# Analysis:  {#analysis .Heading}

# AD669 16-Bit DAC Worst-Case Drift Error. {#ad669-16-bit-dac-worst-case-drift-error. .Heading}

#  {#section .Heading}

  -------------- -------------------------------------------------------------
  **To:**        Gary Drake, Charlie Nelson

  **From:**      Craig Drennan

  **Date:**      May 19, 1997

  **Subject:**   Analysis of the worst-case drift error for the AD669
  -------------- -------------------------------------------------------------

# I. The 16-Bit DAC Circuit

The proposed 16-bit DAC circuit for generating the differential SMQIE
calibration voltage is shown in Figure 1.. This circuit provides for
gain and offset adjustments. This note considers the possible worst case
errors due to inherent non-linearity's and drifts due to changes in
temperature. Data sheets for each component are available. The
specifications used in the analysis is given below.

# AD688AQ, High Precision +/- 10 V Reference

+--------------------------------+-------+-------+-------+------------+
|                                | Min   | Ty    | Max   | Units      |
|                                |       | pical |       |            |
+--------------------------------+-------+-------+-------+------------+
| OUTPUT VOLTAGE DRIFT           | -3    |       | +3    | ppm / deg  |
|                                |       |       |       | C          |
| +10 V, -10 V Outputs           |       |       |       |            |
|                                |       |       |       |            |
| -40 deg C to +85 deg C         |       |       |       |            |
+--------------------------------+-------+-------+-------+------------+
| BUFFER AMPLIFIERS              |       | 1     |       | μV / V     |
|                                |       |       |       |            |
| Offset Voltage Drift           |       |       |       |            |
+--------------------------------+-------+-------+-------+------------+
| LINE REGULATION                | -200  |       | +200  | μV / V     |
|                                |       |       |       |            |
| -40 deg C to +85 deg C         |       |       |       |            |
+--------------------------------+-------+-------+-------+------------+

#  AD669BR, Monolithic 16-Bit DACPORT

+--------------------------------+-------+-------+-------+------------+
|                                | Min   | Ty    | Max   | Units      |
|                                |       | pical |       |            |
+--------------------------------+-------+-------+-------+------------+
| TRANSFER FUNCTION              | -1    |       | +1    | LSB        |
| CHARACTERISTICS                |       |       |       |            |
|                                | -2    |       | +2    | LSB        |
| > (-40 deg C to +85 deg C)     |       |       |       |            |
| >                              | -3    |       | 3     | ppm / deg  |
| > Integral Non-linearity       |       |       |       | C          |
| >                              |       |       | +3    |            |
| > Differential Non-linearity   |       |       |       | ppm / deg  |
| >                              |       |       |       | C          |
| > Unipolar Offset Drift        |       |       |       |            |
| >                              |       |       |       |            |
| > Gain Drift (-40 deg C to +85 |       |       |       |            |
| > deg C)                       |       |       |       |            |
| >                              |       |       |       |            |
| > Mainly Reference related.    |       |       |       |            |
| > Refer to AD688 Output        |       |       |       |            |
| > Voltage Drift.               |       |       |       |            |
+--------------------------------+-------+-------+-------+------------+
| POWER SUPPLY SENSITIVITY       |       | 1     | 3     | ppm / %    |
+--------------------------------+-------+-------+-------+------------+

# OPA27GU, Ultra-Low Noise Precision Operational Amplifier (single)

+--------------------------------+-------+-------+-------+------------+
|                                | Min   | Ty    | Max   | Units      |
|                                |       | pical |       |            |
+--------------------------------+-------+-------+-------+------------+
| OFFSET VOLTAGE                 |       | +/-   | +/-   | μV         |
|                                |       | 25    | 100   |            |
| > Input Offset Voltage         |       |       |       | μV / deg C |
| >                              |       | +/-   | +/-   |            |
| > Average Drift                |       | 0.4   | 1.8   | μV / month |
| >                              |       |       |       |            |
| > Long Term Stability          |       | 0.4   | 2.0   | μV / V     |
| >                              |       |       |       |            |
| > Supply Rejection             |       | +/- 1 | +/-   |            |
|                                |       |       | 20    |            |
+--------------------------------+-------+-------+-------+------------+

# OPA1013CN8, Precision Dual Operational Amplifier

+--------------------------------+-------+-------+-------+------------+
|                                | Min   | Ty    | Max   | Units      |
|                                |       | pical |       |            |
+--------------------------------+-------+-------+-------+------------+
| OFFSET VOLTAGE                 |       | +/-   | +/-   | μV         |
|                                |       | 50    | 300   |            |
| > Input Offset Voltage         |       |       |       | μV / deg C |
| >                              |       | 0.4   | 2.5   |            |
| > Average Drift                |       |       |       | μV / month |
| >                              |       | 0.5   | +/-   |            |
| > Long Term Stability          |       |       | 10    | μV / V     |
| >                              |       | +/-   |       |            |
| > Supply Rejection             |       | 1.4   |       |            |
+--------------------------------+-------+-------+-------+------------+

