WO2021148107A1

WO2021148107A1 - Control-bounded analog-to-digital converter

Info

Publication number: WO2021148107A1
Application number: PCT/EP2020/051369
Authority: WO
Inventors: Hans-Andrea Loeliger; Erik Hampus MALMBERG
Original assignee: Eth Zurich
Priority date: 2020-01-21
Filing date: 2020-01-21
Publication date: 2021-07-29
Also published as: WO2021148300A1

Abstract

Analog-to-digital converters are disclosed that use digitally controlled analog networks. The digital control keeps the internal continuous-time analog states within their proper physical limits. Using many separate controls leads to robust design as the control task is divided and averaged among multiple contributions. Densely interconnected analog networks allow signals to be distributed over multiple physical nodes. Oscillator control enables conversion at a frequency band other than the base band. Additionally, digitally reconfigurable analog networks enable adaptive design options for spectral shaping, effective resolution, and distribution of resources between multiple conversion processes.

Description

Control-Bounded Analog-to-Digital Converter

Technical Field

The invention relates in general to analog-to-digital (A/D) converters, in particular, A/D converters with densely connected analog networks and multiple control loops. Background Art

The proposed A/D converter is related to A/D converters as in [1, 2, 3, 4, 5, 6] and, more particularly, to control-bounded converters as in [7, 8, 9]. A general system description of a control-bounded converter is shown in Fig. 1. For control-bounded converters, the continuous-time input signal u(i) (the signal to be converted) is fed into an analog continuous-time dynamical system, which provides amplification (in certain frequency bands) and interacts with a digital control and estimation unit. The digital control and estimation unit ensures, with suitable digital control signals, that all state variables (voltages and/or currents) of the analog system remain within their proper limits. Based on these control signals, the digital control and estimation unit produces a digital estimate u(t) as described in [7] and [9].

A primary advantage of control-bounded converters is that large amplification in desired frequency bands can be achieved without concerns for stability.

An example of a control-bounded converter with local control is shown in Fig. 3 [8, 9]. In this example, the linear dynamical system is a chain of integrators. Each integrator is controlled individually with the help of a one-bit flash analog-to-digital (A/D) converter and a zero-order hold digital-to-analog (D/A) converter. A proposed circuit implementation of each integrator is shown in Fig. 2. The transfer function (i.e., the Laplace transform of the impulse response) from the input u(t) to the xp_f(t)-th state is

this means, for a sinusoidal input signal with a frequency of / we expect the signal-to-noise ratio (SNR) performance of this converter to be proportional to

where is the frequency band of interest.

The chain of integrators converter, of Fig. 3, achieves performance similar to that of an oversampling converters such as DS modulators [1]. In fact the multi stage noise shaping (MASH) DS modulator and the chain of integrator converter both share performance scaling attributes and their chain like structure,

Disclosure of the Invention The problem solved by the recent invention is to provide a more versatile architecture of this type. This problem is solved by the A/D-converter of claim 1. Accordingly, the A/D-converter has

- an analog converter input for a continuous-time input signal u(Z), with t being the time

- a digital converter output for a digital representation ύ(ί) of the input signal

A converter as described above overcomes the limitations of the chain of integrator converter, e.g. of the type of Figure 3, and may offer favorable properties including robustness against disturbances and imper- fections such as thermal noise, clock jitter, and component mismatch, power efficiency, configurability and multi-input conversion.

Specific advantages may e.g. include the following.

- Interconnections between states of the state vector may suppress the sensitivity to component mismatch, limit cycles and increase robustness against thermal noise.

- Controlling in many overlapping subspaces, as follows from an overcomplete set of column vectors in , suppress sensitivity in component mismatch as well as increases the performance of the whole converter.

- Circuit resources can be shared between multiple conversion processes.

- Configurable analog networks may enable conversion where the power consumption, the frequency tuning, mismatch suppression, and effective resolution can be instantaneously adapted. This leads to a conversion principle that utilize resources after demand. Brief Description of the Drawings

The invention will be better understood and objects other than those set forth above will become apparent when consideration is given to the following detailed description thereof. This description makes reference to the annexed drawings, wherein:

Fig. 1 shows the general architecture of a control-bounded converter as in [8].

Fig. 2 shows an operational amplifier (op-amp) realization of a first order integrator conversion mod- ule.

Fig. 3 shows the chain of integrator converter from [8],

Fig. 4 shows the general system schematic.

Fig. 5 shows a particular implementation where the control observation

and feedback matrix A share a pre-transformation Φ.

