lecture 2 - fundamentals of data converters lecture 2 - fundamentals of data converters dr. mohamed...

Lecture 2 - Fundamentals of Data

Converters

Dr. Mohamed Refky Amin

Electronics and Electrical Communications Engineering Department (EECE)

Cairo University

refky.master@gmail.com

http://scholar.cu.edu.eg/refky/

Outline of the lecture

▪ Previous on ELC 609

▪ Analog to Digital Conversion

• Sampling

• Quantization

▪ ADC Specifications

▪ ADC Types

▪ Figure of Merit

▪ Digital to Analog Conversion

• Reconstruction

▪ Assignment (1)

Dr. Mohamed Refky

Previous on ELC 609

Data converters act as an interpreter between the analog and

digital domains.

Dr. Mohamed Refky

Data Converters

Previous on ELC 609

The Design trend is to increase the digital part of the system. This

means moving the ADC toward the input of the system.

Dr. Mohamed Refky

Data Converters

Previous on ELC 609

The Design trend is to increase the digital part of the system. This

means moving the ADC toward the input of the system.

Moving the ADC towards the input introduces challenges.

Dr. Mohamed Refky

Data Converters

Analog Circuit Digital Circuit

Harder to design Easier to design

Higher power consumption Lower power consumption

Larger IC area Smaller IC area

Immune to noise (Noise margin)

Technology scaling introduces

challenges that need to be deal

with

Gain a lot from technology scaling

(speed, power,…)

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

Analog Domain Digital Domain

Continuous in time by

nature (Asynchronous)

Sampling Discrete in time by

nature (Synchronous)

Continuous in

amplitude

(Infinite Resolution)

Quantization Discrete in amplitude

(Finite Resolution)

Analog to Digital Conversion

Analog to Digital Converter

Sampling is the process of converting the continuous signal into

discrete samples.

Sampling

Dr. Mohamed Refky

Analog to Digital Conversion

Analog to Digital Converter

Sampling

Dr. Mohamed Refky

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

Sampling

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

Sampling

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

Sampling

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

According to the sampling frequency the ADCs are classified into

two groups

For the Nyquist rate ADCs, the sampling frequency is about 5-10

the Nyquist frequency.

Sampling

Analog to Digital Converter

Nyquist rate ADCs Oversampling ADCs:

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

According to the sampling frequency the ADCs are classified into

two groups

For Oversampling ADCs, the sampling frequency is much higher

than the Nyquist frequency (around 50-100 times).

Sampling

Analog to Digital Converter

Nyquist rate ADCs Oversampling ADCs:

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

Quantization

Analog to Digital Conversion

Analog to Digital Converter

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Quantization is the process of rounding up/down the sample to one

of the closest available finite digital levels.

Quantization

Analog to Digital Conversion

Analog to Digital Converter

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Quantization

Analog to Digital Conversion

Analog to Digital Converter

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Quantization

Analog to Digital Conversion

Analog to Digital Converter

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Quantization

The quantization process can be

mathematically modeled by using

a summer

Analog to Digital Conversion

Analog to Digital Converter

Quantization

Power of a

random variable

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Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

Quantization

Analog to Digital Conversion

Analog to Digital Converter

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Quantization

Analog to Digital Conversion

Analog to Digital Converter

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Quantization

Analog to Digital Conversion

Analog to Digital Converter

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Interchange the quantizer and the sampler results in a similar

frequency distribution

Quantization

Quantization error has a uniformly

distribution in frequency domain and

is treated as a white noise

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

Due to non idealities in circuit implementation of the ADC, new

types of errors, other than the quantization error, are introduced.

The ADC specifications are divided into two groups:

▪ Static specifications: these specifications quantify the

errors that appear even when the input is constant.

▪ Dynamic specifications: these specifications quantify the

errors that appear when the input is time varying.

ADC Specifications

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

The offset error is defined as the

deviation of the ADC

characteristic line (the line

connecting the midpoint of the

ADC levels) from the one of the

ideal ADC

Static Specifications

Offset Error

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

After the offset error has been

removed, the gain error is

defined as deviation in the slope

of the ADC characteristic line

from the one of the ideal ADC

Static Specifications

Gain Error

Differential Non-Linearity

Analog to Digital Conversion

Analog to Digital Converter

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Static Specifications

Integral Non-Linearity

Analog to Digital Conversion

Analog to Digital Converter

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Static Specifications

Signal to Noise Ratio

Analog to Digital Conversion

Analog to Digital Converter

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Dynamic specifications

Signal to Noise and Distortion Ratio

Analog to Digital Conversion

Analog to Digital Converter

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Dynamic specifications

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

Direct conversion ADCs convert the analog signal directly into

digital code.

An example of direct conversion ADCs is conventional pipeline

ADC.

ADC TypesAnalog to Digital Converter

Direct Conversion ADCs Indirect Conversion ADCs

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

Indirect conversion ADCs do the conversion in indirect way by first

converting the analog signal into an intermediate representation.

Then, this intermediate representation is converted into digital code.

An example of indirect conversion ADCs is the time based ADC.

ADC TypesAnalog to Digital Converter

Direct Conversion ADCs Indirect Conversion ADCs

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

ADC TypesAnalog to Digital Converter

Direct Conversion ADCs Indirect Conversion ADCs

Nyquist Rate

ADCs

Oversampling

ADCs

Nyquist Rate

ADCs

Oversampling

ADCs

An example of Nyquist rate ADCs is Flash ADC.

An example of Oversampling ADCs is Sigma Delta ADC.

Analog to Digital Conversion

Analog to Digital Converter

Dr. Mohamed Refky

Figure of Merit

Digital to Analog Conversion

Digital to Analog Converter

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Digital Domain Analog Domain

Discrete in time by

nature (Synchronous)

Reconstruction

Continuous in time by

nature (Asynchronous)

Discrete in amplitude

(Finite Resolution)

Continuous in

amplitude

(Infinite Resolution)

Digital to Analog Conversion

Digital to Analog Converter

Dr. Mohamed Refky

Reconstruction

Reconstruction is the process of converting discrete samples into a

continuous signal.

Digital to Analog Conversion

Digital to Analog Converter

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Reconstruction

The easiest way to construct the continuous signal is to use a zero

order hold circuit.

Digital to Analog Conversion

Digital to Analog Converter

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Reconstruction

Digital to Analog Conversion

Digital to Analog Converter

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Reconstruction

For proper operation of the DAC, the output must be updated with

the same rate as the ADC sampling frequency

Digital to Analog Conversion

Digital to Analog Converter

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Reconstruction

The frequency response of the ZOH is Sinc function

The impulse response of the zero

order hold is a gate function

Assignments

Assignment (1)

Dr. Mohamed Refky