As in any electrical system, the structure produces noise. In this article, we examine the resulting noise from a digital-to-analog converter (DAC) system. The DAC system design goal is to minimize the various noise sources as much as possible to achieve optimal performance. To achieve this we start by examining the three major sources of noise contribution: 1) DAC’s internal resistor string and feedback resistor; 2) output amplifier; and 3) voltage reference (**Figure 1** ).

**Figure 1**

This article examines the DAC internal-resistances and output-amplifier noise issues. The next article in this DAC Basics series will examine the impact of the voltage reference noise.

Note that other noise sources can impact the DAC system noise, such as power supply transients and cleanliness of the ground layer. The design of well-regulated supplies and proper layout mitigate the impact of these noise sources. Discussing power and layout noise is beyond the scope of this article.

**Internal DAC resistor string**

Multiplying DACs have the strongest DC specifications of all DAC topologies. These specifications are important in applications where accuracy is critical, such as test and measurement. Along with requiring excellent DC performance, low noise plays a large role in obtaining precision for these applications.

In this discussion, we consider the noise of the multiplying DAC (MDAC) in **Figure 2** . The first source of noise in this circuit is the internal DAC’s resistive noise. Due to digitally-driven switches in **Figure 2** , the MDAC internal R-2R resistor string model is a single equivalent resistor that changes values with changing DAC input codes.

**Figure 2**

In this noise calculation, there is the resistor string and the output amplifier’s feedback resistor (R_{FB} ). The feedback resistor, in combination with the output current (I_{OUT} ) and an external amplifier, creates the DAC’s output voltage.

For full-scale MDAC resistance, all switches connect to the V_{REF} . This action causes associated currents to flow to the I_{OUT} leg instead of ground. Looking back into the MDAC from the IOUT node to the V_{REF} pin, the equivalent full-scale resistance equals the entire resistor chain. In MDAC data sheets, TI specifies this full-scale resistance as the REFERENCE INPUT: Input resistance (**Figure 3** ).

**Figure 3**

With the full-scale resistance, the calculated noise is equal to:

One uses the KN variable to change a “brick wall” output to a real-world filter with attenuation. **Table 1** shows the relationship between filter order, approximate attenuation, and the KN multiple.

**Table 1**

In this article, we use K_{N} = 1.57 to estimate the amplifier fall-off at the amplifier closed-loop bandwidth frequency.

Equation 1 also calculates the noise contribution of the amplifier feedback resistor. The value of the feedback resistor is equal the full-scale DAC resistance value. Adding the noise contribution from both these resistors provides the total noise impact of this resistive system.

As an example, TI’s 16-bit MDAC, DAC811, has a REFERENCE INPUT: Input resistance equaling 5 k-Ohm. The noise contribution of this resistance equals:

The noise contribution of the MDAC’s resistance plus the amplifier’s feedback resistance (R_{FB} ) is equivalent to:

This is consistent with the data sheet, where the specified output spot noise voltage equals:

After we choose an amplifier for the circuit, e_{n-RES} will convert to rms noise with the following formula:

For instance, if the amplifier in the circuit has a close loop bandwidth (f_{CL} ) of 1 MHz this value is equal to:

**Operational amplifier noise**

The external operational amplifier (Figure 1) generates the second source of noise in our study. Figure 4 shows the implementation of an external output amplifier in a MDAC system.

**Figure 4**

In **Figure 4** the 16-bit MDAC drives an output current (I_{OUT} ) through an internal feedback resistor (R_{FB} ). The internal feedback resistor’s relative value and drift characteristics match the DAC’s R-2R resistor string providing high-accuracy DAC results.

The operational amplifier (op amp) is a unity-gain stable amplifier with a 1 MHz gain-bandwidth-product. **Figure 5** shows the input noise characteristics of the op amp. There are two noise regions of interest: 1/f region and broadband region.

**Figure 5**

Red highlights the amplifier’s 1/f noise region. In this region, noise decreases not at a 20 dB per decade, but rather as a multiple of the inverse of frequency. Blue highlights the amplifier’s broadband noise region. In this region, the amplifier’s input noise remains constant across frequency.

*1/f noise*

One can easily calculate the noise underneath the curves 1/f region in **Figure 4** . The first order of business is to determine the input noise density at 1 Hz (see **Figure 5** ). Once you find that value, the simple formula below will provide the integrated rms noise under the curve.

As an example, given the OPA277 1 Hz noise equaling 12 nV/√Hz, the amount of integrated rms noise produced by the amplifier shown in **Figure 5** from 0.1 Hz to 1.6 Hz is equal to:

*Broadband noise*

The amplifier table of specifications gives the input noise density value. This specification is always at a higher frequency. Additionally, you find this specification where the input voltage noise is relatively constant. For this region of the curve, multiplying the square-root of the bandwidth and the noise density derives the noise across a bandwidth. For example, if the noise of the amplifier is 8 nV/ √ Hz @ 10 kHz, the noise from the amplifier across the bandwidth of 1.6 Hz to 1 MHz is equal to:

**Total MDAC system noise (minus voltage reference)**

At this time, we have the noise contributions of the DAC resistor ladder, the feedback resistor, the amplifier 1/f, and the amplifier broadband region. A root-sum-square (RSS) equation combines these three noise sources into a single number:

**Figure 6**

From the above calculation, the MDAC noise dominates with a slight influence from the operational amplifier. These calculations point strongly to finding the lowest noise DAC followed by the lowest noise amplifier for the circuit. But, we may have to wait before we make our final decision. The only component missing in this calculation is the voltage reference circuit. Fortunately, I will review this topic in DAC Basics (Part 7).

**References**

- Baker, Bonnie. Transimpedance strikes again: Current-to-voltage conversion with MDACs, EDN, July 5, 2007
- Mejia, Eugenio. How do you select a multiplying DAC? Think op amp first, TI Precision Hub Blog, October 9, 2015
- Download these datasheets: DAC811, OPA277

The R-2R netowrk requires resistors R in series between the connections to resistors 2R and switches. (Without these, the left-hand 7 switches all have the same effect!)

You are right. I am sending the corrected diagram to AspenCore. You should see the correction soon.

You are right. I am sending the corrected diagram to AspenCore. You should see the correction soon.