Measuring RF circuits exhibiting nonlinear responses combined with short and long term memory effects

All RF circuits that incorporate active devices exhibit nonlinear behavior. Nonlinearities result in signal distortion, and therefore state the upper limit of the dynamic range of the circuits. A measure for linearity used quite commonly in RF is the P1dB and/or IP3 point. These quantities are usually measured using a signal generator and a spectrum analyzer. Depending on the quantity of interest (1 P1dB or IP3), a single or two-tone signal is passed through the system. A shortcoming of this type of measurement is that it only quantifies the magnitude of the distortion, and gives no information about the phase. New measurement methodologies using X-parameters circumvent this shortcoming by including phase information as well. This enables more detailed nonlinear measurements, providing the RF designer with more information leading to a higher predictability of the total RF system. For many RF applications this methodology provides sufficient information. In real-life RF systems, the distortion components (harmonics and intermodulation products) can in principle have any phase due to memory effects. The memory effects can sub-divided into two categories, namely short and long term effects. Short term memory exhibits time constants smaller than the symbol time of the modulated signals of interest, and long term memory has time constants which are spread over multiple symbols. The aforementioned X-parameters include only short term memory effects, leading to a certain phase of the distortion products. This limitation of the approach based on X-parameters is due to the fact that only unmodulated constant envelope signals are used (pure sinusoidal signals) as an excitation. In this paper a measurement setup is proposed that captures both the input and output signals, fully in the time domain. Realistic (and in fact any arbitrary) waveforms can be used as excitation, enabling the extraction of both the short and the long term memory effects that are of increasing importance for future wireless systems with complex wideband modulation techniques. To achieve a high accuracy, a noise minimization technique is applied