Gary is using a 12-bit A/D converter with a range of -10 to 10 V. His input signal comes from a pressure transducer, and has a range of -15 to 15 mV. Gary also has an amplifier circuit (output = G x input, where G is the gain of the amplifier) which he installs in series between the transducer output and the A/D converter input. A switch on the amplifier enables him to select the gain as G = 10, 100, or 1000.
a) Which gain should Gary use to minimize the effect of quantization errors - in other words, to be able to utilize as much of the range of the A/D as possible, so as to sample data with the best precision?
b) When the transducer output is 3.75 mV and using the gain of Part (a), calculate the quantizing error as a percent of the A/D input voltage reading.
c) Consider the best possible situation (best case scenario), defined such that the signal coming into the A/D system uses the entire dynamic range of the A/D system, yet without clipping. Use the same transducer output range of Part (a), but suppose you have an additional piece of electronic equipment that lets you attenuate (reduce the amplitude of) the signal before sending it to the amplifier. In order to use the amplifier gain setting of 1000, by what factor should the signal first be attenuated? Finally, find the quantizing error for this best case scenario as a percent of the A/D voltage reading. Is the error better than that of Part (b)?