  We study the charge noise $S_Q$ in Josephson qubits produced by fluctuating
two level systems (TLS) with electric dipole moments in the substrate. The TLS
are driven by an alternating electric field of angular frequency $\Omega$ and
electric field intensity $I$. It is not widely appreciated that TLS in small
qubits can easily be strongly saturated if $I\gg I_c$, where $I_c$ is the
critical electric field intensity. To investigate the effect of saturation on
the charge noise, we express the noise spectral density in terms of density
matrix elements. To determine the dependence of the density matrix elements on
the ratio $I/I_c$, we find the steady state solution for the density matrix
using the Bloch-Redfield differential equations. We then obtain an expression
for the spectral density of charge fluctuations as a function of frequency $f$
and the ratio $I/I_c$. We find $1/f$ charge noise at low frequencies, and that
the charge noise is white (constant) at high frequencies. Using a flat density
of states, we find that TLS saturation has no effect on the charge noise at
either high or low frequencies.
