I was, "OK, this is feasible," but then I traced how it worked and it simply blocked current through drain and source when a P and N pair are reverse biased. When the other P and N pair are forward biased current flows through forward fiodes, then alternatingly. Then it's the same, one is just using diodes to bridge rectify. Worse still, MOSFETs generally don't have a low diode voltage drop. Maybe I'm missing something here.
The rectifier has no voltage drop at no current. The availability of low RDs on MOSFETs means that the voltage drop could be very low. It can be lower than a Schottky diode. The effective resistance is the sum of the N chan and the P chan. I did this in a previous life but for production I used a dual Schottky instead of the 2 P chan FETs. P channel was a big penalty 25 years ago so I figured that 2 n chans and 1 dual Schottky was better value for money. Everything was fine for 12V 10 ampere battery charger. Nowdays the P chan could be economic depending on your application. Remember that if you do the P chan into a big electrolytic capacitor then you will have to do something about high reverse currents. Maybe a diode connection or some reverse current sense that shuts the gates down.
I tested this rectifier in LTSpice. Using only a resistive load it worked perfectly, generating a full-wave rectified current over the load resistor, with a very small voltage drop in the transistors (depending on on-resistance, not on the body diode forward voltage).
Then I added a capacitor to make it a continous DC current. In that case the rectifier faled totally. When there was a voltage over the capacitor, the MOSFET's was conducting in the wrong direction, making the current flow back to the AC source again.
If you replace the two P-MOS transistors with two diodes, it works, because the diodes will block any reverse current. That's why Autistic's solution worked (described in the last post).
There have been a couple of comments and answers here about the failure of the MOSFET bridge rectifier: That it conducts in both directions, so if you have a capacitor-filtered power supply the capacitors will simply drain on the AC downslope, back to the source.
There are a couple of commercial solutions to this problem: at least two that I know of, the LT4320 and LM74670-Q1.
I stumbled across this in search of low-loss rectification for harvesting. The basic problem with the circuit shown is that any phase shift introduced by the load (e.g., with a filter cap) will cause the FETs to fire when you don't want them to (simulate it here):
With no cap, you get something like fullwave rectification. With it, the FET switching is messed up, allowing the cap to discharge back into the line-in.
Even when it's working, it still has forward drop. First, the FETs won't be conducting near the zero-cross points, as neither the body diode nor the Vgs voltages are met. Note also that the no-cap the peak rectified voltage is less than the input by two body diode drops. This is because during that low voltage time, the Vgs threshold isn't met so the enhancement path is off, so only the forward-biased body diodes (two of them) are conducting. Result? It has forward drop!
In short, it's a pointless circuit by itself. Doesn't work with a real load, and doesn't solve the forward drop.
How to make it work then? Use active control of the FETs to make ideal diodes. The FET based ideal diode lets the body diode behave like diode, and turns the FET on when Vs > Vd (for n-FET), using that FET party trick of conducting in either direction. A comparator monitors Vgs, and turns on the gate for the 'reverse' (drain-to-source) direction, shorting out the body diode and eliminating that pesky forward drop. Voila! Ideal diode.
For a bridge, as it so happens we need just two comparators to monitor Vds of the high-side FETs (simulate it here):
I've left out some details, like powering the comparators and getting them to swing high enough (via bootstrap?) to turn the high-side FETs fully like the commercial bridge ICs do (e.g., LT4320.) But this illustrates the principle. (The low-side FETs actually only need logic-level drive, but will have the same polarity as the high-side drive. This is the case for the LT4320.)