Analog signal processing: blocks, trends and limitationslesim1.ing.unisannio.it/tc4/summer2007/summer06_eng/Links/gasulla... · Analog signal processing: blocks, trends and limitations

Analog signal processing: blocks, trends and limitations

Ramon Pallàs-Areny, Manel GasullaInstrumentation, Sensors and Interfaces Group

Castelldefels School of TechnologyUniversitat Politècnica de Catalunya

Barcelona – Spainhttp://isi.upc.es

Our Campus!!Castelldefels (Barcelona), Spain

R. Pallàs-Areny, M. Gasulla Summer School-Benevento 2007 3

Index1. Function and structure of DAS2. Functions on signal amplitude, level and power3. Functions on signal spectrum: filtering4. Uncertainty and calibration5. Trends in AFE for DAS

Textbook:Analog Signal ProcessingR. Pallàs-Areny and J. G. WebsterNew York: John Wiley & Sons, 1999



Index

1. Function and structure of DAS2. Functions on signal amplitude, level and

power3. Functions on signal spectrum: filtering4. Uncertainty and calibration5. Trends in AFE for DAS


1. Functions and structure of DAS

1.1 Basic functions in measurement systems

1.2 Dynamic range: amplitude and level matching

1.3 Architectures for DAS


Basic functions in measurement systems

For any size or design scale

Sensing Processing Communication

Powersupply

Control/memory


Sensing

Primarysensor

Signalconverter


Powersupply

Control/memory


Processing

ADCAnalogprocessing

Signal-to-symbolconverter


Powersupply

Control/memory


Analog signal processingADCAnalog

processingSignal-to-symbol

converter

Sensorconditioner

Analogprocessor

Excitation/biasAmplificationLevel shiftingFilteringImpedance adaptation

DemodulationLinearizationCompression


Function types

1. Conversion: sensor, ADC, analog processor

2. Adaptation/matching: conditioner + analog processor

Amplitude: attenuator, amplifierLevel: level shifter (amplifier)Power: input/output protectionImpedanceBandwidth: filtersTerminals

Sensor AnalogprocessorConditioner

Dx voyMeasurand ADC

Excitation/bias

AFE


ADC: transfer characteristic

CAD

Vref

LSB

MSB

Vs+ Vs-

vxt1 t2 t3

01111010

t111100101

t211111111

t3

3Q 4Q 5Q 6Q 7Q vx

Codenumber

1

2

3

4

5

6

7

8

Intervalnumber

1 82 3 4 5 6 7

2QQ

vx

eQ

-Q/2

+Q/2

( )

= +

=

ir

ir ref

ent 2 1Nxx

VDV

V VQuantization intervalQ = Vref/2N = 1 LSB

eQ-Q/2 +Q/2

p(eQ)

Quantization noise:var [eQ] = Q2/12


QuantizationAnalogsignal Scale Code

transitionlevels

Codebin

Digitaloutput

ADC

FSR

0

T[2N-1] 2N-1

0

Vmax

Vmin000

111

100

Vx

T[k]k

[ ] ( ) [ ]= × − +1 1T k Q k T

T[1]

k-1

1 100

2N-2 110

011

Input


Resolution in ADCs

N 2N % ×10-6 dB 8 256 0,390 625 3 906,25 -48,2

10 1 024 0,097 656 976,56 -60,212 4 096 0,024 414 244,14 -72,214 16 384 0,006 104 61,04 -84,316 65 536 0,001 526 15,26 -96,318 262 144 0,000 381 3,81 -108,420 1 048 576 0,000 095 0,95 -120,422 4 194 304 0,000 024 0,24 -132,524 16 777 216 0,000 006 0,06 -144,5


Measurement system


Sensing

Functions in DAQ:

• Conversion: sensor, ADC, analog processor• Adaptation/matching: conditioner + analog processor

Amplitude, level, powerImpedanceTerminalsBandwidth


What’s a sensor?

