EP1849213B1 - Multiband-gedruckte dipolantenne - Google Patents

Multiband-gedruckte dipolantenne Download PDF

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Publication number
EP1849213B1
EP1849213B1 EP06709478A EP06709478A EP1849213B1 EP 1849213 B1 EP1849213 B1 EP 1849213B1 EP 06709478 A EP06709478 A EP 06709478A EP 06709478 A EP06709478 A EP 06709478A EP 1849213 B1 EP1849213 B1 EP 1849213B1
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European Patent Office
Prior art keywords
dipole
leg
antenna
dipoles
strands
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EP06709478A
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English (en)
French (fr)
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EP1849213A1 (de
Inventor
Patrice Brachat
Philippe Ratajczak
Frédéric DEVILLERS
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Orange SA
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France Telecom SA
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Publication of EP1849213A1 publication Critical patent/EP1849213A1/de
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    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q9/00—Electrically-short antennas having dimensions not more than twice the operating wavelength and consisting of conductive active radiating elements
    • H01Q9/04—Resonant antennas
    • H01Q9/16—Resonant antennas with feed intermediate between the extremities of the antenna, e.g. centre-fed dipole
    • H01Q9/28—Conical, cylindrical, cage, strip, gauze, or like elements having an extended radiating surface; Elements comprising two conical surfaces having collinear axes and adjacent apices and fed by two-conductor transmission lines
    • H01Q9/285—Planar dipole
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q21/00—Antenna arrays or systems
    • H01Q21/30—Combinations of separate antenna units operating in different wavebands and connected to a common feeder system

