REAL TIME MEASUREMENTS OF HIGH RESOLUTION

MIXED-SIGNAL CIRCUITS FOR SELF AWARE

EMBEDDED SYSTEM

Drago Strle and Janez Trontelj

Department of Electrical Engineering, University of Ljubljana, Trzaska 25, Ljubljana, Slovenia

Keywords: Self aware mixed-signal embedded systems, Fail-safe embedded systems, Real-time-built-in-self-test,

Pseudo random testing of mixed signal circuits, Efficient testing of mixed signal VLSI circuits, Efficient test

of high resolution ΣΔ AD converters.

Abstract: In this paper we discuss a methodology for efficient real-time measurements of high-resolution mixed-

signal circuits implemented on the IC. The methodology could be used for real time built-in self-tests of a

fail-safe mixed-signal integrated circuits and as a measurement part of a self-aware algorithm and

methodology for integrated mixed-signal circuits. We show that a pseudo-random noise signal is a good

option for the signal source and that the methodology leads to the efficient and cost-effective measurements

in real time. The measurement is running in parallel to the main signal processing. The method is

theoretically analyzed and verified using Matlab models and simulations. As an example the response of

high precision, high order Σ-Δ ADC with most important non-ideal effects is compared to the response of a

bit-true model of a reference digital circuit. The differences are demonstrated using simple area-efficient

cross-correlation algorithm that can be implemented in software or in digital hardware.

1 INTRODUCTION

Continuous advances in IC processing technologies

offer a possibility to produce integrated circuits with

increased complexity and performances for reduced

cost. In addition, integrated circuits are more and

more composed of heterogeneous embedded

systems, with different kind of digital, analogue and

mixed-signal circuits and sensors integrated on the

same IC. In future, this number will increase and the

complexity of all modules will increase as well. It is

thus essential, that modules are built in such a way

that monitoring their own states is possible, which

means that the system is capable to measure some of

its performance parameters and act according to that.

Monitoring is an essential part of any self-adaptive

and/or self-aware system. This is new and difficult

topics for digital systems (Santambrogio et al., 2010)

and completely new for embedded analogue and

mixed-signal circuits. The problem of self-

awareness of analogue circuits lies in the fact that

this circuits are not flexible as digital circuits are, it

is very difficult to measure their characteristics

without expensive measurement equipment and

without precision generators and usually they do not

have any “built-in intelligence”. The problem is

even harder if high resolution mixed-signal

embedded modules like Σ-Δ A/D converters are

involved because they are complicated analogue

structures, which are difficult to design and almost

impossible to measure without high resolution

instruments. The modules may also operate at high

frequency, while their power consumption is limited

to a minimum. Fortunately, modern heterogeneous

systems always consists of digital hardware and/or

software signal processing, which provide the

opportunity for evaluation of monitored parameters;

a precision analogue signal source or appropriate

replacement is still needed if someone wants to

measure the parameters of the analogue module. For

systems where human life may be in danger in the

case of the failure, the self awareness and thus the

measurements of the most important parameters

must be executed in real time, that is in parallel to

the real operation of the system. Example of such

self-aware system is for example electronic stability

system in passenger car (Strle, 2007) where the

measurement channels and the sensors are

582

Strle D. and Trontelj J..

REAL TIME MEASUREMENTS OF HIGH RESOLUTION MIXED-SIGNAL CIRCUITS FOR SELF AWARE EMBEDDED SYSTEM .

DOI: 10.5220/0003406205820589

In Proceedings of the 1st International Conference on Pervasive and Embedded Computing and Communication Systems (SAAES-2011), pages

582-589

ISBN: 978-989-8425-48-5

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

monitored in real time in parallel to the real

operation. Many other examples that require fail-

safe operation exist, therefore, it make sense to

develop a methodology and a general frame-work

for RTBIST (real time measurements; we name it

real-time-built-in-self-test) of a mixed signal

circuits. Such real time measurements are the basis

for self-awareness of embedded analogue and

mixed-signal circuits. To be able to measure

characteristics of embedded mixed-signal module, a

high precision generator is needed that is simple to

built, requires small silicon area for the

implementation and needs little power for the

operation. Such generator is one bit pseudo random

(PRN) signal generator described in subsection 2.2.

