DAC frequency response

DAC frequency response

Introduction

The AWG (Arbitrary Waveform Generator) modules of the ATX7006 generate an output signal using a D/A converter. It is important to know the output of a DAC is not flat over the full frequency range. Generally the output signal frequency ranges from DC to halve the samplefrequency (1/2 fs). The frequency response of the D/A converter depends on the sin(x)/x (or sinc) function.

An ideal sampled signal would interpolate the voltage between the sample moments. This will result in a flat frequency response.

An typical D/A converter will hold the output constant till the next sample moment (sample-and-hold output). This will result in a stepped output and causes a non flat frequency response. The less samples per signal the more attenuation in the frequency response

The steps in the time domain of the signal are translated into high frequency spectral images. These images can be found at the samplerate +/- signalfrequency. See image below. The black line close to the y-axis is the signal frequency. The images around the samplefrequency are marked red. Images are also attenuated with the sinc frequency response and are self-evident dependend on the analog (output) bandwidth of an AWG. The effects of images can be reduced through interpolation (digital filtering) and analog filtering. Digital filtering increases the effective samplerate and therefore shifts the image frequencies to higher frequencies. An (low pass) analog filter will smooth the output and therefore suppress the higher frequency signals.

The equation for the sinc function can be found in the image above. The 0.1dB frequency flatness is about 17% of the nyquist frequency (nyquist frequency = 1/2 samplefrequency). There are two methods for compensating the sinc frequency response: digital and analog filtering. Digital filtering or the pre-equalization technique processes the digital data for the DAC and can offer a flatness of 0.1 dB to 96% of the nyquist frequency. Analog filtering or the post-equalization technique processes the analog output data of the DAC and can offer a flatness of 0.1 dB to 50% of the nyquist frequency. Both method reduce (worsen) the SNR at low output frequencies.