Simplifying and interpreting two-tone measurements

Abstract—We develop a mathematical description of the response of weakly nonlinear systems to second-order memory mechanisms. Our description is based on a time-varying gain-mod-ulation function. We show that intermodulation (IM) products arising from interactions at baseband have phase symmetries dif-ferent from both interactions at second harmonic frequencies and gain compression and, thus, may be readily distinguished through measurement. We also demonstrate a technique for measuring and aligning the phase of IM products outside the measurement bandwidth of our instrumentation to identify contributions to memory with broad frequency response. Index Terms—Gain modulation, intermodulation (IM) distortion, large-signal network analyzer, memory effects, nonlinear vector network analyzer (NVNA), two-tone measurements. I