The rest of the paper is organized as follows. In

section 2 the principles of measurements using

pseudo random signal are explained. Section 3 deals

with measurements of high resolution Σ-Δ

modulator using PRN source. Section 4 introduces a

real time measurements of important parameters that

is going on in parallel to the normal operation, while

section 5 deals with implementation of efficient

classification circuit. Section 6 presents one example

and section 7 concludes the article.

2 PRN MEASUREMENTS

The first step to reach or achieve self awareness is to

measure important parameters of embedded mixed-

signal circuit that can be any combination of

interconnected analogue and/or mixed-signal and

digital modules. Generally, to measure

characteristics of such circuit a precision signal

generator is needed with parameters better than the

circuit to be measured. Such signal generator is not

available on chip and would be very difficult,

demanding and expensive to built. In addition,

measured results must be evaluated with high

precision and as fast as possible. Fortunately, on a

mixed signal VLSI circuit a DSP is usually available

and if designed properly it can execute efficiently

the algorithms needed for the evaluation of the

performance measurements in real time.

One possibility to measure the performances of a

high resolution analogue or mixed-signal circuit is to

compare the response of the analogue LTI system

(continuous or discrete time) with digital discrete

time system having the same architecture and equal

coefficients. The system to be measured is high

precision analogue or mixed-signal circuit

implemented on the chip, while reference LTI

system can be implemented on or off the chip in

hardware or in software. If one bit pseudo random

noise (PRN) generator with appropriate

autocorrelation and approx. white PSD is used as a

signal source a high precision and high linearity can

be achieved easily and on a very small silicon area.

2.1 Theory of PRN Measurements

The easiest way to measure analog Linear-time-

invariant (LTI) system (discrete time or continuous

time) is to measure its transfer function in

frequency domain. Such measurements require

precision sine-wave generator and narrow

bandwidth signal or spectrum analyzer or

calculation of the FFT coefficients. Usually a

precision sine-wave generator is not available on-

chip and the measurement need a long time because

the transfer function must be measured at several

different frequencies and amplitudes. Theoretically,

the time needed for the measurements could be

reduced measuring the response



hn to the unit

delta pulse







. In this way, all information of the

LTI system would be obtained in one measurement.

Unfortunately, the method is difficult to use

because it requires huge dynamic range of a system

or the response is covered by the noise and it is

therefore not practical.

Applying Pseudo Random Noise signal (PRN)

with appropriate amplitude and approx. white

spectrum and Gaussian probability density function

(PDF) to the input of an LTI system (Couch, 1993

and Pan, 1997) provides the opportunity to measure

the response





hnof the LTI system. If mixed-

signal LTI is running in parallel to the reference

(digital) LTI as suggested on Figure 1 the

difference between two LTI systems could be

measured efficiently. Input signals are the same for

both systems (with possibly slightly different gain)

and have noise-like properties. They are shaped by

two, generally different deterministic transfer

functions





hnand





hn. Both responses are

exactly the same if transfer functions are the same.

The first response





n corresponds to analog or

mixed-signal discrete or continuous time system

while





n corresponds to “exact” digital discrete

time system. Both have exactly the same

architecture and equal coefficients. The later is

always nominal because it is implemented in digital

hardware or software with sufficient word-lengths

that the quantization noise of the calculations could

be neglected.

REAL TIME MEASUREMENTS OF HIGH RESOLUTION MIXED-SIGNAL CIRCUITS FOR SELF AWARE

EMBEDDED SYSTEM

583

Figure 1: LTI systems driven by signal x[n].

