PCB 布线方法不断改进，灵活的布线技术可以减少布线长度并释放更多的PCB空间。 传统的PCB布线受限于固定的线坐标，缺乏任意角度的线。 消除这些限制可以显着提高布线质量。

Let’s start with some terminology. 我们将任意角度接线定义为使用任意角度段和弧度的接线。 它是一种导线布线，但不限于仅使用 90 度和 45 度角线段。 Topological wiring is wire wiring that does not adhere to grids and coordinates and does not use regular or irregular grids like shape-based wiring. 让我们将术语柔性布线定义为没有固定形状的电线布线，它可以实时重新计算电线形状以实现以下转换可能性。 仅使用来自障碍物的弧及其公共切线来形成线条形状。 (Obstacles include pins, copper foil, forbidden areas, holes and other objects) part of the circuit of two PCB models. 绿线和红线在 PCB 模型的不同层上运行。 The blue circles are the perforations. The red element is highlighted. There are also some red round pins. Use only line segments and models with an Angle of 90 degrees between them. 图 1B 是使用圆弧和任意角度的 PCB 模型。 Wiring at any Angle may seem strange, but it does have many advantages. The way it is wired is very similar to how engineers wired it by hand half a century ago. 展示了 1972 年由一家名为 Digibarn 的美国公司开发的用于完整手工布线的真实 PCB。 This is a PCB board based on Intel8008 computer. 图 2 所示的任意角度布线实际上是类似的。 为什么他们会使用任意角度接线？ 因为这种接线方式有很多优点。 Arbitrary Angle wiring has many advantages. 首先，不使用线段之间的角度可以节省 PCB 空间（多边形总是比切线占用更多的空间）。 Traditional automatic cablers can place only three wires between adjacent components (see left and center in Figure 3). 但是，在任何角度布线时，都有足够的空间在同一路径上铺设 4 根电线，而不会违反设计规则检查 (DRC)。 假设我们有一个正模式芯片并且想要将芯片引脚连接到另外两个引脚。 Using only 90 degrees takes up a lot of space. 使用任意角度布线可以缩短芯片与其他引脚之间的距离，同时减少占用空间。 In this case, the area was reduced from 30 square centimeters to 23 square centimeters. Rotating the chip at any Angle can also provide better results. In this case, the area was reduced from 23 square centimeters to 10 square centimeters. It shows a real PCB. Arbitrary Angle wiring with rotating chip function is the only wiring method for this circuit board. 这不仅是一个理论，也是一个实际的解决方案（有时是唯一可能的解决方案）。 Shows an example of a simple PCB. 拓扑布线器结果，而基于最佳形状的自动布线器结果是实际 PCB 的照片。 An automatic cabler based on optimal shape cannot do this because the components are rotated at arbitrary angles. 您需要更大的面积，如果不旋转组件，设备就必须做得更大。 Layout performance would be greatly improved without parallel segments, which are often a source of crosstalk. The level of crosstalk increases linearly as the length of parallel wires increases. As the spacing between parallel wires increases, crosstalk decreases quadratic. Let’s set the level of crosstalk produced by two parallel 1mm wires spaced d to e. 如果线段之间有一个角度，那么随着这个角度的增加，串扰水平会降低。 The crosstalk does not depend on the length of the wire, but only on the Angle value: where α represents the Angle between the wire segments. 考虑以下三种接线方法。 On the left side of Figure 8 (90 degree layout), there is the maximum wire length and the maximum emi value due to parallel line segments. In the middle of Figure 8 (45 degree layout), the wire length and emi values are reduced. On the right-hand side (at any Angle), the wire length is shortest and there are no parallel wire segments, so the interference value is negligible. So arbitrary Angle wiring helps to reduce the total wire length and significantly reduce electromagnetic interference. You also remember the effect on signal delay (conductors should not be parallel and should not be perpendicular to the PCB fiberglass). Advantages of flexible wiring Manual and automatic movement of components does not destroy the wiring in flexible wiring. 电缆器会自动计算电线的最佳形状（考虑到必要的安全间隙）。 因此，灵活的布线可以大大减少编辑拓扑所需的时间，很好地支持多个重新布线以满足约束条件。 这显示了通过孔和分支点移动的 PCB 设计。 在自动移动过程中，电线分支点和通孔被调整到最佳位置。 In most computer-aided design (CAD) systems, the wiring interconnection problem is reduced to the problem of sequentially finding paths between pairs of points in a maze of pads, forbidden areas, and laid wires. 当找到一条路径时，它被固定并成为迷宫的一部分。 顺序接线的缺点是接线结果可能取决于接线顺序。 当拓扑质量还远未完善时，“卡顿”的问题就出现在局部小范围内。 But no matter which wire you rewire, it’s not going to improve the quality of the wiring. This is a serious problem in all CAD systems using sequential optimization. This is where the bending elimination process is useful. 导线弯曲是指一个网络中的导线必须绕过另一个网络上的对象才能访问对象的现象。 Rewiring a wire will not correct this. 显示了弯曲的示例。 A lit red wire travels around a pin in the other network, and an unlit red wire connects to this pin. 显示自动处理结果。 In the second case (on another layer), a lighted green wire is automatically rewired by changing the wiring layer (from green to red). Eliminate wire bending by automatically optimizing wire shape (approximate arcs with line segments just to show any Angle examples without arcs). (top) original design, (bottom) after eliminating bending design. 红色弯曲的电线突出显示。 在 Steiner 树中，所有线必须作为线段连接到顶点（端点和添加）。 在每个新顶点的顶部，三个线段必须收敛，并且结束的线段不得超过三个。 The Angle between the line segments that converge to the vertex shall not be less than 120 degrees. 构造具有这些充分条件性质的 Steiner 并不是很困难，但不一定是最小的。 Gray Steiner trees are not optimal, but black Steiner trees are. 在实际的通信设计中，必须考虑不同类型的障碍。 它们限制了使用算法和 Steiner 树使用几何方法构建最小生成树的能力。 The obstacles are shown in gray and we recommend starting at any end vertex. If there is more than one adjacent terminating vertex, you should choose one that allows you to continue using the second vertex. It depends on the Angle. 这里的主要机制是一种基于力的算法，它计算作用在新顶点上的力，并将它们反复移动到一个平衡点（力的大小和方向取决于相邻分支点处的线）。 如果连接一个顶点（终点或相加）的一对线段之间的夹角小于120度，则可以增加一个分支点，然后可以使用机械算法来优化顶点位置。 It’s worth noting that simply sorting all angles in descending order and adding new vertices in that order doesn’t work, and the result is worse. After adding a new node, you should check the minimum of a subnet consisting of four pins:

