**Amplifiers/Converters??**

# Use CT delta-sigma ADCs to cut down power consumption

**Keywords:ADC technology?
amplifier?
Continuous time?
CT delta sigma?
CT?
**

**By Mark HoldawayXignal Technologies GmbH**

Continuous time (CT) delta-sigma ADC technology shatters the conventional wisdom that pipeline ADCs are the only conversion technique available for high-speed, dynamic range applications. CT delta sigma technology offers lower-power operation, better dynamic performance and economy of design.

CT delta sigma is an inherently power-efficient architecture that eliminates power-hungry sample-and-hold amplifiers and the wide-bandwidth gain stages essential to the pipeline ADC concept. An alias-free Nyquist sample range is made available by exploiting inherent oversampling and on-chip digital filtering.

Digital filtering permits tailoring of group delay performance and the signal transfer function to specific applications. The integration of a clock and low jitter PLL, elimination of anti-aliasing filters and integration of input gain stages simplify input signal path design of high-resolution data-conversion systems. Switchless design future-proofs continuous delta sigma technology through its easy migration to next-generation CMOS processes, enabling greater speed and power benefits.

The architecture supports high-resolution ADC systems from 10bit to 16bit and beyond with sampling rates up to 100MHz. Today, most ADC designs aim to reduce power, particularly in high-speed conversion, and to minimize the number of comparators needed.

**Pros and cons**

It is broadly assumed that the pipeline converter provides the highest sample rates while yielding a high dynamic range. It is used as a standard in data-conversion applications at 10bit and higher resolutions, and for sample rates from 5MHz to 100MHz or more. The architecture reduces the number of comparators needed by deploying multiple low-resolution flash conversion stages cascaded together to form the pipe.

Although the resolution of each conversion stage is reduced, the first stage must be designed with linearity at least as good as the maximum resolution of the ADC (12bit linearity for a 12bit ADC). Different pipeline implementations exist, but all work by reducing a multibit conversion into several lower-resolution "flashes" that are processed synchronously. At each stage in the pipe, a reconstruction of the previous stage's quantized output generated by a DAC is subtracted from the original input signal.

The residual signal is then amplified before moving onto the next stage for finer quantization. In pipeline conversion, a SHA needs to acquire the input signal and hold it to better than 0.5LSB for the conversion's duration. Once all sub-stages have a valid conversion result, a digital correction block constructs the final multibit result.

The pipeline ADC is capable of high dynamic performance. However, beyond 12bit resolution and as the sampled signal moves through the pipeline, transferring the charge associated with a given signal demands high-gain bandwidth to ensure that stage settling times fall within the limits set by the high-frequency signals being sampled.

To maintain linearity, you need to calibrate and correct for the limits in component matching achievable with current process technologies; it is tough to migrate designs from one process to another. As operating voltages fall from one process generation to the next, the input signal headroom is compressed. Furthermore, designing switches with reduced threshold voltages that work well in deep-submicron processes gets harder.

Remember that pipeline ADCs form only part of a data-conversion system - in addition, you need to find a low-jitter clock source and design input stages that include anti-alias filters (AAFs). In AAF design, steep attenuation characteristics are hard to achieve, tempting you to consider over-sampling the signal of interest. Over-sampling stretches the Nyquist zone, lowering demands on filter roll-off.

**Looking at the trade offs**

But the trade-offs are increased system power and higher processing speeds demanded of the back-end DSP system. With CT Delta-Sigma conversion, on the other hand, you don't need an AAF. The Delta-Sigma converter uses a low-resolution quantizer！often only 1bit！clocked at rates considerably greater than Nyquist demands. The quantizer creates many low-resolution samples that！averaged over time！yield an increased dynamic range.

The analog design is potentially straightforward, given the linearity of a 1bit (2-level) quantizer. In the digital domain, filtering and decimation！the process of sample-rate reduction！are needed to reconstruct output data and remove out-of-band noise. Figure 1 below shows the simplest single-order DS modulator block. It comprises a summing node, integrator and comparator.

Figure 1: The simplest single-order Delta Sigma modulator block components are clocked at oversampling frequency. |

The comparator's output feeds a 1bit DAC that closes the modulator's feedback loop. The modulator compares the input signal against a voltage reference level fed back from the DAC. The comparator is clocked at the oversampling frequency. Assuming enough loop gain, the modulator is a pulse stream, the density of 1s or 0s of which is a direct digital representation of the input signal. The DAC switches between Vref to close the control loop.

For the Delta Sigma ADC, resolution increases are gained by balancing the over-sampling ratio, Delta Sigma modulator order and quantizer resolution. Oversampling allows sample frequency/SNR trade-off and improves dynamic range. It gives a 6dB (or 1bit's worth) SNR improvement for every quadrupling of the sample rate, but dynamic range is more effectively enhanced by increasing the resolution of the quantizer and/or by adding more integration stages to the modulator.

