  A spin-torque nano-oscillator (STNO) driven by a ramped bias current can
perform spectrum analysis quickly over a wide frequency bandwidth. The STNO
spectrum analyzer operates by injection locking to external microwave signals
and produces an output DC voltage $V_{\rm dc}$ that temporally encodes the
input spectrum. We found, via numerical analysis with a macrospin
approximation, that an STNO is able to scan a $10~\rm GHz$ bandwidth in less
than $100~\rm ns$ (scanning rate $R$ exceeds $100~\rm MHz/ns$). In contrast to
conventional quadratic microwave detectors, the output voltage of the STNO
analyzer is proportional to the amplitude of the input microwave signal $I_{\rm
rf}$ with sensitivity $S = dV_{\rm dc}/dI_{\rm rf} \approx 750~\rm mV/mA$. The
minimum detectable signal of the analyzer depends on the scanning rate $R$ and,
at low $R \approx 1~\rm MHz/ns$, is about $1~\rm pW$.
