  We present an extended analysis of the relation between radio surface
brightness and diameter -- the so-called $\Sigma-D$ relation for planetary
nebulae (PNe). We revise our previous derivation of the theoretical $\Sigma-D$
relation for the evolution of bremsstrahlung surface brightness in order to
include the influence of the fast wind from the central star. Different
theoretical forms are derived: $\Sigma \propto D^{-1}$ for the first and second
phases of evolution and $\Sigma\propto D^{-3}$ for the final stage of
evolution. Also, we analyzed several different Galactic PN samples. All samples
are influenced by severe selection effects, but Malmquist bias seems to be less
influential here than in the supernova remnant (SNR) samples. We derived
empirical $\Sigma-D$ relations for 27 sample sets using 6 updated PN papers
from which an additional 21 new sets were extracted. Twenty four of these have
a trivial form of $\beta \approx 2$. However, we obtain one empirical
$\Sigma-D$ relation that may be useful for determining distances to PNe. This
relation is obtained by extracting a recent nearby (< 1 kpc) Galactic PN
sample.
