ELECTRICAL CABLE CONNECTION FOR ELECTRICAL CONTACTING OF A SURFACE ELECTRODE

DE502021007796D1Active Publication Date: 2025-07-10SAINT GOBAIN SEKURIT FRANCE
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Patent Information

Application Number
DE502021007796
Authority / Receiving Office
DE · DE
Patent Type
Patents
Current Assignee / Owner
Priority Date
2020-09-30
Filing Date
2021-09-21
Publication Date
2025-07-10
Estimated Expiration
2041-09-21

AI Technical Summary

Technical Problem

The labor-intensive process of electrical contacting in composite panes with functional elements, particularly in laminated glass panels, where each segment must be individually contacted using flat conductors and manual soldering, is time-consuming and inefficient.

Method used

A substrate with a functional element featuring an electrical line connection with a cross-sectional transition region that includes a plug connection between a flat conductor and a cable, allowing for automatic assembly and eliminating the need for soldering.

Benefits of technology

The plug connection significantly reduces the labor required for electrical connections, saves time, and prevents mechanical stresses associated with soldering, making it suitable for industrial mass production.

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Description

[0001] The invention relates to a substrate with a functional element comprising an electrical line connection with a cross-sectional transition region and a composite pane with at least one such line connection.

[0002] In laminated glass panels, which comprise at least two rigid panes and an intermediate layer connecting them, as well as electrical components, such wiring connections typically involve a transition from a flat ribbon cable to a cable. The components incorporated into a laminated glass panel can include heating components, antenna elements, and flatly installed functional elements that can be electrically contacted via so-called bus bars. Laminated glass panels equipped in this way are used in automobiles as roof, windshield, rear, and side windows, and also in the construction industry.

[0003] Functional elements with electrically controllable optical properties are used in the industrial production of laminated glazing, for example, roof glazing. The functional element is embedded in the laminated glazing. During the manufacture of the laminated glazing, the functional element is cut out of a functional element in the desired size and shape and inserted between the films of the intermediate layer. Typical intermediate layers are polyvinyl butyral films, which, in addition to their adhesive properties, exhibit high toughness and high acoustic damping. The intermediate layer prevents the laminated glazing from disintegrating in the event of damage. The laminated glazing merely develops cracks but remains dimensionally stable.

[0004] Such composite panes contain a functional element, which typically includes an active layer between two surface electrodes. The optical properties of the active layer can be modified by a voltage applied to the surface electrodes. One example of this is electrochromic functional elements, known, for example, from US 20120026573 A1. Another example is SPD (suspended particle device) or PDLC (polymer dispersed liquid crystal) functional elements, known, for example, from EP 0876608 B1 and WO 2011033313 A1. The transmission of visible light through electrochromic or SPD / PDLC functional elements can be controlled by applying a voltage to the surface electrodes.

[0005] SPD and PDLC functional elements are commercially available as multilayer films. The surface electrodes required for applying a voltage are arranged between two PET carrier films. The surface electrodes can be electrically connected to a control module (ECU) via flat conductors outside the laminated pane. The control module is designed to apply the electrical voltage between the surface electrodes. To lead a flexible cable connection as an external connection from the interior of the laminated pane, flat cables are usually used. These consist of at least one thin carrier substrate and a metallic conductor track (conductor strip). An additional cover layer can be provided so that the flat conductor forms a three-layer laminate.The flat conductors are soldered to connection surfaces close to the edge of the composite disc and are led outwards only over this edge, where they are connected to a round cable at a short distance from the edge.

[0006] Electrical contacting is a laborious step in the production of a composite pane with a functional element divided into multiple segments, as each segment must be electrically contacted individually. This is usually achieved using flat conductors connected to the surface electrodes via bus bars, such as strips of an electrically conductive material or electrically conductive prints (e.g., formed by a silver-based screen print). Contacting is performed manually, step by step, and involves many work steps. In particular, the conductors of the round cables must be contacted to the conductor tracks of the flat conductor by manual soldering. This process is very time-consuming and laborious.

[0007] JP 2005 310570 A discloses a terminal structure for connecting a flat cable for a rotary connector.

[0008] EP1237228 A2 discloses a relay connector with an insulating housing having a plurality of connection terminals between flat and round conductors.

[0009] The object of the present invention is to provide an improved electrical line connection which enables electrical contacting of a functional element in a simple manner.