Materialproperties

Geometry

+Physical/chemicalquantity

Electricaloutput

Interfering quantity

Interfering quantity


Sensing methodsSensing: Transduction from non-electrical to electrical quantity1. Material-based sensing: conductors, semiconductors,

insulators, magnetic– Mechanical: piezoresistivity, piezoelectricity…– Thermal: Seebeck effect…– Magnetic: AMR, GMR, Hall effect…– Optical: photoelectric effect…– Chemical (concentration): Nernst equation…

2. Geometry-based sensors (linear or angular displacements):

– Potentiometer– Capacitive– Inductive– Mutual inductance


Sensor classification: power supply

Modulating sensorx y

Excitation

Modulating sensorx y

Excitation

Power flow

Electromagneticsensor

x y

Bias

Electromagneticsensor

x y

Bias

Power flow

Self-generatingsensor

x y Self-generatingsensor

x yPower flow


Sensor classification: output signalAnalogsensorx y

Quasi-digitalsensorx

y

Digitalsensorx 01101

y


Analog signal processing

Conditioner + analog processor functions:

• Sensor excitation (driving) or bias • Adaptation/matching:

Amplitude, level, powerImpedanceBandwidth (filtering)Terminals

• Analog signal processing:Domain conversion (I → V, ac → dc)LinearizationInterference compensation

Sensor AnalogprocessorConditioner

Dz voyMeasurand ADC

Excitation/bias

AFE


(1 - α)RT

VrαRT

ADC

RefD

Excitation/bias

( ) ( )s

r

2 1 2 1N NvD

Vα= − = −

Rin ADC >> RT

Potentiometer: ratiometric measurement

R

Rr

vo

Vr

Resistive sensors

ro

r

max r

Vv R

R RS R R

=+

⇒ =

vs


Wheatstone bridge

0.5 1-0.5-1

Ideal output

Real output0.25

vo

Vr

x

-0.5

-0.25Vr

R2

R3 = R0(1 + x)R4

R1

voi2 i1+-

Ib


o rv V x=

o r 2xv V=

Half-bridge and full-bridge sensors

R0(1 + x)

R0(1 - x)

F

Vr

R0(1 - x)

R0

R0

vo

R0(1 + x)

R0(1 + x)

R0(1 - x)

vo

R0(1 + x)

R0(1 - x)

Vr

• Linear• Higher sensitivity• Temperature compensation


Amplification

If Vo,max – Vo,minn ≤ Vin,max – Vin,minn+1 ⇒Range matching: amplification

Vs+

Vs-

vin vo


Amplification limits

Vout, max < Vs+Vout, min > Vs-

RRIRRO

G(f)

Vs+

Vs-

Vout,max

Vout,min

ZL

IL < Io,max

IL

Vin,max

Vin,min

Voltage headroom

IL comes from the power supply


Level shiftingWe need: Vo,minn = Vin,minn+1

Vo,maxn = Vin,maxn+1

Vref ≠ Vs

G

Vs+

Vs-

+

Vos = αVref

αGVref


Impedance adaptation/matching

1. Signal transfer (undesired attenuations): Vo→ VLIo→ IL

2. Signal integrity (when l > λ/10) ⇒ ZL = ZS

3. Maximal power transfer ⇒ ZL = Z*S

Zo

Vo ZLVL ZoIo ZLIL


Voltage loading effectZo

Vo Zi (ZD)Vi

ZLZL + Zi

A(f) =Source Load

Solution: voltage buffer (impedance transformer)


DC voltage divider effect

i i

o o i

V RV R R

=+

i o io o,FSR

o o

1If when 22

MM

V V RV VV R−

< = ⇒ >

Ro

vo vi Ri


AC voltage divider effect

( )( )

i0

i oi 0

eq io

eq o i 0 o

1

RAR R

V A R CV j

R R R A R

ωτ

ω ωτ

= += =+

= = ×

i oo o,FSR

o

20

If when

2 1 21 1

v vv V

v

A

ε

ε εωτε ε

−< =

+ −< ≈

− −max

eq i

1 22 1

fR C

επ ε

<−

Ro

vo vi Ri Ci


Maximal measurement frequencyε = 2-N 8 10 12 14 16 18 20 22fc/fmax 11.3 22.6 45.5 71 181 362 724 1448

lg f

A0

fc

0.7A0

A


1. A signal generator whose output resistance is 600 Ω is connected to a load resistance of 1 MΩ. Calculate the amplitude attenuation

2. A signal generator is connected to a 12 bit DAS whose input resistance is 1 MΩ. Calculate the maximal output resistance of the signal generator in order for it not to influence the measurement result

3. A grounded signal generator whose output resistance is 600 Ω is connected to an oscilloscope whose input impedance is 1 MΩ in parallel with 20 pF, using 2 m of a coaxial cable whose capacitance is 75 pF/m. If a maximal 0.1 % amplitude attenuation is accepted, what is the maximal signal frequency we can measure?

