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What is the difference between the sampling rate and the bandwidth of a DAC? I have found in one paper a DAC speced as 15GHz 3dB bandwidth, and 64GS/s sampling rate, and I haven't been able to relate them to each other in any way...

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The bandwidth of a DAC is related to the analog filtering on the output. Most often (and in your example), this is specified as the 3 dB point of the analog filters that are part of the DAC. They are there to reject the Nyquist images of the signal that are part of the digital signal spectrum. Analog filters are not usually sharp enough to reject the first image you don't want while retaining the high frequencies of the baseband image that you might want to retain. For this reason, the 3 dB point starts a bit earlier to ensure that the required attenuation can be reached at the first folding band. Trying to output a signal with frequency components higher than this point will result in those components undergoing significant attenuation (resulting in a distorted output signal). Usually, one desires spectral flatness in the passband (low distortion of the time domain signal). In this case, it is recommended to oversample by at least 4 or 8 times (although the actual required amount is application specific). The bandwidth is important. In your example, if you are using a 64 GS/s DAC and want to use it to output signals higher than (or even close to) 15 GHz, then your signals will be output with significant attenuation.

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  • $\begingroup$ why do we need to "oversample by at least 4 or 8 times" ? $\endgroup$ – AlexTP May 16 '17 at 18:27
  • $\begingroup$ See edited answer, and "need" was not used... The word was "recommended" $\endgroup$ – hops May 16 '17 at 18:30
  • $\begingroup$ I mean it would be nice if you are able to elaborate the argument "one desires spectral flatness in the passband (low distortion of the time domain signal). In this case, it is recommended to oversample by at least 4 or 8 times", i.e. the reason of low distortion in time domain is equivalent to spectral flatness in passband and why 4 or 8 times oversampling is enough. Thanks. $\endgroup$ – AlexTP May 16 '17 at 18:52
  • $\begingroup$ First of all, no need to yell... I'm not that old yet. You are requesting information for something that is off topic and may confuse the OP. The spectral flatness is given as one example of a reason why one might care about the 3 dB point. Answering the question, "How much is flat?" is (as stated in the answer) application specific. As no application was specified, and as the question was not asked. The answer would therefore be off topic. Why I say 4 to 8 times, is because that is my engineering rule of thumb, I would obviously refine based on any specific application I used the DAC for. $\endgroup$ – hops May 16 '17 at 19:18
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    $\begingroup$ You are generally correct that the 3 dB bandwidth is usually less than half the sampling rate (to ease further filtering requirements). Oversampling (or using a higher sampling frequency) also helps. Another thing to consider in your analysis is the zero order hold (sinc response) and any additional analog filtering placed at the DAC output. These will all contribute to the overall response and influence how well the system rejects the unwanted Nyquist images. You are also correct that these factors together reduce the effective bandwidth of the device. DSP compensation can help. $\endgroup$ – hops May 17 '17 at 15:56
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The closer the sampling rate is to twice the bandwidth, the steeper the transition band of anti-aliasing filter needs to be, resulting in a more expensive and/or more complicated filter, and/or a worse filter (passband ripples, aliasing, etc.) Thus, the filter can be made better and/or cheaper if the sample rate is higher. And the sampling rate can be implemented arbitrarily higher than twice the bandwidth.

However, the cost of the DAC and the digital path (wires, buffers, memory, digital filters, etc.) feeding the DAC usually goes up with the sample rate.

So there has to be a trade-off, where the DAC sampling rate is higher than twice the needed bandwidth to allow a better or cheaper filter, but not unnecessarily higher (unless perhaps there is "free" excess hardware bandwidth and capability lying around), or else the digital implementation cost explodes.

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