[0010] The object of the present invention is achieved by a substrate with a functional element comprising an electrical conductor connection according to independent claim 1. Preferred embodiments of the invention emerge from the subclaims.

[0011] The invention comprises a substrate with a functional element and an electrical line connection with a cross-sectional transition region from a flat conductor comprising a carrier substrate and at least one conductor track to a cable comprising at least one electrical conductor, wherein at least one electrical connection between the at least one conductor track and the cable is provided in the cross-sectional transition region, and wherein the cross-sectional transition region has a plug connection for establishing an electrical connection between the flat conductor and the cable. The plug connection comprises two connecting elements, wherein in each case a conductor track of the flat conductor is provided for connection to a conductor of a cable via the plug connection.

[0012] It is essential that the cross-sectional transition area has at least one plug connection between the flat conductor and the cable, which is intended to establish the electrical connection between the flat conductor and the cable.

[0013] The advantage of the cable connection according to the invention is that the plug-in connection between the flat conductor and the cable reduces the labor required to create electrical connections, thus saving valuable working time when installing a composite pane. The plug-in connection can be assembled automatically, making it very advantageous for industrial mass production. The use of the plug-in connection eliminates the need for solder, thus preventing the generation of mechanical stresses caused by the introduction of energy during the soldering process.

[0014] The cross-sectional transition area can have a crimp connection (also called a clamp connection or crimp connection) as a joining connection. The use of crimp connections is particularly advantageous in terms of cost-effective production. The cross-sectional transition area has at least one metal part that is crimped, particularly around the cable, which is arranged when the flat conductor is joined to the cable in such a way that a mechanically stable connection is created between the flat conductor and the cable. The joining connection within the cross-sectional transition area is thus secure and reliable because it features a crimp connection.

[0015] The flat conductor (also called a flat cable) comprises at least one electrical conductor track applied to a carrier substrate made of plastic, which can be covered with a cover layer made of plastic. The carrier substrate and the cover layer together form an insulating sleeve which encloses the electrical conductor track. The flat conductor, which is in particular flexible and / or bendable (e.g. FFC = Flexible Flat Cable), is used for the electrical connection to a flat electrode. The flexible flat conductor is a flat body with two opposite sides which can be made either flat or curved. In the flat (i.e. non-curved) state, the flat conductor is arranged in a plane. The flat conductor is generally elongated and has two ends along its direction of extension. The flat conductor can also be provided with a plurality of electrical conductor tracks, in particular running parallel.The flat conductor can preferably have up to 32, particularly preferably 8 to 10, conductor tracks. The conductor tracks are arranged in a common plane. Each conductor track can have a rectangular cross-section. The flat conductor is an elongated electrical component with multiple electrical conductor tracks, the width of which is significantly greater than its thickness. The flat conductor is designed to be so thin (i.e., the thickness is so small) that it is flexible and bendable. Its width can be between 0.8 mm and 100 mm.

[0016] Furthermore, the flat conductor comprises at least two connection areas with contact points of the conductor tracks at two ends of the flat conductor that are opposite in the direction of extension. The connection areas of the flat conductor serve to electrically contact the conductor tracks. For this purpose, the insulating sheath, i.e., carrier layer and / or cover layer, is absent or removed at least at the contact points, so that the conductor tracks are accessible.

[0017] The electrical conductor tracks are arranged adjacent to one another, at least in sections. Each electrical conductor track can be electrically contacted at two contact points spaced apart along the conductor track. The contact points are areas of the conductor tracks where electrical contact is possible. In the simplest design, these are accessible areas of the electrical conductor tracks. It may be necessary and useful to provide a separate cable connection for each pole, so that one conductor track of the flat conductor is provided for connection to a conductor of a cable.

[0018] The conductor tracks are applied using a printing process. Alternatively, the electrical conductor tracks are prefabricated as metal strips made of metal foil and laminated on both sides with a plastic material. In both cases, the electrical conductor tracks are mechanically stabilized and embedded in an insulating sleeve, thus providing electrical insulation from the external environment.

