Lecture 2 - Fundamentals of Data
Converters
Dr. Mohamed Refky Amin
Electronics and Electrical Communications Engineering Department (EECE)
Cairo University
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
Dr. Mohamed Refky
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
Dr. Mohamed Refky
Quantization
Analog to Digital Conversion
Analog to Digital Converter
Dr. Mohamed Refky
Quantization
Analog to Digital Conversion
Analog to Digital Converter
Dr. Mohamed Refky
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
Dr. Mohamed Refky
Analog to Digital Conversion
Analog to Digital Converter
Dr. Mohamed Refky
Quantization
Analog to Digital Conversion
Analog to Digital Converter
Dr. Mohamed Refky
Quantization
Analog to Digital Conversion
Analog to Digital Converter
Dr. Mohamed Refky
Quantization
Analog to Digital Conversion
Analog to Digital Converter
Dr. Mohamed Refky
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
Dr. Mohamed Refky
Static Specifications
Integral Non-Linearity
Analog to Digital Conversion
Analog to Digital Converter
Dr. Mohamed Refky
Static Specifications
Signal to Noise Ratio
Analog to Digital Conversion
Analog to Digital Converter
Dr. Mohamed Refky
Dynamic specifications
Signal to Noise and Distortion Ratio
Analog to Digital Conversion
Analog to Digital Converter
Dr. Mohamed Refky
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
Dr. Mohamed Refky
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
Dr. Mohamed Refky
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
Dr. Mohamed Refky
Reconstruction
Digital to Analog Conversion
Digital to Analog Converter
Dr. Mohamed Refky
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
Dr. Mohamed Refky
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
