superconformal algebras are superextensions of the virasoro algebra. they play an important role in the string theory and conformal field theory. central extensions of contact superalgebras $k(2)$ and $k'(4)$ are known to physicists as the $n = 2$ and the big $n = 4$ superconformal algebras. a remarkable property of $\widehat{k}'(4)$ and the exceptional superconformal algebra $ck_6$ is that they admit embeddings into the lie superalgebras of pseudodifferential symbols on the circle, extended by $n = 2, 3$ odd variables. associated to these embeddings, there are ``small" irreducible representations of these superalgebras and their realizations in matrices of size $2^n$ over a weyl algebra. the general construction of such matrix realizations is connected with the spin representation of $\mathfrak{o}(2n + 1, \mathbb{c})$. we also obtain a realization of the family of simple exceptional finite-dimensional lie superalgebras $d(2; 1; \alpha)$, related to $k(4)$ in matrices over a weyl algebra.