Examples


Bandwidth adaptation

( )

max min

c

c max min c max

max min

11

; often, , : depend on the application

f ff

f f f S f Sf f

>− <

= ≠

Signal bandwidth

Broadband signalNarrow band signal

f

S(f)

fcfmax fmin

S(f)

ffcfmax fmin


Circuit/system bandwidth

C H Lf f f=

|G|/|G0|

0 dB

fL fH lg ffc

3 dB< 3 dB


Bandwidth compatibility

Continuous signal systems: fL < fmin, fH > fmax

fL fH lg ffc

S(f),

fmaxfmin

|G|


Bandwidth compatibility

Sampled systems: fsampling/2 >”Signal BW”


DC and AC coupling

in,maxoff

min

vvkffc

<

<


Minimal measurement frequencyε = 2-N 8 10 12 14 16 18 20 22fmin/fc 11.3 22.6 45.5 71 181 362 724 1448

lg f

A0

fc

0.7A0

A


Terminal matching

(Chassis) (Ground, PE)(Common, signal ground)

Reference point for voltage measurements


Single-ended voltages

(pseudo-differential)

=L "0 V"V

Floating

Zo

vo

Grounded

Zo

vo

Floating with a common-mode voltage

Zo

vo

vc Zc


Differential voltage, floatingvd = vH – vLvc = (vH + vL)/2

Z’o

Zo

Vd/2+

+Vd/2

H

L

C

vc Zc

Zo

Vd/2

Z’o

+

+Vd/2

H

L

C


Differential voltage, grounded


Differential voltage, generalZo

vd/2

Z’o

+

+vd/2

H

L

viso

Ziso

C

vc Zc

vc

vc


Single-ended input

Grounded Floating


Pseudo-differential input

H and L cannot be interchanged

Zin

H

L

ZL

ZH

LH ZZ ≠


Differential input

Grounded Floating

H and L can be interchanged

ZD

H

L

ZC

ZC

COM

ZD

H

L

ZC

ZC

COM

ZISO


Example: pseudo-differential tosingle-ended conversion



1.1 Basic functions in measurement systems1.2 Dynamic range: amplitude and level

matching1.3 Architectures for DAS


Dynamic range: concept

( )

max min max min

irADC

ADC

Measurement rangeDRResolution

2 1DR 2

DR (dB) 20lgDR 6

NN

x x V Vx V

QVQ Q

N

− − = = = ∆ ∆

−= = ≅

= ≅

Sensor Analog

processorConditionerD

x voyMeasurand ADC

DR can be defined at the input and at the output of each stage


Signal-to-noise ratio (SNR)

( )

2s2n

2s s s2n n n

Signal powerSNRNoise power

S/N dB 10lg 20lg 20lgσ

Ψ=

Ψ

Ψ Ψ Ψ= = =

Ψ Ψ

( ) ( ) ( )H

L

2 2 2 2

0 0

1limT f

x x x fTx t dt S f df S f df

Tµ σ

∞

→∞Ψ = = + = ≈∫ ∫ ∫


Application to system design

−=

−max min

max min

y ySx x

MR: xmax - xminResolution: ∆xDR = (xmax-xmin)/∆x

Sensor sensitivity (linear)−

=−

o,max o,min

max min

v vS

x x

System sensitivity (linear)

Sensor Analog

processorConditionerD

x voyMeasurand ADC

Procedure:1. Calculate DR from problem specifications2. Determine N for ADC3. Select a sensor that fulfills the design requirements4. Select/design a signal conditioner to match the output voltage

range of the sensor to the input voltage range of the ADC


ExampleTemperature measurement 0 °C to 100 °C, resolution 0.1 °C.Sensor: sensitivity 1 mV/°C, output 0 V at 0 °C.ADC: input range voltage range [0 V, 10 V].

a) Dynamic range needed for the measurement systemb) Minimal number of bits (N) for the ADCc) Input range and (minimum) resolution at the amplifier inputd) Amplifier gaine) N if no amplifier is used


ExampleTemperature measurement: -40 °C to 60 °C, resolution 0.1 °C. Sensor sensitivity: 1 mV/°C, output 0 V at 0 °C.ADC: input range voltage range [0 V, 10 V].

a) Dynamic range needed for the measurement systemb) Minimal number of bits (N) for the ADCc) Input range and (minimal) resolution at the amplifier inputd) Amplifier gaine) Level shifting needed at the input (output) of the amplifier


