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Supercharger Options
Factory Superchargers
The 3800 came equipped with two different superchargers from the factory. Each supercharger had a few changes over the years to make improvements.
At a high level the series 1 3800 was equipped with the smaller Eaton M62:
The series 2 3800 was equiped with the larger Eaton M90 supercharger:
Other superchargers that have been succesful
In theory you can make any supercharger work on a 3800, the biggest thing to consider is the packaging around it. You will just need to make sure you can get the belt aligned properly and adapt it into the intake manifold correctly. It will also need ot fit into whatever vehicle you are using as well.
Here are a list of aftermarket superchargers that have been documented so far with links and images of such installs:
Eaton M112
Expired - Ford Svt Supercharger Eaton M112 | Mustang Forums at ...
Eaton M122
Whipple
TVS1900
Ford GT Supercharger