#  AD708JN, Ultralow Offset Voltage Dual Operational Amplifier

+--------------------------------+-------+-------+-------+------------+
|                                | Min   | Ty    | Max   | Units      |
|                                |       | pical |       |            |
+--------------------------------+-------+-------+-------+------------+
| OFFSET VOLTAGE                 |       | 30    | 100   | μV         |
|                                |       |       |       |            |
| > Input Offset Voltage         |       | 0.3   | 1.0   | μV / deg C |
| >                              |       |       |       |            |
| > Average Drift (for amp match |       | 0.3   | +/-   | μV / month |
| > as well)                     |       |       | 1.0   |            |
| >                              |       | +/-   |       | μV / V     |
| > Long Term Stability          |       | 0.1   |       |            |
| >                              |       |       |       |            |
| > Supply Rejection             |       |       |       |            |
+--------------------------------+-------+-------+-------+------------+

All of the external resistors are assumed to have +/- 100 ppm / deg C
temperature coefficient.

There are three different op-amps listed above. The OPA27 was listed
because of its exceptional merits, but we will likely just go with a
dual amp package. The AD708's appear to be the best, but they are not
easy to procure. If we put an order in now we will have some (hopefully
all we need) by the end of August. The OPA1013 is a descent amp, has the
same pin out as the AD708 and is readily available through Digi-Key. The
analysis and the initial prototype will use the OPA1013.

# II. Worst-Case Accuracy

The analysis is taken from the Burr Brown Application Bulletin AB-063
"What Designers Should Know About Data Converter Drift", 1977. The
analysis will compute the worst-case accuracy, or worst case full scale
error, resulting from the combined effects of temperature drifts and the
integral non-linearity of the DAC.

The data sheet for the AD669 16-bit DAC states that the gain drift of
this device is attributable in a very large degree to the voltage
reference. Using the AD669's internal 10 V reference the gain drift is
given as +/- 15 ppm / deg C. The data sheet also states that using the
AD688 precision 10 V reference will improve this specification by a
factor of five. The math results in a gain drift of +/- 3 ppm / deg C,
which is the specified voltage drift of the AD688. From all of this you
may assume that the gain drift of the DAC exclusive of the reference is
zero. The analysis will assume +/- 2 ppm / deg C for this gain drift
exclusive of the reference.

The specification for voltage drift of the AD688 reference is a bit
misleading. Figure 7. in the data sheet provides a graph of the typical
voltage variation with respect to temperature. The voltage variation
between 0 deg C and 75 deg C is more like 5.7 ppm / deg C.

The Full Scale Accuracy Drift is,

Ref. Voltage Drift + Exclusive DAC Gain Drift + DAC Offset Drift

= Full Scale Accuracy Drift.

\[5.7 ppm + 2 ppm + 3 ppm\] / deg C

= 10.7 ppm / deg C. = 0.00107% of FSR / deg C

The Worst-Case Accuracy will be the product of the Full Scale Accuracy
Drift times the design temperature range plus the integral non-linearity
of the DAC. The errors due to the op-amps and power supply variations
will be considered separately.

The integral linearity of the DAC is given as +/- 1 LSB or 0.001526 % of
FSR. Therefore,

Worst Case Accuracy =

\[ 0.001526 + 0.00107 \* ∆Temp (deg C)\] % of FSR

For a DAC that is accurate to 13 Bits the Worst Case Accuracy must be
less than 0.012207 % of FSR. This limits the temperature variation
allowed to 10.0 deg C or 18.0 deg F.

For 13 Bit Accuracy: ∆Temp **\<** 10.0 deg C (or 18.0 deg F)

# III. Considerations for the Output Op-Amps

For a 0 V to 5 V input range for the output op-amps 1 μV / deg C voltage
offset drift error between the two op-amps of the dual package is
0.000020% of FSR / deg C. The ratio of the voltage dividers for gain and
offset adjustment are assumed to add an additional 0.0002 % of FSR / deg
C. The variation of the voltage across the offset adjusting resistor can
be determined from Figure 7. of the AD688 data sheet to be 0.000624 % of
FSR / deg C. Adding these errors to the result above gives,

Worst Case Accuracy =

\[ 0.001526 + 0.001914 \* ∆Temp (deg C)\] % of FSR

For a DAC that is accurate to 13 Bits the Worst Case Accuracy must be
less than 0.012207 % of FSR. This limits the temperature variation
allowed to 5.6 deg C or 10.0 deg F.

For 13 Bit Accuracy: ∆Temp **\<** 5.6 deg C (or 10.0 deg F)

# IV. Power Supply Variations

Both the reference and the DAC have a power supply sensitivity of
approximately 200 μV / V. A one bit output change of the DAC is
approximately 152.6 μV. A change of 1 V in the power supply should not
be a problem.

# V. Conclusions and Questions

If the ambient temperature of the electronics will not vary more than 10
deg F there should be no trouble maintaining a DAC calibration accurate
to 13 bits. Does the worst case look good enough to proceed in building
this circuit and doing test of our own? Are there omissions or
misconceptions in the analysis?

![](media/image1.emf)

Figure 1. The proposed 16 Bit DAC SMQIE calibration voltage source.