Analysis and Modeling of the Non-ideal Performance in a Polar Transmitter Caused by Limited Bandwidth and Inaccurate Pulsewidth in a [Delta][Sigma] Envelope Modulator

In this paper, the spectral regrowth issues of the separated broadband signals' magnitude and phase components have been analyzed using stochastic theory for polar transmitters. The analysis shows that limited bandwidth of the low-pass envelope reconstruction filter in the [Delta][Sigma] supply modulator can affect the transmitting signals' fidelity of the polar transmitter, which can be measured by the system specifications of error vector magnitude (EVM) and adjacent channel power ratio (ACPR). The relations between the cut-off frequency of the filter and the specifications of EVM and ACPR have been derived to determine the minimum required filter bandwidth. The relations are verified by simulation examples of wideband WCDMA and WLAN 802.11a signals. In the time-domain, the limited bandwidth of the low-pass filter is verified to be responsible for the quasi-memory effects observed in the input envelope amplitude to output envelope amplitude (AM-AM) relation of the [Delta][Sigma] supply modulator. Through numerical examples, the effects of inaccurate pulsewidth caused by non-zero transistor's rise and fall time have been found to be one of the factors causing nonlinear AM-AM relation of supply modulators. The [Delta][Sigma] envelope modulator restrained by limited envelope bandwidth and inaccurate pulsewidth can be characterized as a nonlinear system with memory, which is modeled by ARMAX Hammerstein systems in this paper. The validity of this model is verified by a simulation example of a WCDMA supply modulator.[PUBLICATION ABSTRACT]