--- title: "R-2R Ladder DACs: How Resistor Conversion Works" description: "How an R-2R ladder turns bits into voltage, why resistor matching is the hard part, and what a ladder DAC genuinely does differently from delta-sigma." url: "https://theaudiostuff.com/glossary/r-2r/" type: "website" author: "Jakub Charkiewicz" --- > Markdown rendering of https://theaudiostuff.com/glossary/r-2r/ > Canonical URL to cite: https://theaudiostuff.com/glossary/r-2r/ > Generated from the published page. Text and links only; see the HTML for layout. Breadcrumb: [Home](https://theaudiostuff.com/) > [Glossary](https://theaudiostuff.com/glossary/) > R-2R Audio glossary # R-2R Ladder DACs: How Resistor Conversion Works An R-2R DAC converts audio with a ladder of precision resistors, one rung per bit, each contributing exactly half the weight of the one above it. It reconstructs the sample directly rather than approximating it with a high-speed pulse stream, and its performance is limited by how precisely those resistors can be matched. ## How the ladder works The name describes the circuit. It is built from resistors of just two values, R and 2R, arranged in a repeating ladder, one rung per bit of the sample. Each rung is switched by its bit. Turn a bit on, that rung contributes current; turn it off, it does not. The ladder is arranged so each rung contributes exactly half the current of the rung above it, matching the binary weighting of the sample itself. Sum the contributions and you have a voltage that directly represents the number. That is the appeal: the conversion is direct. The value you asked for is constructed as a real voltage in one step, with no [oversampling](https://theaudiostuff.com/glossary/#oversampling), no modulator, and no shaped noise to filter away. ## Why it is hard, and expensive The halving has to be exact, and it has to stay exact. For 16-bit conversion, the least significant rung contributes 1/65,536 of full scale. For 24-bit, one part in 16.7 million. Any resistor that is off by more than its rung's contribution introduces an error that is *correlated with the signal*, because it appears whenever that bit is set. Real resistors have manufacturing tolerance, they drift with temperature, and they age. Holding one-part-in-a-million matching across a ladder, across a temperature range, over years, is the entire engineering problem of a ladder [DAC](https://theaudiostuff.com/glossary/#dac). Manufacturers address it by hand-matching resistors, using expensive low-drift types, or trimming and calibrating in production. All of that is why these converters cost what they do. This is also why true 24-bit ladder performance is largely a specification rather than a measurement. The bottom bits are below the achievable matching accuracy. ## What it does differently **Error character.** A ladder DAC's errors come from component mismatch, so they scale with and correlate with the signal. A [delta-sigma](https://theaudiostuff.com/glossary/delta-sigma/) DAC's errors are quantisation noise that has been shaped and pushed out of the audio band. These are genuinely different residuals, and which one a listener prefers is a listening question rather than a measurement one. **Filtering.** Because a ladder does not oversample by nature, it can be run with much gentler reconstruction filtering, and some designs are deliberately non-oversampling. Filter behaviour, particularly [pre-ringing](https://theaudiostuff.com/glossary/#pre-ringing) ahead of transients, is one of the more audible differences between DACs, and a good deal of what gets attributed to "the ladder sound" is really the filter choice that ladder designs make possible. **Low-level linearity.** At very low signal levels a delta-sigma converter is generally more linear, because it has no matching problem to lose to. This is the opposite of the usual folklore and it is what the measurements consistently show. ## What the measurements say On distortion and [noise floor](https://theaudiostuff.com/glossary/#noise-floor) in the audio band, well implemented delta-sigma conversion generally outperforms ladder conversion, and it is not close. The matching problem is real and it sets a ceiling. Ladder DACs remain a deliberate choice because measured superiority in those two axes is not the only thing a listener is buying, and because the filtering freedom the architecture allows is a real design lever. Both of those are defensible. What is not defensible is the claim that [R-2R](https://theaudiostuff.com/glossary/#r-2r) is simply more accurate, because that is the one thing it demonstrably is not. ## Choosing one Judge the converter, not the topology. The filter design, the analogue [output stage](https://theaudiostuff.com/glossary/#output-stage), the clocking and the power supply predict how a DAC performs far better than whether it converts with a ladder or a modulator. A ladder DAC is a legitimate and often excellent choice; it is not a shortcut past listening to it. ## Reviewed gear that shows this 6 reviews in the catalogue. Every score is anchored to the same published reference list. - [HIFIMAN Serenade 9.3/10 · $999](https://theaudiostuff.com/reviews/hifiman-serenade/) - [Denafrips Enyo 15th Anniversary 9.1/10 · $699](https://theaudiostuff.com/reviews/denafrips-enyo-15th/) - [Denafrips Hades 12th 9.0/10 · $1,369](https://theaudiostuff.com/reviews/denafrips-hades-12th/) - [HIFIMAN EF500 8.2/10 · $549](https://theaudiostuff.com/reviews/hifiman-ef500/) - [HIFIMAN EF499 8.1/10 · $299](https://theaudiostuff.com/reviews/hifiman-ef499/) - [HIFIMAN EF400 7.5/10 · $399](https://theaudiostuff.com/reviews/hifiman-ef400/) ## Keep reading - [Best DACs](https://theaudiostuff.com/guides/best-dacs/) - [Full audio glossary](https://theaudiostuff.com/glossary/) - [How we test and score](https://theaudiostuff.com/about/#methodology-title)