AN3853| Application Note
Maxim/Dallas > App Notes > A/D and D/A CONVERSION/SAMPLING CIRCUITS BASESTATIONS / WIRELESS INFRASTRUCTURE DIGITAL POTENTIOMETERS WIRELESS, RF, AND CABLE
HIGH-SPEED SIGNAL PROCESSING
Keywords: pre equalization, post equalization, frequency response, sinx/x, sinc function, interpolation, Nyquist, image frequency, reconstruction filter, FIR, roll-off
Jun 01, 2006
APPLICATION NOTE 3853
Equalizing Techniques Flatten DAC Frequency Response
Digital-to-analog converters (DACs) convert digital data to analog voltage or current in applications such as instrumentation and wireless communications. A DAC's output frequency generally ranges from DC to less than fS/2, where fS is the input-updating frequency. The output frequency response for most DACs, however, rolls off according to the sin(x)/x (sinc) frequency-response envelope. In the generic example of Figure 1, a digital baseband signal is sampled by the DAC. The DAC's frequency response is not flat and attenuates the analog output at higher frequencies. At 80% of fNYQUIST, for instance (fNYQUIST = fS/2), the frequency response is attenuated by 2.42dB. That loss is unacceptable for some broadband applications requiring a flat frequency response. Fortunately, however, several techniques are available for coping with the non-flat frequency response of a DAC. These include increasing the DAC's update rate, as well as using interpolation techniques, pre-equalization filtering, and post-equalization
filtering--all of which reduce or eliminate the effects of the sinc rolloff.
Figure 1. The non-flat frequency response of a DAC attenuates the output signal, especially at high frequencies.
Understanding DAC Frequency Response
To understand the non-flat frequency response of a DAC, consider the DAC input as a train of impulses in the time domain (Figure 2a), and a corresponding spectrum in the frequency domain (Figure 2b). An actual DAC output is a "zero-order hold" (Figure 2c) that holds the voltage constant for an update period of 1/fS. In the frequency domain, this zero-order hold introduces sin(x)/x distortion (also called aperture distortion)[1]. As shown in Figure 2d, the amplitude of the outputsignal spectrum is multiplied by |sin(x)/x| (the sinc envelope), where x = f/fS. The resulting frequency response is given in equation 1 and plotted in Figure 3. Thus, aperture distortion acts like a LPF that attenuates image frequencies, but also attenuates the desired in-band signals.
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