) electrode pair 5 and the s k,i -th conductor 7 are connected to each other via the branch line 7x, and the other electrode 5b of the i-th (i ∈ [e(k)]) electrode pair 5 and the (c(k) + 1)-th conductor 7 are connected to each other via the branch line 7y. k,i -th conductor 7 are connected to each other via the branch line 7x, and the other electrode 5b of the i-th (i ∈ [e(k)]) electrode pair 5 and the (c(k) + 1)-th conductor 7 are connected to each other via the branch line 7y.

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[0039] <Condition 6> The non-negative integer g m,k is determined by Equation (11), and the codeword h(m) is the K non-negative integers g m,kWhen defined by Equation (12) as a sequence of (k ∈ [K]), Equation (13) or Equation (14) holds. Equation (12) means that the codeword h(m) is given as a sequence in which g m,k is arranged in ascending order of the order relation of k ∈ [K]. That is, h(m) = (g m,1 g m,2 ... g m,K ). In Equation (13) or Equation (14), h(m1) ≠ h(m2) means the mismatch between two codewords h(m1) and h(m2). The mismatch between two codewords is defined by Equation (15). Although the codeword is not limited to the concatenation of K non-negative integers, representing the codeword as the concatenation of K non-negative integers does not lose generality.

Number

[0040] Let the interval I(1) be one of the two half-spaces obtained by dividing the space by the plane P(1) and not containing the planes P(2),..., P(M), and let the interval I(m) (m ∈ {x ∈ N: 2 ≤ x ≤ M}) be the space region between the adjacent planes P(m - 1) and P(m), and let the interval I(M + 1) be one of the two half-spaces obtained by dividing the space by the plane P(M) and not containing the planes P(2),..., P(M). Clearly, there exists a bijection between the M + 1 codewords h(m) (m ∈ [M + 1]) and the M + 1 intervals I(m) (m ∈ [M + 1]). However, the image by the bijection of h(m) is I(m) (m ∈ [M + 1]). That is, a one-to-one correspondence holds between the M + 1 codewords h(m) (m ∈ [M + 1]) and the M + 1 intervals I(m) (m ∈ [M + 1]) in the interface sensor 1. Therefore, specifying the position of the interface by the interface sensor 1 is equivalent to specifying the interval, and specifying the interval is equivalent to determining a K-digit codeword based on the physical quantity generated in the electrode pair 5. In other words, by determining a K-digit codeword based on the physical quantity generated in the electrode pair 5, the interval where the interface exists can be specified. This will be described in detail as a method for specifying the position of the interface.

[0041] When Equation (14) holds, the codewords of interval I(1) and interval I(M + 1) are the same as each other. In this case, by measuring the capacitance of any one electrode pair included in any sensor block, the codewords of interval I(1) and interval I(M + 1) can be distinguished.

[0042] Regarding r(k) (k ∈ [K]) defined in Condition 6, when Equation (13) holds, Equation (16) holds, and when Equation (14) holds, Equation (17) holds.

Number

[0043] <Condition 7> max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) = 1 holds. Here, d H (h(m), h(m + 1)) is the Hamming distance between codeword h(m) and codeword h(m + 1). That is, the code system in the first embodiment is Gray code.

[0044] <Condition 8> From Condition 2, the k-th (k ∈ [K]) sensor block B k includes c(k) + 1 conducting wires 7. Therefore, for the total number of conducting wires 7 drawn from the interface sensor 1 to be less than the total number of observation points, that is, the number of planes M, it suffices that Equation (18) holds. By the way, according to Condition 5, in the k-th (k ∈ [K]) sensor block B k the (c(k) + 1)-th conducting wire 7 is connected to e(k) electrode pairs 5. That is, the (c(k) + 1)-th conducting wire 7 gives the reference potential to e(k) electrode pairs 5. Therefore, the (c(k) + 1)-th conducting wire 7 in the k-th (k ∈ [K]) sensor block B k and the (c(j) + 1)-th conducting wire 7 in the j-th (j ∈ [K], j ≠ k) sensor block B j may be connected to each other. In the extreme case, the K conducting wires 7—the k-th (k ∈ [K]) sensor block B kThe collection of the (c(k) + 1)-th conductors 7 in -- can be replaced by one conductor. Therefore, it is sufficient if Equation (19) holds. [Number]

[0045] <Condition 9> Equation (20) holds. Equation (20) corresponds to the above-mentioned condition a). The left side of the inequality in Equation (20) is the maximum value max k on the set [K] of the number e(k) of electrode pairs 5 included in the k-th (k ∈ [K]) sensor block B included in the interface sensor 1 k∈[K] e(k) and the minimum value min k∈[K] e(k). The right side of the inequality in Equation (20) is the same as Equation (6). The value of K in the right side of the inequality in Equation (20) is the same as the value of K in the left side of the inequality in Equation (20). The set F(M, K) is a set having as an element the sum set of singleton sets each having as an element each of the K factors n(k) (k ∈ [K]) of M excluding 1. Note again that the factorization of M is not necessarily uniquely determined. For example, when M = 24 and K = 3, the factorization of M using the K factors excluding 1 is M = 2 × 2 × 6 or M = 2 × 4 × 3 (note that the order of the factors is not considered). Therefore, F(M, K) = {{2, 6}, {2, 3, 4}}. The symbol F of the set F(M, K) is represented in calligraphy in the mathematical formula. The element F of the set F(M, K) is represented by a German letter in the mathematical formula. When M is not represented as the product of K factors excluding 1, the inequality in Equation (20) holds (vacuous truth). [Number]

[0046] [Example of symbol system] As an example, M = 2 KWhen - 1 holds, the code system that gives the codeword h(m) (m ∈ [M + 1]) is a K - digit max({r(k): k ∈ [K]}) - ary counting sequence. Further, as another example, when r(k)=2 for any k ∈ [K] in condition 6, the code system that gives the codeword h(m) (m ∈ [M + 1]) is a K - digit binary Gray code. Further, d H When (h(M + 1), h(1)) = 1 holds, the code system that gives the codeword h(m) (m ∈ [M + 1]) is cyclic. Please refer to Document A for such a code system. (Document A) I Nengah SUPARTA, "Counting Sequences, Gray Codes and Lexicodes", Dissertation at Delft University of Technology, 2006, ISBN 90 - 8559 - 176 - 7

[0047] [Design] An example of the design of the interface sensor 1 will be briefly described. The essence (groundwork) of the design of the interface sensor 1 is to determine the codeword h(m) (m ∈ [M + 1]). When the code system that gives the codeword h(m) (m ∈ [M + 1]) is, for example, balanced Gray codes or uniform counting sequences, the process of determining the codeword h(m) (m ∈ [M + 1]) is disclosed in Document A (In Document A, some examples of balanced Gray codes or uniform counting sequences as transition sequences (for example, see Example 3.2.6) are disclosed). Once balanced Gray codes or uniform counting sequences are determined, it is easy to design the interface sensor 1 that satisfies conditions 1 - 9. For example, when a codeword h(m) (m ∈ [M + 1]) with a predetermined number of digits of 3 or more as balanced Gray codes is determined, K is the number of digits of the codeword h(m) (m ∈ [M + 1]), and M = 2K -1 and condition 7 are naturally determined, and e(k) (k ∈ [K]) is determined from the transition counts of the k-th digit of the codeword h(m) (m ∈ [M + 1]) (that is, the total number of changes from 0 to 1 and from 1 to 0), and the above-mentioned plane P(p k,i )(i ∈ [e(k)]) is determined as the position of the transition (that is, the change from 0 to 1 or from 1 to 0) in the k-th digit of the codeword h(m) (m ∈ [M + 1]). Furthermore, by adopting c(k) = r(k) = 1 + max({g m,k : m ∈ [M + 1]}) = 2 (k ∈ [K]), the interface sensor 1 satisfying conditions 1 to 9 can be easily designed. Let the entire set of configurations of the interface sensor 1 satisfying conditions 1 to 9 be X1, and the entire set of configurations of the interface sensor 1 determined by the balanced Gray codes or uniform counting sequences disclosed in Document A be X2. Then X2 ⊂ X1 holds, but the converse does not hold. Therefore, the configuration of the interface sensor 1 satisfying conditions 1 to 9 is not limited to the configuration of the interface sensor 1 determined by the balanced Gray codes or uniform counting sequences disclosed in Document A.

[0048] Some examples of the interface sensor 1 of the first embodiment will be described with reference to the drawings. In each figure, for the sake of easy viewing of the drawings, when there are two or more identical components, signs are attached to one or more components that are not all of the two or more identical components.

