I have a circuit design that I believe will work, but I need to change the transistor from a BJT to a FET for lower on resistance. Can anyone help?

The circuit is very simple.
It is a transistor PNP with a diode placed between the base and emitter. A rechargeable 12V battery is placed from gnd to the emitter. The base is supplied with 14V and the collector has 12V on it.
Normally the transistor is off and the battery is charged via the diode. When the supply drops out the 14V and 12V supplies go to ground. The battery then turns the transistor on and supplies the power.
I need a fet in place of the transistor to lower the on voltage drops.

 

What is the current through the transistor? You should be able to get less than 0.2V drop across a BJT when it's ON if it is properly sized. You should also have a current limiting resistor in the base of the transistor if the 14V indeed goes to ground when off.

Otherwise you can just substitute a PMOSFET of the appropriate voltage and desired ON resistance.

 

What is the current through the transistor? You should be able to get less than 0.2V drop across a BJT when it's ON if it is properly sized. You should also have a current limiting resistor in the base of the transistor if the 14V indeed goes to ground when off.

Otherwise you can just substitute a PMOSFET of the appropriate voltage and desired ON resistance.

The circuit is to provide a trickle charge into a battery of around 100mA (500mA max), but the circuit will need to provide 4A from the battery on discharge.
The voltage feeding in, is a 12V 5A power supply and this will run a small booster circuit to provide the 14V for charging. I just need some way of providing a battery backup of 4A without any voltage drops. I know that some FET's have very low on resistances and hence low drops. But I have very little experience of using FET's

 

So, can anyone help please.
Are these two circuits the same and will the fet be good for supplying 12V from the battery when the supplies fail at 4A?