Amplification and level shifting circuits

-+

R2R1

vo

R3

vs

voff

-+

R2R1

vo

R3

vs

voff

Non-inverter with level shifting Inverter with level shifting

213 RRR =

off1

2s

1

2o 1 v

RRv

RRv −

+= off

1

2s

1

2o 1 v

RRv

RRv

++−=


Differential amplifier with level shifting

vs2

vs1

vo

R3 R4

R4R3

-+

voff

( ) offs1s23

4o vvvRRv +−=



1.1 Basic functions in measurement systems1.2 Dynamic range: amplitude and level

matching1.3 Architectures for DAS


Basic parameters for DAS (1)1. Functions:

– ADC– DAC– Digital I/O– PWM output– Specific sensor conditioners– Isolation– Event counters– Timers– Triggers


Basic parameters for DAS (2)2. Number of channels: analog mux/demux3. Terminals:

SE, DIF, Pseudo-differential4. Input impedance5. (Voltage) input range: Signals + transients6. Gain(s)7. Resolution (bits) and ENOB8. Sampling speed (Sa/s). Speed-resolution

trade-off9. Accuracy (uncertainty) ≠ resolution


Basic parameters for DAS (3)10.Capability of: memory (Data loggers) or

memory access method, and processing11.Communication interface:

– PCI– USB, EIA-232, RS-485– GPIB– PXI, VXI, LXI– Ethernet

12.Cost: acquisition, technical support


Centralized, decentralized, and distributed systems. Sensor networks

• Centralized: a single processor for processing and control– IC systems: AFE + ADC (+ controller)– Plug-in (snap-on) data acquisition PC cards: ISA, PCI– External modules (USB)– External DAQ system (board-rack system) using

modular buses: VME/VXI, MXI,PCI, PXI. – Discrete (bench/rack) instruments using standalone

buses: IEEE-488 (GPIB), USB, IEEE-1394 (Firewire), Ethernet, Wireless

– Hybrid instruments: measurement instruments with DAQ

R. Pallàs-Areny, M. Gasulla

Summer School-Benevento 200776

Decentralized and distributed systems• Decentralized: several coordinated processors.

Industrial networks– Reduced cabling costs (for more than 100 I/O),

modularity (connectivity via software), easy diagnostic, self-configuration

– External PC buses: EIA-232, RS-422, RS-485, IEEE-488, USB, Ethernet (PoE)

– Fieldbuses: Ethernet/IP, Modbus, Profibus, Foundation Fieldbus, DeviceNet, CANopen, J1939, FlexRay

• Distributed: extended geographical network (WAN)– Signal degradation: attenuation, interference, speed

reduction



Ad-hoc wireless sensor networks (WSN)

1. Self-organizing: rapid deployment and reconfiguration → temporary networks

2. Cooperating nodes within communication range from each other

3. Energy efficiency: multi-hop routing informationRobust to node failureHigh-level of fault tolerance



REALnet: WSN for environmental monitoring

Punt de mesura

Repetidor

Laboratori 123P

Punt de mesura

Repetidor

Laboratori 123P

Punt de mesura

Farola

Punt de mesura

Farola

PFC Joan AlbesaFebruary 2007



Low-level and high-level multiplexingLow-level multiplexingSensor

1

Sensorn

Sensor2

AMUX SHALPF

Digitalcontroller

Systembus

ADCPGA



High-level multiplexing

Sensor

Sensor

Sensor

AMUX SHALPF

Digital

LPF

LPF

LPF

ADC

Sensor1

Sensorn

Sensor2

AMUX SHALPF

Digitalcontroller

LPF

LPF

LPF

ADC

Systembus

Systembus

PGA

G = 1, 2, 4, 8G = 1, 2, 5, 10



Simultaneous samplingSensor

1

Sensorn

Sensor2

LPF

LPF

LPF

SHA

MUX

SHA

SHA Digitalcontroller

Systembus

LPF ADC



(Inherent) digital multiplexingSensor

1

Sensorn

Digitalcontroller

Systembus

LPF

LPF

SHA

SHA

Digitalcontroller

ADC

ADC

Smart sensors: IEEE 1451.X


Index

1. Function and structure of DAS2. Functions on signal amplitude, level

and power3. Functions on signal spectrum: filtering4. Uncertainty and calibration5. Trends in AFE for DAS


