Signal chain basics: Using the digital features of high-speed DACs
Keywords:digital-to-analog converters? interpolation? digital FIR filter?
The first digital block is interpolation, which increases the sample rate of the digital signal inside the DAC. Interpolation typically is done in steps of a two times increase in sample rate. It is accomplished by inserting zeros between the input sample points, which creates two signals at f_{IF} and F_{IN} 每 f_{IF}. Passing through a digital low-pass filter removes the second signal at F_{IN} 每 f_{IF}, leaving only the signal at f_{IF}.
The motivation for using interpolation is related to the zero-order hold output structure used in most high-speed DACs. With a zero-order hold, the DAC sets the output amplitude corresponding to the digital sample at the
beginning of the clock cycle and holds it until the end of the clock cycle and the next output sample. This results in a "stair-step" output with frequency response that follows in Equation 1:
Sin (p x f_{IF}/f_{s}?)/(p x _{IF}/f_{s})
where f_{IF} is the analog output frequency and f_{s} is the sample rate. This response has a low-pass effect (figure 2), with ~3.5 dB loss at f = f_{s}/2 and goes to zero at multiples of f_{s}. Although the DAC output will have images of the signal at N ℅ fs ㊣ f_{IF}, the amplitude of the images in the higher Nyquist zones is significantly lower than the signal at f_{IF} and, therefore, has lower signal-to-noise-ratio (SNR) and potentially a significant amplitude droop.
Figure 2: DAC output spectrum with no interpolation. |
This limits most applications to output signal frequencies less than f_{s}/2. Additionally, the separation between the signal at f_{IF} and the image at f_{s} 每 f_{IF} reduces as f_{IF} approaches f_{s}/2, making an analog filter at the DAC output to remove the unwanted image at f_{s} 每 f_{IF} difficult to build, which limits f_{IF} for most applications to less than f_{s}/3.
Figure 3: DAC output spectrum with 2x interpolation. |
Using interpolation in the DAC to increase the sample rate inside the DAC, the digital interface rate, f_{IN}, to the DAC only needs to be high enough to allow transfer of the signal bandwidth, plus a small amount of additional bandwidth to allow for the interpolation filter transition band (f_{in} > 2.5 ℅ BW for a real signal and f_{in} > 1.25 ℅ BW for a complex signal). Increasing the sample rate with interpolation then places the signal comfortably below f_{s}/2.
Another benefit of increasing the sample rate is to allow digital mixing to increase the output IF to a higher frequency. For example, with 2℅ interpolation, the output frequency can be placed above f_{in}/2, which would not be possible without interpolation (figure 3). Typically a complex input signal is used with a complex mixer to avoid generating images in the mixing process. The mixing output can either be a real IF signal or complex IF signal, useful when following the DAC with an analog IQ modulator.
Using a complex DAC output with an analog quadrature modulator (AQM) highlights another useful digital feature common in high-speed DACs 每 the quadrature modulator correction block. This block corrects for the gain, phase and offset imbalance of the analog quadrature modulator, improving the AQM sideband suppression and LO feedthrough.
Finally, at the end of the digital signal chain is a digital FIR filter to compensate for the sin(x)/x rolloff across the first Nyquist zone. In the DAC34H84 implementation, the filter compensates up to 0.4 ℅ f_{DAC} with less than 0.03dB of error.
As we have seen in this article, there are a lot of digital features included in high-speed DACs like the DAC34H84. These features ease system implementation by reducing data rates and improving output signal characteristics.
- Robert Keller
??Systems and Applications Manager
??Texas Instruments
References
1. "Quad-Channel, 16bit, 1.25 GSPS Digital-to-Analog Converter (DAC)," DAC34H84 datasheet, LIT# SLAS751A, June 2011.
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