DAC Reconstruction Filter

# DAC Reconstruction Filter: Keep the Wanted Band, Reject the Images

A DAC reconstruction filter shapes the analog output spectrum so the receiving circuit sees the intended frequency band with acceptable unwanted content. For baseband output it is commonly a low-pass filter. In systems that deliberately use a higher DAC image, it may instead be a band-pass filter.

The filter is selected from passband accuracy, image rejection, phase, settling and loading requirements. Simply making a staircase look smooth on an oscilloscope is not a complete design criterion.

## 1. Locate the nearest image before choosing a cutoff

Baseband DAC signal band and first image bandConceptual positive-frequency bands for a one hundred megasample-per-second DAC with signal bandwidth ten megahertz. Desired band zero to ten megahertz, first image band ninety to one hundred ten megahertz, eighty megahertz between desired edge and nearest image edge. Heights not to scale.Pass the signal. Attenuate its images.Example: fs = 100 MS/s · desired baseband extends to 10 MHz01090100110Wanted bandFirst image bandMHz80-MHz transition spaceConceptual bands; heights are not spectral amplitudes.Nearest image edge: fs − B = 90 MHzAvailable transition interval: fs − 2B = 80 MHzFor baseband reconstruction with B below fs/2.

*Conceptual positive-frequency band locations. The rectangles indicate occupied frequency intervals, not constant spectral density or measured amplitude. The example assumes a real baseband signal extending from DC to B.*

For a conventional DAC update rate fs and desired bandwidth B below fs/2, the first positive-frequency image band extends from fs − B to fs + B. The nearest unwanted edge is therefore fs − B. The interval between the wanted edge B and that image edge is fs − 2B.

At fs = 100 MS/s and B = 10 MHz, the nearest edge is 90 MHz and the available transition interval is 80 MHz. If B increases toward 50 MHz, the interval shrinks. The analog filter becomes more demanding because it must preserve desired frequencies while rejecting unwanted frequencies much closer to them.

Use the actual DAC core update rate. An upstream input-data rate may differ when digital interpolation is enabled. An interpolation filter can suppress intermediate replicas and increase spacing at the analog output, but its finite rejection and the DAC’s actual pulse mode must be included.

## 2. Quantify passband loss and rejection together

Calculated first and third order Butterworth reconstruction responsesCalculated gain in decibels versus frequency zero to one hundred megahertz for ideal first and third order Butterworth low-pass filters with twenty megahertz cutoff. At ten megahertz losses are0.97and0.067dB; at ninety megahertz attenuations13.3and39.2dB. Excludes DAC hold response and circuit parasitics.Filter order changes rejection and lossIdeal Butterworth low-pass · fc = 20 MHz · no DAC sinc included0-20-40-60020406080100Gain / dBMHz1st order3rd orderAt 10 MHz: −0.97 dB vs. −0.067 dBAt 90 MHz: −13.3 dB vs. −39.2 dBIdeal transfer functions, not a component-level design.

*Calculated ideal analog Butterworth responses. Both have a 20-MHz −3-dB cutoff. These curves exclude DAC sinc droop, finite component Q, amplifier bandwidth and board coupling.*

For an nth-order Butterworth low-pass response, magnitude is 1/sqrt(1 + (f/fc)^(2n)). The chart compares n = 1 and n = 3 at fc = 20 MHz. At the 10-MHz wanted edge, their losses are approximately 0.97 dB and 0.067 dB. At the 90-MHz image edge, their attenuations are approximately 13.3 dB and 39.2 dB.

Neither curve is automatically the right answer. The required passband loss and image limit determine whether either is sufficient. The third-order response achieves stronger frequency separation, but realizing it requires additional circuitry and introduces a different phase and transient response.

Filter attenuation at an image is not, by itself, the final image level relative to the desired signal. Combine the DAC’s image-to-signal ratio with the difference between filter gain at the image frequency and gain at the desired frequency. Perform that comparison over the complete wanted band and relevant image bands.

## 3. Include the DAC hold response

A conventional DAC zero-order hold produces a sinc envelope. It attenuates desired high-frequency components as well as images, but it does not remove every image between its zeros. The DAC, reconstruction network, buffer and load form one combined response.

A simple low-pass filter adds passband loss rather than inherently correcting sinc droop. Equalization can compensate a specified band when there is enough headroom, but it has its own noise and out-of-band consequences. Keep equalization and image rejection explicit in the model instead of treating them as interchangeable functions.

## 4. Select a realizable response and interface

Butterworth designs have a maximally flat magnitude response near DC. Other approximations trade amplitude ripple, transition steepness, group delay and transient behavior differently. Choose the response from the actual signal requirements rather than assuming the steepest rolloff is always best.

Passive networks depend on their source and load impedances; connecting a network intended for one termination to a different load changes its response. Active filters add amplifier noise, distortion, slew and stability constraints. At high frequencies, component self-resonance, finite Q, package parasitics and PCB coupling can limit achievable rejection.

For a current-output DAC, check output compliance and the recommended current-to-voltage interface. For a voltage-output DAC, check load drive and stability. A mathematically correct filter can still overload or destabilize the source that drives it.

## 5. Check time-domain and system consequences

Filtering can reduce the visible peak of a switching disturbance while extending its duration. Include the network when evaluating DAC settling time, pulse fidelity and the observation window of the receiving circuit. A frequency-domain amplitude target alone may not constrain overshoot or delay enough for a control system.

A reconstruction filter acts after conversion. An ADC anti-alias filter acts before sampling. They can use similar circuits, but their positions and error mechanisms differ. Filtering the DAC output cannot undo aliasing that has already corrupted the digital samples.

## 6. Verify the assembled path

Measure passband gain, phase or group delay where relevant, and rejection through the required stopband. Use the intended termination and enough instrument dynamic range to resolve the unwanted components. Check whether fixture leakage or board coupling bypasses the filter and creates a rejection floor.

Test representative DAC tones and waveforms, including band-edge signals. Separate sampling images from harmonics, clock feedthrough and spurs: not every unwanted line follows the same model. Record core rate, interpolation mode, output pulse mode, load, reference level and measurement bandwidth. Compare the complete measured output with the combined DAC-and-filter prediction.

## References

  • [Texas Instruments: DAC Output Response](https://www.ti.com/content/dam/videos/external-videos/en-us/2/3816841626001/5577272810001.mp4/subassets/TIPL4705-DAC-Output-Response.pdf) — DAC images, pulse response and reconstruction filtering.
  • [Analog Devices: Mixed-Signal Components for Digital Communications Systems, Part V](https://www.analog.com/en/resources/analog-dialogue/articles/mixed-signal-components-for-digital-communications-systems-part-v.html) — sample-rate and signal-band spacing for analog reconstruction.
  • [Analog Devices AN-837: DDS-Based Clock Jitter Performance vs. DAC Reconstruction Filter Performance](https://www.analog.com/en/resources/app-notes/an-837.html) — practical rejection limits and layout effects.

Take DAC reconstruction filter further

Ask the copilot about this term, or have our engineers assess it against your process.

Ask CFSGPT about this → Request a technical assessment → Open the CFS app