Analog discrete time system described by





may deviates from nominal because of catastrophic

faults (short or open circuits, etc.) and/or

parametric faults: spread of parameters owing to

process parameter changes, matching and

temperature variations, ageing. Cross-correlation

between input signal and response of each system

is proportional to the impulse-responses





according to (1) and (2) if input signal





has

noise-like properties (5). We used discrete time

convolution (3) to calculate response of discrete

time LTI system to an arbitrary input, (4) to

calculate cross-correlation and (5) to

  

xy x x

mhm hk







 



(1)

  

xy x x

mhm hk







 



(2)

calculate auto-correlation of time-shifted white

noise signal. E{.} is the expectation operator.

  

nxnkhk









(3)















mExnynm 

(4)















xnxn m k m k



   

(5)

Cross-correlations given by (1) and (2) are

proportional to appropriate impulse response





and variance of the noise if the mean value of the

noise signal



approaches zero, which happens

for sufficiently long pseudo random sequence

(

Zepernick, 2005).

The difference of cross-correlations of LTI

systems is proportional to the difference of impulse

responses according to (6) if



is sufficiently

small, which happens for long period of PRN.













 



,1 ,2

,,1,2

xy xy

mmm

hm h m









(6)

In the ideal case, both responses are the same and

the difference is zero (7):





,1 ,2

0, 1, 2,...

xy xy





(7)

If we assume that digital system LTI

has nominal

impulse response









hn hn , while analogue

system described by LTI

has real impulse response

that deviates from the nominal by







then:













hn hn n



. The difference of cross-

correlations is proportional to the deviation







the responses and the variance



of the noise (8).









,1 ,2

xy xy







(8)

Calculation efficiency can be improved by

calculating first the difference of both responses and

then the cross-correlations between noise source and

the difference of the responses. For linear systems

the results are the same as before (9):











 





Exn y n m y n m

hm hm m









  



(9)

It is not possible to calculate the expectation

operator from the definition (4), but for ergodic

random signals the time-average operation is equal

to expectation calculation (Hayes, 1996) (10):













  

lim

Exnyn m

nynm













(10)

For sufficiently large N the estimate of the mean of

the cross-correlation





 (11) is equal to the

cross-correlation (12). This result provides the

opportunity for efficient calculation of cross-

correlation coefficients.

   

   



  

mxnnm

nxnmkk

kxnxnmk









 







 











(11)









Em m





(12)















hHzn

















hHz







   

nxnkhk









   

nxnkhk









PECCS 2011 - International Conference on Pervasive and Embedded Computing and Communication Systems

584

2.2 PRN as a Signal Source

All results in previous subsection are based on the

assumption that the input signal has real “white

noise” properties. In reality, such signal does not

exist and even approximation is hard to implement.

Good approximation, which is easy to built and

requires small silicon area is pseudo random noise

signal (PRN) that under certain conditions possesses

appropriate characteristics (Zepernick, 2005):

 The spectrum is discrete with approximate

“white” power spectrum density (PSD). The spectral

components exist at frequencies





iclk

ff

for



0... 2 1

i ; the sequence is periodic and

repeated every



 clock cycles,



The period is sufficiently long so, that



approaches zero. Inside period the signal appears

random,



All states have approx. equal probability, while

state 0 is not allowed,



The PRN can be single or multi bit, dependent on

the application but the linearity and accuracy

requirements must be maintained,



The sequence with appropriate autocorrelation

properties







for





, otherwise







must be used,



The PRN source must be simple with small

silicon area required for the implementation.

Several useful implementations of PRN exist

(Zepernick, 2005). Converting binary pseudo

random signal into analogue voltage is accomplished

using 1 bit D/A converter that is inherently linear,

very accurate and very simple for the

implementation. Eventual inaccuracy of the gain

coefficient can be corrected during production

calibration phase.

Figure 2: PRN measurements of a modulator.

