Lec. 3: Fundamentals of Data Converters

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Lec. 3:

Fundamentals of Data Converters

Lecturer: Hooman Farkhani

Department of Electrical Engineering Islamic Azad University of Najafabad Feb. 2016.

Email: [email protected]

In The Name of Almighty

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ADC Input-Output Transfer Characteristics

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Least-Significant Bit (LSB) in Volts

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The Ideal A/D Converter & Quantization Error

1

0

( .2 )

N

m

in ref m Q

m

V V B V





  

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Effect of Quantization error on Signal

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Quantization Error

 Assuming a uniform distribution

_1/ _{/ 2} _{/ 2}

( , )

0 P x t x

others

     

 



/ 2 / 2 2

2 2 2 2

,

/ 2 / 2

( , ) . 1

Q rms 12

V Ex x P x t dx x dx

 

 

    

 

 ^V^{Q rms}^, ^ ^₁₂ ^ ^V^LSB₁₂ ^ ₂^N^V^FS₁₂

1LSB

 

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Signal-to-Quantization-Noise Ratio



Assuming uniform distribution of eq and a full-scale sinusoidal

input, we have:

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Quantization noise spectrum



Quantization results in an "infinite" number of harmonics

6.02 1.76

SNR  N  dB

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Performance Metrics of ADCs

 Static specifications

 Offset error

 Gain error

 Monotonicity

 Resolution

 Differential nonlinearity (DNL)

 Integral nonlinearity (INL)

 Dynamic specifications

 SNR

 THD

 SNDR

 ENOB

 SFDR

 ERB

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Static specifications



Offset Error

 Defined as a constant difference, over the whole range of the ADC, betwe en the actual output value and the ideal output value.

 Expressed as number of LSBs (counts) or as percentage of full scale range

 Offset error can be removed by measuring a reference point and subtractin g that value from future samples.

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Static specifications



Gain Error

 Defines as the difference of the slope of the actual output values and the id eal output values.

 Expressed as number of LSBs (counts) or as percentage of full scale range

 Caused by preamplifiers, attenuators, or signal transducers.

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Comments on Offset and Gain Errors



Generally it is non-trivial to build a converter with very good gain/offset specifications

- Nevertheless, since gain and offset affect all codes uniformly, these errors tend to be easy to correct

-E.g. using a digital pre- or post-processing operation - Also many applications are insensitive to a certain level of gain and offset errors

- E.g. audio signals, communication-type signals,…

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Static specifications



Monotonicity

 Monotonicity is a property of certain types of digital-to-analog converter (DAC) circuits.

 In a monotonic DAC, the analog output always increases or remains const ant as the digital input increases.

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Static specifications

● Differential nonlinearity (DNL)

LSB

LSB i

in i

in

i

V

V D

D V

DNL  

 ( ) (

^

) )

(

¹

1. When DNL is large enough, output codes can disappear as the range of inputs able to produce them shrink

2. Any converter with worst-case DNL less than 0.5LSB is guarantee d to have “no missing codes”

3. It doesn’t mean an DNL greater than ½ LSB necessarily produces

Missing code:

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



^k

1 i

i

k

DNL

INL

● Integral nonlinearity (INL)

Static specifications

1. INL acts as an input referred high-order polynomial distortion on the in put, usually larger than DNL

2. INL could add distortion terms of high degree so that while 3rd order IM dominates

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Dynamic specifications

2 2

( )

( ) 10.log

( )

sig spur

V f SFDR dB

V f

 

   ( ) 9

SFDR dB  n c

 SFDR: Spurious-Free Dynamic Range

Only Quantization Noise:

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Dynamic specifications

 SNR: Signal-to-Noise Ratio

10 log (10 ^s ) 6.02 1.76

dB

n

SNR P N dB

 P  

1 2

2

( . )

( )

NH

j

V j f

sig

THD V f



 



 THD: Total Harmonic Distortion

 By convention, total distortion power consists of 2

^nd

thr ough 7

^th

harmonic

Only Quantization Noise:

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) V

V V

log( V 10 SNDR

dist 2 th

, n 2 Q

2

sig2



 

 SNDR: Signal-to-Noise-and-Distortion-Ratio

 ENOB: Effective Number of Bits

02 . 6

76 .

1 dB

ENOB SNDR 



SNDR ≤ SNR

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 ERB: Effective Resolution Bandwidth

 Defined as the input frequency at which the SNDR of a converter has dropped by 3dB

 Equivalent to a 0.5-bit loss in ENOB

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1. SFDR: important for wideband receivers like cellular base-station

due to large interferences; Similarly MTPR for multi-tone receiver s (xDSL)

2. SNDR: important for audio/video applications

3. SNR: important in radar (detecting a target from long distance

means to overcome noise); not too many signal targets for inter- modulations concern

Depending on the application an specific parameter becomes important

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Relationship between INL and SFDR



At low input frequencies, finite SFDR is mostly due to INL



Quadratic/cubic bow gives rise to second/third order harmonic



Rule of Thumb: SFDR≈20 log (2

^N

/INL)



E.g. 1 LSB INL, 10 bits SFDR ≈ 60dB

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References



Professor Boris Murmann Course slides 2012, Stanford University- EE315B course



Dr. Reza Lotfi, ADC course slides 2008.