Test: Digital to Analog Converters - Electronics and Communication Engineering (ECE) MCQ

D/A converter:
D/A converter converts digital or binary data into its equivalent analog data. This analog data is required to drive motors and other analog devices. The converted analog value is either in voltage or current form.
There are two types of D/A converters:

• Weighted Resistor or Resistive Divider type
• R-2R Ladder-type

Weighted resistor DAC:
It uses a summing amplifier with a binary-weighted network as shown below.

For an n-bit ADC,

• If the weight of MSB resistor is 2R, then the weight of the LSB resistor is 2nR.
• We require n number of resistors.
• We require n different values of resistors i.e. 2R, 22R, 23R, …, 2nR.

The accuracy and stability depend on the accuracy of resistors.
The requirement of a wide range of resistor values restricts the use up to 8-bit.
R-2R ladder resistor DAC:
It uses a summing amplifier with an R-2R ladder network as shown below.

For n-bit DAC, it requires only 2 different values of resistors i.e. R and 2R.

• MSB stands for most significant bit is the bit position in a binary number having the greatest value.
• The MSB is sometimes referred to as the high-order bit or left-most bit due to the convention in positional notation of writing more significant digits further to the left.
• The MSB can also correspond to the sign bit of a signed binary number. In one's and two's complement notation, "1" signifies a negative number and "0" signifies a positive number.

Example:
(12)₁₀ = (1100)₂

According to the question, the most significant bit of '100010' binary data is '1'. 

• Let's recall how these two types of ADCs work:
  • Successive Approximation ADC (SAR ADC):
    • Takes fixed number of clock cycles for conversion
    • One cycle per bit
    • Conversion time is independent of input voltage
  • Single Slope Integrating ADC:
    • Works by counting clock pulses during the time taken for a ramp to reach input voltage
    • Conversion time is proportional to input voltage
    • Takes longer for higher voltages
• For SAR ADC:
  • Time is independent of input voltage
  • Therefore, for 6V input: Time = Ta
• For Single Slope ADC:
  • Time is directly proportional to input voltage
  • If 3V takes Tb time
  • Then 6V will take: 2Tb time (doubled)

• Therefore, when input is changed from 3V to 6V:

• SAR ADC will take Ta time
• Single Slope ADC will take 2Tb time

• The answer is: Ta and 2Tb

• The smallest change in the input signal that can be detected by an instrument is referred to as its "resolution."
• The term resolution describes the finest detail that a device or system can detect or measure.
• It is a key parameter for systems that deal with digital signals, as it is directly linked to the quality or level of detail of the output.

For a ladder-type D/A Converter:
Output Voltage (V₀) = Resolution × Decimal Equivalent of binary input.
Where Resolution is given by:

Application:
Given n = 5 and the Digital input = 11010
∵ The Resolution will be:

Since the decimal Equivalent of 11010 = 26
So, V₀ = 26 × 0.3125
V₀ = 8.125 V
Note: If the full-scale voltage is given, then:
Resolution 

Flash ADC (Fastest)

• The flash ADC is the fastest type available. A flash ADC uses comparators, one per voltage step, and a string of resistors.
• Flash-type ADC requires no counter For an n-bit ADC, flash-type ADC requires (2ⁿ – 1) comparators
• A 4-bit ADC will have 15 comparators, and an 8-bit ADC will have 255 comparators.
• The following figure shows a 3-bit flash ADC circuit.

• It is formed of a series of comparators, each one comparing the input signal to a unique reference voltage.
• The comparator outputs connect to the inputs of a priority encoder circuit, which then produces a binary output.
• Vref is a stable reference voltage provided by a precision voltage regulator as part of the converter circuit.
• As the analog input voltage exceeds the reference voltage at each comparator, the comparator outputs will sequentially saturate to a high state.
• The priority encoder generates a binary number based on the highest-order active input, ignoring all other active inputs.

Concept:
For a ladder-type D/A Converter:
Output Voltage (V₀) = Resolution × Decimal Equivalent of binary input.
Where Resolution is given by:

Where, V_fs = Full scale voltage or maximum voltage
Application:
Given n = 6 and the Digital input = 101001
∵ The Resolution will be:

Since the decimal Equivalent of 101001 = 41
So, V₀ = 41 × 0.1587
V₀ = 6.5067 V
V₀ ≈ 6.5 V
Note:  If the reference voltage is given, then:

Resolution: It is defined as the smallest change in the analog output voltage corresponding to a change of one bit in the digital input.
The percentage resolution (%R) of an n-bit DAC is:

The resolution of an n-bit DAC with a range of output voltage from 0 to V is given by:

Calculation:
Number of bits (n) = 8
Resolution 

Resolution: It is defined as the smallest change in the analog output voltage corresponding to a change of one bit in the digital output.
The percentage resolution (%R) of an n-bit DAC is:

The resolution of an n-bit DAC with a range of output voltage from 0 to V is given by:

Hence the difference between analog voltage represented by two adjacent digital codes of an analog to digital converter is called resolution.
Hence option (2) is the correct answer.

It is defined as the smallest change in the analog output voltage corresponding to a change of one bit in the digital output.
The percentage resolution (%R) of an n-bit DAC is:

Calculation:
As we know the formula resolution,

250 = 2^N -1
2^N = 251 ≈ 255 
i.e., 2⁸ = 255
N = 8
Hence the minimum value of N satisfying the condition.