When a magnetic solenoid/relay is energized, a magnetic field has to be formed strong enough to pull the plunger in. When this plunger is pulled in, the power can be reduced to a much lower level to keep it in.
This really cool circuit can do the above. If you pull a line, straight down, just before U5 and then build the circuit on the left, you will have a pulse width controlled relay driver circuit that can handle two relays with a total current of 1.5 amps. There are DRV103 IC's that can handle 3 Amps and by changing your power supply to 3 amps, can pull in really big relays/solenoids.
These PWM relay drivers can be activated by supplying 3 to 5V on pin 8 of U2 and U3. The two red LED's will turn on when an over current or over temperature is detected and will shut the IC's down.
This circuit can be changed to drive 12V relays by changing R1 and R2 resistors on the power supply.
When 3 to 5V is supplied to pin 8 of one of the IC's It will turn on fully, supplying 24V to the relay/solenoid and 22milliseconds later (C4 andC5) will start to pulse the voltage at 5000Hz (R3 and R4) and the duty cycle can be changed by adjusting R5 and R6.
R3 and R4 can be changed to get a different frequency, C4 and C5 can be changed if the relay/solenoid needs more time to pull in before a pulsed signal is supplied, just check out the data sheets.
How to adjust:
Put a voltage of 3 to 5V on pin 8 of the DRV103 IC. When the relay pull in, adjust R5 or R6 until the relay fall out. Set it back a little and energize it again to see if it stays in. If the relay doesn't want to pull in at all then replace C4 and/or C5 with bigger capacitors.
THE GERBER FILES FOR THIS BOARD CAN BE DOWNLOADED HERE