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Artificial neural networks (ANNs) have been widely used to model wireless transmitter low-pass equivalent behavior. However, previously proposed ANNs either do not account for PM-AM and PM-PM distortions or do not satisfy a fundamental constraint imposed by the bandpass nature of wireless transmitters. The purpose of this work is twofold. First, it is shown that PM-AM and PM-PM distortions observed in wireless transmitters excited by wideband signals can have a significant impact on the performance of their behavioral models. Second, a novel ANN topology for wireless transmitter behavioral modeling is proposed. Contrary to previously published ANNs, this one only generates physically meaningful contributions as well as retaining the ability of accounting for PM-AM and PM-PM distortions. The accuracy of the proposed ANN is then compared with two commonly used ANNs of the same computational complexity and for fitting experimental data measured on a GaN-based class-AB amplifier chain. Improvements of up to 7 dB in NMSE and ACEPR results are achieved if the proposed ANN is used instead of a commonly used ANN that neglects the PM-AM and PM-PM distortions. Furthermore, improvements as high as 16 dB in NMSE and ACEPR are achieved by the proposed ANN in comparison with a traditional ANN that also accounts for the PM-AM and PM-PM distortions but does not satisfy the fundamental odd-parity constraint imposed by the bandpass nature of wireless transmitters.