Fig. 6 describes a particular differential circuit implementation of a braided chain converter.

Fig. 7 shows the particular realization of the resistor network from Fig. 6. Namely, the f-th differen- tial input is connected to the k- th differential output via the pair in the matrix.

Fig. 8: shows an oscillator conversion module where the state is two dimensional and the linear dynamic system has a circular feedback pattern.

Fig. 9 shows the amplitude response of a leap frog converter (solid line) in comparison to an integrator- chain converter (dashed line).

Fig. 10 shows the amplitude response of an oscillator chain converter.

Fig. 11 shows a particular realization of a configurable control-bounded converter using differential operational amplifiers.

Modes for Carrying Out the Invention

We begin by reviewing the operation principle of control-bounded converters according to prior art as in Fig. 1 , 2, and 3. We then proceed to a number of examples that illustrate additional specific advantages of the disclosed invention.

1 The Operating Principle of a Control-Bounded Converter

Fig. 1 shows the general system description of a control-bounded converter. As all the devices pre- sented here in are control -bounded converters as in Fig. 1 , we will start by further describing the general operating principle of such a converter and in particular the role of the digital control and estimation unit. As shown in Fig. 1, the system has two parts: the analog linear dynamical system and the digital control and estimation unit. The linear dynamical system takes a continuous-time input signal u(i) (the signal to be converted), and the control and estimation unit provides a digital estimate/representation ύ(ί) of u (t), Furthermore, the linear dynamical system is interactive as it provides N analog observable states and M digital control inputs. As described in [7], the control and estimation unit ensures that all internal states of the linear dynamical system remains within proper limits at all times by observing sampled and quantized representations of the observable states and feeding back suitable control signals. Further- more, the linear dynamical system is such that it provides amplification for certain frequency bands. It follows that the control and estimation unit implicitly collects information about the input signal u(t). Subsequently, the control and estimation unit can produce a digital estimate ΰ (t) as further described in the reconstruction-problem section below. More precisely, the control and estimation unit produces a digital representation of a continuous-time signal ΰ(ί) that approximates u(f). As an example this could be the samples of u(t) evaluated with finite precision at uniformly spaced time instances.

contribution s (t) as previously described in the context of the chain of integrator converter example Fig. 3. Simultaneously, based on the control signal, the DE produces an estimate ύ(ί). In contrast to the analog part of the system, all digital interactions are done in synchronization with a global clock.

As an example the chain of integrators example from Fig. 3 results in the static system description

2.3 Multiple Inputs

It is straightforward to extend the system model for multiple inputs by turning the input vector into a matrix U is the number of inputs. Additionally, control-bounded

converters with multiple inputs enables analog-to-digital conversion where circuit components are shared among multiple conversion tasks.

3 Effective Control

We call a DC effective if it can ensure that the converter maintains a bounded state vector at all times. There are multiple ways to ensure this, as the DC can interact with the linear dynamical system in various ways. However, for a bounded input signal an effective control is such that

Advantages The braided-chain converter shares all the features of the chain of integrators. However, it stands out in its ability to suppresses the impact of physical noise and mismatch by converting in a subspace other than the canonical base where each individual physical state represents a basis. From the distributed design principle, that is the braided chain, it follows that circuit resources optimally are divided uniformly over the involved circuit components. In contrast, a physical chain, that does not have a single limiting node, requires circuit resources to be allocated according to some power law. Furthermore, due to the clear division between the digital control and the analog dynamical system, the braided chain converter naturally enables complex control strategies (such as vector quantization). Additionally, if a known disturbance is situated in a particular subspace, the converter can exclude this subspace and thus further enhance its suppression capabilities. This can be seen as a generalization of principle behind differential instead of single ended amplification configurations where the common mode voltage is suppressed as to enhance the quality of the differential voltage.

An Example

This follows from the fact that a linear transformation can be decomposed in numerous ways comprising multiple sequential linear transformations.

Advantages

The leap frog converter inherits the advantages of the braided-chain converter. In addition, it enables further flexibility as the transfer function G(s) can have larger bandwidth in comparison to the braided chain for the same number of physical states. Furthermore, the transfer function can be designed without concern for stability as the control and estimation unit ensures stability regardless of poles and zero placements. Finally, feedback paths provide additional noise suppression due to noise shaping.

