Steve wrote:

If you use a MULTIPLYING DAC, you can feed the MSB to the first DAC and then the LSB to the second DAC. Vref for the second dac is Vout from the first.

and later:

Incidentally, you don't discuss the method I have used to give high resolution - namely running two multiplying DACs. That way we can get quite high bit resolution, certainly better than 12bit (we use 2 x 12bit AD7537)

Hallo Steve,

I didn't discuss it, because I have never seen this scheme before!

Ok, assume you have two 8bit mulitplying DACs, where the MSB 8bit are fed to the first DAC and then the LSB 8bit to the second, and reference voltage of the second (Vref2) is Vout of the first. Then, total output voltage is:

Vout = Vref2 x LSB / 256 = (Vref x MSB / 256) x LSB / 256 = Vref x MSB x LSB / 65536

Vref is reference voltage of first DAC.

Comparing with a real 16bit DAC, which follows the formula Vout = Vref x CODE / 65536, we see, that MSB x LSB = CODE must be vaild, if this scheme shall represent a 16bit DAC.

Now we ask: Mulitplying MSB by LSB yields 256 x 256 = 65536 combinations, but:

1. Is this scheme free from ambiguities?
2. Is it possible, that MSB x LSB can yield every number between 0 and 65535?

to 1.:

Scheme is NOT free from ambiguities! E.g. CODE = 512 can be achieved by:

4 x 128 = 512
8 x 64 = 512
16 x 32 = 512
32 x 16 = 512
64 x 8 = 512
128 x 4 = 512

to 2.:

255 X 255 yields 65025. So, 65535 can not be achieved. Difference is 65535 - 65025 = 510.
Ok, this could be corrected by adjusting Vref. But what about other values?
From 255 x 254 = 64770, which is the second highest value that can fabricated by MSB x LSB, we see from the difference 65025 - 64770 = 255, that a wide gap is produced while trying to fabricate every integer number in the range of 0, 1, 2, ... 65534, 65535.
So, when MSB is 255, resolution is limited to (65025 - 64770) / 255 = 255, which represents only 8bit resolution!!

16bit resolution is only achieved, when MSB = 1. Because then MSB x LSB = 1 x 0, 1, ... , 255 = 0, 1, 2, ..., 255 and yields steps of Vref x 1 / 65536. But with increasing MSB steps are becoming bigger and resolution decreases. When MSB is near 255 steps are highest and resolution is worst.
Seven highest values which can be fabricated by MSB x LSB are:

65025
         255
64770  
         254
64516
         1
64515
         253
64262
         2
64260
         251
64009

On the right you can see the width of gaps.

So, this scheme does NOT provide real 16bit resolution, with all steps being equidistant! Only if MSB = 1. But if MSB is near 255, only 8bit resolution can be achieved!!


Kai