After discussing the basic two types of data converters, We will now discuss the Digital to Analog converters in a detailed manner.

We will learn the following topics in this lecture:

- The circuit symbol of D to A converters
- Block diagram
- types of D to A converters
- Specification for D to A converter
- Sources of Error in D to A converter
- Application of D to A converter

**Learn about the Data Converters Here: Data Converters**

Let’s discuss the above topics one by one in detail.

## Circuit Symbol :

The circuit symbol and input-output characteristics of a 4-bit DAC are as shown in the figure.

There are four digital inputs and one analog output.

“d_{0}” is the most significant bit MSB and “d_{3}” is the least significant bit LSB.

The 4-bit digital word will have sixteen different possible combinations from 0000 to 1111.

## Block Diagram of DAC (Digital to Analog Converter):

The block diagram of a resistive type DAC is shown in the figure below:

The basic building blocks of a DAC are a resistive network, digitally controlled electronics switches, a voltage reference, and a current to voltage converter.

A digital input code is applied to the resistive network via the digitally controlled switches.

The digitally controlled switches are turned on or off by the digital input bits (0’s and 1’s)

The output of the resistive network is in the form of current. It can be converted into proportional voltage with the help of a current to voltage converter. Thus we obtain an analog output voltage proportional to the digital input code.

The actual digital to analog conversion takes place within the resistive network.

## Types of DAC (Digital to Analog Converters):

Depending on the type of resistive network used, we have different types of Digital to Analog converter circuits.

- Binary weighted resistor DAC
- R-2R ladder type DAC

Comparison of both Digital to Analog converters are as below:

Sr. No | Parameter | Weighted Resistor DAC | R-2R Ladder DAC |

1 | Simplicity | Simple | Slightly complicated |

2 | Range of resistor values | A wide range is required | Resistors of only two values are required |

3 | Number of resistor per bit | one | Two |

4 | Ease of expansion | Not easy to expand for more bits | Easy to expand |

## Specification for DAC (Digital to Analog Converter):

The designers of the DAC converter specify the following important specification of a Digital to Analog converter:

- Resolution
- Accuracy
- Linearity
- Temperature sensitivity
- Settling Time
- Speed
- Long term drift
- Supply rejection

Let us discuss them one by one.

**1. Resolution:**

- Resolution describes the smallest possible change in the analog output voltage. Resolution should be as high as possible.
- Its value depends on the number of bits in the digital input applied to DAC. Higher the number of bits, the higher the resolution.
- Resolution of DAC can be defined in two different ways:
- Resolution is the number of different analog output voltage values that can be provided by a DAC. For n-bit DAC,

Resolution = 2^n

- Hence the resolution of 4-bit DAC is 2^4 = 16 and that of a 3-bit DAC is 2^3 = 8. hence
**the resolution increase with the increase in the number of bits.** - Resolution is defined as the ratio of change in analog output voltage resulting from a change of 1 LSB at the digital input.
- To calculate the resolution with this definition, we need to know the full-scale analog output voltage V
_{FS}and the number of digital inputs “n”. - The full-scale analog output voltage V
_{FS}is defined as the output voltage corresponding to the digital input with all digits 1. Therefore the resolution is given by,

\boxed{Resolution =\large \frac{V_{FS}}{2^n - 1}}

where, n= Number of digital inputs

**Resolution can be treated as the smallest change in the analog output voltage. The resolution will improve with a reduction in the smallest change in the output voltage.**

**2. Accuracy:**

- Accuracy indicates how close the analog output voltage is to its theoretical value. In short, it indicates the deviation of actual output from the theoretical value.
- Accuracy depends on the accuracy of the resistor used in the ladder, and the precision of the reference voltage used.
- Accuracy is always specified n terms of the percentage of the full-scale output that means maximum output voltage. e.g. if the full-scale output s 15V and accuracy is ±0.1 percent then a maximum error is given by 0.001 x 15 = 0.015V or 15 mV

**3. Linearity:**

- The relation between the digital input and analog output should be linear. However, practically it is not so due to the error in the values of resistor used for the resistive network.

**4. Temperature Sensitivity:**

- The analog output voltage of the Digital to Analog converter should not change due to changes in temperature. But practically the analog output is a function of temperature. It is so because the resistance values and Op-Amp parameters change with changes in temperature.

**5. Settling Time:**

- Theoretically, the analog output voltage should change instantaneously in response to the change in its digital input.
- Practically the analog output of the Digital to Analog converter does not change instantaneously. Due to the resistor and Op-Amp in the circuits, oscillations are observed at the output.
- The time required to settle the analog output within 1/2 LSB of the final value, after the change in digital input is called settling time.
**The settling time should be as short as possible.**

**6. Speed:**

- It is defined as the time needed to perform a conversion from digital to analog. It is also defined as the number of conversions that can be performed per second. The speed of DAC should be as high as possible.

**7. Long Term Drift:**

- These results are mainly due to resistor and semiconductor aging and can affect all the characteristics. Characteristics mainly affected are linearity, speed, etc.

**8. Supply Rejection:**

- It indicates the ability of DAC to maintain scale, linearity, and other important characteristics when the supply voltage is varied. Supply rejection is usually specified as a percentage of full-scale change at or near full scale 25
^{0}C.

## Source of Errors in DAC (Digital to Analog Converter):

There are three types of errors in the transfer characteristics of DACs. They are linearity, offset and gain error. Let us discuss them one by one.

**1. Linearity Error:**

- This is defined as the amount by which the actual output of a DAC differs from the ideal straight-line transfer characteristics.
- This error is introduced due to the error in the current source resistance values. The figure shows the linearity error in the transfer characteristics of a DAC.

**2. Offset Error:**

- When all the digital inputs are 0, the analog output also is expected to be 0. But practically it does not happen. As shown in the figure, some non-zero analog output voltage is present even for a zero digital input. This is called an offset error.
- Thus the offset error is defined as the non-zero level analog output when all the digital inputs are 0. The offset error is due to the offset voltages of Op-Amps and leakage currents n the switches.

**3. Gain Error:**

- In a DAC we use a current to voltage converter. The gain of this converter determines the analog output voltage of the DAC.
- The gain error is defined as the difference between the calculated gain and the practically obtained gain of the I to V converter.
- This error exists due to the error in the feedback resistor value. The gain error is as shown in the figure below:

## Application of DAC (Digital to Analog Converter):

- In any digital processing system to convert digital command signal into analog one. (e.g. Motor speed control)
- In the A to D converters, such as counter ADC or Successive approximation type ADC
- For displaying information on CRT or XY plotter
- In computers
- In the electronic equipment such as curve tracers etc.

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