For a complete explanation of the mechanism you can get a copy of the original U.S. Divers service manual available for free in the catalogs and manuals section of Vintage Double Hose website.
In a nutshell the single stage regulator takes the high pressure air from the cylinder and reduces it to ambient pressure delivered to the diver in one step. Unlike a two stage regulator there is no second stage and no intermediate pressure to change or adjust. Below you can see there are two types of single stage double hose regulators but very few are of the down stream type.
Dr Ed in the Philippines made a nice video for VDH showing the simple mechanics of the single stage upstream regulator. Click Here to see it.
The single stage is not without is drawbacks though. Since there is no intermediate pressure available you cannot use a safe 2nd stage, BCD or Drysuit inflator unless you are carrying a pony bottle with another 1st stage on it or using doubles with a separate post and another first stage.
Most, but not all single stage regulators came with short yokes on them and these do not allow enough room to fit a banjo fitting for your pressure gauge between the regulator and valve face. I have manufactured a new yoke nut that allows use of the more plentiful two stage long yokes so this problem is much easier to overcome than it used to be.
Since the regulator reduces the cylinder pressure in one step the work of breathing is slightly higher when used with higher pressure cylinders. The single stage really comes into it's own when used with low pressure cylinders 2500 psi and below. Not to say you can't use them on higher pressure cylinders (Cousteau reportedly used La Spirotechnique Mistrals up to 5000 psi) but your work of breathing is going to be harder until the pressure drops.
Here is a PDF of the popular U.S.Divers family of single stage regulators. The Mistral being the most popular and plentiful. It has a great venturi nozzle and was made in the thousands.
Voit made copies of the US Divers single stage mechanicals and also made a Down Stream regulator for a few years. Click Here for the Voit Family of regulators and more information.
La Spirotechnique made their version of the Mistral and Royal Mistal for years and was the regulator used most often by the Cousteau divers. Click Here for more info.
Most double hose divers have at least one single stage in the collection and diving one is a real treat! Single stage regulators go WOOOOOSH on inhalation when the veturi kicks in and is a sound unique to them. You can even hear the difference in video clips of single stage and two stage divers swimming side by side.
Single Stage regulators were made by almost every manufacture but parts for lesser known brands are not always available and some are impossible to find parts for. I am partial to La Spirotechnique Royal Mistrals but even with those you must be careful as some have the first stage sized for European valves and won't work on US valves unless modified.
If you are looking for an economical way to get started in double hose diving then a U.S.Divers Mistral is a great way to start. Inexpensive, plentiful, all parts are available and for many people they are the first regulator they ever do their own service on. Don't get hung up on serial number date of manufacture nonsense! U.S. Divers Mistrals are all the same on the inside and the only thing that would make one more desirable than the other is a factory installed long yoke.
I hope you find this overview helpful and use it as a segue to doing more research and reading on the Vintage Double Hose website and website message forum.