2. Functions on signal amplitude, level and power

2.1 Voltage attenuation2.2 Differential voltage amplification

and level shifting2.3 Input circuit protection


Voltage attenuation

2 i 2

o 1 2 i 1 2

in 1 2 i

Z Z ZAZ Z Z Z Z Z

Z Z Z Z

= ≈+ + +

= +

o in

i 2

Z ZZ Z

<<

>>

Zo

vo

Zivi

Z1

Z2

Zin

A : attenuator “gain”“Attenuation” : 1 - A


DC voltage attenuator

2 i 2

o 1 2 i 1 2

in 1 2 i

R R RAR R R R R R

R R R R

= ≈+ + +

= +vo

vi

RinRo

R1

R2 Ri


AC voltage attenuator

( )

( ) ( )

1 1 2 i i

eq 2 i

1 eq 1 2 i

in 1 2 i 1 i

Compensation:

o

R C R R C

Z R RA

Z Z Z R R R

Z R R R C C

=

= ≈+ + +

= + ⊕

Zo

vo

vi

Zin

R1

R2 Ri

C1

Ci


AC voltage attenuator (2)

( ) ( )

1 1 i i

eq i

1 eq 1 i

in 1 i 1 i

Compensation:

o

R C RCZ RA

Z Z Z R R

Z R R C C

=

= ≈+ + +

= + ⊕

Zo

vo

vi

Zin

R1

Ri

C1

Ci Useful for “small” Ri


Frequency-compensated attenuator

Vo CinCc Rin

Vin

Ro

Vo CinCc

Rin

Vin

R

9 MΩ

1 MΩC

Ro

Passive oscilloscope probe (1:10)


Attenuator adjustment

1 kHz






Fully-differential amplifier

iD iH iL

iH iLiC

oDoH oC

oDoL oC

2

2

2

v v vv vv

vv v

vv v

= − +

= = + = −

ic iD

ic iD

oD oCDD CC

iD iC0 0

oC oDCD DC

iD iC0 0

v v

v v

V VG GV V

V VG GV V

= =

= =

= =

= =


Ideal differential amplifier

oD DD iD DC iC DD iD

oC CD iD CC iC CC iC

DC

CD

DD

CC

0 Ideal

0

Discrimination factor: 1

V G V G V G VV G V G V G V

GG

GDG

= + = = + =

= =

= >>


Figures of merit

( )

( )

DD

DC

CD

DD

iCoD DD iD DC iC DD iD

oC CD iD CC iC CC iC iD

CMRR

Gf CG

GEG

VV G V G V G VC

V G V G V G V V ED

= =

=

= + = +

= + = +


Example: independent stages

voH

voLG2

G1

viH

viL( )( )

DD

CC

DD 1 2

DC 1 2

1 2CD

DD 1 2

1

12

4 12 4

GDGG G GCG G G

G GGEG G G C

= =

+= =

−

−= = =

+


Example: coupled stages

DD 1 2

CC

DC

1 2CD

' "2 2

1 21 1

110

2

,

G G GGG

G GG

R RG GR R

= + + = =

− =

= = ( )

DD

DC

DD1 2

CC

CD 1 2

DD 1 2

1

2 1

GCGGD G GGG G GEG G G

= = ∞

= = + +

−= =

+ +viL

viH voH

voL

R'2

R''2

R1

-

+VFA

-

+VFA


Input impedances

voH

voL

vc vd/2

vd/2+

+

Zo

Z'o

ZD

L

H

ZC

Z'C

viH

viL

GCC

GDC

GCD

GDD


Input impedances: differentialZC → ∞


Input impedances: common mode

voH

voL

vc vd/2

vd/2+

+

Zo

Z'o

ZD

L

H

ZC

Z'C

viH

viL

GCC

GDC

GCD

GDD


Input impedances: common mode

voH

voL

vc vd/2

vd/2+

+

Zo

Z'o L

H

ZC

Z'C

viH

viL

GCC

GDC

GCD

GDD

A

B


Effect of common-mode input impedances

viH

viL

Z o

Z'o

Z C

Z'C

B

A

C oC Ca o oa

' 'C oC oa o oa

2 2

2 2

Z ZZ Z Z Z

Z ZZ Z Z Z

∆ ∆= + = +

∆ ∆= − = −


Effective CMRR( ) ( )

( )

( )

