Some more things for consideration:

It is very common in German framework, and almost universal in Switzerland, for the braces to stretch from the sill to the plate, creating very long slanted braces. There is a very good reason behind this. These braces are resisting storm loads in buildings that are using relatively small posts for support, which are joined above and below with short tenons. By not having the braces brace into the posts, they are not required to handle any extra loading during storms or high winds, but rather the brace loading is transferred directly to the length of the horizontal timbers. This, however, has the disadvantage of not forming triangles.

Braces can be slanted inwards and join to wall posts, forming true triangles. The same problems still apply but are alleviated by having an opposing brace press against the other side of the same post. This requires a lot of wall space, and so is not always practical. The former setup has proven itself to be more than efficient, and is the dominant technique used in nearly all non-decorative Fachwerk buildings.

As for the small posts, there are two reasons why this is used:

1, as mentioned earlier it allows you to use smaller and lower grade materials without detrimental effects.
2. Apparently one of the primary factors in developing this system was to create interior walls that are free from intruding projections. IF the timbers are seen on the inside of a German house, they are flush with the wall surface.

In the case of barns and utility buildings this is not a concern. These buildings are very often built with more of a bent-profile style of construction, or at least a Fachwerk style wall with much larger timbers. It is rare, however, to see barns in the Canton of Bern. The common farm setup in most of the region is the large Bauernhause, which has a two level structure which serves on one end as the stables and on the other as the living quarters, and has a large upper level (the Heustock) that provides storage for hay and farm equipment. This upper level is accessed by a large framed and usually fully enclosed ramp.

What is interesting about the Bauernhaus is it appears to be descended from a Medieval predecessor that was typically built of stone. These stone houses were limited to the wealthier farmers, and the advancements in timber framing allowed this type of farm setup to be used by everybody.

One thing about posts, there are 3 categories that posts in the typical Fachwerk wall (Fachwerkwand) can be put in.
1 The Ecktänder, or corner post. These are generally the biggest posts. They must be made of adequate size and proportion to resist forces in two directions.
2: The Bundständer. These are posts where two walls come together. Very often they are somewhat wider than the the other posts to accommodate the thickness of the adjoining wall.
3: the regular old Ständer. These are the posts that aren't in the corners or aren't at the junction of two walls. They are typically rectangular in cross section, as they only need to be able to resist lateral forces in 1 direction. They mark the inner and outer surfaces of the wall, and they depth determines the dimensions of everything else as it is desirable in Fachwerk to have smooth inner and outer walls.

I also found this good picture, which does a good job of illustrating the setup and joinery of a simple wall. In particular pay attention to the different scarf joints used for the sills and the plates, reflecting the differences in the loads they are expected to bear. Also pay attention to the fact that the 'Riegel' around the bress is let in (verblattung) rather than mortised in.