[0049] Fig. 7 shows the first example of the first embodiment. In the first example, K = 4 M = 15 e(1) = 4, e(2) = 3, e(3) = 4, e(4) = 4, Σ k∈[K] e(k) = 15 c(1) = 2, c(2) = 2, c(3) = 2, c(4) = 2 p 1,1 = 4, p 1,2 = 9, p 1,3 = 11, p 1,4 = 14 p 2,1 =3, p 2,2 =5, p 2,3 =10 p 3,1 =2, p 3,2 =6, p 3,3 =8, p 3,4 =12 p 4,1 =1, p 4,2 =7, p 4,3 =13, p 4,4 =15 s 1,1 =1, s 1,2 =2, s 1,3 =1, s 1,4 =2 s 2,1 =1, s 2,2 =2, s 2,3 =1 s 3,1 =1, s 3,2 =2, s 3,3 =1, s 3,4 =2 s 4,1 =1, s 4,2 =2, s 4,3 =1, s 4,4 =2 r(1) = 2, r(2) = 2, r(3) = 2, r(4) = 2 h(16) = 0100 h(15) = 0101 h(14) = 1101 h(13) = 1100 h(12) = 1110 h(11) = 0110 h(10) = 0010 h(9) = 1010 h(8) = 1000 h(7) = 1001 h(6) = 1011 h(5) = 1111 h(4) = 0111 h(3) = 0011 h(2) = 0001 h(1) = 0000 max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) = 1 This is the case. It can be easily confirmed that equations (13), (16), and (19) hold. Since M is not expressed as the product of K factors excluding 1, equation (20) holds (vacuous truth). The code system of the first example is cyclic 4-bit binary Gray codes.

[0050] Fig. 8 shows a second example of the first embodiment. In the second example, K = 3 M = 23 e(1) = 8, e(2) = 8, e(3) = 7, Σ k∈[K] e(k) = 23 c(1) = 3, c(2) = 2, c(3) = 4 p 1,1 = 5, p 1,2 = 8, p 1,3 = 10, p 1,4 = 11, p 1,5 = 14, p 1,6 = 16, p 1,7 = 18, p 1,8 = 20 p 2,1 = 4, p 2,2 = 6, p 2,3 = 9, p 2,4 = 13, p 2,5 = 15, p 2,6 = 19, p 2,7 = 21, p 2,8 = 23 p 3,1 = 1, p 3,2 = 2, p 3,3 = 3, p 3,4 = 7, p 3,5 = 12, p 3,6 = 17, p 3,7 = 22 s 1,1 = 1, s 1,2 = 2, s 1,3 = 3, s 1,4 = 1, s 1,5 = 2, s 1,6 = 3, s 1,7 = 1, s 1,8 = 2 s 2,1 = 1, s 2,2 = 2, s 2,3 = 1, s 2,4 = 2, s 2,5 = 1, s2,6 = 2, s 2,7 = 1, s 2,8 = 2 s 3,1 = 1, s 3,2 = 2, s 3,3 = 3, s 3,4 = 4, s 3,5 = 1, s 3,6 = 2, s 3,7 = 3 r(1) = 3, r(2) = 2, r(3) = 4 h(24) = 203 h(23) = 213 h(22) = 212 h(21) = 202 h(20) = 102 h(19) = 112 h(18) = 012 h(17) = 011 h(16) = 211 h(15) = 201 h(14) = 101 h(13) = 111 h(12) = 110 h(11) = 010 h(10) = 210 h(9) = 200 h(8) = 100 h(7) = 103 h(6) = 113 h(5) = 013 h(4) = 003 h(3) = 002 h(2) = 001 h(1) = 000 max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) = 1 That is. It can be easily confirmed that equations (13), (16), and (19) hold. Since M is not expressed as the product of K factors excluding 1, equation (20) holds (vacuous truth). The coding system of the second example is a 3-digit maximum quaternary code.

[0051] Figure 9 shows the third example of the first embodiment. In the third example, K = 5 M = 32 e(1) = 6, e(2) = 6, e(3) = 6, e(4) = 6, e(5) = 8, Σ k∈[K] e(k) = 32 c(1) = 2, c(2) = 2, c(3) = 2, c(2) = 2, c(3) = 2 p 1,1 = 2, p 1,2 = 8, p 1,3 = 12, p 1,4 = 17, p 1,5 = 27, p 1,6 = 32 p 2,1 = 6, p 2,2 = 14, p 2,3 = 20, p 2,4 = 22, p 2,5 = 25, p 2,6 = 31 p 3,1 = 3, p 3,2 = 9, p 3,3 = 16, p 3,4 = 18, p 3,5 = 21, p 3,6 = 29 p 4,1 = 5, p 4,2 = 7, p 4,3 = 11, p 4,4 = 23, p 4,5 = 26, p 4,6 = 28 p 5,1 = 1, p 5,2 = 4, p 5,3 = 10, p 5,4 = 13, p 5,5 = 15, p 5,6 = 19, p 5,7 = 24, p 5,8 = 30 s 1,1 = 1, s 1,2 = 2, s 1,3 = 1, s 1,4 = 2, s 1,5 = 1, s 1,6 = 2 s 2,1 = 1, s 2,2 = 2, s 2,3 = 1, s 2,4 = 2, s 2,5 = 1, s 2,6 = 2 s3,1 =1, s 3,2 =2, s 3,3 =1, s 3,4 =2, s 3,5 =1, s 3,6 =2 s 4,1 =1, s 4,2 =2, s 4,3 =1, s 4,4 =2, s 4,5 =1, s 4,6 =2 s 5,1 =1, s 5,2 =2, s 5,3 =1, s 5,4 =2, s 5,5 =1, s 5,6 =2, s 5,7 =1, s 5,8 =2 r(1) = 2, r(2) = 2, r(3) = 2 h(33) = 00000 = h(1) h(32) = 10000 h(31) = 11000 h(30) = 11001 h(29) = 11101 h(28) = 11111 h(27) = 01111 h(26) = 01101 h(25) = 00101 h(24) = 00100 h(23) = 00110 h(22) = 01110 h(21) = 01010 h(20) = 00010 h(19) = 00011 h(18) = 00111 h(17) = 10111 h(16) = 10011 h(15) = 10010 h(14) = 11010 h(13) = 11011 h(12) = 01011 h(11) = 01001 h(10) = 01000 h(9) = 01100 h(8) = 11100 h(7) = 11110 h(6) = 10110 h(5) = 10100 h(4) = 10101 h(3) = 10001 h(2) = 00001 h(1) = 00000 max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) = 1 That is. It can be easily confirmed that equations (14), (17), and (19) hold. Since the factorization of M using K factors excluding 1 is only M = 2 × 2 × 2 × 2 × 2, F(M, K) = {{2}}. Therefore, equation (20) holds. The code system of the third example is 5-bit binary balanced Gray codes.

[0052] [Method and Algorithm for Specifying the Position of the Interface] Next, an example of a method for specifying the position of the interface using the interface sensor 1 will be described. In the following example, for any k ∈ [K], 2 ≤ e(k) and 2 ≤ c(k). In the k-th sensor block B k (k ∈ [K]), a measurement circuit (not shown) for measuring capacitance is connected to each of the electrode pairs 5 connected to the s k (s k ∈ [c(k) - 1])-th conductor 7. The synthesis (e.g., synthesized capacitance) C(s k ) of the physical quantities generated in each of the electrode pairs 5 and the synthesis (e.g., synthesized capacitance) C(s k +1) of the physical quantities generated in each of the electrode pairs 5 connected to the s k +1-th conductor 7 are measured, and the difference C(s k ) - C(s k +1) is compared with the threshold value δ. The threshold value δ is determined in advance considering the relative permittivity of the first substance, the relative permittivity of the second substance, the measurement error, the number of electrode pairs 5 connected to one conductor 7, etc. As a result of the comparison, when C(s k ) - C(s k +1) ≥ δ holds, the k-th non-negative integer of the code word h(m) (m ∈ [M + 1]) is s kis determined. Note that s k ∈[c(k)-1], if C(s k ) - C(s k +1)≧δ does not hold, the k-th non-negative integer of the codeword h(m) (m∈[M + 1]) is determined to be 0. By performing such measurement processing in each sensor block B k (k∈[K]), a K-digit codeword is uniquely determined. Among the M + 1 codewords h(m) (m∈[M + 1]), there is an interface in the interval corresponding to the same codeword h(m) as the uniquely determined K-digit codeword. For example, in the interface sensor 1 shown in FIG. 7, when the K-digit codeword is determined to be 1010 as a result of the measurement processing, the interface exists in the interval I(9) (that is, between the plane P(8) and the plane P(9)). Note that when the K-digit codeword is 0000, since the interface exists in the interval I(1), it has not reached the plane P(1), and when the K-digit codeword is 0100, since the interface exists in the interval I(16), it has exceeded the plane P(15). The one-to-one correspondence between the M + 1 codewords h(m) (m∈[M + 1]) and the M + 1 intervals I(m) (m∈[M + 1]) is stored in a memory (not shown) as a look-up table, and an arithmetic circuit (not shown) specifies the interval corresponding to the K-digit codeword obtained by the measurement processing of the measurement circuit by referring to the look-up table.

[0053] The measurement circuit may be a component of the interface sensor 1 or may be an independent physical entity from the interface sensor 1. In the latter case, the measurement circuit may be a component of the liquid level gauge including the interface sensor 1. The measurement circuit measures C(s k ) for each s k ∈[c(k)], and the difference C(s k ) - C(s k ) for each s kIt is not limited to a measurement circuit including a comparator that compares with (+1) and a threshold value δ, and may further include an AC signal generator that generates an AC signal to be applied to the (c(k)+1)-th conductor 7 for each k∈[K], or may be a measurement circuit of the prior art, or may be a measurement circuit including a PLD (programmable logic device). Examples of PLDs include FPGAs (field-programmable gate arrays).

