Keywords: unipolar, DAC, bipolar, analog IC, op amp, voltage reference, Kirchhoff current law, resistor matching, tolerance, temperature coefficient, offset, gain error, INL, DNL, calibrate, feedback, single supply
Related Parts 


Challenge the Conventional  Make Unipolar DACs Bipolar

A similar version of this article was published March 3, 2014 in EE Herald.
The trend in analog ICs is toward singlesupply digitaltoanalog converters (DACs). A DAC with only a positive 5V supply is convenient, but it limits the available applications to those not requiring highvoltage, highcurrent, or bipolar (±) outputs. In this application note, we illustrate how an external operational amplifier can transform a unipolar DAC to provide bipolar operation.
The expression “up the down staircase” comes from a movie, a play, and a book by the same name.^{1} It is a comedy based on a school in New York City. The title recalls a rule that penalized students for going up the staircase reserved for coming down. It is always a great temptation for a youngster to run up stairs, or escalators (Figure 1), that are going down. Some might say that the child is “thinking outside the box” or breaking the rules, and perhaps he is. Clearly, he is challenging the expected or mandated flow, the common thinking. He also shows how with some daring, a goal can be attained by an unconventional route. There is a lesson here for us engineers.
Figure 1. The boy running up this escalator is using an unconventional way to reach his goal, probably the toy section. We engineers can take note and try to solve problems with unconventional methods.
Sometimes when we design analog circuits, the design “elements” just do not want to fit together. The solution seems unusually elusive. An example situation is when we need a bipolar output from a unipolar DAC. The industry’s trend today is toward smaller, lower power, and higher performance devices, which is excellent when that resolves a solution problem. However, this same lowvoltage, unipolar DAC cannot function directly in highperformance, highvoltage, highcurrent, or bipolar applications. Any additional circuits must not degrade the DAC’s performance. In such a case, it is time to go up that escalator, to try something different. We show you how to make a bipolar output from a unipolar DAC by adding a highvoltage op amp.
A simple bipolar output circuit is shown in Figure 2. It contains a unipolar DAC, a precision voltage reference, and a precision op amp.
Figure 2. Typical bipolar output operating circuit.
The output functionality of this circuit can be derived by making two common assumptions about an ideal op amp:
Following Kirchhoff’s current law, the equation for the V node is:
(Eq. 1) 
Solving Equation 1 for V_{OUT} and replacing the V with V_{DAC}:
(Eq. 2) 
In fact, we have derived the equation of a differential amplifier where the first element is the noninverting input and the second element is the inverting component, each with their gains.
Since the DAC output, V_{DAC}, is a function of the input code and the supplied reference voltage, Equation 2 can be rewritten as:
(Eq. 3) 
If R_{FB} = R_{INV} and their ratio becomes 1, this equation can be further simplified to:
(Eq. 4) 
Thus, bipolar operation allows the output to swing from V_{REF} to +V_{REF} with the unity gain. Table 1 shows the ideal bipolar output data versus code based on Equation 4, for the ideal 16bit DAC with 2.5V V_{REF} in Figure 2.
Table 1. Bipolar Output versus Code (V_{REF} = 2.5V)
Decimal Code  Binary Code  Hex Code  V_{OUT} (V) 