3 PRN MEASUREMENTS

Measurement of high precision and high resolution

A/D converter requires a precision measurement

system. For fail-safe electronic system the status of

the system and also the status of the ADC must be

checked in parallel to the normal operation; any

deviation from optimum behaviour must be noticed

immediately, therefore important parameters must

be measured constantly without the presence of high

precision measurement system. One possibility is

shown on Figure 2, where basic idea for efficient

measurements of a - modulator is presented.

Analogue modulator in grey box is implemented on

silicon together with PRN generator (PRS source)

that fulfils conditions defined in subsection 2.2. We

can assume that after calibration the constants k

ditha

and k

are exact. The PRN signal is used in any case

as a dither signal to prevent limit cycles (Reefman,

2005) and to linearize the quantizer (Widrow, 2008),

so it is already present in the circuit. If a multi-bit

internal D/A converter is needed, than appropriate

linearization or dynamic element matching

technique must be used (Jiang, 2007). Dither signals

are always connected to the modulator’s dither

inputs, usually in front of the internal quantizer. The

second modulator, outside the gray area is a

reference digital modulator that can be implemented

on the chip or off the chip in digital hardware or

software algorithm; it should have exactly the same

architecture and exactly the same coefficients as the

analogue modulator that we want to measure.

Two measurements are generally needed. At

first, both inputs are connected to zero (U

=0, U

=0),

while PRS is connected to dither inputs through k

dith

and therefore, the noise transfer function or the

difference of NTFs is measured. If PRN signal is

connected to the inputs through coefficient k

and at

the same time to dither inputs through k

dithx

, the

signal transfer function or the difference of STFs is

measured. The digital modulator has exactly the

same structure as the analogue modulator with

equivalent coefficients, but it is built with digital

hardware or software with sufficient word-lengths to

render negligible any quantization noise owing to

fixed-point arithmetic. The digital modulator

together with classification block can be

implemented outside the chip as a hardware or

software module or in case of RTBIST it can be

included on-chip together with analogue modulator.

It is estimated, that in modern 90nm CMOS

technology the area of digital modulator is only one

half of the area of the analogue modulator. In both

cases, the digital modulator is running in parallel to

REAL TIME MEASUREMENTS OF HIGH RESOLUTION MIXED-SIGNAL CIRCUITS FOR SELF AWARE

EMBEDDED SYSTEM

585

the analogue modulator using the same or

synchronized PRN signal. Both bit-streams and PRN

signals are monitored with classification block that

calculates cross-correlation coefficients and decides

if analogue modulator fits the requirements despite

the changes caused by process parameters, matching

effects, temperature drift, ageing etc. The behaviour

of digital modulator is assumed to be stable, while

analogue modulator is subject to changes and this

changes we want to measure.

 modulators are non-linear systems so the

theoretical background described in subsection 2.1

could be used only if the module is linearized. This

is achieved by adding dither signal to the input of

the modulator’s quantizer; in this way eventual

limit-cycles are de-correlated (Reefman, 1997) and

the operation is linearized (Widrow, 2008). In that

case the modulator can be approximated as linear

system in z domain (Hamoui, 2004) according to

(13), (14), (15) and (16):





















  



aaa

Yz STFzU z Rz

NTF z z P z





(13)

 





  



Yz STFz

NTF z z P z





(14)

The relations between





Hz,



STF z and





NTF z

are given in (15) and (16) for both modulators,

where index x=a stands for analogue and x=d for

digital modulator.



Rz represents input-referred

circuit noise of the analogue modulator and





represents pseudo-random noise used for dither.



STF z NTF z





(15)



NTF z





(16)

It is assumed that digital and analogue quantization

noises are not equal

 

Qz Qz because internal

states might be different even if applied input signals

are exactly the same. We need to do two tests to be

able to measure both transfer functions (STF and

NTF). For the first test the input signals are set to

zero (





un ,





un ), the PRN is applied to

both dither inputs so





NTF z

and



NTF z

or their

difference can be determined. The cross correlation

can be determined using (17), (18) and (5). We

assumed, that





pn is not correlated to any other

noise source:





rk,





qk and





qk.

