A matrix whose spectral norm is logarithmic in its size?

Question

I'm trying to find a kernel function $f(x,x')$ such that the N by N kernel matrix $A_{i,j} = f(x_i,x_j)$, where $x_i=i/N$, has a spectral norm (largest singular value) of $O(log N)$.

Could anyone find me an example of such a kernel?

Thank you!