PGA309: Actual Gain DAC and Zero DAC calculation from lookup table

Hoda,

1. The PGA309 assumes the numbers stored in the EEPROM table are 16 bit signed binary numbers.  The number 0x851F would be interpreted by the PGA309 as -31457.
2. During the calibration process, you will need to determine the gain and offset required to correct your errors over temperature.  The calibration algorithm given in the PDF below illustrates how you would calculate the gain and offset based on measurements with minimum and maximum applied pressure.  Normally this procedure is done at 2 or 3 temperatures and the polynomial interpolation is used to determine the gain and offset at other temperatures.  
3. Once you have the table with all the temperature, gain, and offset values you will calculate the slope values for the zero dac and gain dac.  The PGA309 users guide provides the equations to calculate the slopes. I attached an excel spreadsheet that calculates the same example from the users guide.  
4. Once you have the table of gain and offset slopes, these are written into the PGA309 EEPROM.  Since the EEPROM holds 8 bit words at each address you will need to split the 16 bit words in half (MSB and LSB).  The write EEPROM PGA309 command will allow writing the MSB and LSB into two different locations in the EEPROM.  Note, the 16 bit word written into the EEPROM is a signed binary word.  Thus writing 0x851F will be written into two locations as 0x85 and 0x1F, but the PGA309 will read back 0x851F and interoperate it as -31457.
5. Once the EEPROM table has been fully written the PGA309 will read the table on power-up.  The PGA309 will interpret all numbers in the table as signed binary numbers.  The PGA309 will use this table to adjust gain and offset over temperature to correct for sensor drift.

I hope that helps.  You may consider getting the EVM to see how the algorithm works for an actual calibration with your sensor.  You can also download the labview source code and use this to understand the calibration algorithm.  Below is the calibration algorithm and the EEPROM table example.

Best regards, Art

sbou024b-pga309-calibration-algorithm.pdf

PGA309 TABLE.xlsx

Hoda,

1. A common way digital systems use signed numbers is the "two's compliment method".  That is how the PGA309 handles signed numbers.
   1. The length of the word is a fixed length.  In this case the length of the word is 16 bits.
   2. The most significant bit in the word is the sign bit.  If the sign bit = 1, the word is negative, if the sign bit = 0.  Then the word is positive.
   3. For a 16 bit signed word the range of values is:  -32768 to 32767.  This is represented in hex by 0x8000 to 0x7FFF.
2. The way the numbers are used internally in twos complement systems is covered in this lecture:  Lecture on signed numbers.  This is not necessary critical to understand, to use the PGA309, but you want to know how the PGA309 interoperates signed numbers and in a very basic sense, this is what is happening internally. 
3. Another explanation of two's compliment is given in wikipedia:  Wikipedia on signed numbers. 
4. In short the number 0xC292 will be interoperated as -15726 by the PGA309 because the PGA309 knows the number is a twos compliment 16 bit number.  Note that 0xC292 is equal to 11000010 10010010, and the Most significant bit is "1".  Thus the number is negative.
5. This tool can help you translate decimal to hex and binary for twos compliment 16 bit numbers:  tool for conversions 
6. The vast majority of digital systems handle signed numbers this way.  For another example of a device that uses signed numbers see:  ADS1220 is another device using signed numbers.  This device uses 24 bit signed numbs.  Thus for this device the number 0xFFFFFF is equal to -1 in decimal.  You can look at this to see other examples of signed numbers.  The key point is that the used of 2's compliment signed numbers is common in digital systems.

I hope this helps.  I think your main questions relates to trying to understand how 2's compliment signed numbers work.  You may want to read through some of the literature in the links above.

Best regards,

Art

Hoda,

1. Regarding the number 41943, and the number -47104:  You found an error in the document.  Both of these numbers are outside of the allowable range of -32768 to +32767.  If the device slope exceed the allowable range, the PGA309 would not be able to compensate for that drift level.
2. Regarding the first row in the table.  This row is not a slope.  This value is a gain value.  All other values in the table are slopes.  So, G0 is the initial gain value at -40C, but all the other values are slopes.  The actual gain DAC value is not a signed integer.  The Gain DAC value is always positive.  A gain of  0x0000 = gain of 0.333333,  GAIN of 0xFFFF - gain of 1.000000.
3. The PGA309EVM software is written in labview.  In labview, and in other software languages, you can define a variable type to be a signed 16 bit integer.  When you define a variable as a 16 bit signed integer in software it will automatically limit the value from -32768 to +32767.  If you develop your own software to build the table it should use 16 bit signed integers.  If you are familiar with LabView, you could download the source code for the EVM and use the section that builds the table:  https://www.ti.com/lit/zip/sboc394 
4. Here is a link to a modified spreadsheet.  The excel file has two tabs.  One that matches the existing PGA309 users guide table 3-3, and a modified one that uses gain changes that do not violate the maximum allowable slope.  I added an error test column so that you can see the issues with the existing table and also see that the new table is ok.  PGA309 TABLE-good-vs-bad.xlsx
5. My apologies, for this error.  I can definitely see how this is very confusing, and I will look into getting the document changed.

Best regards,

Art