Definitions

  • the present invention relates to a multi-band printed dipole antenna for a telecommunications signal reception and / or transmission network capable of radiating radio fields in several frequency bands.
  • Such an antenna is for example intended to operate in a first frequency band of a cellular radio communication network according to the DCS-1800 standard and / or of the CDMA type and in a second frequency band for a cellular radio communication system according to the standard GSM-900.
  • the invention can also be applied to the field of measurement probes.
  • a printed antenna comprises a t-shaped conductor element which extends over the upper portion of a dielectric substrate and which has an axial slot separating two radiating strands from the tee.
  • the conductive element is fed by a coaxial feed line extending on the underside of the substrate.
  • This dipole uses the principle of double stub adaptation and a wide frequency band.
  • multiband operation can be achieved by introducing localized elements, by series supply of several dipoles or by deformation of a main strand.
  • the antenna described in the above-mentioned patent and article provides only one frequency band operation, and all the above-mentioned solutions have the disadvantage of having narrowband multifrequency operation.
  • a multiband printed dipole antenna according to the invention comprises first and second dipoles supported by a dielectric substrate and each having a manner known from the French patent. 2,713,020 a t-shaped conductive element comprising a leg and two radiating strands separated by a coupling slot in the leg, and a feeding line which may extend substantially parallel to the leg.
  • the invention improves it by the presence of a second dipole whose leg and strands are respectively longer than the leg and the strands. of the first dipole.
  • the antenna according to the invention is characterized by a superposition of the leg of the first dipole and a base of the leg of the second dipole, an alignment of the coupling slots, and a decoupling notch formed in the leg of the second dipole and in which the coupling slot of the first dipole opens by superposition.
  • the notch in the second dipole has a bottom substantially aligned with the slot of the first dipole.
  • the antenna according to the invention is very compact while providing operation in different frequency bands.
  • the antenna can reach a stationary wave rate of less than 2 over more than 50% of the bandwidth in each of the bands.
  • the first dipole radiates in the frequency bands of DCS-1800, UMTS and WLAN networks and the second dipole in the GSM-900 network frequency band.
  • the antenna according to the invention retains the bandwidth performance of the known antenna according to the French patent 2,713,020 and offers a considerable space saving due to the superposition of the two dipoles, the thickness of the antenna being negligible in front of the length or the width thereof.
  • the decoupling notch discovers by completely superimposing the coupling slot of the first dipole, and the dielectric substrate comprises two dielectric layers and the dipole supply lines extend between faces facing the two dielectric layers, or the dielectric substrate comprises for each dipole a dielectric layer having faces respectively supporting the feed line and the conductive element of the dipole, and a dielectric layer extending between the layers supporting the dipoles .
  • the conductive elements of the dipoles extend on a common face of the dielectric substrate, the leg of the first dipole and the base of the leg of the second dipole are merged, and the supply lines extend on the other side of the dielectric substrate.
  • This embodiment has the advantage of having a single substrate, which provides space saving and less space.
  • a metal plane may extend perpendicularly to the faces of the substrate, the dipole having the strands farthest from the metal plane operating at the lowest frequencies.
  • the invention also relates to an antenna array comprising a plurality of antennas, each printed antenna being supported by a dielectric substrate and comprising first and second dipoles each having a t-shaped conducting element and comprising a leg and two radiating strands separated by a coupling slot formed in the leg, and a feeding line, the leg and the strands of the second dipole being respectively longer than the leg and the strands of the first dipole.
  • the network is characterized in that in each antenna, the leg of the first dipole and a base of the leg of the second dipole are superimposed, the coupling slots are aligned, and a decoupling notch is formed in the leg of the second dipole and the coupling slot of the first dipole opens by superposition in the decoupling notch, and the faces of the antenna substrates are parallel to each other and the coupling slots of the dipoles are oriented parallel.
