  We study analytically the features of the Cauchy horizon (CH) singularity
inside a spherically-symmetric charged black hole, nonlinearly perturbed by a
self-gravitating massless scalar field. We derive exact expressions for the
divergence rate of the blue-shift factors, namely the derivatives in the
outgoing direction of the scalar field $\Phi$ and the area coordinate $r$. Both
derivatives are found to grow along the contracting CH exactly like $1/r$. Our
results are valid everywhere along the CH singularity, up to the point of full
focusing. These exact analytic expressions are verified numerically.
