Envelope and phase path recombination in ADPLL-based wideband polar transmitters

We investigate the recombination of the RF envelope and phase/frequency paths in a polar transmitter, which is based here on an all-digital phase-locked loop (ADPLL) with a wideband modulation capability. Direct phase/frequency modulation of the digitally-controlled oscillator (DCO) is achieved by means of a two-point modulation scheme of the ADPLL. This scheme views the ADPLL as an all-pass digital filter for the discrete-time baseband phase samples but a low-pass reconstruction filter in the continuous-time domain of the RF DCO output. It is shown analytically that the DCO gain estimation highly affects the interpolative behavior of the ADPLL, which under exact gain estimation, is equivalent to a linear interpolator with sinc
²
(
f
)-type transfer function. Given this low-pass behavior of the ADPLL, simple quantitative analysis indicates that optimum phase and RF envelope recombination is achieved when the digital baseband envelope is reconstructed with a filter that closely approximates the ADPLL interpolative transfer function. Furthermore, the cumulative low-pass behavior of the digital polar transmitter mandates the baseband processing rate of the envelope and, more importantly, the phase, be high enough (on the order of a few hundred MHz) so that the recombined RF spectrum meets the stringent performance requirements of emerging communications standards, such as LTE and WiMAX. Fortunately, the use of envelope and phase pre-distortion counterbalances the need for excessively high baseband processing rates.