Delta-sigma demystified: Basics behind high-precision conversion

Delta-sigma (ΔΣ) converters may sound complex, but at their core, they are all about precision. In this post, we will peel back the layers and uncover the fundamentals behind their elegant design.

At the heart of many precision measurement systems lies the delta-sigma converter, an architecture engineered for accuracy. By trading speed for resolution, it excels in low-frequency applications where precision matters most, including instrumentation, audio, and industrial sensing. And it’s worth noting that delta-sigma and sigma-delta are interchangeable terms for the same signal conversion architecture.

Sigma-delta classic: The enduring AD7701

Let us begin with a nod to the venerable AD7701, a 16-bit sigma-delta ADC that sets a high bar for precision conversion. At its core, the device employs a continuous-time analog modulator whose average output duty cycle tracks the input signal. This modulated stream feeds a six-pole Gaussian digital filter, delivering 16-bit updates to the output register at rates up to 4 kHz.

Timing parameters—including sampling rate, filter corner, and output word rate—are governed by a master clock, sourced either externally or via an on-chip crystal oscillator. The converter’s linearity is inherently robust, and its self-calibration engine ensures endpoint accuracy by adjusting zero and full-scale references on demand. This calibration can also be extended to compensate for system-level offset and gain errors.

Data access is handled through a flexible serial interface supporting asynchronous UART-compatible mode and two synchronous modes for seamless integration with shift registers or standard microcontroller serial ports.

Introduced in the early 1990s, Analog Devices’ AD7701 helped pioneer low-power, high-resolution sigma-delta conversion for instrumentation and industrial sensing. While newer ADCs have since expanded on their capabilities, AD7701 remains in production and continues to serve in legacy systems and precision applications where its simplicity and reliability still resonate.

The following figure illustrates the functional block diagram of this enduring 16-bit sigma-delta ADC.

Figure 1 Functional block diagram of AD7701 showcases its key architectural elements. Source: Analog Devices Inc.

Delta-sigma ADCs and DACs

Delta-sigma converters—both analog-to-digital converters (ADCs) and digital-to-analog converters (DACs)—leverage oversampling and noise shaping to achieve high-resolution signal conversion with relatively simple analog circuitry.

In a delta-sigma ADC, the input signal is sampled at a much higher rate than the Nyquist frequency and passed through a modulator that emphasizes quantization noise at higher frequencies. A digital filter then removes this noise and decimates the signal to the desired resolution.

Conversely, delta-sigma DACs take high-resolution digital data, shape the noise spectrum, and output a high-rate bitstream that is smoothed by an analog low-pass filter. This architecture excels in audio and precision measurement applications due to its ability to deliver robust linearity and dynamic range with minimal analog complexity.

Note that from here onward, the focus is exclusively on delta-sigma ADCs. While DACs share similar architectural elements, their operational context and signal flow differ significantly. To maintain clarity and relevance, DACs are omitted from this discussion—perhaps a topic for a future segment.

Inside the delta-sigma ADC

A delta-sigma ADC typically consists of two core elements: a delta-sigma modulator, which generates a high-speed bitstream, and a low-pass filter that extracts the usable signal. The modulator outputs a one-bit serial stream at a rate far exceeding the converter’s data rate.

To recover the average signal level encoded in this stream, a low-pass filter is essential; it suppresses high-frequency quantization noise and reveals the underlying low-frequency content. At the heart of every delta-sigma ADC lies the modulator itself; its output bitstream represents input signal’s amplitude through its average value.

A block diagram of a simple analog first-order delta-sigma modulator is shown below.

Figure 2 The block diagram of a simple analog first-order delta-sigma modulator illustrates its core components. Source: Author

This modulator operates through a negative feedback loop composed of an integrator, a comparator, and a 1-bit DAC. The integrator accumulates the difference between the input signal and the DAC’s output. The comparator then evaluates this integrated signal against a reference voltage, producing a 1-bit data stream. This stream is fed back through DAC, closing the loop and enabling continuous refinement of the output.

