When I think of economizer circuits for solenoids and relays, I’m reminded of the phrase, “you can’t have your cake and eat it, too.” This phrase comes to mind because if you use a solenoid economizer, it doesn’t apply!
In engineering, as in baked goods, there are always tradeoffs that affect your decisions. While you can’t have your cake and eat it, too, you can use an economizer for a strong initial pull-in force while still driving your solenoid with low current in the long run.
The Physics
If I want to have a strong pull-in force for my solenoid, I need to drive it with a large current. That’s because the strength of the magnetic force is proportional to the current squared. At the beginning of the solenoid’s stroke, the armature or plunger has to overcome friction and spring force. In addition, the force at the beginning of the stroke is weak because it depends on the size of the gap (see equation below). This is why a large current is required for initial pull-in.