  • a dual-band printed dipole antenna according to the first embodiment of the invention is described below in detail with reference to Figures 1 to 5 .
  • the antenna comprises two stacked rectangular dielectric substrate layers CS1 and CS2, and two superposed printed dipoles D1 and D2.
  • the dipoles radiate in different frequency bands BF1 and BF2 and therefore have different dimensions.
  • the first dipole D1 the smallest, extends on the lower face of the first layer CS1 and is intended to radiate in a first frequency band BF1, for example between 1.5 and 2.5 GHz approximately in order to to cover a band combining the DCS 1800, UMTS and WLAN bands.
  • the second dipole D2 extends on the upper face of the second layer CS2 and is intended to radiate in a second frequency band BF2 which is less than the first frequency band BF1 and understood as an example between 0.7 and Around 1.0 GHz to cover the GSM-900 band.
  • the supply lines LA1 and LA2 extend between the facing faces of the first and second dielectric layers CS1 and CS2.
  • the facing faces of the dielectric layers are the faces opposite to the faces on which the dipoles extend, and all the faces of the layers are parallel to each other.
  • the layers CS1 and CS2 are for example a Duroid substrate with a relative dielectric permittivity of 2.2 and a thickness of about 0.75 mm.
  • the layers CS1 and CS2 are in different relative dielectric permittivity substrates and / or have different thicknesses.
  • each dipole D1, D2 comprises a flat-shaped conductor element in the form of a tee comprising a leg J1, J2 and two lateral strands B1, B2 constituted by wings of the tee perpendicular to the leg and separated by an axially arranged coupling slot FC1, FC2 at the top of the leg.
  • the leg J1, J2 constitutes a ground plane for the corresponding feed line LA1, LA2.
  • the songs of the bases of the legs J1 and J2 are coplanar in a plane perpendicular to the layers, and the strands B2 of the largest dipole D2 are located in front of the strands B1 of the smaller dipole D2 in the direction of radiation.
  • the legs for example, have identical widths and collinear edges when viewed from above, as shown in FIGS. Figures 1 and 2 , the longest leg J2 covering the shorter leg J1 to confer a high compactness to the antenna.
  • the lateral strands B1, B2 constitute the radiating part of the conductive element.
  • the coupling slots FC1 and FC2 are of rectangular shape and very narrow, for example having a width of 0.5 mm.
  • the lateral strands B1, B2 of each dipole D1, D2 preferably have identical lengths.
  • the sum of the lengths of the strands is substantially equal to half the wavelength corresponding to the center frequency of the operating band of each dipole.
  • the strands B1 of the first dipole D1 are shorter than the strands B2 second dipole D2.
  • the length of the leg J1, J2 is equal to about half of said wavelength, although this length of the leg is less critical since it does not intervene in a dominant way in the radiation of the antenna.
  • the width of the legs J1, J2 is for example substantially double the width W1, W2 side strands B1, B2 so that the legs cover the feed lines LA1 and LA2 extending longitudinally between the legs.
  • the feed lines LA1 and LA2 extend parallel to the legs of the dipoles D1 and D2 and are printed with the triplate technology dipoles for which the legs J1 and J2 play the role of ground plane.
  • the supply line LA1 of the first dipole D1 extends on the leg J1 between an access end E11 and a U-shaped end E12 symmetrically to the line LA2 with respect to an axial longitudinal plane P of the common antenna. legs and coupling slots.
  • the access end E11 is located at the edge of the antenna and is to be connected by a connector to a first microwave signal generator for the BF1 band.
  • the U-shaped end E12 has a perpendicularly crossing core by superimposing the coupling slot FC1 and located axially under the birth of the strands B1 and is terminated by a short terminal branch extending substantially parallel to the coupling slot FC1 and near the LA2 power line.
  • the end E12 is folded in U towards the supply line LA2 of the second dipole in order to maintain a high compactness of the antenna, avoiding to discard the feed lines LA1 and LA2 juxtaposed parallel between the dielectric layers CS1 and CS2 and therefore to widen the legs J1 and J2, while ensuring efficient excitation of the B1 strand over which the other feed line LA2 and thus the two quarter-wave strands B1 coupled by a slit line FC1.
  • the length of the coupling slot FC1 and the dimensions of the U-shaped end E12 of the feed line LA1 are chosen in order to adapt the dipole D1 to a wide band BF1.
  • the feed line LA2 of the second dipole D2 extends under the leg J2 between an access end E21 and a right angled end E22, symmetrically to the line LA1.
  • the access end E21 is located at the edge of the antenna and connected by a connector to a second microwave signal generator for the BF2 band.