[0054] Table 1 shows an algorithm for specifying the position of the interface using the interface sensor 1. The exemplary algorithm is an algorithm corresponding to the above-described position specifying method. In the algorithm, h = "" represents setting an empty character for h, and h = h + g represents obtaining a new code word h which is a code word obtained by concatenating the non-negative integer g as a character to the code word h. LOOKUP(h, TABLE) represents a process of determining the section corresponding to the code word h by referring to TABLE. The section, that is, the position of the interface, is specified by this algorithm. Note that the exemplary TABLE is based on the example shown in FIG. 7. [Table 1]

[0055] [Variation 1] A method for easily creating a variation from one embodiment in the case of a cyclic code system or when h(1)=h(M + 1) is explained.

[0056] Step A) In the case of a cyclic code system, to make the explanation more specific, as an example, the first example shown in FIG. 7 is adopted. In the first example shown in FIG. 7, M = 15. The first example shown in FIG. 7 has a cyclic code system. In the case of a cyclic code system, one new electrode pair 5 is added to the (M + 1)-th plane P(M + 1). As a result, a codeword h(M + 2) is also added. The added codeword h(M + 2) is the same as the codeword h(1). The sensor block to which one new electrode is added is the k-th sensor block B determined by k in Equation (21) under the condition of h(1) = h(M + 2). k That is. In this example, since k = 2, one new electrode is added to the second sensor block B2 (see FIG. 10). The configuration shown in FIG. 10 is also an example of the first embodiment. [Number]

[0057] Step B) In the configuration obtained by adding one new electrode pair 5 to the (M + 1)-th plane P(M + 1), the M + 1 codewords h(m) (m ∈ [M + 1]) excluding the codeword h(M + 2) are shifted by a ∈ N. That is, if the M + 1 codewords in the variation configuration are h v (m) (m ∈ [M + 1]), then h v (m) = h(1 + ((M + m - a) mod (M + 1))) (m ∈ [M + 1]) h v (M + 2) = h(1) That is, specifically, when a = 5, h v (17) = h(1) = 0000 h v (16) = h(11) = 0110 h v (15) = h(10) = 0010 h v (14) = h(9) = 1010 h v (13) = h(8) = 1000 h v(12) = h(7) = 1001 h v (11) = h(6) = 1011 h v (10) = h(5) = 1111 h v (9) = h(4) = 0111 h v (8) = h(3) = 0011 h v (7) = h(2) = 0001 h v (6) = h(1) = 0000 h v (5) = h(16) = 0100 h v (4) = h(15) = 0101 h v (3) = h(14) = 1101 h v (2) = h(13) = 1100 h v (1) = h(12) = 1110 is as follows.

[0058] Regarding condition 6), h(1) must be a concatenation of K zeros, but the codeword h v (1) is not a concatenation of K zeros. However, by applying the remainder operation of the divisor r(k) to each digit of the codeword h v (m) (m ∈ [M + 1]), the codeword h v (m) (m ∈ [M + 1]) can be rewritten as a codeword h r (m) (m ∈ [M + 1]) that satisfies condition 6). Specifically, if the k-th non-negative integer of the m-th codeword h v (m) is g v m,k then the codeword h r (m) (m ∈ [M + 1]) is obtained by Equation (22). Specifically, in this example, r(1) = 2, r(2) = 2, r(3) = 2, r(4) = 2, g v 1,1 = 1, g v 1,2 = 1, g v 1,3 = 1, g v1,4 Since it is = 0, h r (17) = 0000 h r (16) = 1000 h r (15) = 1100 h r (14) = 0100 h r (13) = 0110 h r (12) = 0111 h r (11) = 0101 h r (10) = 0001 h r (9) = 1001 h r (8) = 1101 h r (7) = 1111 h r (6) = 1110 h r (5) = 1010 h r (4) = 1011 h r (3) = 0011 h r (2) = 0010 h r (1) = 0000 is obtained. These codewords are shown in FIG. 11.

Number

[0059] The configuration of this variation is shown in FIG. 11. Since the codeword h r (m) (m ∈ [M + 2]) is determined, as described above, e(k) (k ∈ [K]) is determined from the k-th digit transition counts of the codeword h r (m) (m ∈ [M + 2]) (that is, the total number of non-negative integer changes), and the above-mentioned plane P(p k,i )(i ∈ [e(k)]) is the codeword h rIt is determined as the position of the transition (i.e., the change of non - negative integers) in the k - th digit of (m) (m ∈ [M + 2]). Further, by adopting c(k)=r(k)=1 + max({g m,k :m ∈ [M + 2]})(k ∈ [K]), the interface sensor 1 satisfying conditions 1 - 9 can be easily designed. In the configuration of the variation shown in FIG. 11, K = 4 M = 16 e(1)=4, e(2)=4, e(3)=4, e(4)=4, Σ k∈[K] e(k)=16 c(1)=2, c(2)=2, c(3)=2, c(4)=2 p 1,1 =3, p 1,2 =9, p 1,3 =14, p 1,4 =16 p 2,1 =5, p 2,2 =8, p 2,3 =10, p 2,4 =15 p 3,1 =1, p 3,2 =7, p 3,3 =11, p 3,4 =13 p 4,1 =2, p 4,2 =4, p 4,3 =6, p 4,4 =12 s 1,1 =1, s 1,2 =2, s 1,3 =1, s 1,4 =2 s 2,1 =1, s 2,2 =2, s 2,3 =1, s 2,4 =2 s 3,1 =1, s 3,2 =2, s 3,3 =1, s 3,4 =2 s 4,1 =1, s 4,2 =2, s 4,3 =1, s 4,4 =2 r(1)=2, r(2)=2, r(3)=2 max({d H (h(m),h(m + 1)):∀m ∈ [M]}) = 1 is true. Since the total number of variations by this method matches the possible values of the shift number, it is M + 1. In the configuration shown in FIG. 11, it can be easily confirmed that equations (14), (17), and (19) hold. Note that in this example, M appearing in equations (14), (17), and (19) is the value of M + 1 (i.e., M + 1 = 15 + 1 = 16). Since the factorization of M + 1 using K factors excluding 1 is only M + 1 = 2 × 2 × 2 × 2 × 2, F(M, K) = {{2}}. Therefore, equation (20) holds. The coding system of this example is 4 - bit binary balanced Gray codes.

[0060] An example of the configuration obtained by removing the electrode pair 5 located on the plane P(16) from the configuration example shown in FIG. 11 is also an example of the first embodiment.

[0061] When h(1) = h(M + 1) is satisfied, to obtain the variation configuration, only step B) needs to be performed. Specifically, shift the M codewords h(m) (m ∈ [M]) except for the codeword h(M + 1) by a ∈ N. That is, if the M codewords in the variation configuration are h v (m) (m ∈ [M]), then h v (m) = h(1 + ((M + m - a - 1) mod (M))) (m ∈ [M]) h v (M + 1) = h(1) is true. The conversion from the codeword h v (m) (m ∈ [M]) to the codeword h r (m) (m ∈ [M]) follows equation (22).

[0062] [Variation 2] Another method for easily creating its variation from a certain example will be described. In the second direction orthogonal to the first direction, by rearranging the K sensor blocks {B k : k ∈ [K]}, variations can be obtained. The K sensor blocks {Bk : The total number of possible arrangement patterns of {k ∈ [K]} is K!, that is, Π k=1 K k.

[0063] [Equivalent configurations related to the first embodiment] Next, "configurations equivalent to the configuration that satisfies all of condition 1, condition 2, condition 3, condition 4, condition 5, condition 6, condition 7, condition 8, and condition 9" and specific examples thereof will be described. "Configurations equivalent to the configuration that satisfies all of condition 1, condition 2, condition 3, condition 4, condition 5, condition 6, condition 7, condition 8, and condition 9" are configurations that have different configurations from "the configuration that satisfies all of condition 1, condition 2, condition 3, condition 4, condition 5, condition 6, condition 7, condition 8, and condition 9" but have the same function from the perspective of an electric circuit. Since it is impossible to list all "equivalent configurations", in addition, since a person skilled in the art can easily implement various equivalent configurations, only some examples of the "equivalent configurations" of the first example of the first embodiment will be described.

[0064] max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) is less than K, the electrode pairs 5 can be arranged in Y columns. Y is an integer that satisfies max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) ≤ Y ≤ K - 1. In the first example of the first embodiment, since max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) = 1, 1 ≤ Y ≤ K - 1 = 3. Therefore, the electrode pairs 5 can be arranged in 1 column. This configuration is shown in FIG. 12.

[0065] Furthermore, as described in <condition 8>, since the collection of the (c(k) + 1)-th conductor 7 in the K conductors 7 - the k-th (k ∈ [K]) sensor block B k can be replaced with 1 conductor, the configuration shown in FIG. 12 may be changed to the configuration shown in FIG. 13.

