The Circuit Network is a network you can create by connecting Red Wires and Green Wires to different entities. Before the 0.12 release the only things that could connect to this network were Smart Chests, Smart Inserters and Logistics Chests. However after the update, Combinators were added which creates a whole new realm of possibilities. As well as adding Combinators, the 0.12 update now allows the ability to connect Lamps, Pumps, and Storage Tanks to the network.
The Circuit Network allows you to put limits on items using Red and Green Wires similar to how you can with the Logistics Network. On top of that, the Combinators allow very complex systems that automate production even further without any waste. You can also use them to balance production so that it only works when some other product reaches a certain amount. For example you can use the Combinators to only allow the cracking of Light Oil into Petroleum if Petroleum drops below 1000. That is just one example of the many different things you can do with the Circuit Network.
Now that the general concepts of the Circuit Network are explained let’s start with the simplest part, the Smart Inserters and Green/Red Wire connections. Smart Inserters were already explained earlier in the Logistics System section, so I'm going to assume you know how they work already. In addition to being able to set conditions in the Logistics Network on a Smart Inserter, you can also set Red and/or Green Wire conditions. Just with this you can set something to work if there is more than “>” or less than “<” of the desired item within that specific Circuit Network. This will make more sense as we continue.
In order to accomplish this task you will need a Smart Inserter, Smart Chest or Logistic Chest, and some Red or Green Wire. Let’s use the same example as we did in the Logistics System section of an Assembling Machine making Piercing Ammo. In this example let's say that you want to limit the amount of Piercing Ammo to 75 but you don't have a Logistics Network setup yet. So what you want to do is use your Smart Chest as the output chest from the assembler, and the Smart Inserter taking the ammo from the assembler and putting it into the Smart Chest (picture below).
Now obviously the Inserter won't work without a condition so now it is time to connect the wires so we have a small Circuit Network and can set a condition. For this example we will use Red Wire. Youwill need two Red Wires to actually make this work. First you will need to connect one of the wires between the Inserter and a nearby power pole. To do this just have the wire in your hand and click the power pole and then click the Inserter. You will see the Red Wire connecting the two.
The next step is to connect the second wire from the same power pole to the Smart Chest. Just do this the same way. Now there should be two wires, one from the pole to the Inserter, and another from the pole to the Chest:
It's really as simple as that. Once you have done this, if you check the Inserter you will see that you can set a Circuit Network condition. In our example we want the Inserter to only work if there is less than 75 Piercing Ammo in that chest, so just select Piercing Ammo in the item slot and then set the amount to 75. So even though there is no Logistics Network to set a condition in, you can still limit the amount of items in a chest to very specific amounts using the Smart Inserter and wire conditions.
The next part of the Circuit Network is the use of Combinators .This is where it gets very cool but also quite complicated as well. To be completely honest this is not my main area of expertise so I will do my best to explain what each Combinator does, and perhaps provide an example for each. I will also link to multiple different tutorials and guides that can explain it far better.
As of right now there are three different Combinators each with specific tasks or processes it can perform. Let's start with the simplest of the three which is the Constant Combinator. This one sends out specified signals each with specific items counts, so it basically acts like a Smart Chest but without having to put anything in it. That is literally all it does by itself. Here is an example of what that might look like:
The second type is a Decider Combinator. It has a similar function as the Smart Inserter in that it compares item signals. Here is an example of that (picture below):
In this example it is saying that if Plastic is more than 1000, send out a Blue Science Pack signal. Essentially this is saying that Blue Science Packs can only be grabbed by the Smart Inserter if there is more than 1000 Plastic in the connected chest. You can't see it, but there is 1.1k Plastic in that chest so the Inserter is working. For the Inserter condition in this example, it is just set to Blue Science Packs = 1 because the output signal on the Combinator is set to output a signal of 1 Blue Pack if the parameters are met.
You can also compare one item to another rather than an item to a number. Here is an example of that:
In the above example it is saying if Green Circuits are less than Red Circuits then send out a Copper Wire signal of 1. Essentially it is saying that if Green Circuits go lower than the amount of Red Circuits then Copper Cables can be grabbed by the Smart Inserter that is connected. Currently there are more Green Circuits in the chest than there are Red Circuits so the Inserter isn't working. However, once the amount of Greens drop below the amount of Reds, the Inserter will start grabbing Cable again from the Machine.
The last Combinator is the Arithmetic Combinator. It just performs basic Arithmetic operations (+, -, /, *). Here is an example:
In this one it is summing the amount of Green Circuits and Red Circuits and outputting that number as Blue Circuits.
The second parameter can also be a number if you want. So in the following example it is multiplying the amount of Red Science Packs by 2 and outputting that number as Basic Inserters.
One last very important thing to note about the Decider Combinator and the Arithmetic Combinator is that they don't read colors of wires. In other words, if you have a Red and Green wire both going from one thing to the Combinator it will sum the inputs of them together. So if you are only hooking it up to one thing, you only need one color wire, using two will essentially double the input since it is summed from both wires.
Circuit network improvements of 0.13
The 0.13 update brings with it a large number of additions and changes to the circuit network system. Most notable is allowing more entities to be connected to the circuit network. Connecting an entity now also shows a small connector sprite, to allow you to more easily see what you have connected. These entities can also be connected to a logistic network if they are within range.
There is also the addition of the circuit network entity gui, which is a way to easily change and configure the behaviour of a connected entity.
There is also the addition of the new power switch. This can be used to manually or automatically connect and disconnect multiple electric networks. This is especially useful for implementing emergency backup power, but can be used flexibly for any number of tasks.
With these changes comes some removals. Since all inserters and chests can now be connected to the circuit network, the smart chest and smart inserter have both been removed. The smart inserter has no been replaced by the filter inserter, and any chest can match the smart chests functionality.
There are multiple links below that help explain actual uses for Combinators. Some are videos and some are forum posts or articles that explain it.