# What are the DNL and INL specifications of a DAC? No…

This article discusses the DNL and INL specifications of a digital-to-analog converter (DAC).

We can use several different specifications to characterize the performance of a data converter. Depending on the application, some of these specifications may be more important than the others.

This article discusses the DNL (differential non-linearity) and INL (integral non-linearity) specifications of a DAC. These specifications are generally important in measurement and control applications where there is generally an error budget for an ideal transfer characteristic.

### Introduction to Output Voltage on a Three Bit Unipolar DAC

A digital-to-analog converter (DAC) receives data represented as a digital code and produces an equivalent analog output (see Figure 1 below).

##### Figure 1. Image courtesy of Analog Devices.

The above ideal transfer function corresponds to a three-bit unipolar DAC. Various structures, such as a Kelvin divider or an R-2R architecture, can be used to obtain the above input-output characteristic.

In order to illustrate the DNL and INL specifications, we will consider a simple structure based on current sources, as shown in Figure 2.

##### Figure 2

This three-bit DAC uses binary weight current sources to produce the eight different analog levels in Figure 1. Here, I is the unit current that can produce the smallest voltage step at the DAC output. Therefore, sw0 and sw2 correspond respectively to the least significant bit (LSb) and the most significant bit (MSb) of the input code.

As an example, if the digital input code is 101, the switches sw0 and sw2 turn on and the load current is I + 4I = 5I. This produces an output voltage equal to 5I âœ– RL. Similarly, other combinations of the digital input code will produce one of the eight different levels in Figure 1.

### How to characterize non-ideal output voltage levels

The older model of a three-bit DAC in Figure 2 is too idealistic; In reality, there are many factors that limit the accuracy of the system. For example, although we want a set of current sources weighted in binary form, the values â€‹â€‹of the current sources may be slightly different from those in Figure 2.

An exaggerated case is shown in Figure 3.

##### figure 3

The input-output characteristic of this non-ideal DAC is shown in Figure 4. Ideally, the output voltage levels should be on the dashed straight line; however, due to the mismatch, we get the voltage levels indicated by the solid dots.

##### Figure 4

The DNL and INL specifications of a DAC allow us to characterize such non-ideal output voltage levels.