  We present the design and the circuit details of a high-sensitivity microwave
vector detection system, which is aiming for studying the low-dimensional
electron system embedded in the slots of a coplanar waveguide at low
temperatures. The coplanar waveguide sample is placed inside a phase-locked
loop; the phase change of the sample may cause a corresponding change in the
operation frequency, which can be measured precisely. We also employ a
double-pulse modulation on the microwave signals, which comprises a fast pulse
modulation for gated averaging and a slow pulse modulation for lock-in
detection. In measurements on real samples at low temperatures, this system
provides much better resolutions in both amplitude and phase than most of the
conventional vector analyzers at power levels below -65 dBm.
