Diamond Systems 16-Channel 12-Bit Analog Output PC/104 Module LSB = 1/2048 x Full-Scale Voltage

Offset Binary Coding (for bipolar output ranges)

This method takes into account the fact that the lowest output voltage is not zero but a negative value. The output voltage is given by:

Output Voltage = (Output Code / 2048) x Full-Scale Voltage - Full-Scale Voltage

Example:	Output code = 1024, full-scale voltage = 5V
	Output voltage = (1024 / 2048) x 5 - 5 = (0.5 x 5) - 5 = -2.500V

Note the difference between this output voltage to the output voltage using straight binary coding shown above using the same output code.

Conversely, the output code for a desired output voltage is given by:

Output Code = (Desired Output Voltage / Full-Scale Voltage) x 2048 + 2048

Example:	Desired output voltage = 0.485V, Full-scale voltage = 2.5V
	Output Code = (0.485 / 2.5) x 2048 + 2048 = 0.194 x 2048 + 2048 = 2445
	(rounded down)

The relationship between D/A resolution and Full-scale voltage is:

1 LSB = 1/2048 x Full-Scale Voltage

Example: Full-scale voltage = 5V; 1 LSB = 5V / 2048 = 2.44mV

The reason that 1 LSB for a bipolar range is twice the magnitude of 1 LSB for a unipolar range with the same full-scale voltage is that for the bipolar range, the full voltage span is twice the magnitude. For example, a unipolar range with a full-scale voltage of 5V has a range of 0V to 5V, for a total span of 5V. However, a bipolar range with a full-scale voltage of 5V has a range of ±5V, for a total span of 10V. Here is a brief overview of the relationship between output code and output voltage:

Output Code	Explanation	Output Voltage for ±5V Range
0	Negative full scale	-5V
1	Negative full scale + 1 LSB	-4.9976V
2047	-1 LSB	-.0024V (-2.44mV)
2048	0V	0V
2049	+1 LSB	+.0024V (+2.44mV)
4095	Positive full scale - 1 LSB	+4.9976V

⇒Note: Again, an output code of 4096 would be required to generate the positive-full-scale output voltage, but since that is impossible, the maximum output voltage is 1 LSB less then positive full scale.

Copyright 2001 Diamond Systems Corp. Ruby-MM-1612 User Manual V1.1 P. 15