# Digital Electronics: Data Converters Study Notes

By Yash Bansal|Updated : September 10th, 2021

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DAC and ADC: It is possible to convert the analog signal to digital and vice-versa. We can get analog from digital through DAC and can get digital from analog through ADC.

Digital to Analog Converter (DAC): D/A converter (also called a DAC) accepts an n-bit digital word and produces an analog sample.

where, k = Proportionality factor, bn = 1;if nth bit of digital input is 1, bn = 0; if nth bit of digital input is 0.

Classification of DAC:

Weighted Resistor DAC (N – bit):

• A DAC can be constructed by using a Summing Amplifier and a set of resistors R, 2R, 4R, 8R, etc as its inputs.
• The circuit consists of a reference voltage Vf, N binary-weighted resistors R, 2R, 4R, 8R, . . . , 2(N-1) R, N single-pole double-throw switches, and an Op-amp together with its feedback resistance R = R/2.
• The switches are controlled by an N-bit digital input word D.

V0 = -Rf If = -Vf D

LSB resistance = (2N – 1) MSB resistance.

• The accuracy of the DAC depends critically on the accuracy of the Reference voltage, the precision of the binary-weighted resistors, and the perfection of the switches.
• A disadvantage of the binary-weighted resistor network is that for a large number of bits (N > 4) the spread between the smallest and largest resistances becomes quite large. This implies difficulties in maintaining accuracy in resistor values.

R – 2R Ladder DAC: Non-Inverting OP-amp type DAC

Inverting Amplifier

Inverted Ladder R – 2R Circuit

Specifications for DAC:

• Resolution in DAC is changed in analog output with corresponding to 1 LSB bit increment at the input.
• Resolution = weight of LSB =
• V= Voltage corresponding to logic N = Number of bits.
• Analog Output Analog output = resolution x decimal equivalent of binary data
• Maximum Analog Output Voltage (VFS) VFS is the maximum analog output voltage of DAC.

VFS = Vr

• Percentage Resolution:

• Maximum Error Maximum error acceptable in ADC and DAC equals to resolution.
• Resolution (R-2R ladder type) =

Analog to Digital Converter:

• A/D converter (also called an ADC) accepts an analog sample Vand produces an N-bit digital word.
• Examples of ADC usage are digital volt meters, cell phone, thermocouples, and a digital oscilloscope.
• Types of A/D Converters: Dual Slope A/D Converter, Successive Approximation A/D Converter, Flash A/D Converter, Delta-Sigma A/D Converter, etc.

• In N-bit counter type ADC:
• Maximum number of clock pulses required for conversion = 2N -1
• Maximum time required for conversion = (2N -1) TCLK
• Minimum number of clock pulses = 1
• Average number of clock pulses = 2N-1

• It is faster than digital ramp ADC.
• Conversion time (tc) is independent of the value of the analog input voltage (Va).
• It has fixed conversion time.

• Maximum number of clock pulses = N for conversion
• Maximum conversion time = N.TCLK

• It is also known as Parallel-comparator type ADC or Simultaneous converter.
• Functional component
• It utilizes 2N -1 comparators to compare the input signal level with each of the 2N -1 possible quantization levels.
• The outputs of the comparators are processed by an encoding-logic block to provide the N bits of the output digital word.
• Complete conversion can be obtained within one clock cycle.
• For N-bit comparator:
• Total number of comparators = 2N -1,
• Total number of resistors = 2N,
• Total number of priority encoders = 1 (2N × N)

2-bit Flash Converter:

• It has slowest conversion time but has relatively low cost.
• The following components are present in the Dual slope A/D converter:
• Integrator
• Electronically Controlled Switches
• Counter
• Clock
• Control Logic
• Comparator

where, n = Count recorded in the counter.

• Total number of clock pulses = 2N + n
• Maximum number of clock pulses = 2N + 2N - 1 = 2N + 1 -1== 2N + 1

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