A/D and D/A converters Study Notes for GATE EE Exam

By Yash Bansal|Updated : September 19th, 2021

A/D and D/A converters Study Notes for GATE EE Exam: In this article, you will find the Study Notes on Data Converters which will cover the topics such as DAC & ADC, Classification of DAC, Weighted Resistor and R-2R ladder circuits, Inverting Circuits, Types of ADC and CMOS Logic implementations.

Table of Content


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

Digital to Analog Converter (DAC)

DAC converter (also called D/A) accepts an n-bit digital word or input and produces an analogue sample.



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

Classification of DAC


Weighted Resistor DAC (N – bit):

  • A DAC can be implemented 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 & 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 completeness of the switches.
  • A disadvantage of the binary-weighted resistor network is that for a large number of bits (N > 4), the difference between the smallest and largest resistances becomes quite large. This denotes 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 exchanged in analogue output corresponding to 1 LSB bit increase in the input.
  • Resolution = weight of LSB =image017
  • 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 analogue output voltage of DAC.


VFS = Vr

  • Percentage Resolution:


  • Maximum Error Maximum error acceptable in ADC and DAC equals resolution.
  • Resolution (R-2R ladder type) = image020

Analog to Digital Converter

  • A/D converter (also called an ADC) accepts an analogue sample Vand produces an N-bit digital word.
  • Examples of ADC usage are cellphone, thermocouples, digital voltmeters, 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.

Counter type ADC:

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

Successive Approximation Type ADC:

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


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

Flash Type ADC:

  • It is also known as Parallel-comparator type ADC or Simultaneous converter.
  • It is the highest speed ADC (fastest ADC)
  • Functional component
  • It utilizes 2N -1 comparators to compare the input signal level with each of the 2N -1 possible quantization levels.
  • The output of the comparators is 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:


Dual Slope Integrating Type ADC:

  • It has the slowest conversion time but has a 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.

Dual Slope Integrating Type ADC:

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


CMOS: Complementary Metal Oxide Semiconductor

CMOS inverter



CMOS contains two types of power dissipation

  1. Static power dissipation During logic 0 or logic 1
  2. Dynamic power dissipation Occurs during transitions and it is given by image029 where C is the capacitance of MOSFET

Other Logic Gates by CMOS


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