  The complex conductivity of YBa$_2$Cu$_3$O$_{7-\delta}$ samples representing
the optimally doped, the underdoped and the overdoped stoichiometry was
measured using time-domain terahertz spectroscopy. In the normal state, the
frequency dependence is described by the Drude model. Below the critical
temperature $T_\mathrm{c}$, the two-fluid model was successfully employed to
fit all the spectra, from 5 K up to $T_\mathrm{c}$. The temperature behaviour
of fundamental parameters such as the scattering time $\tau$, the superfluid
fraction $f_\mathrm{s}$ and the conductivity $\sigma$ was investigated at given
frequencies. The real part of the conductivity $\sigma_1(T)$ exhibits a
coherence-like peak at low frequencies, which slightly shifts with increasing
frequency whereas its height decreases. It can be observed for all three
stoichiometries and its exact shape depends on the quality of the sample. A
further analysis shows that this peak is a consequence of the competition
between the scattering time $\tau(T)$ and the superfluid fraction
$f_\mathrm{s}(T)$. The decrease of the superfluid fraction towards
$T_\mathrm{c}$ depends on the reduced temperature with a power law close to 2,
suggesting a dirty d-wave superconductor case for all levels of doping.