' 'C C o C C o Ca

iC ooa C Ca o oa

Ca oa

DD DDi DC CDie -1 -1

DD DCi DC CCi i a i a

12

1 14

Z Z Z Z Z Z ZC Z ZZ Z Z Z ZZ Z

G G G GCG G G G C C C C

+ + += ≅

∆ ∆∆ − ∆ −

+= = +

+ + +

A finite ZD does not affect this result

e i a

1 1 1C C C

≅ +


Cascade differential amplifiers

1T

1

1 1CMRR CMRR

CMRR

n

i ij i

i i jj

C D

=

<

=

≅

=

∑

∏


Additional errors: instrumentation amplifier

vo-

+IA

vL

vH

Ref

Don’t use “dc blocking” capacitors!

vc vd/2

vd/2

+

VioZo

Z'o

Ip

In

Vs+

Vs-

+vo

-

+IA

Ref

ZD

'onopioIZE RIRIV −+=


Instrumentation amplifier: deviations

( )o ref H L DDV V V V G− = −

( ) c s+ s-d ni

e + -

e front IA

1 IZE " "CMRR PSRR PSRR

1 1 1CMRR CMRR CMRR

o Gv V Vv G v Eε

∆ ∆= + + + + + +

= +


Instrumentation amplifier: frequency response

vo-

+IA

vL

vH

Ref

f 'af ''a fa

lg f

G

G''0

G0

G'0

( )

( )

o ref H L DD

0 aH L

a

V V V V GG fV Vjf f

− = −

= −+


DC level shifters

R

-

+Vs-

Vs+

VFA

Vs+

VrefIo

1ref 0

1 2

RV VR R

=+






Input circuit protection

Devicesto be

protected

Overcurrentprotection

Ove

rvol

tage

prot

ectio

n


Overvoltage protection

• Problems:– Damaged pn junctions by excessive reverse voltage– Dielectrics breakdown– Overcurrents– Circuit malfunctioning

• Solution: voltage transient suppressors– Transient attenuators: passive low-pass filters– Transient diverters:

• Voltage clamping devices: MOV, Transzorb®, Zener diodes• Foldback/crowbar circuits: GDT


Overcurrent protection

• Problems:– Excessive heating by Joule’s effect– IC degradation (input current >1 mA)

• Solution: current limiters– Fuses– Series resistors– Resettable fuses (PPTC, NTC thermistor)


First-level protection1 k , 1 W

+t° +t° MOV15 V


First-level protection + LPF

LPFGDT


Differential input protection


Second-level protection

R2

Vs-

Vs+

R1

D1

D21-100 k 1-10 k

Op ampIAAMUX


Integrated devices


Circuit isolation basics


Grounded measurements


Isolated measurements with a battery-supplied DMM


Isolated measurements


Isolated USB DAQ module


Summary

1. Compensate ac attenuators2. Use differential amps whenever possible3. Beware of unexpected ac attenuations4. Keep differential circuits balanced5. Ensure input protection6. Consider isolation in industrial settings


Index


power3. Functions on signal spectrum:

filtering4. Uncertainty and calibration5. Trends in AFE for DAS


3. Functions on signal spectrum: filtering

3.1 Frequency filtering fundamentals3.2 Differential filters


Filtering

• Linear filters discriminate signals based on their frequency.

• Used for:– Antialias filters– Interference and noise reduction

• Design of filters:– Approximation problem: filter shape– Realization problem: circuit implementation


Antialias filters

Source: IEEE Instrumentation & Measurement Magazine, October 2005


Ideal filters

f

Phase

Groupdelay

|H|

ffc

Passband Stopband

Low pass |H|

ffc

PassbandStopband

High pass

|H|

ffcfL fH

StopbandStopband

BW= fH - fL

Bandpass

LHc fff =

|H|

ffc

Passband Passband

Band reject

[ ]( )fd

fHdT

π2)(arg

gd −=


Frequency response for actual filters1. Amplitude deviations in the passband2. Finite stopband transmission3. Transition band4. Group delay: not constant

Trade-off between amplitude response (flatness, attenuation), and phase response (or group delay) / transient response (settling time)

fp f

dB

0

A

0 fs

Passband Transitionband

Stopband

H(f )


Frequency response

( ) A jBH fC jD

+=

+

2 22

2 2( ) A BH fC D

+=

+

arg ( ) arctan arctanB DH fA C

= −

( )gd

arg ( )2

d H fT

d fπ = −


Butterworth LPF

( )2

2c

1( )1 nH f

f f=

+

c

arg ( ) arctann

fH ff

= −


Chebyshev LPF

2

2 2c

1( )1 n

H fC f fε

=+

( ) ( )2dB 10lg 1R ε= +


Bessel filters: attenuation


Analog LPF: amplitude response


Analog LPF: group delay


Analog LPF: step response


Comparative• Bessel:

