  We discuss the distributions of three functionals of the free Brownian
bridge: its $\L^2$-norm, the second component of its signature and its L\'evy
area. All of these are freely infinitely divisible. We introduce two
representations of the free Brownian bridge as series of free semicircular
random variables are used, analogous to the Fourier representations of the
classical Brownian bridge due to \ts{L\'evy} and \ts{Kac}.