[0066] [Second embodiment] The interface sensor 2 of the second embodiment is an interface sensor having a configuration determined by the adopted coding system and its specific code words, and with respect to the number t(j) of electrode pairs connected to the j-th conductor (j ∈ [J] = [Σ k∈[K] c(k)]) (excluding the conductors connected to the e(k) electrode pairs or electrical conductors included in the k-th sensor block (k ∈ [K])), the difference between the maximum value max j∈[J] t(j) and the minimum value min j∈[J] t(j) on the set [J] of the number t(j) is smaller than the value of Equation (7). In this regard, the second embodiment is different from the first embodiment.

[0067] Here, the substantial differences between the first and second embodiments are explained, and for other technical matters, the description of the first embodiment is applied mutatis mutandis to the description of the second embodiment. Therefore, the description of the first embodiment, except for the substantial differences, is incorporated herein mutatis mutandis by making the necessary changes. By applying the description of the first embodiment mutatis mutandis to the description of the second embodiment, for example, "interface sensor 1" is changed to "interface sensor 2".

[0068] The interface sensor 2 of the second embodiment is a sensor having a configuration that satisfies all of the following Conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent thereto. First, the configuration of "satisfying all of Conditions 1, 2, 3, 4, 5, 6, 7, and 8" and its specific example are explained, and then the "equivalent configuration" and its specific example are explained.

[0069] <Condition 1> to <Condition 7> Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, and Condition 6 in the second embodiment are the same as Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, and Condition 6 in the first embodiment, respectively. Condition 7 in the second embodiment is the same as Condition 8 in the first embodiment. Therefore, the descriptions of Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, and Condition 8 in the first embodiment are applied mutatis mutandis to the descriptions of Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, and Condition 7 in the second embodiment. In the second embodiment, Condition 7 and Condition 9 in the first embodiment are unnecessary. Condition 8 in the second embodiment is as follows.

[0070] <Condition 8> Equation (23) holds. Equation (23) corresponds to the above-mentioned condition b). The set S is the union of the sets Z(k) and is defined by Equation (24). The set S and the set Z(k) are represented by German letters in the mathematical formula. The symbol a|b represents that the integer a is a divisor of the integer b. The combined symbol of the symbol | and the symbol / represents that the integer on the left of the combined symbol is not a divisor of the integer on the right of the combined symbol. The left side of the inequality in Equation (23) is the maximum value max k∈[K] t(j) of the number t(j) of electrode pairs 5 connected to the j-th (j ∈ [J] = [Σ j∈[J] c(k)]) conductor 7 (excluding the conductors connected to the e(k) electrode pairs or electrical conductors included in the k-th (k ∈ [K]) sensor block) in the interface sensor 2, with respect to the set [J] of the number t(j), and the minimum value min j∈[J] t(j) is specifically represented using sets. The right side of the inequality in Equation (23) is the same as Equation (7). When M is not represented as the product of K - 1 factors excluding 1, the inequality in Equation (23) holds (vacuous truth).

Number

[0071] With reference to the drawings, some examples of the interface sensor 2 of the second embodiment will be described. In each figure, in consideration of the legibility of the drawings, when there are two or more identical components, reference numerals are attached to one or more components that are not all of the two or more identical components.

[0072] The first example of the second embodiment is the configuration shown in FIG. 7, the second example is the configuration shown in FIG. 8, the third example is the configuration shown in FIG. 9, the fourth example is the configuration shown in FIG. 10, and the fifth example is the configuration shown in FIG. 11. In the configuration shown in FIG. 7, since M is not represented as the product of K factors excluding 1, Equation (23) holds (vacuous truth). In the configuration shown in FIG. 8, since M is not represented as the product of K factors excluding 1, Equation (23) holds (vacuous truth). In the configuration shown in FIG. 9, since the factorization of M using K factors excluding 1 is only M = 2×2×2×2×2, F(M, K) = {{2}}. Furthermore, S = {3, 4}. Therefore, Equation (23) holds. In the configuration shown in FIG. 10, since the factorization of M using K factors excluding 1 is only M = 2×2×2×2, F(M, K) = {{2}}. Furthermore, S = {2}. Therefore, Equation (23) holds. In the configuration shown in FIG. 11, since the factorization of M using K factors excluding 1 is only M = 2×2×2×2, F(M, K) = {{2}}. Furthermore, S = {2}. Therefore, Equation (23) holds. These examples of the interface sensor 2 of the second embodiment include the examples of the interface sensor 1 of the first embodiment, but the second embodiment does not necessarily mean that it includes the first embodiment.

[0073] FIG. 14 shows a sixth example of the second embodiment. In the sixth example, K = 4 M = 15 e(1) = 8, e(2) = 7, e(3) = 8, e(4) = 7, Σ k∈[K] e(k) = 30 c(1) = 2, c(2) = 2, c(3) = 2, c(4) = 2 p 1,1 = 1, p 1,2 = 2, p 1,3 = 4, p 1,4 = 8, p 1,5 = 9, p1,6 = 10, p 1,7 = 12, p 1,8 = 14 p 2,1 = 3, p 2,2 = 5, p 2,3 = 6, p 2,4 = 9, p 2,5 = 12, p 2,6 = 13, p 2,7 = 14 p 3,1 = 1, p 3,2 = 4, p 3,3 = 7, p 3,4 = 8, p 3,5 = 10, p 3,6 = 11, p 3,7 = 12, p 3,8 = 15 p 4,1 = 1, p 4,2 = 2, p 4,3 = 6, p 4,4 = 7, p 4,4 = 9, p 4,4 = 13, p 4,4 = 14 s 1,1 = 1, s 1,2 = 2, s 1,3 = 1, s 1,4 = 2, s 1,5 = 1, s 1,6 = 2, s 1,7 = 1, s 1,8 = 2 s 2,1 = 1, s 2,2 = 2, s 2,3 = 1, s 2,4 = 2, s 2,5 = 1, s 2,6 = 2, s 2,7 = 1 s 3,1 = 1, s 3,2 = 2, s 3,3 = 1, s 3,4 = 2, s 3,5 = 1, s 3,6 = 2, s 3,7 = 1, s 3,8 = 2 s 4,1 = 1, s 4,2 = 2, s 4,3 = 1, s 4,4 = 2, s 4,5 = 1, s4,6 = 2, s 4,7 = 1 r(1) = 2, r(2) = 2, r(3) = 2, r(4) = 2 h(16) = 0101 h(15) = 0111 h(14) = 1010 h(13) = 1111 h(12) = 0001 h(11) = 0011 h(10) = 1001 h(9) = 0100 h(8) = 1110 h(7) = 1101 h(6) = 1000 h(5) = 1100 h(4) = 0110 h(3) = 0010 h(2) = 1011 h(1) = 0000 max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) = 3 It can be easily confirmed that equations (13), (16), and (19) hold. Since M is not represented as the product of K factors excluding 1, equation (23) holds. The column h(m) in the sixth example is a 4-bit binary counting sequence.

[0074] The descriptions of [Example of coding system], [Design], [Method and algorithm for specifying the position of the interface], [Variation 1], and [Variation 2] in the first embodiment are applied mutatis mutandis to the descriptions of [Example of coding system], [Design], [Method and algorithm for specifying the position of the interface], [Variation 1], and [Variation 2] in the second embodiment.

[0075] [Equivalent configurations related to the second embodiment] Next, a configuration "equivalent to a configuration that satisfies all of Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, and Condition 8" and specific examples thereof will be described. A configuration "equivalent to a configuration that satisfies all of Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, and Condition 8" has a configuration different from the "configuration that satisfies all of Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, and Condition 8", but has the same function from the viewpoint of an electric circuit. Since it is impossible to enumerate all "equivalent configurations", and in addition, a person skilled in the art can easily implement various equivalent configurations, only an example of the "equivalent configuration" of the sixth example of the second embodiment will be described.

[0076] max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) is less than K, the electrode pairs 5 can be arranged in Y columns. Y is an integer that satisfies max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) ≤ Y ≤ K - 1. In the sixth example of the second embodiment, since max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) = 3, 3 ≤ Y ≤ K - 1 = 3. Therefore, the electrode pairs 5 can be arranged in 3 columns. Further, the collection of the (c(k) + 1)-th conductors 7 among the K conductors 7--the k-th (k ∈ [K]) in the sensor block B k can be replaced with one conductor. Therefore, the example of the "equivalent configuration" of the sixth example (FIG. 14) of the second embodiment has the configuration shown in FIG. 15.

[0077] [Third Embodiment] The interface sensor 3 of the third embodiment is different from the first embodiment in that all the other electrodes 5b are replaced with the first electrical conductor. Therefore, here, the substantial differences between the first embodiment and the third embodiment will be described, and for other technical matters, the description of the first embodiment will be applied mutatis mutandis to the description of the third embodiment. Therefore, the description of the first embodiment, except for the substantial differences, is incorporated herein by changing what should be changed (mutatis mutandis). By applying the description of the first embodiment to the description of the third embodiment, for example, "interface sensor 1" is rephrased as "interface sensor 3".

