  Amplification is usually necessary when measuring the frequency instability
of microwave signals. In this work, we develop a flicker noise free frequency
measurement system based on a common or shared amplifier. First, we show that
correlated flicker phase noise can be cancelled in such a system. Then we
compare the new system with the conventional by simultaneously measuring the
beat frequency from two cryogenic sapphire oscillators with parts in 10^15
fractional frequency instability. We determine for low power, below -80 dBm,
the measurements were not limited by correlated noise processes but by thermal
noise of the readout amplifier. In this regime, we show that the new readout
system performs as expected and at the same level as the standard system but
with only half the number of amplifiers. We also show that, using a standard
readout system, the next generation of cryogenic sapphire oscillators could be
flicker phase noise limited when instability reaches parts in 10^16 or better