Following the delta-sigma modulator, the 1-bit data stream undergoes decimation via a digital filter (decimation filter). This process involves data averaging and sample rate reduction, yielding a multi-bit digital output. Decimation concentrates the signal’s relevant information into a narrower bandwidth, enhancing resolution while suppressing quantization noise within the band of interest.

It’s no secret to most engineers that second-order delta-sigma ADCs push noise shaping further by using two integrators in the modulator loop. This deeper shaping shifts quantization noise farther into high frequencies, improving in-band resolution at a given oversampling ratio.

While the design adds complexity, it enhances signal fidelity and eases post-filtering demands. Second-order modulators are common in precision applications like audio and instrumentation, though stability and loop tuning become more critical as order increases.

Well, at its core, the delta-sigma ADC represents a seamless integration of analog and digital processing. Its ability to achieve high-resolution conversion stems from the coordinated use of oversampling, noise shaping, and decimation—striking a delicate balance between speed and precision.

Delta-sigma ADCs made approachable

Although delta-sigma conversion is a complex process, several prewired ADC modules—built around popular, low-cost ICs like the HX711, ADS1232/34, and CS1237/38—make experimentation remarkably accessible. These chips offer high-resolution conversion with minimal external components, ideal for precision sensing and weighing applications.

Figure 3 A few widely used modules simplify delta-sigma ADC practice, even for those just starting out. Source: Author

Delta-sigma vs. flash ADCs vs. SAR

Most of you already know this, but flash ADCs are the speed demons of the converter world—using parallel comparators to achieve ultra-fast conversion, typically at the expense of resolution.

Flash ADCs and delta-sigma architectures serve distinct roles, with conversion rates differing by up to two orders of magnitude. Delta-sigma ADCs are ideal for low-bandwidth applications—typically below 1 MHz—where high resolution (12 to 24 bits) is required. Their oversampling approach trades speed for precision, followed by filtering to suppress quantization noise. This also simplifies anti-aliasing requirements.

While delta-sigma ADCs excel in resolution, they are less efficient for multichannel systems. Architecture may use sampled-data modulators or continuous-time filters. The latter shows promise for higher conversion rates—potentially reaching hundreds of Msps—but with lower resolution (6 to 8 bits). Still in early R&D, continuous-time delta-sigma designs may challenge flash ADCs in mid-speed applications.

Interestingly, flash ADCs can also serve as internal building blocks within delta-sigma circuits to boost conversion rates.

Also, successive approximation register (SAR) ADCs sit comfortably between flash and delta-sigma designs, offering a practical blend of speed, resolution, and efficiency. Unlike flash ADCs, which prioritize raw speed using parallel comparators, SAR converters use a binary search approach that is slower but far more power-efficient.

Compared to delta-sigma ADCs, SAR designs avoid oversampling and complex filtering, making them ideal for moderate-resolution, real-time applications. Each architecture has its sweet spot: flash for ultra-fast, low-resolution tasks; delta-sigma for high-precision, low-bandwidth needs; and SAR for balanced performance across a wide range of embedded systems.

Delta-sigma converters elegantly bridge the analog and digital worlds, offering high-resolution performance through clever noise shaping and oversampling. Whether you are designing precision instrumentation or exploring audio fidelity, understanding their principles unlocks a deeper appreciation for modern signal processing.

Curious how these concepts translate into real-world design choices? Join the conversation—share your favorite delta-sigma use case or challenge in the comments. Let us map the noise floor together and surface the insights that matter.

T.K. Hareendran is a self-taught electronics enthusiast with a strong passion for innovative circuit design and hands-on technology. He develops both experimental and practical electronic projects, documenting and sharing his work to support fellow tinkerers and learners. Beyond the workbench, he dedicates time to technical writing and hardware evaluations to contribute meaningfully to the maker community.