[0078] The interface sensor 3 of the third embodiment includes, as will be described later, the first electrical conductor 50a and Σ k∈[K] e(k) second electrical conductors 50b and the conducting wire 70. Between the first electrical conductor 50a and Σ k∈[K] e(k) second electrical conductors 50b, Σ k∈[K] e(k) electrode pairs are formed. The identification of the position of the interface between the first substance and the second substance is achieved by utilizing the physical quantity generated in the electrode pair according to the property of the first substance or the second substance existing between the two electrodes constituting the electrode pair (that is, the first electrical conductor 50a and any one of the Σ k∈[K] e(k) second electrical conductors 50b). For the reasons described above, capacitance is adopted as the physical quantity generated in the electrode pair, and the description of the example in which electrical resistance is adopted as the physical quantity is omitted.

[0079] The interface sensor 3 is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, 9, or a configuration equivalent thereto. First, the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, 8, 9" and its specific example will be described, and later, the "equivalent configuration" and its specific example will be described.

[0080] <Condition 1> The interface sensor 3 includes the first electrical conductor 50a and K sensor blocks {B k: k ∈ [K]}, where K is a predetermined integer satisfying 2 ≤ K < M. K preferably satisfies the above formula (8). M is a predetermined integer satisfying 8 ≤ M except when K = 2, and is a predetermined odd integer satisfying 9 ≤ M when K = 2. M determines the resolution of the interface sensor 3. That is, M corresponds to the total number of the above-mentioned "observation points".

[0081] The first electrical conductor 50a is, for example, a metal. The first electrical conductor 50a may be a single electrical conductor or may include two or more electrical conductors.

[0082] When the first electrical conductor 50a is a single electrical conductor, the shape of the first electrical conductor 50a is not limited to the following examples and may be a flat plate or a cylinder. When the first electrical conductor 50a has a cylindrical shape, the cross-sectional shape of the cylinder in a cross-section perpendicular to the longitudinal direction of the cylinder is, for example, a circle or a rectangle. When the first electrical conductor 50a has a cylindrical shape, the K sensor blocks {B k : k ∈ [K]} are usually arranged inside the first electrical conductor 50a, but this is not the case.

[0083] When the first electrical conductor 50a includes two or more electrical conductors, the shape of each of the electrical conductors included in the first electrical conductor 50a is not limited to the following examples and may be a flat plate or the shape of each component for constituting the above-mentioned cylinder (for example, the shape of an object obtained by cutting the above-mentioned cylinder in a direction perpendicular to its longitudinal direction (that is, a cylinder shorter than the above-mentioned cylinder), the shape of an object obtained by cutting the above-mentioned cylinder in its longitudinal direction (for example, in the case of a cylinder, a 1 / 4 cylinder shape)). When the first electrical conductor 50a includes two or more electrical conductors, the two or more electrical conductors may be independent of each other. However, it is desirable that the two or more electrical conductors included in the first electrical conductor 50a have the same potential as each other, for example, by contacting each other.

[0084] Hereinafter, from the perspective of ease of understanding of the interface sensor 3, in the example shown in FIG. 16 and the example shown in FIG. 17, the first electrical conductor 50a is one electrical conductor. In FIGS. 16 and 17, for ease of viewing the figure, the edge of the first electrical conductor 50a is explicitly illustrated, and the first electrical conductor 50a is drawn as if it were transparent.

[0085] <Condition 2> For any k ∈ [K], among the K sensor blocks {B k : k ∈ [K]}, the k-th sensor block B k includes e(k) second electrical conductors 50b and c(k) conductive wires 70. e(k) is a predetermined integer satisfying 1 ≤ e(k) < M. c(k) is a predetermined integer satisfying 2 ≤ c(k) ≤ e(k) except when e(k) = 1, and is 1 when e(k) = 1.

[0086] The K sensor blocks {B k : k ∈ [K]} are formed on Q substrates 9 having a flat plate shape without being limited to the following example. That is, the second electrical conductors 50b and the conductive wires 70 are formed on the substrate 9. The substrate 9 is waterproof-coated except for the second electrical conductor 50b. Q is a predetermined integer satisfying 1 ≤ Q ≤ K. When Q < K, there are substrates 9 having two or more sensor blocks. In the example shown in FIG. 16 and the example shown in FIG. 17, Q = 1. When Q ≥ 2, the Q substrates 9 may be arranged on one plane, may be arranged like angle steel or channel steel, or may be arranged like triangular pipes or square pipes without being limited to the following example.

[0087] The second electrical conductor 50b is, for example, metal. The shape of the second electrical conductor 50b may be a rectangular flat plate or a circular flat plate without being limited to the following example. The k-th (k ∈ [K]) sensor block B kIn this case, e(k) electrode pairs are formed between the first electrical conductor 50a and the e(k) second electrical conductors 50b. When e(k) ≠ 1, in a state where each of the e(k) gaps between the e(k) electrode pairs - in other words, the e(k) gaps formed by the first electrical conductor 50a and the e(k) second electrical conductors 50b - are filled with, for example, a first substance, the e(k) electrode pairs have the same capacitance C with respect to each other. k Stated from another perspective, when e(k) ≠ 1, for the purpose of satisfying the condition that "in a state where each of the e(k) gaps between the e(k) electrode pairs are filled with, for example, a first substance, the e(k) electrode pairs have the same capacitance C with respect to each other" k the area of the i-th (i ∈ [e(k)]) second electrical conductor 50b among the e(k) second electrical conductors 50b included in the k-th (k ∈ [K]) sensor block B k and the distance between the i-th (i ∈ [e(k)]) second electrical conductor 50b and the first electrical conductor 50a are appropriately set. For example, when the e(k) second electrical conductors 50b included in the k-th (k ∈ [K]) sensor block B k have the same area, if the distance between any one of the e(k) second electrical conductors 50b and the first electrical conductor 50a is equal to the distance between the other one and the first electrical conductor 50a, the above-mentioned condition is achieved. In the example shown in FIG. 16 and the example shown in FIG. 17, the shape of the first electrical conductor 50a is a rectangular flat plate having an area larger than the area of the substrate 9. In the example shown in FIG. 16 and the example shown in FIG. 17, the k-th (k ∈ [K]) sensor block B k is located on one surface of the substrate 9, the first electrical conductor 50a is located parallel to and facing one surface of the substrate 9. When looking directly at the interface sensor 3 (that is, when looking at the paper surface of FIGS. 16 and 17 from the front), the first electrical conductor 50a covers the Σ k∈[K] e(k) second electrical conductors 50b included in the interface sensor 3, and the distance between the edge of the first electrical conductor 50a and each second electrical conductor 50b is sufficiently large. The capacitance C of each of the e(k) electrode pairs included in the k-th sensor block B k is kis the electrostatic capacitance C of each of the e(j) electrode pairs included in the j-th (j≠k) sensor block B j which may be the same as or different from that. Each of the c(k) conductors 70 is a conductor drawn from any one of the K sensor blocks {B j : k∈[K]} and is connected to at least one of the e(k) second electrical conductors 50b of the interface sensor 3 as will be described later in relation to Condition 5 k . The c(k) conductors 70 are connected to the measurement circuit described above. In the figure, for the sake of clarity of the figure, only some of the second electrical conductors and some of the conductors are labeled k∈[K] .

[0088] <Condition 3> to <Condition 4> Condition 3 and Condition 4 in the third embodiment are the same as Condition 3 and Condition 4 in the first embodiment, respectively. Therefore, the descriptions of Condition 3 and Condition 4 in the first embodiment are applied mutatis mutandis to the descriptions of Condition 3 and Condition 4 in the third embodiment. By applying the description of the first embodiment to the description of the third embodiment, for example, "interface sensor 1" is changed to "interface sensor 3", and "electrode pair 5" is changed to "second electrical conductor 50b".

[0089] <Condition 5> For any (k, i) ∈ [K] × [e(k)], in the k-th sensor block B k of the K sensor blocks {B k : k∈[K]}, the i-th second electrical conductor 50b of the e(k) second electrical conductors 50b is connected to the s k,i -th conductor 70 of the c(k) conductors 70. s k,i is represented by the above formula (10). In this example, the i-th (i∈[e(k)]) second electrical conductor 50b and the s k,i -th conductor 70 are connected to each other via the branch line 70x

[0090] <Condition 6> to <Condition 7> Condition 6 and Condition 7 in the third embodiment are the same as Condition 6 and Condition 7 in the first embodiment, respectively. Therefore, the descriptions of Condition 6 and Condition 7 in the first embodiment are applied mutatis mutandis to the descriptions of Condition 6 and Condition 7 in the third embodiment. By applying the description of the first embodiment to the description of the third embodiment, for example, "interface sensor 1" is replaced with "interface sensor 3", and "electrode pair 5" is replaced with "second electrical conductor 50b".

[0091] <Condition 8> From Condition 2, the k-th (k ∈ [K]) sensor block B k includes c(k) conductive wires 70. Therefore, for the total number of conductive wires 70 drawn from the interface sensor 3 to be less than the total number of observation points, that is, the number of planes M, it is sufficient that Equation (25) holds.