An Example

Advantages

The main advantage of the oscillator converter, compared to bandpass ΔΣ converters or systems that down-modulates the signal before analog-to-digital conversion, is that the modulation is done in the control path and not the signal path. Subsequently, the digital control can be operated without requiring excessively fast or precise sampling operations in the included analog-to-digital converter. Additionally, the analog multipliers (the control observation matrix) do not need to be implemented at the same level of precision as the rest of the dynamical system as they are not part of the signal path and their output is only used by the low complexity analog-to-digital converter. In contrast, the digital multiplication (the control input matrix) can more easily be implemented as shown in the example below. Furthermore, the signal path is not degraded by the modulation and can be a part of a larger control-bounded converter structure. Additionally, as both modulation and demodulation is done with the same oscillator, synchronization and phase alignment of the oscillator do not impact the performance of the converter, i.e. a free running oscillator can be used for modulation.

An Example A particular example of an oscillator converter is shown in Fig. 8. The linear dynamical system has two states that are interconnected such that the states resonate at the angular frequency ω. Furthermore, both the in-phase and quadrature signal part (where one could be a dummy signal) are equally amplified by b. The system input and dynamics can therefore be summarized as

The control uses a free running oscillator sin( ωt + Φ) of the same frequency as the resonance fre- quency of the dynamical system. Furthermore, as both the control input and observation matrix is imple- mented with the same oscillator, the unknown phase f is immaterial for the control. Another key point of this implementation is that the analog multiplication in the control observation is not required to be implemented with the same precision as the rest of the analog part of the circuit. On the other hand the digital multiplication in the control input matrix, which should be implemented with precision, can be realized by switching between different phase shifted versions of the oscillators output. The proposed design can be summarized by the control input and observation matrix

With two one-bit AD and DA converters converting each of their inputs and outputs separately and a control policy of .

5.4 Oscillator Chain Converter

The oscillator chain converter is a control-bounded converter that makes us of multiple oscillator converters. This leads to a converter structure that achieves high performance conversion at frequency bands not centered around zero. As a single oscillator converter requires two states, the length of the state vector of oscillator chain converter will be 2 N instead of N. The oscillator chain converter’s dynamical system can be written as

frequency of th oscillator node of the chain

represent the connection

angles between pairs of oscillator states. Furthermore, the control input and observation matrix can be written as

Advantages

The oscillator-chain converter, much like the braided-chain converter, provides an exponential res- olution increase in the order of chain nodes N, However, unlike the chain of integrator converter, the oscillator chain converts a signal centered at one or several carrier frequencies. The main advantage of the oscillator chain compared to first demodulating and then applying conventional A/D conversion at baseband, is that the modulation does not appear in the signal path in the oscillator chain. Subsequently, the modulation (control observation matrix) does not need to be implemented with the same level of precision as the overall converter. Note that the same does not apply for the control input matrix as the resulting signal enters the signal path directly. However, this can be done more simply as illustrated in the oscillator converter example since it requires a digital multiplication instead of an analog one. Addi- tionally, in comparison with an undersampling approach, the sampling at the control interface needs not be as precise as its input is effectively down converted (demodulated) before feed to the low complexity AD converter.

An Example

Additionally or alternatively thereto, the effective conversion resolution can be adapted for each con- version processes without changing the joint effective conversion resolution or the power consumption of the converter. A particularly advantageous scenario would be a multi-input conversion task where the scalar input signals are not all active at the same time. In that case, a larger average effective conversion resolution can be achieved (for the same power budget) by constantly reallocating the circuit resources to the signals that are active at any given time. Furthermore, the signal activation can be evaluated by the digital control and estimation unit via the estimate u (t).

Formal Definition

and estimation unit is adapted to bring said converter into at least two different configurations wherein said two different configurations have different elements in at least one of A, B, G, and G.

In particular, said at least two different configurations may have different zero elements in at least one of

In

particular, said at least two different configurations may have a power consumption differing by a factor F > 1.2, in particular F > 1.5, in particular F > 2, and in particular F > 10.

In particular, said at least two different configurations may differ in effective conversion resolution

for at least one scalar input signal.

Advantages

The fully configurable converter enables us to do adaptive conversion where the analog network can be updated to further enhance the signal characteristics that are observed by the control and estimation unit. It can also be used for adaptive power management where only a subset of the involved circuit resources are utilized until the control and estimation unit detects the presence of an input signal and subsequently additionally resources are activated. Furthermore, an adaptive analog network can be used to share the circuit resources between multiple conversion processes (multiple input signals) and adapt the allocation of signal dimension used in each process in accordance with each input dimension’s activ- ity, signal conditioning demand, or power and performance constraints.

An Example

allocated adaptively to these two conversion processes, i.e. the available configurations are

and a static input matrix

Furthermore, the control contribution is generated with the same control as in Section 5.1 with input matrix and output matrix as in (24) and (25).

