Homework Assignment ML12b temperature sensor In order to per

Homework Assignment ML1.2b temperature sensor In order to perform temperature measurements one can use a platinum resistance-temperature detector (RTD or Pt100). We assume a resistance-temperature curve to be linear according to R_1 = R_0 (1 + At) where R_t resistance [Ohm] of the Pt100 at t degree C, R_0 resistance of the Pt100 at 0 degree C, equal to 100 Ohm, A coefficient set to 0.003908 [degree C^-1], t temperature in degree C, t> 0 degree C. A known current can be applied to a Pt100 and a voltage across the resistance is measured. A low excitation current of 0.15 mA minimizes the self-heating effect and the voltage to measure is not larger than 25 mV. In Matlab: Create variables R0, A, and I (current), with appropriate values Create variable V (voltage), and set it to its maximum value. Calculate the according temperature t. Redefine V to 18 mV, what is the according temperature? Calculate which voltage corresponds to 0 degree C? Now change the definition of V from a single value into an array V=Vmin:Vstep:Vmax. Calculate the according temperatures. Show your results to a teaching assistant.

Solution

Matlab Code:

% Matlab three variable declarations
R0=100;
A=0.003908;
I=0.15;
% max voltage given is 25
V=25;
% calculating the Resistance Using formula
Rt=V/I;
% A display to the console
disp \'Temperature at max voltage : 25\'
% formula to calculate the temperature
t=((Rt/R0)-1)/A
% redefining voltage to 18
V=18;
Rt=V/I;
disp \'Temperature at voltage : 25\'
% temperature to the console after calculation
t=((Rt/R0)-1)/A
% now to calculate voltage
% the temparature given is 0
t=0;
disp \'Voltage when temperature =0\'
% from the given formula
V=I*R0*(1+A*t)
% array of volts
array=[0 18 25];
disp \'Using arrays\'
% for loop to calculate for each element
for volt=array
% finding resistance first
Rt=volt/I;
%calculating temperature
t=((Rt/R0)-1)/A
% end of the for loop
end

Output:

Temperature at max voltage : 25                                                        

t =  170.59                                                                            

Temperature at voltage : 25                                                            

t =  51.177                                                                            

Voltage when temperature =0                                                            

V =  15                                                                                

Using arrays                                                                           

t = -255.89                                                                            

t =  51.177                                                                            

t =  170.59