Equation

[0092] <Condition 9> Condition 9 in the third embodiment is the same as Condition 9 in the first embodiment. Therefore, the description of Condition 9 in the first embodiment is applied mutatis mutandis to the description of Condition 9 in the third embodiment. By applying the description of the first embodiment to the description of the third embodiment, for example, "interface sensor 1" is replaced with "interface sensor 3", and "electrode pair 5" is replaced with "second electrical conductor 50b".

[0093] An example of the interface sensor 3 of the third embodiment will be described with reference to the drawings. As described above, the third embodiment is different from the first embodiment in that all the other electrodes 5b are replaced with the first electrical conductor. Therefore, only an example of the interface sensor 3 based on the first example (see FIG. 7) of the first embodiment is shown in FIG. 16. In FIG. 16, for the sake of clarity of the drawing, when there are two or more identical components, reference numerals are attached to one or more components that are not all of the two or more identical components.

[0094] The descriptions of [Examples of symbol systems], [Design], [Methods and algorithms for specifying the positions of interfaces], [Variation 1], and [Variation 2] in the first embodiment are applied mutatis mutandis to the descriptions of [Examples of symbol systems], [Design], [Methods and algorithms for specifying the positions of interfaces], [Variation 1], and [Variation 2] in the third embodiment.

[0095] [Equivalent configurations related to the third embodiment] Next, a configuration equivalent to the configuration that satisfies all of "Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, Condition 8, and Condition 9" and specific examples thereof will be described. The configuration equivalent to the configuration that satisfies all of "Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, Condition 8, and Condition 9" is a configuration that has a different configuration from the configuration that satisfies all of "Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, Condition 8, and Condition 9" but has the same function from the perspective of an electric circuit. Since it is impossible to list all "equivalent configurations", in addition, since a person skilled in the art can easily implement various equivalent configurations, only the example of the interface sensor 3 shown in FIG. 16 and an example of an "equivalent configuration" will be described.

[0096] max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) is less than K, the second electrical conductor 50b can be arranged in Y columns. Y is an integer that satisfies max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) ≤ Y ≤ K - 1. In the example of the third embodiment, max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) = 1. Therefore, 1 ≤ Y ≤ K - 1 = 3. Therefore, the second electrical conductor 50b can be arranged in one column (see FIG. 17).

[0097] [Fourth embodiment] The interface sensor 4 of the fourth embodiment is an interface sensor having a configuration determined by the adopted coding system and its specific code words, and has a configuration in which the above-mentioned condition b) is satisfied. In this regard, the fourth embodiment is different from the third embodiment. Stated from another perspective, the fourth embodiment is different from the second embodiment in that all the other electrodes 5b are replaced with the first electrical conductor.

[0098] Here, the substantial differences between the third embodiment and the fourth embodiment will be described, and for other technical matters, the description of the third embodiment will be applied mutatis mutandis to the description of the fourth embodiment. Therefore, the description of the third embodiment, except for the substantial differences, is incorporated herein with the necessary changes made mutatis mutandis. Furthermore, through the incorporation of the description of the third embodiment, the description of the first embodiment is also incorporated herein with the necessary changes made mutatis mutandis. By applying the descriptions of the first embodiment and the third embodiment mutatis mutandis to the description of the fourth embodiment, for example, "interface sensor 1" and "interface sensor 3" are respectively rephrased as "interface sensor 4".

[0099] The interface sensor 4 of the fourth embodiment is a sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent thereto. First, the "configuration that satisfies all of conditions 1, 2, 3, 4, 5, 6, 7, and 8" and its specific example will be described, and later, the "equivalent configuration" and its specific example will be described.

[0100] <Condition 1> to <Condition 7> Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, and Condition 6 in the fourth embodiment are the same as Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, and Condition 6 in the third embodiment, respectively. Condition 7 in the fourth embodiment is the same as Condition 8 in the third embodiment. Therefore, the descriptions of Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, and Condition 8 in the third embodiment are applied mutatis mutandis to the descriptions of Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, and Condition 7 in the fourth embodiment. In the fourth embodiment, Condition 7 and Condition 9 in the third embodiment are unnecessary. Condition 8 in the fourth embodiment is as follows.

[0101] <Condition 8> Condition 8 in the fourth embodiment is the same as Condition 8 in the second embodiment. Therefore, the description of Condition 8 in the second embodiment is applied mutatis mutandis to the description of Condition 8 in the fourth embodiment.

[0102] An example of the interface sensor 4 of the fourth embodiment will be described with reference to the drawings. Since the fourth embodiment differs from the second embodiment in that all the other electrodes 5b are replaced with the first electrical conductor as described above, only an example of the interface sensor 4 based on the sixth example (see FIG. 14) of the second embodiment is shown in FIG. 18. In FIG. 18, for the sake of clarity of the drawing, when there are two or more identical components, reference numerals are attached to one or more components that are not all of the two or more identical components.

[0103] The descriptions of [Example of symbol system], [Design], [Method and algorithm for specifying the position of the interface], [Variation 1], and [Variation 2] in the first embodiment are applied mutatis mutandis to the descriptions of [Example of symbol system], [Design], [Method and algorithm for specifying the position of the interface], [Variation 1], and [Variation 2] in the fourth embodiment.

[0104] [Equivalent configurations related to the fourth embodiment] Next, a configuration "equivalent to a configuration that satisfies all of Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, and Condition 8" and specific examples thereof will be described. A configuration "equivalent to a configuration that satisfies all of Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, and Condition 8" has a configuration different from the "configuration that satisfies all of Condition 1, Condition 2, Condition 3, Condition 4, Condition 5, Condition 6, Condition 7, and Condition 8", but has the same function from the perspective of an electric circuit. Since it is impossible to list all "equivalent configurations", in addition, since a person skilled in the art can easily implement various equivalent configurations, only examples of "equivalent configurations" of the example of the interface sensor 4 shown in FIG. 18 will be described.

[0105] max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) is less than K, the second electrical conductor 50b can be arranged in Y columns. Y is an integer that satisfies max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) ≤ Y ≤ K - 1. In the example of the fourth embodiment, max({d H (h(m), h(m + 1)): ∀m ∈ [M]}) = 3. Therefore, 3 ≤ Y ≤ K - 1 = 3. Therefore, the second electrical conductor 50b can be arranged in 3 columns (see FIG. 19).

[0106] <Addendum 1> The technical features disclosed in the above-described various embodiments and their modifications are not necessarily mutually exclusive. As long as there is no contradiction from a technical perspective, the technical features of a certain embodiment or its modification may be applied to the technical features of other embodiments or their modifications.

[0107] The claims recited in the claims of the present application at the time of filing do not necessarily comprehensively claim all the inventions disclosed in this specification. In this regard, it should not be understood or interpreted that the applicant of the present application has waived the right to obtain a patent for inventions not claimed at the time of filing of the present application before filing. As long as the laws and regulations or treaties of the country or region that has accepted the present application permit, the applicant of the present application reserves the right to obtain a patent for inventions not claimed in the present application, the right to file a divisional application for the invention, the right to claim the invention by amendment, and all other rights. However, this is not the case when the applicant of the present application has made an express and definite statement of opposition.

[0108] An example of the summary of the present disclosure based on another perspective is as follows.

[0109] A sensor based on a first perspective is a sensor for specifying the position of the interface between a first substance and a second substance, and has a configuration that satisfies all of the following Conditions 1, 2, 3, 4, 5, 6, 7, 8, 9, or has a configuration equivalent to the said configuration. Condition 1) The said sensor includes K sensor blocks {B k : k ∈ [K]}. However, K is a predetermined integer that satisfies 2 ≤ K < M, M is a predetermined integer that satisfies 8 ≤ M except when K = 2, and in the case of K = 2, M is a predetermined odd number that satisfies 9 ≤ M. The symbol [X] represents the set {x ∈ N: 1 ≤ x ≤ X} determined by the positive integer X, and N is the set of all positive integers. Condition 2) For any k ∈ [K], the k-th sensor block B among the said K sensor blocks k includes e(k) electrode pairs and c(k) + 1 conducting wires. However, e(k) is a predetermined integer that satisfies 1 ≤ e(k) < M, c(k) is a predetermined integer that satisfies 2 ≤ c(k) ≤ e(k) except when e(k) = 1, and in the case of e(k) = 1, it is 1. Condition 3) Σ that the said sensor hask∈[K] Each of the e(k) electrode pairs is located on one of M planes that do not coincide with each other and are parallel to each other. However, the M planes are arranged in an order according to the order relation of the elements of the set [M], and for each of the M planes, the above Σ k∈[K] At least one of the e(k) electrode pairs is located. Condition 4) For any k ∈ [K], the k-th sensor block B among the K sensor blocks k When the i-th electrode pair among the e(k) electrode pairs included in is located on the p k,i -th plane of the M planes, ∀k ∈ [K], i, j ∈ [e(k)], i > j ⇒ p k,i > p k,j holds. However, ∀(k, i) ∈ [K] × [e(k)], p k,i ∈ [M]. Condition 5) For any (k, i) ∈ [K] × [e(k)], in the k-th sensor block B among the K sensor blocks k One electrode of the i-th electrode pair among the e(k) electrode pairs is connected to the s k,i -th conductor among the c(k) + 1 conductors, and the other electrode is connected to the (c(k) + 1)-th conductor among the c(k) + 1 conductors. However,