0  0000 0000 0000 0000  0  2.50000000 
1  0000 0000 0000 0001  1  2.49992370 
2  0000 0000 0000 0010  2  2.49984741 
3  0000 0000 0000 0011  3  2.49977111 
4  0000 0000 0000 0100  4  2.49969482 
5  0000 0000 0000 0101  5  2.49961852 
6  0000 0000 0000 0110  6  2.49954223 
7  0000 0000 0000 0111  7  2.49946593 
8  0000 0000 0000 1000  8  2.49938964 
9  0000 0000 0000 1001  9  2.49931334 
10  0000 0000 0000 1010  A  2.49923705 
11  0000 0000 0000 1011  B  2.49916075 
12  0000 0000 0000 1100  C  2.49908446 
13  0000 0000 0000 1101  D  2.49900816 
14  0000 0000 0000 1110  E  2.49893187 
15  0000 0000 0000 1111  F  2.49885557 
.  .  .  . 
.  .  .  . 
.  .  .  . 
32767  0111 1111 1111 1111  7FFF  0.00003815 
32768  1000 0000 0000 0000  8000  0.00003815 
32769  1000 0000 0000 0001  8001  0.00011444 
.  .  .  . 
.  .  .  . 
.  .  .  . 
65534  1111 1111 1111 1110  FFFE  2.49992370 
65535  1111 1111 1111 1111  FFFF  2.50000000 
As we see, it was easy to convert our ideal unipolar DAC. However, we are living in the real world where nothing is ideal. Each component in Figure 2 brings its own level of accuracy, which collectively contributes to the DAC’s final output accuracy. Each system must be characterized and calibrated to the accuracy required by the application. As a result, even though you might select a highprecision 16bit DAC, special attention should also be paid to selecting the appropriate voltage reference, amplifier, and feedback resistors. Which component contributes the most to inaccuracy? Which parameters are most critical for bipolar applications? These are neither simple, nor trivial questions. An inexperienced engineer might be surprised to learn that even simple resistors can be very critical to this design modification.
Resistance matching, tolerance, and temperature coefficient are the most important parameters in any precision application. These parameters contribute to circuit errors, offset, gain error, and gain stability over the temperature range. Each parameter needs to be considered.
There is a wide range of resistor types available, from thin film to metal foil and with tolerance from 1% down to 0.01%. Temperature coefficients range from 300ppm/°C to 0.2ppm/°C with costs that track the precision. However, the most important parameter for setting gain might not be cited explicitly in the resistor’s data sheet: the resistor’s matching to another resistor. For production of more than a few pieces where the resistors can be handmatched, one must assume that two resistors are at opposite ends of the tolerance. This is the only assumption that allows safe operation in the worstcase situation. Precisionmatched resistor pairs can be expensive, depending on the manufacturing process. The great advantage of using a semiconductor fabrication process is that the resistors are made in a photoduplication process and manufactured simultaneously on the same substrate. There are two ways to accomplish this. One method uses a product with just two resistors in the package.^{2} The other method uses multiple resistors and a DAC that are matched in the same package. We explain this second method below.
Selecting the right amplifier can also be challenging, especially for a 16bit and higher precision DAC. Close attention must be paid to the input parameters. There are many: input bias current, input offset voltage, input offsetvoltage drift, input voltage range, input capacitance and settling time, and input current and voltage noise density. Other parameters are equally important: commonmode rejection ratio (CMRR) and powersupply rejection ratio (PSRR), total harmonic distortion (THD) and gain bandwidth, slew rate, and output transient recovery time. A detailed explanation of each of these parameters lies outside the scope of this article and requires a thorough examination of the amplifier’s data sheet.^{3}
There are several key specifications for choosing a voltage reference,^{4} and you need to consult the data sheet for each: output voltage accuracy, output voltage temperature coefficient, line and load regulation, and output voltage noise and longterm stability. After all this, there is yet another consideration. External forces can degrade some voltage reference parameters.^{5} For example, load regulation can become an issue if the DAC’s structure changes the load on the voltage reference.
To better understand this process, we consider three different scenarios.
Unipolar, 16bit, unbuffered DACs can perform bipolar operation with the addition of an external precision op amp. Two examples of such a configuration are the 16bit MAX542 and MAX5442 DACs which use integrated 0.015% (max) matched scaling resistors, R_{FB} and R_{INV}, for an easy bipolar output swing (Figure 3). Use of these DACs eliminates duplication of output buffers, saves PCB real estate, and provides an easytouse and costeffective solution for our customers.
Figure 3. These 16bit DACs use an external op amp to provide a bipolar output.
This solution requires the latest generation of op amps, such as the MAX9632. The INL and DNL graphs of bipolar operation for the DACs in Figure 3 are shown in Figures 4 to 7. The INL calculation was made using nonadjusted data measured by an Agilent^{®}HP^{®} 3458A multimeter and utilizing the endpoints method.
Figure 4. Bipolar output INL for the MAX542A.
Figure 5. Bipolar output DNL for the MAX542A.
Figure 6. Bipolar output INL for the MAX5442A.
Figure 7. Bipolar output DNL for the MAX5442A.
Although not as simple in a realworld scenario, converting a unipolar DAC for use in applications that require bipolar operation is doable if you think outside the box, or about walking up the down staircase. By adding resistors, a precision voltage reference, and a precision op amp to a unipolar DAC, we succeeded in doing just that.
References
Related Parts  
MAX542  +5V, SerialInput, VoltageOutput 16Bit DACs  Samples 
MAX5442  +3V/+5V, SerialInput, VoltageOutput, 16Bit DACs  Samples 
MAX5444  +3V/+5V, SerialInput, VoltageOutput, 16Bit DACs  Samples 
MAX5490  100kΩ PrecisionMatched ResistorDivider in SOT23  Samples 
MAX5491  PrecisionMatched ResistorDivider in SOT23  Samples 
MAX5492  10kΩ PrecisionMatched ResistorDivider in SOT23  Samples 
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© Mar 10, 2015, Maxim Integrated Products, Inc. 
APP 5581: Mar 10, 2015
APPLICATION NOTE 5581, AN5581, AN 5581, APP5581, Appnote5581, Appnote 5581 