[0019] Such flexible flat conductors have a connection area (contact point) at both ends, which has at least one cutout in the cover film. In the cross-sectional transition area, the flat conductor has a cutout in the cover film and carrier substrate, so that the conductor track does not include an insulating sheath in this area. The flat conductor has a first connecting element, in particular a plug contact as the male part of the plug connection, for establishing the plug connection. Such a connecting element creates a simple and cost-effective option for a plug connection, which preferably has the first connecting element as a male part and a second connecting element as a female part.

[0020] The cable has the second connecting element, which comprises a receptacle for connection to a first connecting element, in particular a socket for receiving a plug contact. In addition to an electrically conductive conductor (inner conductor or also called core, wire or core), the cable can comprise an insulating, preferably polymeric cable sheath, wherein the insulating cable sheath is preferably removed in the end region of the cable in order to enable an electrically conductive connection between the conductor of the cable and a connecting element. The electrically conductive conductor of the cable can contain, for example, copper, aluminum and / or silver or alloys or mixtures thereof. The cable preferably has a round or oval cross-section, which is, for example, 0.3 mm² to 6 mm².

[0021] The cross-section transition area can be protected by a plastic sheath. The electrically insulating sheath minimizes the risk of short circuits. The sheath can be designed as a rectangular housing, which can also enclose several parallel lines in the cross-section transition area if necessary.

[0022] The invention further relates to a composite pane comprising the substrate according to the invention. The substrate is formed as a first pane, wherein the composite pane has a second pane and two intermediate layers between the first pane and the second pane. The functional element is arranged between the two intermediate layers, wherein the flat conductor is electrically connected at one end to a surface electrode of the functional element.

[0023] The functional element has electrically controllable optical properties and comprises a first carrier film, a first surface electrode, an active layer, a second surface electrode, and a second carrier film arranged one above the other. According to one embodiment of the composite pane according to the invention, the functional element is a so-called PDLC (Polymer Dispersed Liquid Crystal) functional element.

[0024] The active layer has variable optical properties that can be controlled by an electrical voltage applied to the active layer. For the purposes of the invention, electrically controllable optical properties are understood to mean those properties that can be continuously controlled, but equally those that can be switched between two or more discrete states. The optical properties relate in particular to light transmission and / or scattering behavior.

[0025] The first and second carrier films are, in particular, polymeric or thermoplastic films. The carrier films, in particular, contain or consist of a thermoplastic material. The thermoplastic material can be a thermoplastic polymer or a mixture of two or more thermoplastic polymers. In addition to the thermoplastic material, the carrier film can also contain additives, such as plasticizers. The thermoplastic material of the carrier films is preferably polyethylene terephthalate (PET), as is common in commercially available functional elements.

[0026] The thermoplastic material of the carrier film may also contain or consist of blends of PET with other thermoplastic polymers and / or PET copolymers. The thermoplastic material of the carrier film may also contain or consist of, for example, PU, ​​polypropylene, polycarbonate, polymethyl methacrylate, polyacrylate, polyvinyl chloride, polyacetate resin, fluorinated ethylene propylene, polyvinyl fluoride, and / or ethylene tetrafluoroethylene. The thickness of each carrier film is preferably in the range of 0.03 mm to 0.4 mm, more preferably 0.04 mm to 0.2 mm.

[0027] The surface electrodes of the functional element comprise an electrically conductive coating on the carrier foil. The side of the carrier foil with the electrically conductive coating forming the surface electrode then faces the active layer.

[0028] In a further advantageous embodiment, the functional element can be divided into segments by insulation lines. The insulation lines are particularly incorporated into the surface electrodes so that the segments of the surface electrode are electrically insulated from one another. The individual segments can be connected independently of one another via a connection area and the flat conductor to an external voltage source so that they can be controlled separately during operation. A segment of the functional element has two connection areas. Each connection area has a contact. In this way, for example, different areas of the functional element, e.g. as a sun visor, can be switched independently.

[0029] In a further preferred embodiment, the functional element is a PNLC or SPD functional element. In SPD functional elements, the active layer contains suspended particles, whereby the absorption of light by the active layer can be modified by applying a voltage to the surface electrodes. PNLC functional elements (PNLC = polymer network liquid crystal) contain an active layer in which the liquid crystals are embedded in a polymer network, with the functionality otherwise being analogous to that of PDLC functional elements.

