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

ADC and DAC

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, b_n = 1, k = Proportionality factor; b_n = 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 V_f, 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_f  = R/2.
• The switches are controlled by an N-bit digital input word D.

V₀ = -R_f I_f = -V_f D

LSB resistance = (2^N–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 =
• V= Voltage corresponding to logic
• N = Number of bits.
• Analog Output Analog output = resolution x decimal equivalent of binary data
• Maximum Analog Output Voltage (V_FS) V_FS is the maximum analogue output voltage of DAC.

V_FS = V_r

• Percentage Resolution:

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

• A/D converter (also called an ADC) accepts an analogue sample V_A and 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.

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

Successive Approximation Type ADC:

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

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

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 2^N -1 comparators to compare the input signal level with each of the 2^N -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 = 2^N -1,
  • Total number of resistors = 2^N,
  • Total number of priority encoders = 1 (2^N × 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 = 2^N + n
• Maximum number of clock pulses = 2^N + 2^N – 1 = 2^{N + 1} -1== 2^{N + 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 where C is the capacitance of MOSFET

• Power dissipation is lowest in CMOS.
• P_diss = 0.01mW Figure of merit = 0.7 PJ
• Noise margin =V_DD/2
• t_pd = 70 ns Fan-out = 50

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