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Introduction to Analog-to-Digital

Converters

Shraga Kraus

ADC

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Contents

Background Some Basic Analog

Circuits ADC Architectures

Flash ADC Folding ADC Algorithmic ADCs Pipeline ADC

Time-Interleaved Structure

Characterization in the Lab

Discussion

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Background

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ADC Model (1/2)

Analog signal: continuous both in time and value

Digital signal: discrete both in time and value

Discrete time (sampling) aliasing Discrete value (resolution)

quantization

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ADC Model (2/2)

Modeled as a linear system + quantization noise

For easy analog treatment, noise is input-referred noise

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Sampling for Dummies (1/3)

Sampling = multiplication by an impulse train

Y (t ) = X (t ) · S (t ) Ts = sampling interval fs = 1/Ts = sampling frequency

t

Ts

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Sampling for Dummies (2/3)

In the frequency domain: Y (f ) = X (f ) * S (f )

“Aliasing” is evident

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Sampling for Dummies (3/3)

Nyquist sampling:

Over-sampling:

Under-sampling:

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Anti-Aliasing Filter Nyquist

sampling:

Over-sampling:

Under-sampling:

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Incoherence – by Comics

Consider the following sinusoidal inputs, sampled at fs:

t

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Quantization (1/4)

Δ = LSB m = num of

bits Full scale

amplitude:2

2

m

A

0

Δ

A

76543210

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Quantization (2/4)

For incoherent sinusoidal input: Assuming uniform distribution of

quantization noise from –Δ/2 to +Δ/2

–Δ/2 +Δ/20

1/ΔFqn

x

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Quantization (3/4) For incoherent sinusoidal input

with full scale amplitude: Signal power:

Noise power:

2

2 2 2 31 1 22

2 2 2

mm

sigP A

3 22 2

2 2

2 2

1 1 1

3 4 12qn qnP F x x dx x dx

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Quantization (4/4) SNR:

Effective number of bits (ENOB):

2 2 32

2

10

2 322

1210log 6.02 1.76

msig m

qn

dB

PSNR

P

SNR SNR m

1.76

6.02dBSNR

ENOB

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Example Simulated ideal 7-bit ADC:

SNR = 43.8 dB ENOB = 7

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Practical Over-Sampling Out-of-band noise is filtered out digitally

OSR = 2 SNR x2 (+3dB) ENOB +½

1.76

6.02dBSNR

ENOB

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What is ½ Bit?

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Non-Linear Effects (1/2)

Integral Non-Linearity (INL)

Vin

outputcode

76543210

Vref0

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Non-Linear Effects (2/2)

Differential Non-Linearity (DNL)

Vin

outputcode

76543210

Vref0

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Some Basic Analog Circuits

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Differential Pair

The core of every op amp Finite gain (Av = gmRD) Finite bandwidth Finite slew rate Input capacitance Non-linearity

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Voltage Buffer (1/2)

Theoretically Vout = Vin

Finite gain results in output offest Finite bandwidth (esp. with 2 stages) Finite settling time Input capacitance

reduced by feedback, but still exists

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Voltage Buffer (2/2) Settling time:

Time

Outp

ut

Volt

age

slew rate

damping

Tsettling

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Switch (CMOS Only!) (1/2)

Has finite resistance Resistance depends on the input

voltage (linearity issues) Parasitic capacitances result in

charge sharing Complicated

correction circuits

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Switch (CMOS Only!) (2/2)

Resistance depends on the input voltage (linearity issues)

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Comparator

Basically an open-loop op amp Must make a decision quickly Memory effect Input capacitance not reduced

by feedback Latched comparator –

triggered by clock

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Sample & Hold

Triggered by clock Finite settling time Must be very accurate when

placed at the ADC’s input (noise/linearity)

Speed and accuracy are achieved only by very complicated circuits

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10-Minute Break

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ADC Architectures

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Implementation Methods Discrete time

Requires switches Takes advantage of

switched capacitors Continuous Time

1 clock cycle / decision

Frequencies set by absolute R-C values

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Flash ADC Continuous Time No. of comparators

