Digital-to-analog in the loop: Closed, open, and 'set and forget' systems

Choosing a DAC at different resolutions involves trade-offs for price, package size, reference accuracy, and output impedance.

7The accuracy of a control system depends on how predictable the load is, the control architecture selected, and the precision of the components executing control. The following overview provides tips on selecting digital-to-analog converters for various control-loop applications.

When it comes to selecting a Digital-to- Converter (), designers can choose from a wide range of ICs. DACs can be divided into many different categories for specific applications. The field can be narrowed by differentiating between those needed for DC or low-speed adjustments versus those needed for high-speed waveform generation. This article focuses on those needed for low-speed applications, whether low resolution or high resolution or coarse or fine adjustment.

In terms of selecting a low-speed DAC, it is important to determine whether the design is a closed-loop, open-loop, or “set and forget” system. Each of these will require a DAC with key specifications.

Closed-loop systems

Closed-loop systems include a feedback path to sense and correct for any errors. A sensor monitors the output from a physical parameter such as a servo motor, flow valve, or temperature-sensing element. The sensor then feeds the data back to a controller, which uses this information to determine if a correction is necessary.

DACs and Analog-to-Digital Converters (ADCs) are key components at the heart of a closed-loop system. While a DAC is used in the feed-forward path to make adjustments to the system, an is used in the feedback path to monitor the effect of those adjustments. Together, they force and sense the analog control signals to make real-world adjustments to the parameter they’re controlling.

Motor control is one example of a closed-loop system, as detailed in Figure 1. First, a desired output (set point) is applied to the controller, which compares this to the feedback signal. If a correction is required, the controller will adjust the input code to the DAC, which then produces an analog voltage at its output. The DAC output voltage is amplified through a power amplifier to provide the required drive current to the motor.

Figure 1: In a closed-loop system, the ADC digitizes the tachometer’s output and sends the data to the controller, where an algorithm determines if a correction should be made.
(Click graphic to zoom by 1.9x)

At the next stage of this closed-loop system, a tachometer is used to measure the rotational speed of the motor. The rotation signal is the actual output, or process variable, of the closed-loop system. An ADC digitizes the tachometer’s output and sends the data to the controller, where an algorithm determines if any correction needs to be made at the DAC output, and ultimately, the motor. In this way, the error is reduced to an acceptable level. Feedback ideally allows the closed-loop system to cancel out all errors, effectively limiting the effects from any errant sources of noise, temperature, force, or other unwanted signals.

A closed-loop system’s performance depends on an accurate feedback path, including the sensor and ADC. In essence, the feedback path compensates for errors in the feed-forward path. Because the DAC is in the feed-forward path, its Integral Non-Linearity (INL) error is automatically compensated for. INL error is the deviation of the actual transfer function at the DAC output from the ideal transfer function.

The DAC must have adequate Differential Non- Linearity (DNL) and be monotonic to the number of bits specified in the data sheet. DNL error is the difference between the actual voltage change at the DAC analog output versus an ideal voltage step equal to a 1 Least Significant Bit (LSB) step in the DAC input code. A monotonic DAC means the analog output always increases or stays the same with an increase in the digital code (and vice versa). A DNL spec that is always greater than -1 LSB implies monotonicity. Figure 2 shows the transfer function of DAC analog output voltage versus DAC input code.

Figure 2: DNL error is the difference between actual voltage change at the DAC analog output versus a 1 Least Significant Bit (LSB) step in the DAC input code.
(Click graphic to zoom by 1.3x)

If the DAC is not monotonic, there will be a region where negative feedback turns into positive feedback. This can lead to oscillation that could eventually destroy the motor.

Open-loop systems

Open-loop systems do not have a feedback path. This means the system must be accurate on its own. Open-loop control is useful for well-defined systems where the relationship between the input code and the resulting action on the load is known. If the load is not very predictable, it’s best to use closed-loop control.

An example of an open-loop system is shown in Figure 3. In this example, the DAC drives the SET voltage pin of linear regulator LT3080. The SET pin is the input to the error amplifier and the regulation set point for the output voltage. The LT3080’s output voltage range is from 0 V to the absolute maximum rated output voltage.

Figure 3: In an open-loop system, the DAC drives the SET voltage pin of a linear regulator (LT3080).
(Click graphic to zoom by 1.8x)

The resolution of the DAC determines the step size for adjustments to the SET pin. For example, an 8-bit DAC with a 5 V reference has an LSB size of 5 V/28 = 19.5 mV. A 12-bit DAC with the same 5 V reference has an LSB size of 1.2 mV, and a 16-bit DAC has an LSB size of 76 mV. This means that for an ideal DAC, every increase in the digital code should increase the analog output 76 mV.

Other important parameters in an open-loop system are offset, gain error, error of the reference voltage, and the stability of these parameters over time and temperature. INL is of particular importance because in contrast to the closed-loop system, the INL of the DAC has a direct bearing on the overall linearity of the system.

Set and forget systems

A third application where DAC linearity plays an important role is set and forget systems. In these systems, an adjustment or calibration is made once, perhaps at the time of manufacture or during installation. This system starts life as a closed-loop system and then goes open loop. Thus, any parameter related to initial accuracy (offset, gain error, INL) is not critical, as it is compensated for during the adjustment. But once the feedback is removed, stability becomes key. Data sheet specifications that indicate stability are gain error drift, offset drift, and reference drift.

