Each DUC in the DAC38RF8x has digital quadrature modulator (DQM) blocks with independent Numerically Controlled Oscillators (NCO) that converts the complex input signal to a real signal with flexible frequency placement between 0 and fDAC/2. The NCOs are enabled by fields NCOAB_ENA and NCOCD_ENA in register MULTIDUC_CFG2 (8.5.14). The NCOs have 48-bit frequency registers (FREQ_NCOAB (8.5.25) and FREQ_NCOCD (8.5.26)) and 16-bit phase registers (PHASE_NCOAB (8.5.23) and PHASE_NCOCD (8.5.24)) that generate the sine and cosine terms for the complex mixing. The NCO block diagram is shown in Figure 42.
Synchronization of the NCOs occurs by resetting the NCO accumulators to zero. The synchronization source is selected by fields SYNCSEL_NCOAB and SYNCSEL_NCOCD in register SYNCSEL1 (8.5.29). The frequency word in the FREQ_NCOAB and FREQ_NCOCD registers are added to the accumulators every clock cycle, fDAC.
The frequency and phase offset of the NCOs are:
Treating the complex channels as complex vectors of the form I + j Q, the output of the DQM is:
Where t is the time since the last resetting of the NCO accumulator and the fields MIXERAB_GAIN and MIXERCD_GAIN in register MULTIDUC_CFG2 (8.5.13) are either 0 or 1.
The maximum output amplitude of the DQM occurs if IIN(t) and QIN(t) are simultaneously full scale amplitude and the sine and cosine arguments are equal to an integer multiple of π/4.
With MIXERAB_GAIN or MIXERCD_GAIN = 0, the gain through the DQM is sqrt(2)/2 or -3 dB. This loss in signal power is in most cases undesirable, and it is recommended that the gain function be used to increase the signal by 3 dB to compensate. With MIXERAB_GAIN or MIXERCD_GAIN = 1, the gain through the DQM is sqrt(2) or +3 dB, which can cause clipping of the signal if IIN(t) and QIN(t) are simultaneously near full scale amplitude and should therefore be used with caution.