A load sensor has a full scale range of 80 kN and a response function of 25 mV/k

Question

A load sensor has a full scale range of 80 kN and a response function of 25 mV/kN. The rated accuracy of the sensor is 0.01% of the full scale. We would like to digitize this signal for subsequent readout on a computer, so we are using an ADC converter with the following possible ranges: +/- 500 mV, +/- 1 V, and +/- 2V. Based on the best choice of range, Determine the number of bits of resolution are required such that the ADC (which is uncertain in its least significant bit) has a resolution sufficient to measure 100N load differences at a) 26kN and b) 61kN. Explain your analysis and any assumptions made. Repeat the analysis to find the number of bits needed at those two loads such that the load sensor resolution limits the measurement. (Again consider the least significant bit uncertain)

Explanation / Answer

We are given following data:

Load sensor full scale range : 80 KN

Load sensor response function : 25 mV / KN

Accuracy of sensor : 0.01 % of full scale value

ADC ranges for digitization a) +/- 500 mv b) +/- 1V c) +/- 2V

We need to select one best range out of these three ranges depending on maximum sensor voltage.

Let's calculate Load full scale range votage

Load sensorl full scale voltage = ( load sensor full scale range ) x ( load cell response function)

                                      = 80 KN x 25 mV / KN

                                      =2000 mV = 2V

Hence we need to select ADC for digitization with a range of +/- 2 V

1) We need to find out number of bit of resolution required for 100 N load difference at 26 KN & 61 KN

Now 100 N load diffrence is equivalent to voltage = 100 N x Response factor of load sensor

= 0.1 KN x 25 mV / KN

= 2.5 mV

Therefore 100 N load difference is equivalent to 2.5 mV voltage

ADC must be able to measure voltage resolution in steps of 2.5 mV

Hence Number of steps = ( full scale range ) / (resolution of one step )

Number of steps = 2000 mV / 2.5 mV = 800

Now 9 bit ADC has 29 =512 steps and 10 bit ADC has 210 =1024

Hence to accomodate 800 steps we choose 10 bit ADC.

So we need 10 bits of resolution for 100 N load difference at 26 KN & 61 KN.

2) We need to find out number of bits required at 26 KN & 61 KN such that sensor resolution limits the   measurement

Load sensor accuracy in mV    = (full scale voltage ) x load sensor accuracy

                                             = 2000 mV x 0.01 %

                                             = 0.2 mV

We need to have ADC with number of bits in a way that it's able to measure change in step of 0.2 mV which is accuracy of load sensor.

Number of steps = full scale voltage / load sensor accuracy

                        = 2000 mV / 0.2 mV

Number of steps = 10000

Now 13 bit ADC has 213 =8192 steps and 14 bit ADC has 214 =16384

So we need 14 bits at 26 KN & 61 KN loads such that load sensor resolution limits the measurement.             

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