= 2m – 1 Output in

thermometer code Thermometer code

is converted to binary by simple logic

Fastest topology0011111 = ‘101 = 5

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Flash ADC Limitations Many comparators

– a lot of area & power

Resistors must be matched (area)

Input drives comparators’ capacitances

Number of bits is limited (~ 5 bits)

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Non-Linearity of Flash ADC Resistor ladder

mismatch Input buffer CLK/vin skew

or input S&H non-linearity

Comparators’ “memory effect”

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Folding ADC Continuous Time No. of

comparators = 2m/ 2 (approx.)

Fast with quite a high resolution

Common in instrumentation

vout

vin

VREF

VREF

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Folding ADC Limitations

Flash drawbacks are alleviated, but still there

The folding amplifier must fold accurately and be linear

The folding amplifier introduces a delay and result in skew between the two flash ADCs

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Non-Linearity of Folding ADC

Inherited flash non-linearity

Non-linearity of the folding amplifier

CLK/vin skew between the two flashes or input S&H non-linearity

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Algorithmic ADCs Discrete Time Small No. of comparators (reduced area &

power) High resolution (up to 16 bits) Digital circuitry, usually plenty of switches Output data rate = fs /m or fs /2m (= slow…) Types: single/dual slope, successive

approximation register (SAR), integrating (Agilent’s patent)

Common in slow instrumentation and consumer devices (e.g. digital cameras)

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Example: Single-Slope ADC

t

VREF

vin

Start!

• Counter reset to 0 and starts counting• Slope triggered

Stop!

• Comparator’s output flips • Counter stops

S&H

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Single-Slope ADC Limitations

Calibrations are required: Absolute R-C or L-C values Non-linearity of the slope

Maximum time per decision: 2m clock cycles (sloooooooooooow)

S&H must be as accurate as the ADC

However : one slope + one counter can be used for many ADCs

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Non-Linearity of Single-Slope

Non-linearity of the slope Input S&H non-linearity Incomplete capacitor discharge

(“memory effect” of the slope)

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Pipeline ADC Discrete Time No. of comparators = m Switched capacitor circuitry Common in CMOS

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C0x2

‘1’

C1

–VREF/2thenx2

‘0’

Pipeline ADC – ExampleVREF = 1 Vvin = 0.65 VDout = ‘101

C2

‘1’

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Pipeline ADC Limitations

Speed limited by switches and op amp settling time

The first comparator must be extremely accurate (1½ bit arch.)

Switches and op amps are lousy in contemporary CMOS technologies

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Non-Linearity of Pipeline ADC

Input S&H non-linearity (if exists) Amplifiers’ gain error (low gain) Amplifiers’ gain different than x2

(feedback capacitor mismatch) Amplifiers’ settling time Inaccuracy in VREF /2 subtraction

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Time-Interleaved Structure

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The Principle

Using many slow ADCs Each ADC samples the signal

at a different phase

t

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The Structure

τ

τ

τ

ADC 1

ADC 2

ADC 3

ADC 4

vin

CK

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Limitations

Many ADCs – area, power Signal and clock distribution

networks are required Signal and clock distributed

with different delays Advanced RF techniques Complicated calibration

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Characterization in the Lab

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Pure Sine

Effective Number of Bits

Signal Generator

Signal Generator

ADC

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Dual Tone

Linearity

Signal Generator

Signal Generator

ADC

SFDR

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Discussion

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Periodic Non-Uniform Sampling

Recall the example from Moshiko’s presentation: L = 7 p = 3 C = {0, 2, 3}

Are there two adjacent elements from L in C ?

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Two Adjacent Samples C = {0, 2, 3}

Speed constraints on the ADC are not relaxed

Time-interleaved structure can benefit from omitting some of the ADCs

0123456

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No Adjacent Samples C = {0, 2, 5}

Speed constraints on the ADC are now relaxed

Clock generator implemented by a simple logic circuit

Time-interleaved structure can benefit from omitting some of the ADCs

0123456

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