  The interlayer exchange coupling confers specific properties to Synthetic
Antiferromagnets that make them suitable for several applications of
spintronics. The efficient use of this magnetic configuration requires an
in-depth understanding of the magnetic properties and their correlation with
the material structure. Here we establish a reliable procedure to quantify the
interlayer exchange coupling and the intralayer exchange stiffness in synthetic
antiferromagnets; we apply it to the ultrasmooth and amorphous
Co$_{40}$Fe$_{40}$B$_{20}$ (5-40 nm)/Ru/ Co$_{40}$Fe$_{40}$B$_{20}$ material
platform. The complex interplay between the two exchange interactions results
in a gradient of the magnetization orientation across the thickness of the
stack which alters the hysteresis and the spin wave eigenmodes of the stack in
a non trivial way. We measured the field-dependence of the frequencies of the
first four spin waves confined within the thickness of the stack. We modeled
these frequencies and the corresponding thickness profiles of these spin waves
using micromagnetic simulations. The comparison with the experimental results
allows to deduce the magnetic parameters that best account for the sample
behavior. The exchange stiffness is established to be 16 $\pm$ 2 pJ/m,
independently of the Co$_{40}$Fe$_{40}$B$_{20}$ thickness. The interlayer
exchange coupling starts from -1.7 mJ/m$^2$ for the thinnest layers and it can
be maintained above -1.3 mJ/m$^2$ for CoFeB layers as thick as 40 nm. The
comparison of our method with earlier characterizations using the sole
saturation fields argues for a need to revisit the tabulated values of
interlayer exchange coupling in thick synthetic antiferromagnets.
