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A polar modulator for wireless RF transmitters nonlinearly transforms complex-valued Cartesian baseband modulating signal into amplitude and phase components of the polar coordinate representation before they are recombined in a power amplifier. The resulting explosion in the bandwidth requirements of the polar components can so far be only tolerated for narrowband transmitters, such as EDGE of the 2G cellular. To enable polar topology for wideband transmitters, we propose a technique that alters the signal trajectory such that it avoids crossing (and proximity) of the constellation origin. The resulting substantial decrease of the polar modulator bandwidth is traded off against slight increase of in-band modulation distortion and adjacent channel leakage. We illustrate effectiveness of this method using wideband CDMA (WCDMA) of the 3G cellular. The technique is first mathematically analyzed for various tradeoffs followed by high-level modeling and simulation results. Since the technique is fully contained in the digital domain, its performance effects on the entire RF transmitter can be accurately simulated. A digital architecture to implement the proposed technique is also presented.