battery charging - Switching Between Two Power Supplies Without Reverse Current

I'm new to electronics, so I'm bound to have gotten something wrong.

I'm designing a basic sensor and want it to be powered by USB by default, but use a lithium polymer battery when not connected via USB.

I designed a very basic circuit which uses two enhancement-mode P-channel MOSFETs, with uses fewer parts than most circuits I've found. What am I doing wrong? Below is a picture of my circuit. The grounds of both power sources are connected together, and both MOSFETs have a low VGS threshold.

I'm using a MOSFET as a rectifier. I figured this from here. My main concern is does this circuit prevent power from flowing from USB to the battery?

Answer

I believe you can solve this with two ideal diodes.

Here's a question on this site asking/showing ideal diodes.

Here's two of those put in parallel with a \$5 V_{DC}\$ source and a \$5 V_{DC} + \frac{sin(2\pi500t)}{2} V_{AC}\$

As you can see, whenever the sign of the sine function is negative, it will be less than 5 V, then the other voltage source will take over. Whenever the sign of the sine function is positive, it switches to it.

The major flaw of this system is that you need logic level MOSFET's, like AO3401.

Another flaw is that there will be some quiescent power consumption due to the resistors.

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Another way of doing this would be to actually get IC's made for this single purpose. Such as this one, for an example.