How it works · Part 2 of 6

Can your circuit be built on one layer?

In short

• Some circuits cannot be wired on a single-sided perfboard, however you arrange the parts. This is a fact of geometry, not a weakness of the software.
• boardroute checks this before searching. If your circuit fails, it names the parts and nets that form the conflict.
• Simple rule of thumb: a part whose pins sit in neighbouring holes acts like a fixed link between its nets. A part with a free hole between its pins is invisible to the check, because wires can pass between its legs.

#The three-utilities puzzle

There is an old riddle: three houses each need a line to the water works, the gas works and the power station. Can you draw all nine lines without any two crossing? You can't, and mathematicians proved it long ago. The pattern of three-connected-to-three, called K3,3, simply can't be drawn flat. Neither can five points that are all connected to each other (K5). And in 1930 Kazimierz Kuratowski showed that these two patterns are the only reasons a network can't be drawn flat: every network that can't be drawn without crossings contains one of them, perhaps stretched out.

A single-sided perfboard is a flat drawing. So if your circuit contains one of these patterns, it can't be built without a jumper wire. The search can't change that. What matters is finding out which part of the circuit has the pattern.

#What blocks a wire on a perfboard

To turn a circuit into "a network that must be drawn flat", we need to know what a wire can and cannot get past.

• A pin blocks the hole it sits in. No wire of another net can pass through it.
• Two pins in neighbouring holes form a wall. There is no hole between them for a wire to pass through. A row of header pins, one side of a DIP chip, or a capacitor with 2.54 mm lead spacing are all walls.
• Pins with a free hole between them are not a wall. A resistor bent to 10 mm spacing has three holes between its legs. Wires can pass under it as if it weren't there.
• A net can run through its own pins. Two neighbouring pins of the same net are already connected; the copper goes straight from one to the next.
• Part bodies don't block, because the wiring is on the other side. A part that does block (for example something mounted flat with pads underneath) can be marked with "routeUnder": false, and then its whole outline counts as a wall.

#The check

boardroute builds a small network from your circuit:

1. Every net becomes a single dot. Think of shrinking all the copper of that net, wires and pins together, into one point.
2. Every wall stays what it is: a chain of holes. Where a wall contains a pin, the chain passes through that net's dot.

If your circuit can be built, then the finished board is a flat drawing of this network, because shrinking copper together never creates a crossing. So if the network can't be drawn flat, no placement and no board size will ever work. boardroute tests this with a planarity algorithm and, if the test fails, extracts the smallest offending piece (a stretched K5 or K3,3). The parts and nets in that piece are what you see in the red notice.

This check takes milliseconds, so it always runs before the search.

#Examples

Ten capacitors, five nets. Take five nets A to E and put a 2.54 mm ceramic capacitor between every pair. That's ten capacitors. Each one is a wall linking two nets, and the result is five dots all connected to each other: K5. Not buildable on one layer.

The same with resistors. Replace the capacitors with 10 mm resistors. Now wires can pass between every pair of legs, the parts are invisible to the check, and boardroute finds a layout of 40 holes.

Nine capacitors, the utilities puzzle. Nets A, B, C on one side, X, Y, Z on the other, a capacitor for every pair: K3,3, not buildable. Remove any one capacitor and it becomes buildable (20 holes).

Three transistors in parallel. Three TO-220 transistors with all gates, all drains and all sources connected looks exactly like the utilities puzzle: three walls (the transistors), three nets. But it is buildable. Stand the transistors side by side and each net runs straight across through its own pins:

S S S
D D D
G G G

This is why the check shrinks each net together with its pins: a net may pass through its own pins, and the check must allow that.

The DIP chip that runs out of room. An L293D motor driver next to a Wemos D1 mini passes the check, yet boardroute never found a layout in twenty minutes of searching. The reason is room, not topology: a standard DIP-16 has only two free holes between its pin rows, and this circuit needs to send more wires between the rows than fit. With the rows widened by one hole, a layout is found every time. The planarity check can't see this kind of capacity problem. boardroute notices it differently: when no layout without crossings turns up within ten seconds, it starts allowing jumper wires (see below), and then this circuit fits with two or three of them.

#Jumper wires: what boardroute does when a circuit can't be built

A jumper is a short piece of insulated wire on the component side of the board. It is soldered into two free holes and arches over whatever runs underneath. It is the standard perfboard fix for two wires that have to cross.

boardroute places jumpers by itself:

• If the planarity check fails, jumpers are allowed from the start.
• If the check passes but no layout without crossings turns up within ten seconds, jumpers are switched on then.
• Otherwise boardroute never uses them, even if one would make the board a little smaller.

The router treats a jumper as one more way to get from a hole to another hole in a straight line, two to five holes away. The holes it spans may carry other nets' wires, but no part and no pin, because the jumper lies on the same side as the parts. Each jumper costs about as much as a six-hole detour, so the router only uses one where going around is clearly worse, and the search counts every jumper against the layout, so it keeps their number low.

For the ten-capacitor K5 and the nine-capacitor utilities puzzle, boardroute finds layouts with a single jumper. One is also the mathematical minimum, because both patterns can be drawn with exactly one crossing.

In the app, jumpers are drawn as arcs over the wiring, and the notice tells you how many were added. In the solder-side view they show as dashed lines between their two legs.

#Avoiding jumpers

• Change a footprint. Bending a capacitor's legs to 5 mm, or using a resistor instead of a wire link, turns a wall into a part wires can pass. Often one changed part is enough to break the pattern.
• Check DIP chips with many signals. If several nets have to reach pins on both sides of a chip, there may not be enough room between the rows. A socket with wider spacing, or a different pin assignment, can help.

#Rules of thumb

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