– Excellent step response (low distorsion)– Bad flatness and attenuation– Use where transient response is important

• Chevyshev:– Good attenuation– Ripple in pass-band and ringing in step response– Steeper attenuation at the cost of more passband

ripple (ε↑).• Butterworth:

– Good compromise between all parameters. – Good first choice general purpose filter


Circuit topologiesFirst-order (n=1) and second-order (n=2), low-pass RC passive filters

Second-order (n=2), low-pass active filters

VCVS, Sallen-KeyMultiple feedback (MFB)


Cascading of basic blocs


Filter design1. Determine design requirements: amplitude, group delay

(phase linearity), transient response2. Select an appropriate transfer function (approximation

problem): Butterworth, Chebyschev, Bessel…3. Determine filter order (n) from graphics, tables,

equations…4. Filter implementation (realization problem, filter

synthesis) ⇒ circuit topology: passive/active, Sallen-Key (VCVS, MFB,…), biquad, state variable…

5. Circuit design: use appropriate software from IC manufacturers (FilterCAD®, Filterlab®, FilterPro®, FilterWizard®…)


Noise bandwidth

( ) 2

2 00

1B G f dfG

∞= ∫

( )

c

H L

-3 dB

-3 dB3

LPF-1:2

BPF-1: 2

LPF-2: 1.224 2 1

3LPF-3: 1.1516 2 1

B f

B f f

B f

B f

π

π

π

π

=

= +

= ≈−

= ≈−


3. Functions on signal spectrum: filtering

3.1 Frequency filtering fundamentals3.2 Differential filters


Differential filters


Differential filters: independent stages

( ) ( ) ( )( ) ( )

1 2

1 2

1CMRR2

H jf H jfjf

H jf H jf+

=−


Bad differential passive filter

voHviH

voLviL

R1

R'1

C1

C'1

( ) ( )( )

'

1 ' 11CMRR '2 '

'Example:

0.01, 0.05

CMRR = 60 dB 0.01

R C

R C

R C

t t ss

t t ss sRC

t t

RCω ω

+ +=

+

=

= =

⇒ = =


Bad input ac coupling


Differential filters: coupled stages

( )CMRR jf = ∞


Differential LP passive filter

voHviH

voLviL

R1

R'1

C1

C'1 ( )oH oL

'' 1 1iH iL

1 1 '1 1

1

1

v vC Cv v s R R

C C

−=

−+ +

+

( )CMRR jf = ∞


Input RFI filter

( )c '0 0

12

fR R Cπ

=+


Differential HP filter: coupled stages + bias network

( )1a 2 1a2 2CMRR

R C

j f R R Ct t

π +≈

+


Differential ac coupling

v1

vo

R1

C1

-

+IA

v2

R'1

C'1

R2

( )1a 2 1ai

2π 2

R C

j f R R CC

t t+

≈+

e i IA

1 1 1C C C

= +

L ' '' 1 1 1 1

1 1 '2 1 1

TH

1

2πf

R R C CR RR C C

ffG

=

+ + +

=


Differential ac coupling network

( )( )

'2 2oH oL

'iH iL 2 2 1

s R R Cv vv v s R R C

+−=

− + +

C

R2

R'2

C

R1

R'1

viH

viL

voH

voL

( )CMRR jf = ∞


Differential ac coupling

e i IA

1 1 1C C C

= +

( )L '

' 1 12 2 '

1 1

TH

1

2πf

C CR RC C

ffG

=+

+

=


Active LP differential filter

+

-

47 nF

39.2 kΩ 280 kΩ

+

-

4.7 nF

47 nF

39.2 kΩ 280 kΩ

Low-pass, 2nd order, Butterworth, BW: 70 Hz


Summary

1. Filter selection: attenuation, ripple, group delay and transient response

2. Avoid non-coupled differential filters3. Don’t forget input currents4. Reduce differential input impedances as

much as feasible5. Reduce bandwidth as much as possible


Index




Uncertainty sources

• Systematic effects– Offset (voltage, bias and leakage currents)– Component tolerance– Temperature coefficients (θ measurement)– Reduction: static calibration

• Random effects– Noise– Interference– Environmental noise (pseudonoise)


Accuracy → Uncertainty

Measurand (Result of a) measurement[Ma, Mb] Instrument loading [Va, Vb] M = V ± U [M]- Undisturbed value V: measured value (central)