[0030] The surface electrodes are designed to be electrically connected to an external voltage source. Contacting the surface electrodes is preferably achieved by (ultrasonic) soldering, crimping, or gluing. For this purpose, a conductive material, in particular a paste, or a solder contact is applied to at least one of the surface electrodes. The paste contains silver or a silver-containing alloy. The conductive material is connected to the surface electrodes as so-called bus bars, for example, strips of electrically conductive material or electrically conductive prints. The surface electrodes can each be electrically contacted by means of a bus bar.

[0031] In an alternative embodiment of the bus bars, thin and narrow metal foil strips or metal wires are used, which preferably contain copper and / or aluminum; in particular, copper foil strips with a thickness of approximately 50 µm are used. The width of the copper foil strips is preferably 1 mm to 10 mm. During further processing of the functional element, the metal foil strips or metal wires are applied to the surface electrode in a composite of thermoplastic layers. In the subsequent autoclave process, a secure electrical contact between the bus bars and the coating is achieved through the action of heat and pressure. The electrical contact between the surface electrode and the bus bar can alternatively be established by soldering or gluing with an electrically conductive adhesive.

[0032] The bus bars are attached to the surface electrodes by cutting out the carrier foil, one surface electrode, and the active layer, leaving the other surface electrode with its associated carrier foil protruding. This can preferably be done along an edge area of ​​the respective side of the functional element. A bus bar can then be attached to the protruding surface electrode, or the flat conductor can be directly contacted with the surface electrode. On the opposite side of the respective functional element, another bus bar is attached to the other surface electrode in a similar manner.

[0033] In an advantageous embodiment, the functional element is a PDLC functional element, in particular one that switches at least one region of the laminated pane or a glazing unit from a transparent to an opaque state and vice versa. The active layer of a PDLC functional element contains liquid crystals embedded in a polymer matrix. The thickness of the functional element is, for example, between 0.09 mm and 1 mm.

[0034] The invention is explained in more detail below with reference to figures and exemplary embodiments. The figures are schematic representations and not to scale. The figures do not limit the invention in any way.

[0035] They show: Figure 1 shows a schematic representation of a flat conductor, Figure 2 shows a schematic representation of a cable, Figure 3 shows an embodiment of a cable connection according to the invention, and Figure 4 shows a representation of the cable connection according to the invention with a sheath, Figure 5 shows a second embodiment of the flat conductor, and Figure 6 shows a second embodiment of the cable.

[0036] The invention is described in more detail below with reference to the figures. It should be noted that various aspects are described, each of which can be used individually or in combination. This means that any aspect can be used with different embodiments of the invention unless explicitly presented as a mere alternative.

[0037] Numerical values ​​are generally not to be understood as exact values, but also include a tolerance of + / - 1% to + / - 10%.

[0038] Figure 1shows a flat conductor 1 having 32 parallel conductor tracks 1.2. The conductor tracks 1.2 are evenly spaced from one another and each have a rectangular cross-section. The conductor tracks 1.2 are enclosed by an insulating sheath 1.3 consisting of a carrier layer and a cover foil. At its two opposite ends in the direction of extension, the flat conductor 1 has a plurality of connection areas 1.1 with contact points of the conductor tracks 1.2. The connection areas 1.1 of the flat conductor 1 serve to electrically contact the conductor tracks 1.2. The insulating sheath 1.3 is at least partially removed at the contact points so that the conductor tracks 1.2 are accessible.

[0039] The electrical conductor tracks 1.2 are arranged side by side. Each electrical conductor track 1.2 can be electrically contacted at two connection areas 1.1 spaced apart along the conductor track 1.2. Each conductor track 1.2 is provided for connection to a conductor (2.1) of a cable 2.

[0040] Such flexible flat conductors 1 have a contacting side corresponding to the side of the cover layer having a recess in a cross-sectional transition region 11. The flat conductor 1 has a plug contact, i.e., a male part, as a first connecting element 1.4 A. The plug contact is provided for establishing a plug connection.

[0041] Figure 2shows a plan view of an embodiment of a cable 2. The cable 2 comprises, in addition to an electrically conductive conductor 2.1, an insulating, polymeric cable sheath. The insulating cable sheath is removed in the end region of the cable to enable an electrically conductive connection between the conductor 2.1 of the cable 2 and a second connecting element 2.2. The electrically conductive conductor 2.1 of the cable 2 contains copper. The cable 2 has a round cross-section, which is, for example, 5 mm².