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[0110] The sensor based on the second perspective is a sensor for identifying the position of the interface between the first substance and the second substance, and has a configuration that satisfies all of the following Conditions 1, 2, 3, 4, 5, 6, 7, and 8, or has a configuration equivalent to that configuration. Condition 1 The above sensor includes \(K\) sensor blocks \(\{B k :k\in[K]\}\). Here, \(K\) is a predetermined integer that satisfies \(2\leq K\lt M\), \(M\) is a predetermined integer that satisfies \(8\leq M\) except when \(K = 2\), \(M\) is a predetermined odd number that satisfies \(9\leq M\) when \(K = 2\), the symbol \([X]\) represents the set \(\{x\in N:1\leq x\leq X\}\) determined by the positive integer \(X\), and \(N\) is the set of all positive integers. Condition 2 For any \(k\in[K]\), the \(k\)-th sensor block \(B\) among the above \(K\) sensor blocks k includes \(e(k)\) electrode pairs and \(c(k)+1\) conducting wires. Here, \(e(k)\) is a predetermined integer that satisfies \(1\leq e(k)\lt M\), \(c(k)\) is a predetermined integer that satisfies \(2\leq c(k)\leq e(k)\) except when \(e(k)=1\), and \(c(k)=1\) when \(e(k)=1\). Condition 3 The Σ that the above sensor has k∈[K] Each of the e(k) electrode pairs is located on one of M planes that do not coincide with each other and are parallel to each other. However, the above M planes are arranged in an order according to the order relation of the elements of the set [M], and for each of the above M planes, the above Σ k∈[K] At least one of the e(k) electrode pairs is located. Condition 4) For any k ∈ [K], the k-th sensor block B among the above K sensor blocks k When the i-th electrode pair among the e(k) electrode pairs included in it is located on the p k,i -th plane of the above M planes, ∀k ∈ [K], i, j ∈ [e(k)], i > j ⇒ p k,i > p k,j holds. However, ∀(k, i) ∈ [K] × [e(k)], p k,i ∈ [M]. Condition 5) For any (k, i) ∈ [K] × [e(k)], in the k-th sensor block B among the above K sensor blocks k One electrode of the i-th electrode pair among the e(k) electrode pairs is connected to the s k,i -th conductor among the above c(k) + 1 conductors, and the other electrode is connected to the (c(k) + 1)-th conductor among the above c(k) + 1 conductors. However,

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[0111] The sensor based on the third aspect is a sensor for specifying the position of the interface between the first substance and the second substance, and has a configuration that satisfies all of the following Conditions 1, 2, 3, 4, 5, 6, 7, 8, 9, or a sensor having a configuration equivalent thereto. Condition 1 The above sensor includes a first electrical conductor and K sensor blocks \(\{B\) k : \(k\in[K]\}\). However, K is a predetermined integer satisfying \(2\leq K\lt M\), M is a predetermined integer satisfying \(8\leq M\) except when \(K = 2\), and M is a predetermined odd number satisfying \(9\leq M\) when \(K = 2\). The symbol \([X]\) represents the set \(\{x\in N:1\leq x\leq X\}\) determined by the positive integer X, and N is the set of all positive integers. Condition 2 For any \(k\in[K]\), the k-th sensor block \(B\) among the above K sensor blocks k includes \(e(k)\) second electrical conductors and \(c(k)\) conducting wires. However, \(e(k)\) is a predetermined integer satisfying \(1\leq e(k)\lt M\), \(c(k)\) is a predetermined integer satisfying \(2\leq c(k)\leq e(k)\) except when \(e(k)=1\), and \(c(k)=1\) when \(e(k)=1\). Condition 3 The \(\sum\) that the above sensor has k∈[K]Each of the e(k) second electrical conductors is located in one of M planes that do not coincide with each other and are parallel to each other. However, the M planes are arranged in an order according to the order relation of the elements of the set [M], and for each of the M planes, the above Σ k∈[K] at least one of the e(k) second electrical conductors is located. Condition 4) For any k ∈ [K], the k-th sensor block B among the K sensor blocks k when the i-th second electrical conductor among the e(k) second electrical conductors included in it is located in the p k,i -th plane of the M planes, ∀k ∈ [K], i, j ∈ [e(k)], i > j ⇒ p k,i > p k,j holds. However, ∀(k, i) ∈ [K] × [e(k)], p k,i ∈ [M]. Condition 5) For any (k, i) ∈ [K] × [e(k)], in the k-th sensor block B among the K sensor blocks k the i-th second electrical conductor among the e(k) second electrical conductors is connected to the s k,i -th conductor among the c(k) conductors. However,

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[0112] The sensor based on the fourth aspect is a sensor for specifying the position of the interface between the first substance and the second substance, and has a configuration that satisfies all of the following Conditions 1, 2, 3, 4, 5, 6, 7, and 8, or has a configuration equivalent to the said configuration. Condition 1 The said sensor includes a first electrical conductor and K sensor blocks {B k : k ∈ [K]}. Here, K is a predetermined integer satisfying 2 ≤ K < M, M is a predetermined integer satisfying 8 ≤ M except when K = 2, M is a predetermined odd number satisfying 9 ≤ M when K = 2, the symbol [X] represents the set {x ∈ N: 1 ≤ x ≤ X} determined by the positive integer X, and N is the set of all positive integers. Condition 2 For any k ∈ [K], the k-th sensor block B k among the said K sensor blocks includes e(k) second electrical conductors and c(k) conducting wires. Here, e(k) is a predetermined integer satisfying 1 ≤ e(k) < M, c(k) is a predetermined integer satisfying 2 ≤ c(k) ≤ e(k) except when e(k) = 1, and c(k) is 1 when e(k) = 1. Condition 3 The Σ that the above sensor has k∈[K] Each of the e(k) second electrical conductors is located in one of M planes that do not coincide with each other and are parallel to each other. However, the M planes are arranged in an order according to the order relation of the elements of the set [M], and for each of the M planes, the above Σ k∈[K] At least one of the e(k) second electrical conductors is located. Condition 4) For any k ∈ [K], the k-th sensor block B among the above K sensor blocks k When the i-th second electrical conductor among the e(k) second electrical conductors included in is located in the p k,i -th plane among the above M planes, ∀k ∈ [K], i, j ∈ [e(k)], i > j ⇒ p k,i > p k,j holds. However, ∀(k, i) ∈ [K] × [e(k)], p k,i ∈ [M]. Condition 5) For any (k, i) ∈ [K] × [e(k)], among the above K sensor blocks, the k-th sensor block B k In, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i -th conductor. However,

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[0113] The sensor based on the fifth aspect is a sensor based on the third or fourth aspect, for any \(k\in[K]\), the distance between any one of the \(e(k)\) second electrical conductors included in the \(k\)-th sensor block \(B\) of the above \(K\) sensor blocks and the above first electrical conductor is equal to the distance between the other one and the above first electrical conductor. k This is the sensor characterized by this.

[0114] The liquid level gauge of the present disclosure includes a sensor based on any one of the first to fifth aspects, the first substance is a liquid, the second substance is a gas. This is the liquid level gauge characterized by this. In this liquid level gauge, the normal direction of the above \(M\) planes in the sensor based on any one of the first to fifth aspects may be the vertical direction.

[0115] <Addendum 2> The present invention has been described with reference to exemplary embodiments, and those skilled in the art will understand that various changes can be made and its elements can be replaced with equivalents without departing from the scope of the present invention. Furthermore, many modifications can be made to adapt a particular system, device, or its components to the teachings of the present invention without departing from the essential scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed for carrying out the present invention, but is intended to cover all embodiments included within the scope of the appended claims.

[0116] Furthermore, the use of terms such as "first", "second", etc., when used in this specification and / or the appended claims, does not indicate order or importance, and the terms "first", "second", etc. are used to distinguish elements. The terms used in this specification are for the purpose of describing embodiments and are in no way intended to limit the present invention. The term "comprising" and its inflected forms, when used in this specification and / or the appended claims, disclose the presence of the recited features, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof. The term "and / or" includes any and all combinations of one or more of the associated listed elements, if any. In the claims and the specification, unless otherwise specified, "connected", "coupled", "joined", "linked", or their synonyms, and all of their inflected forms, do not necessarily negate the existence of one or more intermediate elements between, for example, two that are "connected" or "coupled" to each other or "linked" to each other. In the claims and the specification, the term "any", if any, should be understood as a term having the same meaning as the universal quantifier ∀, unless otherwise specified. For example, the expression "for any X" has the same meaning as "for all X" or "for each X". Expressions such as "at least one of A, B, C" (in English, for example, expressions such as "at least one of A, B and C", "at least one of A, B or C", "at least one of A, B and / or C") mean, if any, and unless otherwise stated, arbitrarily selecting one element from the set P obtained by removing the empty set φ from the power set 2 S of the set S that contains all the listed elements as its basis. In the case of this example, S = {A, B, C}, 2 S={φ, {A}, {B}, {C}, {A, B}, {A, C}, {B, C}, {A, B, C}}, P = {{A}, {B}, {C}, {A, B}, {A, C}, {B, C}, {A, B, C}}, and this example means that one element (for example, {A, C}) is arbitrarily selected from the set P.

