Understanding Oversampling in DACs: Theory and Practical Benefits

In this tutorial we’re going to explore how oversampling in digital-to-analog converters (DACs) can improve signal fidelity. It does this by making reconstruction or anti-image filter design less complex and improving overall signal to noise ratio (SNR) for the DACs analog output signal. The main tradeoff of oversampling is getting a faster DAC to support the faster sampling rate. 

If you’re working with waveform generation—whether for audio, communications, or precision instruments —this is a technique that can make a big difference in the signal fidelity of your design.

What Does a DAC Do and what is Oversampling?

A digital-to-analog converter (DAC) takes digital input data and produces an analog output signal at a given clock rate or sample rate.

Figure 1. DAC overview

A DAC's output analog signal bandwidth is going to be limited by its sample rate. According to the Nyquist Sampling Theorem:

  • Maximum theoretical output signal bandwidth = sample rate / 2

However, the Nyquist Sampling Theorem is theoretical and due to non-ideal aspects of all  real-world DAC circuits, you typically need more than 2 samples to produce an accurate analog waveform. The concept of DAC oversampling is all about going well beyond the Nyquist sampling rate.

Oversampling means using more samples than is required to accurately generate an AC analog signal. For example, you can create an accurate sinewave with a DAC using 4–8 points per cycle. But with oversampling you would want to push that sample count to 12, 24, or even 32 points per cycle. One important point is you are still trying to generate the same analog signal at the same frequency or bandwidth. But you are doing it at a higher sampling rate allowing you to add more points to a given waveform cycle. 

DAC Image Frequencies and Reconstruction Filter Design

DAC outputs are not smooth—they produce a step waveform, as shown in the figure 2 sine wave in orange below. which introduces unwanted frequency components called image frequencies. Most applications want to filter out these image frequencies and get a smooth analog signal like the one in figure 2 in blue. 

Figure 2. Sinewave from DAC before and after reconstruction filter

Figure 3 features a frequency domain look at a DAC outputting a sine wave with no reconstruction filter and where the resulting Image frequencies occur at. The spectral content in figure 3 is shown within a Sinc envelope which can be used to define the roll off of the images as frequency increases.  

Figure 3. Frequency domain view of a DAC's output with no reconstruction filter

The frequency values where the images occur can be calculated using the following formula. 

f=k⋅fs±fsignalf = k \cdot f_s \pm f_{signal}

Where:

  • fsf_s = DAC sample rate
  • kk = integer harmonic
  • fsignalf_{signal} = desired output frequency

Example:

  • Sample rate = 60 MHz
  • Sine wave signal frequency = 10 MHz

The image frequencies will appear at:

  • 50 MHz, 70 MHz
  • 110 MHz, 130 MHz
  • etc.

If you are interested in the math behind how this image frequency formula was derived check out this Wikipedia article on the Whittaker-Shannon Interpolation Formula.

How Oversampling makes Filtering Out Image Frequencies Easier

To filter unwanted image frequencies out a Reconstruction filter (low-pass filter) is employed. These filters often have more than one stage and require a steep roll off to ensure good attenuation of the first image frequency. Referring back to the example of creating 10MHz signal, what if we doubled the sample rate of the DAC? If we went from a sample rate of 60 MHz to 120 MHz, the first image frequency would not occur until 110 MHz instead of 50 MHz. That would allow us to use a filter with a longer roll off and still obtain better image frequency attenuation. This reduces the cost and complexity of the DAC's reconstruction filter. 

Without oversampling:

  • Image frequencies are close to the signal
  • Requires high cost and more complex filter circuits with a steep roll off

With oversampling:

  • Image frequencies move farther away from the signal of interest (in the frequency domain)
  • Allows simpler, lower-order filters

The following is a demonstration of the benefits of oversampling for filtering out image frequencies and increasing signal to noise ratio (SNR). In this demo we use Anabit's Reflex DAC reference design which does not have a reconstruction filter. A ESP32-S3 board was used to setup and control the Reflex DAC via SPI communication. Finally a Moku Go instrument is used, which  includes an adjustable digital filter and a spectrum analyzer. See the demo set up in figure 4. 

 

Figure 4. DAC oversampling demo setup

Figure 5 shows a screen shot from the Moku Go's spectrum analyzer capturing the DAC's output with no filtering. The sinewave frequency is about 22.8 kHz with about a 20 dBm power level on the far left of the spectrum. The sample rate of the DAC is about 180 kHz and you can clearly see the image frequencies around the sample rate as well as its 2nd, 3rd, and 4th harmonics. 

 

Figure 5. Reflex DAC generating 22.8 kHz sine wave at a sample rate of ~180 kHz, no reconstruction filter

Next we apply a 3rd order cascaded filter to the signal with a cutoff frequency of about 58.5 kHz. The resulting spectrum is shown in figure 6. Note that the image frequency's have been attenuated to the point that you can no longer see some of the higher frequency images. But you can still see some of the image frequencies with one closet to our sine wave frequency showing a power level of about -30 dBm. 

Figure 6. Reflex DAC output with 3 pole low pass filter

Next, to show the benefits of oversampling, we increased the sample rate by a factor of 4x but kept the same sine wave frequency of 22.8 kHz. The resulting frequency spectrum of the signal with no filter can be seen in figure 7. Note that the image frequencies are further away in the frequency spectrum from the sine wave frequency. Also note that between figure 5 and 7 you can see that the overall noise floor of the signal dropped a bit leading to an improved SNR.  

Figure 7. Reflex DAC outputting 22.8 kHz sine wave with 4x faster sample rate (oversampling)

In figure 8, with the same 58.5 kHz 3rd order filter applied to the oversampled signal, we can no longer see the image frequencies. The only frequency component we can see is the 22.8 kHz sine wave. 

Figure 7. Reflex DAC outputting 22.8 kHz sine wave with 4x faster sample rate and 3 pole filter

As you can see from this simple demo, oversampling allowed us to increase signal fidelity of the DAC's analog output signal using a simple 3rd order filter. 

DAC oversampling summary

From this tutorial you can see how employing oversampling in your DAC circuits can help  increase the analog signal fidelity and reduce filter design complexity. Oversampling is a valuable tool in applications such as communications, audio signal generation, and test and measurement instruments. The main tradeoff of using oversampling is the need for a DAC with a faster sample rate. When moving to a DAC with a faster sample rate the cost of that DAC will go up (all other things being equal). Some of that increase in DAC cost may be offset by the reduced complexity and cost of the reconstruction filter circuit. 

Questions or comments from this tutorial? Post them on Anabit's Forum

Click here for more information on oversampling with DACs check out this Analog Devices MT-017 tutorial entitled "Oversampling Interpolating DACs" by Walt Kester

Click here to check out Anabit's DAC reference designs

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