A signal conditioning system converts a temperature (T) between 20 degree C and

Question

A signal conditioning system converts a temperature (T) between 20 degree C and 80 degree C into a 2V~8V signal (V_T). This signal in turn is fed to an 8 bit ADC with a 5V reference (V_ADC). (1) What is the relationship between temperature T and its voltage output V_T? (2) What is the relationship between the V_T and V_ADC? (3) What is the voltage resolution of V_ADC? (4) What is the corresponding resolution of the measured temperature T? (5) What temperature does a binary output of 10100101 represent? (6) What binary output results from 45 degree C?

Explanation / Answer

1)What is the relation between temperature T and it's voltage output VT ?

We are given data that signal conditioning circuit converts temperature T 20 deg.c to 80 deg.c in to 2 to 8 V Signal VT,

Slope of the line is ,m= (8 - 2) / (80 - 20 )

                               = 6 / 60

                          m = 0.1 V / deg.C

Therefore equation of line i.e. relation beween VT & T is

VT = mT

VT = 0.1T                                      ..............1

This is the required relation between Temperature T and it's voltage output VT

2) What is the relation between VT & VADC

Now we are given data that

2 to 8V of sensor signal voltage corresponds to 0 to 5 V of Analon signal conditioning ( refer diagram given)

slope of this line ,m1 = (5 - 0 ) / (8 -2)

                          m1=0.833

Now at 2V of input out put should be zero hence we need to substract equivalent bias voltage to get that value

VADC =m1VT - b

Now pur VADC =0 , m1=0.833 & VT =2

We obtain b = 1.666

Therefore

VADC = 0.833*VT - 0.833                         .............2

This is the required relation between VT & VADC

c)What is the resolution of VADC

We are given 8 bit ADC therefore it will have 28 = 256 steps

Resolution of ADC = (1/256) *Full scale voltage

Therefore Resolution of VADC = 5 / 256 V

Resolution of VADC = 0.0195 V                          ..................3

This is the required Resolution of VADC

d) What is the corresponding resolution of measured temperature T

Now 5 V ADC output corresponds to 80 deg.C of temperature

Resolution in deg. C = ( 80 /5)*Resolution of VADC

                                        =( 80 /5)*0.0195

Resolution in deg. C for temperature T = 0.31 deg.C                  ........4

This is the required resolution of the measured temperature T

  

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