  Charge equilibration between quantum-Hall edge states can be studied to
reveal geometric structure of edge channels not only in the integer quantum
Hall (IQH) regime but also in the fractional quantum Hall (FQH) regime
particularly for hole-conjugate states. Here we report on a systematic study of
charge equilibration in both IQH and FQH regimes by using a generalized Hall
bar, in which a quantum Hall state is nested in another quantum Hall state with
different Landau filling factors. This provides a feasible way to evaluate
equilibration in various conditions even in the presence of scattering in the
bulk region. The validity of the analysis is tested in the IQH regime by
confirming consistency with previous works. In the FQH regime, we find that the
equilibration length for counter-propagating $\delta \nu $ = 1 and $\delta \nu
$ = -1/3 channels along a hole-conjugate state at Landau filling factor $\nu $
= 2/3 is much shorter than that for co-propagating $\delta \nu $ = 1 and
$\delta \nu $ = 1/3 channels along a particle state at $\nu $ = 4/3. The
difference can be associated to the distinct geometric structures of the edge
channels. Our analysis with generalized Hall bar devices would be useful in
studying edge equilibration and edge structures.