  

axp

py xp a a

m ntf m ntf k











(17)

  

dxp

py xp d d

m ntf m ntf k











(18)

If sufficiently long PRS sequence is used, the mean

value of PRS signal is approaching zero



 and

cross correlation become proportional to

corresponding impulse response of the noise-transfer

function. The difference of both cross-correlations is

proportional to deviation of analogue noise-transfer

function from digital noise-transfer function

according to (19) and (20):









,1 ,1

pya pyd

xp ntf





 

(19)













ntf a d

mntfmntfm





(20)

For test 2, the PRN signal is connected to both

inputs in addition to both dither inputs, so cross-

correlations are ((21), (22)).

















...

pya xp a a

m stf m ntf m







(21)

















...

pyd xp d d

m stf m ntf m







(22)

Moreover, the difference is (23):

















,2 ,2

pya pyd

xp stf ntf

mmm

 





(23)

From (19) and (23) one can estimate deviation of

signal and noise transfer functions of analog

modulator from the reference modulator and since

we know





ntf



it is easy to calculate





stf



4 RTBIST

Real time monitoring of some performance

parameters of the mixed-signal circuit in parallel to

the normal operation comes from the fail-safe

system requirements and the name RTBIST (

Real-

Time-Built-In-Self-Test) reflects that. We could

also name it real-time-self-aware (RTSA) system

taking into considerations that higher level functions

are implemented in dedicated hardware or software.

Here, we are dealing only with methodology, which

is based on ideas presented in sections 2 and 3 with

the following differences:



As explained in section 3 both modulators are

implemented on chip,



The LTI

(analogue modulator) process the input

analogue signal and in parallel the small amount of

PRN, while digital modulator with the same

PECCS 2011 - International Conference on Pervasive and Embedded Computing and Communication Systems

586

architecture and equal coefficients, process only the

PRN noise.



During production the cross correlation

coefficients of the PRN and the difference of the

responses for NTFs and STFs at nominal conditions

are calculated and stored.



During real measurements, the NTF is not

measured explicitly because it can be calculated

from the relation between STF and NTF given in

(15):







NTF z STF z



For S-C implementation we know that the gain

factor for the PRN connected to the input is very

accurate (0.1%) and has a very low temperature

coefficient.



The correlation between PRN and input signal is

assumed negligible.



The amplitude of PRN signal is small so that

only a very small fraction of a mixed-signal circuit

dynamic range is consumed by the test source PRN.

5 CLASSIFICATION

A classification circuit can be implemented

according to Figure 3, which closely follows

equation (11). The average is replaced by moving

average or the first order filter.

Figure 3: Possible classification circuit.

The signal PRN is delayed instead of





n to

simplify the hardware: this is possible for ergodic

signals; PRS signal is simply delayed using



bit

shift register because only

1pq

samples of unit

step response are needed for LTI systems having p

poles and q zeroes, so that the transfer function is

correctly represented (Hayes, 1996). Multiplication

is performed by simple exchange of the signs as

dictated by the PRN. In addition, for one-bit

modulators the bit-streams



n and



n are

also 1 bit, so the result of the subtraction is within

















2, 0, 2

yn y n y n; the multiplication

circuitry is very simple. Each product



vn is then

LP- filtered. It requires a small portion of FPGA

and/or little silicon area. If needed, a higher order

digital-averaging filter could be built. The digital

comparator then decides if all results are within the

limits

L :





; 1, 2,....

nLn





(24)

How many samples do we need for reliable

classification? Is the number of correlation

coefficients sufficient? What time do we need for

the measurement? What is the probability of

classifying correctly? The answers to these questions

are not simple and are still under consideration.

Available time and hardware resources are limited.

