Now its time to add an active sensor. Open the Create Research Project window again, using either the Design button on the Economics window or Ctrl-F6 from the main menu. The first item in the Research Project Type list is active sensors, which is useful as that is what we need. There are five dropdowns this time. Lets make the size of the Antenna 2 HS. This increases the Sensor Strength of the component to 20, which our current Active Grav Sensor Strength of 10 multiplied by the 2 HS. In the text area that shows the details of the new active sensor, several of the fields are the same as the engines so I won't bother describing them again. New information includes the chance of destruction by electronic damage (from microwave weapons), the Resolution and the Range. Resolution Zero is actually resolution 1 but it is described as zero because it treats anything less than 1 as equal to 1.
The Range of an active sensor is equal to Resolution x Sensor Strength x 10,000. So by increasing the resolution you can dramatically increase the range. At the moment, the range is 1 (resolution) x 20 (strength) x 10,000 = 200,000 km. Try changing the resolution to 100 (or 5000 tons). Now the range is 20,000,000 km. So why, you are no doubt asking, wouldn't you have the highest resolution possible? Good question!
An active sensor is able to detect any ship of a size that is equal to or greater than its resolution at its maximum range. So this sensor could detect a ship of 5000 tons or greater (size 100) at 20m km. If the target is smaller than the resolution, the maximum detection range is equal to Max Range x (Target Size / Resolution) ^2. So using this sensor against a target that was size 80, the formula would be:
20m km x (80/100)^2 or 20m x 0.8 x 0.8, which equals 12.8 million kilometers
Against a target of size 20 (1000 tons), the max detection range would be 20m x 0.2 x 0.2 or 0.8 million kilometers
Against a missile (size 1 unless it's huge), 20m x 0.01 x 0.01 = 0.002m, or just 2000 km.
So you need to design active sensors based on the role intended for that sensor. An area search sensor might be designed with a large resolution to find large enemy ships while a sensor designed to detect fast attack craft, which are 1000 tons or less would need a resolution of approximately 20. Missile detection sensors are usually resolution zero. In this case, we want a general search sensor so lets stick with resolution 100. If we encounter an enemy that likes to design ships of 4000 tons or 6000 tons we can modify future sensor designs to take the best advantage of an appropriate resolution (80 or 120).