You are using a 0 to 5 Volt, 8-bit analog to digital converter (ADC) to read and

Question

You are using a 0 to 5 Volt, 8-bit analog to digital converter (ADC) to read and store values from a potentiometer-based position measurement system. A colleague has provided you with the following calibration equation relating position and voltage: V = 3.2 Volt/cm X + 0.03 Volt What is the quantization interval for this system (in Volts)? What measurement will error (in cm) the maximum quantization error result in? Suppose the main limitation of the resolution of this measurement system is quantization. What is the resolution of the system? Your colleague took 3 measurements and saved them to a file, but the output of the microcontroller was a positive integer, and he is not sure how to interpret this. Fill in the table below with the corresponding stored voltage for each integer code. Your colleague is catching on but would like to know what to expect next. He is going to put in some test voltages into the ADC and wants to know the integer code he should expect. Also, he has connected a DAC (digital to analog converter) which is also 0-5V and has 8 bits of resolution. Fill in the expected integer codes and what the output voltage will be if those integers are sent to the DAC.

Explanation / Answer

Hello,

Ans (1):- the number of quantization intervals / voltage levels can be given by,

2M   = 28 = 256.   here M = bits of ADC; in this case it is 8 bits ADC

Ans (3) :- the resolution of the system can be given by,

Q = (5-0) / 256 = 19.5 mV. i.e (voltage range / quantization intervals (codes) )

Ams (2) :- LSB voltage = Q of ADC. So, LSB = 19.5 mV

now quantization errors can be = -1/2 * 19.5 to 1/2 * 19.5 = - 9.75 to 9.75 mV.

in equation 3.2 V /cm , so in cm the error will be 0.00304 cm.

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