For the modeling of power amplifiers (PAs) using sub-Nyquist-rate sampling (sub-sampling), a quadratic down-converting architecture with a parallel-cascade method is suggested. Its performance was analyzed regarding the sampling rate below the input Nyquist rate. As a result, the model from the sub-sampling below the input Nyquist rate characterized long-term memory effects whereas the memoryless model could not. The measurement results from RF PAs with the mWiMAX signal verified the modeling performance of this architecture. Also, for the modeling of memoryless PAs, it was shown that this sub-sampled model is still effective regardless of the sampling rate.