frequency doubling with a ring mixer

A ratrace coupler is not a nonlinear element so it can by itself not do 
mixing, or can it?

Basically you can do frequency doubling with any non-linear element. 
Feeding your signal through a diode is enough already to get a component 
with twice the frequency (as well as other harmonics). All you need is a 
filter to select the harmonic you want.

Hm, wiki (http://en.wikipedia.org/wiki/Rat-race_coupler) sais: "Rat-race 
couplers are used to sum two in-phase combined signals with essentially 
no loss". Is that wrong?

But I will also keep the hint with the diode and the filter network in 
mind. Thank you :)

Aah... the "sum" is not the sum of the frequency, just of the voltage, 
right?

OK, I got my mistake. In some radar applications ratrace couplers are 
used as mixers but they always have diodes at their ports. Now I 
understand why. The diodes do the mixing! :)

Yes, exactly. Whenever a device generates frequencies at its output 
which are not present at its input, there must be a non-linear device 
(such as a diode) involved, and a microstrip arrangement is to my 
knowledge never non-linear.

And yes, the sum is of the frequencies, not the voltages; you need to 
multiply the voltages to get the mixing effect. You can most easily see 
that by denoting the signal as sin(w*t) and then looking at sin(w*t) + 
sin(w*t) = 2+sin(w*t) (no new frequency components) and sin(w*t) * 
sin(w*t) = 1/2 (1-cos(2*w*t)), which contains half the amplitude in the 
difference frequency (the "1", which is DC because your two frequencies 
are equal) and half in the sum frequency 2*w, which is exactly what an 
ideal frequency mixer would give you.