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https://www.electronicdesign.com/power-management/article/21805068/reap-the-benefits-of-economizers-for-solenoidrelay-drivers
https://e2e.ti.com/blogs_/b/industrial_strength/archive/2017/03/16/liberate-your-solenoid-or-relay-from-the-bonds-of-supply-voltage
http://www.ti.com/lit/ds/symlink/drv120.pdf

EV200HAANA: https://www.te.com/commerce/DocumentDelivery/DDEController?Action=srchrtrv&DocNm=EV200_R_TBD_KILOVAC_EV200_Ser_Contactors&DocType=CS&DocLang=English
Inrush Current: 3.8A
Hold Current: 0.13A

Inrush to hold current ratio = 3.8 / 0.13 = 29.2

The relay was tested with the BK Precision power supply, and drew 1.6W when holding the contact. With a driving voltage of 12V, we get a hold current of 1.6W / 12V = 0.133A

These relays have a built-in economizer that reduces the holding current of the coil. The main chips on the board are a PIC12C672 microcontroller, an IRF7341 Dual N-FET, and a 5V LDO. So likely PWM across the coil with the FETs, and controlled with the PIC to provide a delay, the PIC being powered from the LDO.

G9EJ-1-DC12: https://www.mouser.ca/datasheet/2/307/en-g9ej-1-e-371299.pdf
Inrush Current = Coil Drive Voltage / Coil Resistance = 12V / 120Ohm = 0.1A
The datasheet does not give a value for the hold current, so we will go with a similar ratio to the EV200HAANA as our minimum hold current, and add a safety factor.
Hold Current = 0.1A / 29.2 = 3.5mA.
This seems extremely low, so lets go with a value of around 25mA - roughly 1/4 of the inrush current.

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