Noise shaping is a property of Delta Sigma ADCs resulting from the application of feedback that extends dynamic range. This feature is best illustrated by the mathematical analysis of the feedback control loop of the Delta Sigma modulator as modeled in the frequency domain (Figure 2).

Figure 2: The quantization error is modeled as Q added to the modulator output. |

This model reveals the key value of the Delta Sigma modulator. A closed loop modulator works as a high-pass filter to quantization noise and as a low-pass filter to the input signal. The effect of this is a further increase in dynamic range of 9dB for each doubling of the sample rate. Additional integrators within the loop can increase the steepness of the noise characteristic, giving further dynamic range increases.

Figure 3 below shows simulation results for the noise power density for the Delta Sigma modulator used in a CT Delta Sigma ADC. This FFT plot (with 65k points) of the modulator illustrates the noise power density (per FFT bin) relative to the input signal frequency. The simulation was driven with an input signal frequency of approximately 4.8MHz.

Figure 3: The quantization noise simulation result hints at the unrealized dynamic range of a multibit Delta Sigma modulator used in a CT Delta Sigma ADC. |

The minimum noise power density achieved by this modulator is 166dBc/Hz (in the pass band). Note the characteristic of the out-of-band noise！i.e. those frequencies above 20MHz. Here, noise power levels rise at the rate of 21dB/octave, a telltale sign of a third order modulator.

Deployed within this ADC design is a 16-level (or 4bit) quantizer that delivers 14bit dynamic range at modest over sampling rates. Having established a modulator system capable of achieving these low noise levels, the next stage is to apply filtering to eliminate out-of-band noise and decimation to resample the data.

A digital filter must reject all signal components within the serial data stream that occurs beyond the Nyquist bandwidth. Simplistically, two frequency-selective filter structures can be implemented in the digital domain. They are the finite and infinite impulse response filter systems (FIRs and IIRs, respectively). FIRs are more widely used because they are simpler and have a linear phase response. IIR filter design is more complicated by virtue of the feedback included.

The potentially infinite response of the IIR filter means that there is always a possibility for the filter to become unstable. In addition, group delay can become significant and have adverse effects on performance in some systems. Many degrees of freedom exist for signal transfer function optimization in a CT Delta-Sigma ADC by combining different filter algorithms. However, optimal solutions may require many cascaded stages of FIR and IIR sections. Digital filtering allows for the data reduction or downsampling necessary to provide output data at the originally intended sample rate.

In summary, the basic elements of a Delta-Sigma ADC are over-sampling, noise shaping and digital filtering. Oversampling spreads quantization noise; noise shaping reduces the in-band noise at the expense of higher out-of-band noise; and digital filtering attenuates out-of-band noise and signal components.

**CT vs. discrete time systems**

Most Delta-Sigma converters found in audio and precision applications exploit switched capacitor, discrete time (DT), loop filters within the modulator for noise shaping. Switched capacitor filters create their own mixing products, and the DT Delta Sigma design is susceptible to this type of noise aliasing. But the advantage of DT schemes is their relatively simple architecture - the way that increased sample rates produce dynamic range improvements and their compatibility with VLSI CMOS processes.

However, the switched capacitor stages act as a limit on the maximum signal bandwidth in the DT Delta-Sigma ADC. Moving to CT loop filters opens up new application possibilities including wide baseband sampling out to several tens of MHz to under-sampling RF signals in bandpass designs. Pipeline and DT Delta-Sigma ADCs have a common design thread. In discrete time, sampling an input signal requires the signal to be acquired at a precise moment.

For an accurate representation of the input signal, the input stages should settle to a finite level, dictated by the accuracy limits of the system and a time period driven by the system sample-rate needs. This settling time eats into the sample time period of the system.

At 40MSps, a conversion system can have a sample period of just 25ns, setting the maximum time limits for circuit settling. At higher resolutions, this drives the need for very high gain bandwidth circuits within the acquisition signal path. In fact, the converter system must be designed with circuits that work with bandwidths many times that of the input signal.

Thus, discrete time circuits have to burn excess power to process a given bandwidth. The move to a CT strategy eliminates the settling time issue altogether, allowing either a lower-power CT Delta-Sigma ADC implementation vs. discrete time, at a given sample rate or a higher sample rate for a given power budget. There is no acquisition phase in CT Delta-Sigma , so a high performance sample-and-hold stage is eliminated. CT does not require the high-gain bandwidth stages necessary to force rapid settling, so power in these stages is reduced.

