12v lead acid battery uninterruptible power supply circuit design.

Hi!
I am designing a PIR sensor based security alarm system that works of 230Vac. This alarm should have an uninterruptible 12v power supply. I want to use a 3Ah 12v lead acid battery as the backup power system, however, I am not sure about the charging of the battery and the power supply of the whole circuit. The circuit has an overall low power consumption about 9mA for the PIR sensor and even less for the ATmega328 microcontroller because it will be in sleep mode most of the time. I have to make a PCB based design so I can't really use chargers, boost converters, and other handy modules. I have looked around various forums including this one and made(taken and modified) a circuit. However, I am not sure if this circuit will charge the battery because from what I have read you need more than 12v to charge a 12v battery. Another question is could I replace the transformer/full bridge rectifier with a 5W SMPS such as https://goo.gl/DtFqxV and could I replace LM7805 with a switching regulator such as this one https://ie.rs-online.com/web/p/switching-regulators/6664379/.

In the attached circuit con 1 A and B is where the 12v SLA battery would connect.

Any help would be appreciated thanks in advance

 

That is true.
A lead-acid battery needs about 14.5V to fully charge.
Then the voltage should be dropped to about 13.5V trickle-charge to maintain the charge.

What is the maximum voltage the PIR circuit can tolerate?

 

How could I set up that trickle charge? The PIR tolerates 9-16 V

 

Here's a charge circuit using an LM317 regulator that gives a constant-current charge to 14.5V and then drops to a 13.5V trickle-charge.
For your size battery, change the value of R4 to 2Ω, to give a maximum charge current of about 300mA.

The circuit requires at least 17.5Vdc which could be provided by a SMPS.

Just connect your circuit directly to the battery.
Normally the charger will keep the battery charged as well as providing the circuit current.