[0117] Unless otherwise noted, all terms used in this specification (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. Further, terms such as those defined in commonly used dictionaries should be interpreted as having a meaning that coincides with their meaning in the context of the related art and this disclosure, and should not be interpreted ideally or overly formally unless explicitly defined otherwise.

[0118] In the description of the present invention, it will be understood that many techniques and steps are disclosed. Each of these has individual advantages and can also be used in combination with one or more, or in some cases all, of the other disclosed techniques. Therefore, to avoid complication, this specification refrains from describing every possible combination of the individual techniques or steps. Nevertheless, the specification and claims should be read with the understanding that such combinations are fully within the scope of the present invention and the claims.

[0119] In the following claims, all corresponding structures, materials, acts, and equivalents of the functional elements combined with the means or steps are intended to include, if any, structures, materials, or acts for performing the functions in combination with other elements.

[0120] The embodiments of the present invention have been described above. However, the present invention is not limited to these embodiments. Various changes and modifications are permitted without departing from the gist of the present invention. The selected and described embodiments are for explaining the principle of the present invention and its practical applications. The present invention can be used in various embodiments with various changes or modifications, and such changes or modifications are determined according to the expected uses. It is intended that all such changes and modifications be included within the scope of the present invention defined by the appended claims, and that the same protection be provided when interpreted in accordance with the breadth given fairly, legally, and equitably.

Explanation of Reference Numerals

[0121] 1 Interface sensor 2 Interface sensor 3 Interface sensor 4 Interface sensor 5 Electrode pair 5a Electrode 5b Electrode 7 Conductive wire 9 Substrate 50a First electrical conductor 50b Second electrical conductor 70 Conductive wire B k Sensor block

Claims

1. The sensor is for identifying the position of an interface between a first substance and a second substance, and has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or has a configuration equivalent to said configuration. Condition 1) The sensor is divided into K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) electrode pairs and c(k)+1 conductors, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case c(k) is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) electrode pairs is located in one of M planes that are mutually disjoint and parallel to each other. However, the M planes are arranged in order according to the original ordering relationship of the set [M], and the Σ k∈[K] At least one electrode pair of the e(k) electrode pairs is located. Condition 4) For any k∈[K], the k-th sensor block B k The i-th electrode pair among the e(k) electrode pairs included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i) ∈ [K] × [e(k)], p k,i ∈[M]. Condition 5) For any (k, i) ∈ [K] × [e(k)], the k-th sensor block B k In the above, one electrode of the i-th electrode pair among the e(k) electrode pairs is s of the c(k)+1 conductors. k,i The other electrode is connected to the c(k)+1-th conductor of the c(k)+1 conductors. [0048] Condition 6) non-negative integer g m,k of, [0049] and the codeword h(m) is defined by [Number 50] In the case specified by a)m 1 ,m 2 ∈[M+1],m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 )、 or b) m 1 , m 2 ∈[M], m 1 ≠ m 2 ⇒ h(m 1 )≠h(m 2 ), and h(1)=h(M+1), holds true. Condition 7) max({d H (h(m),h(m+1)):∀m∈[M]})=1. H (h(m), h(m+1)) is the Hamming distance between codeword h(m) and codeword h(m+1). Condition 8) [0051] holds true. Condition 9) [0052] holds true.

2. The present invention relates to a sensor for identifying the position of an interface between a first substance and a second substance, the sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent to said configuration. Condition 1) The sensor is divided into K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) electrode pairs and c(k)+1 conductors, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case c(k) is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) electrode pairs is located in one of M planes that are mutually disjoint and parallel to each other. However, the M planes are arranged in order according to the original ordering relationship of the set [M], and the Σ k∈[K] At least one electrode pair of the e(k) electrode pairs is located. Condition 4) For any k∈[K], the k-th sensor block B k The i-th electrode pair among the e(k) electrode pairs included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i) ∈ [K] × [e(k)], p k,i ∈[M]. Condition 5) For any (k, i) ∈ [K] × [e(k)], the k-th sensor block B k In the above, one electrode of the i-th electrode pair among the e(k) electrode pairs is s of the c(k)+1 conductors. k,i The other electrode is connected to the c(k)+1-th conductor of the c(k)+1 conductors. [0,53] Condition 6) non-negative integer g m,k of, [0,54] and the codeword h(m) is defined by [0.55] In the case specified by a)m 1 ,m 2 ∈[M+1],m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 )、 or b) m 1 , m 2 ∈[M], m 1 ≠ m 2 ⇒ h(m 1 )≠h(m 2 ), and h(1)=h(M+1), holds true. Condition 7) [0,56] holds true. Condition 8) [0.57] holds true.

3. The sensor is for identifying the position of an interface between a first substance and a second substance, and has a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, 8, and 9, or has a configuration equivalent to said configuration. Condition 1) The sensor includes a first electrical conductor and K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) second electrical conductors and c(k) conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case c(k) is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) second electric conductors is located in one of M planes that are mutually disjoint and parallel to each other. However, the M planes are arranged in an order according to the ordering relationship of the elements of the set [M], and the Σ k∈[K] At least one second electrical conductor is located among the e(k) second electrical conductors. Condition 4) For any k∈[K], the k-th sensor block B k The i-th second electrical conductor among the e(k) second electrical conductors included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i) ∈ [K] × [e(k)], p k,i ∈[M]. Condition 5) For any (k, i) ∈ [K] × [e(k)], the k-th sensor block B k In the above, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i connected to the 1st conductor, except that [0,58] Condition 6) non-negative integer g m,k of, [0,59] and the codeword h(m) is defined by [0.60] In the case specified by a)m 1 ,m 2 ∈[M+1],m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 )、 or b) m 1 , m 2 ∈[M], m 1 ≠ m 2 ⇒ h(m 1 )≠h(m 2 ), and h(1)=h(M+1), holds true. Condition 7) max({d H (h(m),h(m+1)):∀m∈[M]})=1. H (h(m), h(m+1)) is the Hamming distance between codeword h(m) and codeword h(m+1). Condition 8) [0061] holds true. Condition 9) [0062] holds true.

4. The present invention relates to a sensor for identifying the position of an interface between a first substance and a second substance, the sensor having a configuration that satisfies all of the following conditions 1, 2, 3, 4, 5, 6, 7, and 8, or a configuration equivalent to said configuration. Condition 1) The sensor includes a first electrical conductor and K sensor blocks {B k : k∈[K]}, where K is a predetermined integer satisfying 2≦K<M, M is a predetermined integer satisfying 8≦M except when K=2, and is a predetermined odd number satisfying 9≦M when K=2, the symbol [X] represents a set {x∈N:1≦x≦X} determined by positive integers X, and N is the set of all positive integers. Condition 2) For any k∈[K], the k-th sensor block B k includes e(k) second electrical conductors and c(k) conducting wires, where e(k) is a predetermined integer satisfying 1≦e(k)<M, and c(k) is a predetermined integer satisfying 2≦c(k)≦e(k) except when e(k)=1, in which case c(k) is 1. Condition 3) The above sensor has Σ k∈[K] Each of the e(k) second electric conductors is located in one of M planes that are mutually disjoint and parallel to each other. However, the M planes are arranged in an order according to the ordering relationship of the elements of the set [M], and the Σ k∈[K] At least one second electrical conductor is located among the e(k) second electrical conductors. Condition 4) For any k∈[K], the k-th sensor block B k The i-th second electrical conductor among the e(k) second electrical conductors included in k,i When it is located in the th plane, ∀k∈[K],i,j∈[e(k)],i>j ⇒ p k,i >p k,j where ∀(k, i) ∈ [K] × [e(k)], p k,i ∈[M]. Condition 5) For any (k, i) ∈ [K] × [e(k)], the k-th sensor block B k In the above, the i-th second electrical conductor among the e(k) second electrical conductors is the s k,i connected to the 1st conductor, except that [0063] Condition 6) non-negative integer g m,k of, [0,64] and the codeword h(m) is defined by [0.65] In the case specified by a)m 1 ,m 2 ∈[M+1],m 1 ≠m 2 ⇒ h(m 1 )≠h(m 2 )、 or b) m 1 , m 2 ∈[M], m 1 ≠ m 2 ⇒ h(m 1 )≠h(m 2 ), and h(1)=h(M+1), holds true. Condition 7) [0.66] holds true. Condition 8) [0.67] holds true.

5. The sensor according to claim 3 or claim 4, For any k∈[K], the k-th sensor block B k a distance between one of any two second electrical conductors among the e(k) second electrical conductors included in the first electrical conductor is equal to a distance between the other second electrical conductor and the first electrical conductor; Sensor.

6. A liquid level gauge comprising: A sensor according to any one of claims 1 to 4, the first substance is a liquid; The second substance is a gas; Liquid level gauge.

7. 7. The liquid level meter according to claim 6, The normal direction of the M planes is the vertical direction. Liquid level gauge.

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