A little more power is demanded from the post modulator digital filter stages, but the CT loop filter reduces the power demands of the modulator and eliminates the additional discrete time-sampling effects seen in the DT DS ADC. In addition, there is no down-mixing of noise, eliminating any additional spectral spurs in the baseband.

With CT Delta-Sigma the filter performance is dependent on conventional active filter design rules. If the sample rate is changed to match input signal bandwidth, the CT filter must be tuned. Thus, a potential limit on the CT Delta-Sigma implementation is how to ensure that a wide range of sample rates can be supported from a single product platform. This problem is solved using adaptive filter combined with calibration techniques.

For high-resolution implementations, the loop filter must have significant gain to obtain high linearity. This is provided using multipath and cascaded gain stages operating at 1.2V and delivering 80dB of gain for a 30MHz bandwidth. This has been clearly demonstrated as possible in 0.1?m CMOS. The first product to implement CT Delta-Sigma conversion offers a low-power alternative to the pipeline converter. It is said to be a complete data-conversion system, designed to operate seamlessly over a wide range of sample rates without high-performance, expensive and external components.

**Simplify application**

Xignal's implementation of a CT Delta-Sigma quantizer and digital filtering supports resolutions up to and beyond 14bits. The general-purpose ADC core is combined with several features designed to simplify its application. It consumes less power - 60mW for the ADC core, leading to an energy figure of merit (FOM) of 0.79pJ/conversion.

The CTDS ADC architecture eliminates complex input filtering due to the effect of oversampling in combination with digital filtering (Figure 4, below). With filter performance characteristics set in the digital domain, a very high level of pass-band flatness and steep roll-off is possible. The current digital filter allows 90 percent of the first Nyquist zone to be exploited whilst offering a pass-band ripple of only ＼0.0002dB and 80dB stop-band attenuation. Group delay for this filter is only 0.33 samples.

Figure 4: CT Delta Sigma ADC eliminates complex input filtering. |

A third-order CTDS modulator is used, designed around a 4bit quantizer stage achieving dynamic range at an oversampling rate of 16. The differential input signal path has a bandwidth of 30MHz. The internal sample clock operates at 640MHz. Today's technology allows for increased sample rates to 80MSps (at 14bits) with an over-sampling clock rate of approximately 1.3GHz. Through self-adaptive tunable loop filter components, the ADC is optimized for sample rates of 20MSps to 40MSps.

The clock source is integrated on-chip with the ADC core. The ADC just needs a low-cost crystal, parallel connected to its clock input. The clock is connected to a high-performance PLL block that uses an on-chip LC-tuned circuit to create a high-Q resonator, creating a precise clock source.

Alternatively, an external clock can drive the ADC. High-frequency jitter from an external distributed clock tree will be removed, provided its jitter falls outside the 350kHz PLL bandwidth of the jitter cleaner circuit. However, an advantage of the on-chip precision clock is that it can be routed to external circuits. Furthermore, it can be used as a system reference clock for other time-critical parts of the system, potentially eliminating the extra cost of a low-jitter source, saving both design effort and board area.

A low-jitter clock is a crucial function in all high-speed, high-resolution data-conversion systems. Phase accuracy of the sample clock has a major impact on measured performance. In fact, decibels of dynamic range are easily sacrificed by picoseconds of phase jitter.

Figure 5 below shows the mathematical derivation of maximal clock jitter for a given resolution and input signal frequency. For a 10MHz bandwidth signal, at 12bit resolution, clock jitter must be less than 3ps rms. For 14bits, this demand drops to 1ps rms.

Figure 5: For a 10MHz bandwidth signal, at 12bit resolution, clock jitter must be less than 3ps rms. |

The initial results are encouraging and better than the FOMs achieved by contemporary pipeline ADC designs. Furthermore, the architecture has the ability to scale with CMOS process developments and to yield further increases in efficiency and speed. This is important as pipeline design will become more challenging within the restrictive confines of the CMOS process roadmap with its sub-bandgap threshold requirements.

The ongoing development at Xignal shows that the ADC core can be successfully combined with input signal path components to provide a high level of integration. The digital processing (filtering and decimation) provided also shows that in the future, it is possible for system designers to tailor-transfer functions for a given application. Finally, the elimination of external anti-alias networks and the inclusion of a high-performance PLL significantly ease the design of a high-resolution, high-speed sampling system.

The quantization noise simulation result hints at the unrealized dynamic range of a multibit DS modulator. There is some room for further dynamic range improvements with careful design, particularly with thermal noise - the dominant noise source in this design today. Although complex, the deployed CTDS ADC has been implemented in such a way to be transparent to the user.

**About the authorMark Holdaway** is director of product marketing, ADC Products at Xignal Technologies GmbH, now a subsidiary of National Semiconductor.

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