In this example the DC chooses the configuration by evaluating the signal activity of the estimates u. Namely, in case one of them falls below a threshold, and is thereby classified as not active, the DC switches to the configuration where the other input uses three signal dimensions instead of two. This yields a substantial increase in conversion performance for the latter input. Note that even though less resources are used for the signal that was classified as not active, it is still being converted and contin- uously monitored (using one signal dimension). In the case the signal becomes active again, the DC switches into a configuration where two or three signal dimension are utilized for this input depending on the classification of the other input at that time.

5.6 Effective Control Converter

Most DS modulators do not have guaranteed stable operations. That means that the modulator might occasionally stall and hang in a particular state when a particular input signal is fed into the system. Both excessive simulation at the design stage, to make sure that signals of interest do not exhibit this behaviour, and continuous monitoring and resets during operations are standard techniques to manage such instabilities. These techniques can be extended and used for the same purpose in all the previously proposed converters Additionally, the control-bounded converter makes it possible to ensure an effective control as is described in Section 3.

Formal Definition

An effective control converter is a control-bounded converter wherein

Advantages

The main advantage of having an effective control is the fact that converter is guaranteed to not stall or hang during its normal operations. This means that the design can be made without the addition of excessive simulations and the uncertainty of not having simulated enough relevant signals of interest.

Examples All the necessary conditions for an effective control can been explicitly stated in the context of each previously presented converter example as follows:

- the control of the braided-chain converter example from Section 5.1 can be made effective by

given that the elements of the state vector and input signal are bounded by the same bound. - The control of the leap-frog converter example from Section 5.2 can be made effective by setting T = 0.476/j seconds where T is the time period between control updates.

- The control of the oscillator converter example from Section 5.3 can be made effective by

given that both the elements of the state vector and input signal are bounded by the same bound.

- The control of the oscillator-chain converter example from Section 5,4 can be made effective by T — 0.5 m seconds,

- The control of the configurable converter example from Section 5.5 can be made effective by making sure that for any of its configurations (78) holds. 5.7 Overcomplete Control

For control-bounded converters, higher order quantizers may be used to improve the performance and stability of the conversion. The main drawback of a high order quantizer is the higher order DAC that is required in the feedback path. The precision that such an DAC can be implemented with is typically a limiting factor when increasing the number of bits in the quantizer. The control-bounded converter can also make use of higher order quantizers. More so it offers an alterative approach by controlling in overlapping subspaces of the state space rather than increasing the quantization in a single physical space (as described above). The overlapping control spaces are realized by choosing

where M is larger than N and the non-zero column vectors of G form an overcomplete set respectively. Furthermore, the DC uses one-bit DA converters to ensure an effective control. Performance and stability may be enhanced further by using hysteresis (Schmitt triggers) in the AD conversion of the control observation. Note that introducing such hysteresis does not alter the estimation task from Section 4. Note any control -bounded converter may benefit from an overcomplete control independently of their A and B matrix structure.

Formal Definition

In a control-bounded converter with overcomplete control the columns of G form a set of vectors U such that the span of U and the span of U \ {u} are identical for any u ∈ U. Advantages

A control-bounded converter utilizing an overcomplete control enhances robustness as the control effort is distributed over multiple overlapping control inputs. Furthermore, the sensitivity to circuit im- perfections, relating to the control input matrix, is reduced as the impact of each individual control input is reduced. Additional performance follows from the fact that the control discretize the state space in finer partitions.

An Example

A particular example would build upon a braided chain converter utilized with a Hadamard basis as in (22) and (23). However, to make use of an overcomplete control, the control input and observation matrix follows as

With this setup sufficient conditions for an effective control are

given that the elements of the state vector and input signal are bounded by the same bound. Notes

While there are shown and described presently preferred embodiment of the invention, it is to be distinctly understood that the invention is not limited thereto but may be otherwise variously embodied and practiced within the scope of the following claims. References

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Claims

1. An analog-to-digital converter having

10. The analog-to-digital converter of claim 9 wherein said at least two different configurations have different zero elements in at least one of

11. The analog-to-digital converter of any of the claims 9 or 10 wherein said at least two different configurations have a power consumption differing by a factor F > 1.2, in particular F > 1.5, in particular F > 2, and in particular F > 10.

12. The analog-to-digital converter of any of the claims 9 to 11 wherein said at least two different configurations differ in effective conversion resolution for at least one scalar input signal.

13. The analog-to-digital converter of any of the claims 9 to 12 wherein

with

a static input matrix