  • the U-shaped end E22 is terminated by a small rectilinear section situated axially under the birth of the strands B2, and crossing perpendicularly by superposing the coupling slot FC2 to extend also under the strand B2 of the same side of the axial longitudinal plane P of the antenna, and thus excite the two radiating strands B2 in quarter-wave stubs coupled by a slot line FC2.
  • a decoupling slot ED for example rectangular is provided in the leg J2 of the second dipole D2 ( figure 4 ) extending on the leg J1 of the first dipole D1 and beyond the top of the leg J1 including the coupling slot F1 of the first dipole D1.
  • the notch ED is formed in the edge of the leg J2 of the second dipole D2 closest to the feed line LA1 and discovers a portion of the line end E12 from the coupling slot FC1, and substantially the slot of FC1 coupling itself.
  • the notch ED completely overlaps the coupling slot FC1 and has a bottom which is located substantially in a plane perpendicular to the dielectric layers and containing the side of the coupling slot FC1 closest to the other line. LA2 power supply.
  • the decoupling notch ED decouples the ground plane constituted by the leg J2 of the second dipole D2 with respect to the coupling slot FC1 of the strands B1 of the first dipole D1 so that it can radiate.
  • the dipole antenna printed according to the first embodiment of the invention combines in a compact manner two superimposed and decoupled printed dipoles D1 and D2 respectively operating in the frequency bands BF1 and BF2, according to the principle of the double stub adaptation.
  • the printed dipole antenna typically extends over a maximum length of about 150 mm and a maximum width of about 150 mm, preferably respecting a square shape, and has a thickness of about 1.5 mm to provide a bulk minimum.
  • the printed dipole antenna described above has a stationary wave ratio of less than 2 over more than 50% bandwidth in each of the two frequency bands BF1 and BF2, and guarantees a decoupling level. better than -20 dB between E21 access for BF1 (GSM) and E11 for BF2 (DCS + UMTS + WLAN).
  • the feed lines LA1a and LA2a of the dipoles D1a and D2a of the antenna have a common access end E1, as shown in FIGS. Figures 6 and 7 .
  • the common access end E1 situated between the bases of the legs J1a J2a of the dipoles D1a, D2a is collinear with one LA2a of the supply lines, and the other supply line LA1a has a sinuous end for bypass the bottom of the decoupling slot FC1a
  • the Figures 8 and 9 illustrate the second embodiment of the antenna according to the invention.
  • the antenna feed is performed on separate layers.
  • the antenna comprises a third dielectric substrate layer CS3, the second layer CS2 extending between the first and third layers CS1 and CS3.
  • One D1b of the dipoles extends on the outer face of one CS1 of the first and third layers, and the other dipole extends between the two other layers CS2 and CS3.
  • the supply line LA1b relating to the first dipole D1b extends respectively between said one CS1 of the first and third layers CS1 and CS3 and the second intermediate layer CS2, on the leg J1b of the dipole D1b and under the leg J2b of the dipole D2b, and the feed line LA2b relative to the other dipole D2b extends on the outer face of the other CS3 of the first and third layers, on the legs J1b and J2b of the dipoles D1b and D2b.
  • the LA2b power line is printed in technology microstrip while the LA1b feed line is printed in triplate technology.
  • the second embodiment offers more decoupling between dipoles D1b and D2b but to the detriment of a thicker antenna compared to the first embodiment shown in FIGS. Figures 1 and 2 .
  • the conductive element of the dipole D1b and the feed line LA1b are interchanged, the conducting element of the dipole D1b being located between the layers CS1 and CS2 and the feed line LA1b being located under the layer CS1, the outside of the stack of layers, and / or the conductive element of the dipole D2b and the feed line LA2b are interchanged, the feed line LA2b being located between the layers CS3 and CS2 and the conductive element of dipole D2b being located on the CS3 layer, outside the stack of layers.
  • the Figures 10 and 11 illustrate the third embodiment of the antenna with dielectric structure monolayer and microstrip according to the invention.
  • the two printed dipoles D1c and D2c are etched on the same face of a single substrate S and the feed lines LA1c and LA2c are etched on the other side of the single substrate S.
  • the leg J1c of the smallest dipole D1c is used also an extreme portion of the leg J2c of the largest dipole D2c so that the legs J1c and J2c are coaxial and the bases of the legs J1c and J2c are merged on the access ends E11c and E21c feed lines LA1c and LA2c.
  • the decoupling notch EDc which can still be rectangular is practiced in the edge of the leg J2c of the second dipole D2c in front of the strand B1 on the line end E12c and located between this strand B1 and the bottom of the coupling slot FC2c.