In addition, the accuracy of a decision and its speed

conflict with each other. For our self-aware and/or

fail-safe system we need the information about the

system behaviour as fast as possible, thus,

appropriate selection of conflicting parameters

(time, accuracy of classification, hardware resources

available, etc.) must be optimized for particular

application. For example, a decision that is more

accurate needs more time or a more elaborate

averaging process and higher order filters. Fast

decision usually leads to poor accuracy of

classification, which could be improved by

appropriate higher order filtering which in turn

needs more hardware resources.

6 EXAMPLES

A fifth-order, single-loop, discrete-time Σ-Δ

modulator implemented in S-C technique with one-

bit internal quantizer and feed-forward structure to

reduce power consumption is used as an example.

Over-sampling frequency is 32MHz and the band

of interest is from 20kHz up to 400kHz. The

problem of efficient testing of such modulator is

that we cannot measure internal signals because we

would destroy the operation (internal S-C stages

have capacitances from 0.5pF down to 50fF) and

-1

x(n)

x(n-1)

x(n-2)

x(n-p-q)

(n) y

(n)

y(n)=y

(n)-y

(n)

-1

















































pq pq





























OK?

Limits

REAL TIME MEASUREMENTS OF HIGH RESOLUTION MIXED-SIGNAL CIRCUITS FOR SELF AWARE

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587

the power consumption is restricted. To verify

presented methodology we have built Simulink

models of the modulators and classification circuit.

For LTI

the most important analog performances

of opamps (kT/C noise, thermal noise A0, GBW,

offset, slew-rate, non-linearity) and quantizer

(offset, hysteresis, noise, latency) are modeled.

Capacitor ratios can be perturbed according to the

technology and size of unit capacitor. The digital

modulator and classification circuit are with bit-

true models that calculate in real time eleven cross-

correlation coefficients





through





using

first order moving average filter with pole:





 . Moving average filter needs approx.

2ms for the transient; the results after that time

could be used for the comparison. We have run

several simulations, trying to imitate different

problems of analog modulator related to the

production spread as well as to temperature drift

and other possible problems. A summary of

simulation results is presented on Figure 4 for noise

transfer function and on Figure 5 for the signal

transfer function. The following experiments were

simulated: (a) nominal circuit with no kT/C noise,

no op-amp noise, and ideal op-amp characteristics,

(b) real op-amp characteristics inside allowed

ranges, (c) allowed kT/C and op-amp noise with

other conditions as before, (d) the same as (c) with

kT/C 10 times bigger (out of specs), (e) the same as

the min allowed, (f) the same as (c) but one

capacitor changed by 30%, (g) limit of the 1

amplifier reduced to 0.4V from 0.5V, (h) Monte-

Carlo run with capacitor ratio changes

35%





proportional to unit cap size (the spread is

intentionally exaggerated to get some out-of-range

results). On both figures, cross-correlation

coefficients are plotted for different experiments

marked with triangles. We can see that in both

cases some of the results are out of the limits

marked with dots inside the squares. The limits

were defined according to the specifications using

Matlab simulations.

7 CONCLUSIONS

In this article a possibility for real-time

measurements of high resolution mixed-signal

circuits have been investigated. The basic idea and

the theory behind it have been explored for simple

LTI system as well as for more complex mixed-

signal module (Σ-Δ modulator). A block diagram

of efficient measurements has been presented

together with possible implementation of

classification circuitry. The aim of presented

methodology is to pave the way for real time built-

in self test (RTBIST) of such embedded modules

and to real time self aware (RTSA) methodology

measurements.

Figure 4: Classification result for NTF.

Figure 5: Classification results for STF.

The investigation is far from finished. We

believe that only basic steps were analyzed in this

work. Many other problems still need to be

investigated, like for example: optimization of

classification algorithm according to required

speed and accuracy, influence of properties and

length of PRN sequence to the accuracy and speed

of measurements, influence of nonlinearities.

PECCS 2011 - International Conference on Pervasive and Embedded Computing and Communication Systems

588

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