1. If a vertex is added to the vicinity of another newly added vertex, check for the smallest four-pin network.

2. If the four-pin network is not minimal, select a pair of “diagonal” (belonging to the quadrilateral diagonal) endpoints or virtual terminal nodes (virtual terminal nodes – wire bends).

3. The line segment that connects the endpoint (virtual endpoint) to the nearest new vertex is replaced by the line segment that connects the endpoint (virtual endpoint) to the distant new vertex.

4. Use mechanical algorithms to optimize vertex positions.

This method does not guarantee to build the smallest network, but compared with other methods, it can achieve the smallest network length without grazing. 它还允许禁止端点连接的区域，并且端点节点的数量可以是任意的。

Flexible wiring at any Angle has some other interesting advantages. For example, if you can automatically move many objects with the help of automatic real-time wire shape recalculation, you can create parallel serpentine lines. This cabling method makes better use of space, minimizes the number of iterations, and allows for flexible use of tolerances. If there are two serpentine lines interlaced with each other, the automatic cabler will reduce the length of one or both, depending on rule priority.

Consider the wiring of BGA components. In the traditional peripheral-to-center approach, the number of channels to the periphery is reduced by 8 with each successive layer (due to a reduction in perimeter). For example, a 28x28mm component with 784 pins requires 10 layers. 图中的某些层没有布线。 图 16 显示了四分之一的 BGA。 同时，在采用“中心到外围”布线方式时，需要退出到外围的通道数不会因层而异。 这将大大减少层数。 对于 28x28mm 的组件尺寸，7 层就足够了。 对于更大的组件，这是双赢的。 Figure 17 shows a quarter of the BGA. An example of BGA wiring is shown. When using the “center to periphery” cabling approach, we can complete the cabling of all networks. 任意角度拓扑自动电缆器可以做到这一点。 Traditional automatic cablers cannot route this example. Shows an example of a real PCB where the engineer reduced the number of signal layers from 6 to 4 (compared to the specification). In addition, it took engineers only half a day to complete the wiring of the PCB.