[0042] The cable 2 can, in principle, be any connecting cable known to those skilled in the art for making electrical contact with a functional element and suitable for being connected to a connecting element (also called a crimp contact) by crimping or clamping. The conductor 2.1 (also referred to as the core or core) of the cable 2 is stripped at its end facing the flat conductor 1 and has the second connecting element 2.2. The second connecting element 2.2 is crimped around the conductor 2.1 of the cable 2 in the end region of the cable 2, creating a permanent, stable, electrically conductive connection between the second connecting element 2.2 and the cable 2. Crimping is carried out using a suitable crimping tool known to those skilled in the art, for example crimping pliers or a crimping press.The crimping tool typically comprises two working points, for example, the jaws of a crimping pliers, which are guided against each other, exerting mechanical pressure on the second connecting element 2.2. The second connecting element 2.2 is thereby plastically deformed and squeezed around the cable 2.

[0043] The second connecting element 2.2 comprises a socket 2.3 B, i.e. a female part, for receiving the plug contact 1.4 A and an area 2.4 crimped around the cable 2 (the so-called crimp, i.e. the area deformed by the crimping process), so that the second connecting element 2.2 is connected to the cable 2 by crimping. The crimp connection is simple, cost-effective and easy to automate. Complex additional process steps, such as soldering or welding the connecting element 2.2 to the cable 2, can thus be avoided. The socket 2.3 B is arranged on the side of the crimped area 2.4 that is opposite the direction of extension of the cable 2 to a control unit (not shown here). The cable 2 is intended to electrically connect the functional element to the control unit, for example a power supply, via the flat conductor 1.For this purpose, the cable 2, starting from the flat conductor 1, is preferably arranged over a side edge of a substrate 100 or a composite disc 101 (in . Figures 3 and 4 shown) away from the substrate 100 or the composite disc 101.

[0044] Figure 3shows an embodiment of a cable connection 10 according to the invention with a cross-sectional transition area 11. The cable connection 10 comprises the cable 2 with the second connecting element 2.2 and the flat conductor 1 with the first connecting element 1.4 A. Furthermore, the cable connection 10 comprises a plug connection between the first connecting element 1.4 and the second connecting element 2.2. The first connecting element 1.4 can form an electrical plug connection as a plug contact (male part) with the socket 2.3 B (female part). One conductor track 1.2 of the flat conductor 1 is stripped at its end pointing towards the round cable 2. The first connecting element 1.4 A (plug contact) can be pushed into the socket 2.3 B. The first connecting element 1.4 A (plug contact) then represents the Figure 3In the end position shown, an electrical contact is established between the socket 2.3 B and the conductor track 1.2. A first connecting element 1.4 A is inserted as a plug contact into each socket 2.3 B.

[0045] Figure 4 shows an embodiment of the cable connection 10 with a sheath 12.

[0046] The cross-sectional transition area 11 can be protected by a plastic sheath 12. The electrically insulating sheath 12 minimizes the risk of short circuits. The sheath 12 is designed as a rectangular housing that can enclose several parallel line connections 10 in the cross-sectional transition area 11.

[0047] The cable connection 10 according to the invention with the cross-sectional transition region 11 can be manufactured simply and cost-effectively and allows a space-saving, flexibly usable and permanently stable electrical contacting of a functional element arranged in a composite pane 101.

[0048] Figure 5 shows a second embodiment of the flat conductor 1. In contrast to Figure 1 The flat conductor 1 has a first connecting element 1.4 B in the form of a socket as the connection area 1.1. The first connecting element 1.4 B (socket) is intended to receive a second connecting element 2.3 A in the form of a plug contact. The first connecting element 1.4 B is crimped around a conductor track 1.2 in the end area of ​​the flat conductor 1 by means of a crimping tab 1.6, so that a permanent, stable, electrically conductive connection is created between the first connecting element 1.4 B and the flat conductor 1.

[0049] Figure 6shows a second embodiment of a cable 2. In contrast to Figure 2 The cable has 2 in Figure 6 via the second connecting element 2.2 in the form of a plug contact.

