DAC Interpolation

# DAC Interpolation: More Updates, Easier Image Filtering

DAC interpolation increases the digital sample rate before analog conversion by computing additional samples with a digital filter. For an integer factor L, the DAC core can update at L times the input sample rate while representing the same intended signal band.

The extra samples do not create new source information. They provide a higher-rate representation of the existing bandlimited signal. This can move core-rate analog images farther from the desired band and reduce zero-order-hold droop at a given analog frequency.

## 1. Separate zero insertion from filtering

*Conceptual integer-rate baseband interpolator. The displayed zeros are mathematical sequence values; a particular interface may encode zero amplitude differently, such as midscale in offset-binary coding.*

Upsampling by L inserts L − 1 zeros between original samples. In the discrete-time spectrum, this creates repeated copies of the input spectrum across the higher-rate frequency range. A digital low-pass interpolation filter passes the wanted copy and attenuates the intermediate images.

Zero insertion alone is not a completed reconstruction of the signal at the higher rate. It also changes amplitude normalization. In the usual zero-insertion convention, the interpolation filter has passband gain L to preserve the amplitude of the represented waveform. A device implementation may distribute scaling among stages, so confirm its documented gain and full-scale behavior.

Efficient polyphase filters combine upsampling and filtering without explicitly storing and processing all the inserted zeros. Cascaded stages can achieve larger factors with different clock rates and filter structures. The conceptual model remains useful for checking spectra and gain.

## 2. Compare the image locations

*Calculated frequency-band locations, not amplitude spectra. The lower diagram assumes adequate digital suppression of the intermediate replicas; a finite filter leaves residuals that must be checked.*

For a wanted baseband from DC to B, the first image band around a conventional DAC core rate fs extends from fs − B to fs + B. In the example, a 25-MS/s input with B = 5 MHz has a nearest image edge at 20 MHz without interpolation. Raising the core rate to 100 MS/s with proper 4× interpolation moves that core-rate edge to 95 MHz.

The analog transition interval from the wanted edge to the nearest core-rate image edge increases from 15 MHz to 90 MHz. This can relax a DAC reconstruction filter. It does not mean all unwanted content below 95 MHz vanishes: residual intermediate images, harmonics, spurs and clock-related feedthrough still require evaluation.

## 3. Recompute hold droop using the core rate

For a conventional DAC zero-order hold, normalized magnitude is |sin(πf/fs)/(πf/fs)|. At the fixed analog frequency 5 MHz, that factor is about 0.935, or −0.58 dB, for fs = 25 MS/s. At fs = 100 MS/s it is about 0.996, or −0.036 dB.

These are ideal hold-only calculations. Digital passband ripple, optional inverse-sinc compensation, the analog output stage and the reconstruction network modify the complete response. Return-to-zero or other pulse modes use a different hold response. Use the actual selected mode and core rate rather than the data-port rate.

## 4. Respect the original signal bandwidth

Increasing the rate does not recover information already lost to aliasing or increase the original source’s independent signal bandwidth. A conventional baseband interpolator must accommodate a wanted band that fits within the input sampling constraints and its own specified passband.

An interpolation filter also needs a transition region between its passband and stopband. A filter cannot both preserve and reject content at the same frequency boundary with zero transition width and finite length. Read the supported signal bandwidth, passband flatness and stopband rejection for each interpolation mode.

Some converters include digital mixers or high-pass interpolation modes for frequency translation and image selection. Those require their own frequency plan. The low-pass baseband example does not describe every RF DAC operating mode.

## 5. Budget gain, headroom and latency

Filter output samples can exceed the largest original sample value for some sequences. Allow numerical and analog headroom, check fixed-point scaling, and test for clipping with representative signals. More sample positions alone do not imply more effective resolution, lower distortion or a guaranteed signal-to-noise improvement.

Digital filtering adds latency and a phase response. A linear-phase FIR of length M at a specified stage rate has group delay (M − 1)/2 samples at that rate; cascaded stages require converting their delays to a common time reference. Converter pipeline delay and interface buffering add further latency. Use documented timing for the actual mode when synchronizing channels or closing a control loop.

Higher core rate can also change power, clocking requirements and implementation limits. Check supported input rates, interpolation factors and clock relationships together rather than selecting each independently.

## 6. Verify each boundary of the path

Test input tones and representative modulated signals near the passband edges. Confirm gain, clipping margin, image suppression and latency in the selected mode. Measure both the desired output and residual replicas related to the input rate, as well as images around the DAC core rate.

Record input rate, interpolation factor, core rate, filter mode, digital gain, output pulse mode and analog termination. Compare the measured output with a model containing the interpolation filter, DAC hold and analog network. That combined model distinguishes successful rate conversion from simply clocking a zero-stuffed sequence faster.

## References

• [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) — interpolation filtering and analog image spacing.
• [Analog Devices AD9775 data sheet](https://www.analog.com/media/en/technical-documentation/data-sheets/ad9775.pdf) — a concrete interpolating DAC with selectable rates and filter modes; implementation details are device-specific.
• [Texas Instruments: Interpolation Filters in RF Sampling DACs](https://www.ti.com/document-viewer/lit/html/SSZTAF1/GUID-9E2A6DC6-AE7A-431F-AE9D-5CF7EC0B7AA3) — cascaded interpolation and digital filter structures.