Figure 4 shows an example of a set and forget application. In this figure, a lower-resolution DAC drives an amplifier that sets the voltage at an offset adjustment pin for a precision DAC. The lower-resolution DAC is used to effectively calibrate the gain offset out of the precision DAC during initial system calibration. This adjustment code can be stored in nonvolatile memory and loaded each time the system is powered up.

Figure 4: In a set and forget system, a lower-resolution DAC calibrates the gain offset out of the precision DAC during initial system calibration.
(Click graphic to zoom by 1.9x)

Home in on DAC DC specifications

Once the type of closed-loop, open-loop, or set and forget system has been determined, it’s time to select the best DAC for the job. As mentioned previously, some applications call for coarse adjustment, meaning the system only needs a limited amount of variable settings. In this case, a DAC with 8 bits or 10 bits of resolution is typically sufficient. For systems that need finer control, a 12-bit DAC may offer enough resolution. Sixteen and 18-bit DACs offer the finest resolution per LSB size on the market today.

The LTC2600 is a 16-bit octal DAC for closed-loop systems. This is evident in looking at its DC specifications. Typical INL is ±12 LSB, with a maximum of ±64 LSB. These specifications, along with a typical INL curve versus input code, are shown on the bottom row in Figure 5. The 16-bit monotonicity and ±1 LSB DNL error allow precision control in the feed-forward path. As mentioned previously, feed-forward error is not critical for a closed-loop system, so long as the DAC is monotonic.

Figure 5: While the LTC2600 DAC offers ±12 LSB, the new LTC2656 offers ±4 LSB INL error for all eight DACs.
(Click graphic to zoom by 1.9x)

Conversely, the new LTC2656 is an octal DAC that offers 16 bits of monotonicity and an excellent ±4 LSB INL error for all eight DACs, making it a potential fit for both open- or closed-loop systems. The LTC2656 typical INL versus code plot is shown in Figure 5 across all eight DACs in the package. The LTC2656 offers the best INL in its class of 16-bit octal DACs.

Achieving high linearity on eight DACs in a single package is not an easy design task. Package stress and voltage shifts over temperature must be accounted for in the design. It is much easier for a single DAC to achieve tighter INL specifications. For example, the LTC2641 from is a single 16-bit DAC that offers maximum DC specifications of ±1 LSB INL and DNL.

Besides INL and DNL, the other important DC specifications to consider are offset error (or zero-scale error) and gain error (or full-scale error). Offset error indicates how well the actual transfer function matches the ideal transfer function at or near the zero-scale input code. Offset error is very important for applications that need precision control down to ground. The LTC2656 shown in Figure 6 offers a very low ±2 mV maximum offset error.

Figure 6: The LTC2656 DAC offers ±2 mV maximum offset error and ±64 LSB maximum gain error.
(Click graphic to zoom by 1.9x)

Gain error indicates how well the slope of the actual transfer function matches the slope of the ideal transfer function. Gain error and full-scale error are sometimes used interchangeably, but full-scale error includes both gain error and offset error. The LTC2656 offers ±64 LSB maximum gain error, which equates to a very low maximum of 0.098 percent of full scale (64/65,536).

A DAC with good offset and gain errors can allow the system to avoid running a calibration cycle in software in the controller or . A DAC that drifts very little over time and temperature also makes design simpler, as the system engineer doesn’t need to calibrate as often.

±10 V output DACs

The DACs mentioned previously are useful for single supply or unipolar 0 V to 5 V systems. However, some closed-loop, open-loop, or set and forget systems require ±10 V DACs instead. For these high-voltage systems, designers can use either a unipolar 0 V to 5 V DAC with a programmable gain amplifier to perform gain and level shifting, or the DAC can provide a ±10 V signal directly.

Linear Technology offers a choice of single, dual, and quad DACs that provide up to ±10 V at their outputs. The LTC1592 is a single 16-bit DAC that includes two unipolar and four bipolar software programmable output ranges. These output voltage ranges include 0 V to 5 V, 0 V to 10 V, ±2.5 V, ±5 V, ±10 V, and -2.5 V to 7.5 V. Therefore, the same DAC can be used for both unipolar and bipolar systems without needing to completely reprogram the controller. For example, changing the DAC output range from 0 V to 5 V to ±10 V only requires changing a couple of bits in the serial bit stream to the DAC.

Look beyond just the bits

DACs are key components in open-loop, closed-loop, or set and forget systems. Each of these systems requires a different level of accuracy and resolution from the DAC. At a particular resolution, there are also trade-offs for factors such as price, package size, reference accuracy, and output impedance.

For the highest-precision systems, it’s important to choose a DAC not only based on how many bits are on the front page of the data sheet, but also on how accurate the DC specifications such as INL, DNL, offset error, and gain error are. IES

Mark Thoren is applications engineering manager for products at Linear Technology. Mark tries to keep a lab bench well stocked with equipment that was obtained in a broken state and brought back to life. He has a BS in Agricultural/Mechanical Engineering and an MS in Electrical Engineering, both from the University of Maine.

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