  • the bottom of the notch EDc is set back with respect to the aligned slots FC1c and FC2c so that the coupling slot FC1c of the first dipole D1c opens into the notch EDc and the first dipole D1c can radiate.
  • a second coupling slot F1 similar to the first slot FC1c is formed axially in the base of the leg J1c opposite the first slot FC1c and collinearly to that and two slots F2 are provided at the end of a leg portion J2c of the dipole D2c located in front of the strand B1 under which the feed line LA1c and LA2c pass in order to form a narrowing of the leg J2c in a corner of the EDc notch to the width of the LA2c power line and above it.
  • the figure 12 presents an alternative embodiment comprising a metal ground plane PS extending perpendicularly to the faces of the substrate distributed in one, two or three layers and therefore to the flat conductive dipoles. It was assumed in the figure 12 that the antenna was in accordance with the first embodiment shown in figure 1 .
  • the ground plane PS serves as a means of reflection to remove a back radiation of the dipoles and direct the radiation forward of the dipoles opposite the floor plane PS, in the axial direction of the opening of the coupling slots FC1 and FC2.
  • the ground plane PS aims to increase the directivity of the antenna of the order of 2 dB, while maintaining broadband performance of the antenna.
  • the largest B2 strands of the antenna radiating at the lowest frequencies are the farthest from the ground plane PS.
  • the PS ground plane is located at a distance from the rear AC access side of the antenna by about one-third of the wavelength corresponding to the highest frequency of the operating band of the antenna and therefore frequency band BF1 of the smaller dipole.
  • the antenna is introduced into a metal cavity CV or a waveguide, as shown in dotted lines in the figure 12 , in order to obtain a frequency-doubled feed system in a guided structure.
  • the radio performance of the bi-band printed dipole antenna described above is maintained when a plurality of dual-band printed dipole antennas according to the invention are juxtaposed to form a frequency band network BF1 and BF2.
  • the figure 13 presents an example of a one-dimensional RE network of dipole antennas printed in two-band mode according to the first embodiment of the invention.
  • the network comprises a column of dual-band printed dipole antennas whose faces of the substrates are mutually parallel and preferably coplanar and whose axial planes P of coupling slots FC1, FC2 of the dipoles are oriented in parallel.
  • the antennas preferably have common substrate layers extending perpendicularly to a metal ground plane PS that can be the bottom of a cavity CV.
  • the LA1 feed lines of the dipoles D1 of all the antennas are connected to a first common access end and feed lines LA2 dipoles D2 of all the antennas are connected to a second common access end.
  • the first and second common access ends may be interconnected.
  • This network can constitute, for example, an antenna for a base station for the GSM, DCS and UMTS radiocommunication networks and a terminal for a WLAN network (IEEE 802.xx).
  • a base station for the GSM, DCS and UMTS radiocommunication networks and a terminal for a WLAN network (IEEE 802.xx).
  • IEEE 802.xx Depending on the orientation of the antenna, it has a directional diagram in elevation DE and a wide azimuth diagram DA for the two frequency bands BF1 and BF2.
  • a dual-polarization and two-frequency antenna array (not shown) consists of a first column of first dual-band printed dipole antennas which are oriented in the same way as in FIG. figure 13 and a second column of second dual-band printed dipole antennas which are oriented in the same fashion and perpendicular to the orientation of the first antennas.
  • the dipoles D1 and D2 of the first column radiate an electric field polarized and crossed perpendicularly with the electric field radiated respectively by the dipoles D1 and D2 of the second column for respective operations in the first common frequency band BF1 and the second band of common frequency BF2.
  • the dual polarization and thus two-dimensional network may comprise several parallel columns alternating on a plane.
  • the antenna according to the invention can be extended to a structure multiband by introducing as many dipole levels as desired operating bands, and as many dielectric layers as desired operating bands for the first embodiment, or as many pairs of dielectric layers as desired operating bands for the second embodiment, or as many dipoles as desired operating bands for the third embodiment. It is then necessary that one or more decoupling notches are formed in the legs of the dipoles of the upper levels so that they do not cover the coupling slots of the dipoles of the lower levels.

