# Dac Error Sources

**DAC Error Sources**

For a given digital word, the analog output voltage from a DAC would not be exactly equal to what is given by the analytical formulas that were derived earlier. The difference between the actual output and the ideal output is the error. The DAC error could be normalized with respect to the full-scale value.

There are many causes of DAC error. Typical error sources include parametric uncertainties and variations, circuit time constants, switching errors, and variations and noise in the reference voltage. Several types of error sources and representations are discussed below.

**1. ****Code Ambiguity:**In many digital codes (e.g., in the straight binary code), incrementing a number by an LSB will involve more than one bit switching. If the speed of switching from 0–1 is different from that for 1–0, and if switching pulses are not applied to the switching circuit simultaneously, the switching of the bits will not take place simultaneously. For example, in a 4-bit DAC, incrementing from decimal 2 to decimal 4 will involve changing the digital word from 0011–0100. This requires two bit-switching from 1–0 and one bit switching from 0–1. If 1–0 switching is faster than the 0–1 switching, then an intermediate value given by 0000 (decimal zero) will be generated, with a corresponding analog output. Hence, there will be a momentary code ambiguity and associated error in the DAC signal. This problem can be reduced (and eliminated in the case of single bit increments) if a gray code is used to represent the digital data (See Chapter 7). Improving the switching circuitry will also help reduce this error.

**2. ****Settling Time**: The circuit hardware in a DAC unit will have some dynamics, with associated time constants and perhaps oscillations (under damped response). Hence, the output voltage cannot instantaneously settle to its ideal value upon switching. The time required for the analog output to settle within a certain band (say ±2% of the final value or resolution), following the application of the digital data, is termed settling time. Naturally, settling time should be smaller for better (faster and more accurate) performance. As a rule of thumb, the settling time should be approximately half the data arrival time. Note that the data arrival time is the time interval between the arrival of two successive data values, and is given by the inverse of the data arrival rate.

**3. ****Glitches: **Switching of a circuit will involve sudden changes in magnetic flux due to current changes. This will induce the voltages that produce unwanted signal components. In a DAC circuit, these induced voltages due to rapid switching can cause signal spikes, which will appear at the output. The error due to these noise signals is not significant at low conversion rates.

**4. ****Parametric Errors:**As discussed before, resistor elements in a DAC might not be very precise, particularly when resistors within a wide range of magnitudes are employed, as in the case of weighted-resistor DAC. These errors appear at the analog output. Furthermore, aging and environmental changes (primarily, change in temperature) will change the values of circuit parameters, resistance in particular. This also will result in DAC error. These types of errors due to imprecision of circuit parameters and variations of parameter values are termed parametric errors. Effects of such errors can be reduced by several ways including the use of compensation hardware (and perhaps software), and directly by using precise and robust circuit components and employing good manufacturing practices.

**5. ****Reference Voltage Variations: **Since the analog output of a DAC is proportional to the reference voltage uref, any variations in the voltage supply will directly appear