[0050] The cable 2 further comprises an electrically conductive conductor 2.1 and an insulating cable sheath, which is removed in the end region of the cable 2. The end of the cable 2 pointing towards the flat conductor 1 has the stripped conductor 2.1. The second connecting element 2.2 comprises the plug contact 2.3A, i.e. a male part, and an area 2.4 crimped around the cable 2, wherein the second connecting element 2.2 is connected to the cable 2 by crimping. The second connecting element 2.2 is provided to enable an electrically conductive connection between the conductor 2.1 of the cable 2 and the first connecting element 1.4B. The flat conductor 1 therefore has the first connecting element 1.4B in the form of a matching socket. List of reference symbols:

[0051] 1Flat conductor 1.1Connection area 1.2Conductor track 1.3Insulation sheath 1.4AFirst connecting element (plug contact) 1.4Bursting connecting element (socket) 1.5Crimped area (flat conductor) 1.6Crimping tab 2Cable 2.1Cable conductor 2.2Second connecting element 2.3ASecond connecting element (plug contact) 2.3BSocket 2.4Crimped area 10Cable connection 11Cross-sectional transition area 12Sheath 100Substrate 101Laminated pane

Claims

1. Laminated pane (101) comprising a substrate (100) having a functional element, • the substrate comprising an electrical line connection (10) having a cross-sectional transition region (11) from a flat conductor (1) comprising a carrier substrate and at least one conductor track (1.2) to a cable (2) comprising at least one electrical conductor (2.1), • at least one electrical connection being provided between the at least one conductor track (1.2) and the cable (2) in the cross-sectional transition region (11), • the cross-sectional transition region (11) having a plug connection for establishing an electrical connection between the flat conductor (1) and the cable (2), • the plug connection comprising two connecting elements (1.4 A, 1.4 B, 2.2, 2.3 A, 2.3B, 2.4), • a conductor track (1.2) of the flat conductor (1) being provided for connection to a conductor (2.1) of a cable (2) via the plug connection, characterized in that • the cable (2) has a second connecting element (2.2, 2.3 A, 2.3B, 2.4), which in particular has a receptacle for connection to a first connecting element (1.4 A, 1.4 B) in the form of a socket (2.3 B) or a plug contact (2.3 A), and in that the substrate (100) is designed as a first pane and the laminated pane (101) has a second pane and two intermediate layers between the first pane and the second pane, the functional element being arranged between the two intermediate layers and the flat conductor (1) being electrically conductively connected at one end to at least one planar electrode of the functional element and being provided with another end via the cable (2) for connection to a supply voltage of a vehicle.

2. Laminated pane (101) according to claim 1, wherein a joining connection is provided for connecting one of the two connecting elements (1.4 A, 1.4 B, 2.2, 2.3 A, 2.3B, 2.4) to the cable (1) or to the flat conductor (1).

3. Laminated pane (101) according to claim 2, wherein the joining connection has a crimped connection, in particular a crimped region (1.5, 2.4).

4. Laminated pane (101) according to any of the preceding claims 1 to 3, wherein the flat conductor (1) has a cover film for electrically insulating the at least one conductor track (1.2), which has a recess in the cross-sectional transition region (11).

5. Laminated pane (101) according to any of the preceding claims 1 to 4, wherein the flat conductor (1) has a first connecting element (1.4 A, 1.4 B), in particular a plug contact (1.4 A) or a socket (1.4 B), for establishing the plug connection.

6. Laminated pane (101) according to any of the preceding claims 1 to 5, wherein the flat conductor (1) has a plurality of parallel, in particular 1 to 32, preferably 8 to 10, conductor tracks (1.2).

7. Laminated pane (101) according to any of the preceding claims 1 to 6, wherein the cross-sectional transition region (11) has a plastics material sheath (12) for electrical insulation.

8. Laminated pane (101) according to claim 7, wherein the sheath (12) is designed as a rectangular housing.

9. Laminated pane (101) according to any of the preceding claims 1 to 8, wherein the functional element has electrically controllable optical properties and comprises, arranged one above the other in terms of area: - a first carrier film, - a first planar electrode, - an active layer, - a second planar electrode and - a second carrier film, wherein the functional element is a PDLC functional element.

10. Laminated pane (101) according to any of the preceding claims 7 to 9, wherein the sheath (12) is designed as a rectangular housing which encloses a plurality of parallel line connections (10) in the cross-sectional transition region (11).

11. Laminated pane (101) according to any of the preceding claims 1 to 10, wherein the conductor tracks (1.2) are evenly spaced from one another and each have a rectangular cross-section.