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Claims (9)

  1. Gedruckte Antenne, die erste und zweite Dipole (D1, D2) aufweist, die von einem dielektrischen Substrat getragen werden und je ein leitfähiges Element in Form eines T, das einen Fuß (J1, J2) und zwei strahlende Einzeldrähte (B1, B2) aufweist, die von einem in dem Fuß angeordneten Koppelschlitz (FC1, FC2) getrennt werden, und eine Speiseleitung (LA1, LA2) haben, wobei der Fuß (J2) und die Einzeldrähte (B2) des zweiten Dipols (D2) länger sind als der Fuß (J1) und die Einzeldrähte (B1) des ersten Dipols (D1), und eine Überlagerung des Fußes (J1) des ersten Dipols und einer Basis des Fußes (J2) des zweiten Dipols, eine fluchtende Ausrichtung der Koppelschlitze (FC1, FC2) und eine Entkopplungsaussparung (ED) aufweist, die in dem Fuß (J2) des zweiten Dipols eingerichtet ist und in die der Koppelschlitz (FC1) des ersten Dipols durch Überlagerung mündet.
  2. Antenne nach Anspruch 1, bei der die Entkopplungsaussparung (ED) durch Überlagerung den Kopplungsschlitz (FC1) des ersten Dipols (D1) völlig freilegt.
  3. Antenne nach Anspruch 1 oder 2, bei der das dielektrische Substrat zwei dielektrische Schichten (CS1, CS2) aufweist, und die Speiseleitungen (LA1, LA2) der Dipole (D1, D2) sich zwischen einander gegenüberliegenden Seiten der zwei dielektrischen Schichten (CS1, CS2) erstrecken.
  4. Antenne nach Anspruch 1 oder 2, bei der das dielektrische Substrat für jeden Dipol (D1b, D2b) eine dielektrische Schicht (CS1, CS3), die Seiten besitzt, die die Speiseleitung bzw. das leitfähige Element des Dipols tragen, und eine dielektrische Schicht (CS2) aufweist, die sich zwischen den die Dipole tragenden Schichten (CS1, CS3) erstreckt.
  5. Antenne nach Anspruch 1, bei der die leitfähigen Elemente der Dipole (D1c D2c) sich auf einer gemeinsamen Seite des dielektrischen Substrats (S) erstrecken, wobei der Fuß (J1c) des ersten Dipols und die Basis des Fußes (J2c) des zweiten Dipols zusammenfallen, und die Speiseleitungen (LA1c, LA2c) sich auf der anderen Seite des dielektrischen Substrats erstrecken.
  6. Antenne nach einem der Ansprüche 1 bis 4, bei der im zweiten Dipol eingerichtete Aussparung (ED, EDc) einen Boden im Wesentlichen in Flucht mit dem Schlitz (FC1, FC1c) des ersten Dipols hat.
  7. Antenne nach einem der Ansprüche 1 bis 6, bei der ein Ende (E12) der Speiseleitung (LA1) des ersten Dipols zur Speiseleitung (LA2) des zweiten Dipols U-förmig umgebogen ist und einen Steg hat, der lotrecht durch Überlagerung den Koppelschlitz (FC1) des ersten Dipols kreuzt, und einen kurzen Endschenkel hat, der sich im Wesentlichen parallel zum Koppelschlitz (FC1) des ersten Dipols erstreckt.
  8. Antenne nach einem der Ansprüche 1 bis 7, bei der eine metallische Ebene (PS) sich lotrecht zu den Seiten des Substrats (CS1, CS2) erstreckt, wobei die am weitesten von der metallischen Ebene entfernten Einzeldrähte des Dipols (D2) mit den niedrigsten Frequenzen arbeiten.
  9. Antennennetz mit mehreren Antennen, wobei jede gedruckte Antenne von einem dielektrischen Substrat getragen wird und erste und zweite Dipole (D1, D2) aufweist, die je ein leitfähiges Element in Form eines T, das einen Fuß (J1, J2) und zwei strahlende Einzeldrähte (B1, B2) aufweist, die von einem in dem Fuß angeordneten Koppelschlitz (FC1, FC2) getrennt werden, und eine Speiseleitung (LA1, LA2) haben, wobei der Fuß (J2) und die Einzeldrähte (B2) des zweiten Dipols (D2) länger sind als der Fuß (J1) und die Einzeldrähte (B1) des ersten Dipols (D1), und derart hergestellt, dass
    in jeder Antenne der Fuß (J1) des ersten Dipols und eine Basis des Fußes (J2) des zweiten Dipols überlagert sind, die Koppelschlitze (FC1, FC2) fluchtend ausgerichtet sind, und eine Entkopplungsaussparung (ED) im Fuß (J2) des zweiten Dipols eingerichtet ist, und der Koppelschlitz (FC1) des ersten Dipols durch Überlagerung in der Entkopplungsaussparung (ED) mündet, und
    die Seiten der Substrate der Antennen parallel zueinander sind und die Koppelschlitze der Dipole parallel ausgerichtet sind.
EP06709478A 2005-02-18 2006-02-03 Multiband-gedruckte dipolantenne Active EP1849213B1 (de)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
FR0501814A FR2882468A1 (fr) 2005-02-18 2005-02-18 Antenne dipole imprimee multibandes
PCT/FR2006/050099 WO2006087488A1 (fr) 2005-02-18 2006-02-03 Antenne dipole imprimee multibande

Publications (2)

Publication Number Publication Date
EP1849213A1 EP1849213A1 (de) 2007-10-31
EP1849213B1 true EP1849213B1 (de) 2008-07-23

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US (1) US7432873B2 (de)
EP (1) EP1849213B1 (de)
AT (1) ATE402500T1 (de)
DE (1) DE602006001942D1 (de)
FR (1) FR2882468A1 (de)
WO (1) WO2006087488A1 (de)

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RU2712798C1 (ru) * 2019-05-20 2020-01-31 Федеральное Государственное Бюджетное Образовательное Учреждение Высшего Образования "Новосибирский Государственный Технический Университет" Двухдиапазонная антенна
CN113451788B (zh) * 2020-03-24 2022-10-18 华为技术有限公司 天线、天线模组及无线网络设备
CN114665261B (zh) * 2020-12-22 2023-03-28 华为技术有限公司 一种天线和通信设备

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US7432873B2 (en) 2008-10-07
ATE402500T1 (de) 2008-08-15
FR2882468A1 (fr) 2006-08-25
US20080030418A1 (en) 2008-02-07
WO2006087488A1 (fr) 2006-08-24
DE602006001942D1 (de) 2008-09-04
EP1849213A1 (de) 2007-10-31

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