- Intrinsic uncertainty U: uncertainty (dispersion)Confidence level: 95 %

Alternative method:• Standard uncertainty: u = σ(v)• Uncertainty: U = k×u; k = coverage factor (k = 2 →95.42 %)


Calibration diagram and curve

Vi: measured valueUi: intrinsic uncertainty (instrument)

Alternatives to calibration diagrams:- Calibration table- Algebraic equation

Sensitivity (linear): RSV

∆=

∆

Readings or indicationsin output units

R

Mea

sure

d va

lues

, in

mea

sure

men

t uni

ts

M

∆Rj

Vj

Ri

ViUiUi

Calibrationcurve

Calibration diagram

Reference conditions

Vj: conventional “true” valueUj < 0.1Ui


Uncertainty of measurement

InstrumentMeasurand[Interval]

Calibration curve

Calibrationdiagram

Reading

R

V

U

Indicatedvalue

UncertaintyMeasurement span Uncertainty limits

Operation conditions

M = V ± UResult

Influence quantities

Influence coefficients


Uncertainty limits

• (Absolute) uncertainty:U = a × R + AU = a × R + b × Vf Vf: fiducial value

• Relative uncertainty: U/V

• Fiducial uncertainty: U/Vf


Uncertainty propagation

• Indirect measurement:• Each direct measurement:• Measured value:• Measurement uncertainty:

Xi independent Xi correlated (ρ = +1)

( )= 1 2, ... NY f X X X[xi – Ui, xi + Ui] ( )= 1 2, ... Ny f x x x

1

N

ii i

fU Ux=

∂= ∂

∑2

2 2

1

N

ii i

fU Ux=

∂= ∂

∑


Static calibration

Expected transfer characteristic:

y by mx b xm−

= + ⇒ =

( ) ii i i o

o i

'' : y bx y y xm

e x x

−→ ≠ =

= −

Aim: from reading y’ obtain corrected xo such that e = 0

Actual transfer characteristic:


Two-point calibration

x

y, y'1

y'i

xi xo

y'o

00 1

Actual

Ideal

x

y, y*1

y'i

xi xo

00 1

( )

( )

2 1o 1 1

2 11 1

2 2 FSo 0

FS 0

' '' ''

'' '

' '

x xx y

xx y

y x

y

y yx x yx

yx y

y

− = − + −= → → = →= −

−

CalibrationGain deviation/error

FSR FSR

When 0, When ,

x y bx x y mx b

= ≠ = ≠ +


Optimal two-point calibration

ISE

IAE

LMEx2x1

c 2 1xx

k∆

−+

c 2 1xx

k∆

++

c 4xx ∆

− c 4xx ∆

+

c 2 3xx ∆

− c 2 3xx ∆

+

FS

0

FS

0

0 FS max c

2

LME:

IAE =

ISE =

x

x

x

x

e e k e k e

edx

e dx

= = × = ×

∫

∫FS 0

0 FSc 2

x x xx xx

∆ = −

+=


Static calibration DAQ system


Index




Quasi-digital light sensor (TSL220)

C

vo, fo+

-

tmi(t)


Quasi-digital temperature sensor(TMP03/04)

+-

+

-

1 bitDAC

TemperatureSensor

Digitalfilter

Clockgenerator

T1 T2

Out

modulatorΣ

×° = − 1

2

400( C) 235 TTT


Direct sensor-µC interface


Pt1000 thermometerRange: -45 °C to +120 °C [825 Ω to 1470 Ω]

RB7

RB0/INT

RB6

RB4

CC PIC

Rx

Rc2

R0

RB5 µC: AVR AT90S2313 and PIC16F873

Timer1: 16 bitTwo-point calibration: Rc1 = 909 Ω, Rc2 = 1330 ΩThree-signal method: Rc2 = 1470 Ω, R0 = 330 ΩR: 0,1 %, 15 × 10-6/°CC = 2,2 µF, 5 %, 100 × 10-6/°CThermal shieldingNx, Nc1, Nc2: 100 readings → ( ),x xR s R∗ ∗


Accuracy and resolution

800 900 1000 1100 1200 1300 1400 15000

50

100

150

200

250

Actual Resistance (Ohms)

Rel

ativ

e er

ror (

x10

)ExperimentalTheoretical

-6

Maximal deviation: 0,075 °CResolution: 0,075 °CResolution (n = 10): 0,025 °C


Mixed-signal µC


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