Mesure de température avec une thermistance CTN

Composant très bon marché, la thermistance permet de mesurer la température avec une précision suffisante dans de très nombreuses situations et ce d'autant plus que sa forte non linéarité peut aisément être compensée par son exploitation judicieuse dans un diviseur de tension. La vidéo suivante s'intéresse à différentes possibilités de modélisation de la thermistance CTN (coefficient de température négatif = la résitance diminue lorsque la température augmente) : deux programmes Arduino sont également proposés pour la mise en oeuvre de ces modèles.

Pour ceux que cela intéresse, voici le code Scilab en vrac que j'ai utilisé pour tracer les caractéristiques :

PAS1 = 25;
PAS2 = 100
T25 = 25+273.15;
R25=10000;
B = 3950;
VCC = 5;
R0 = 10000;
clf;
T=-10+273.15:0.1:50+273.15;
//T=-2+273.15:0.1:12+273.15;
axeT = T-273.15;

// 1/T = 1/T25 + 1/B * ln(Rt/R25)
// B*(1/T - 1/T25) = ln(Rt/R25)
// R25*exp(B*(1/T - 1/T25)) = Rt
Rt = R25*exp(B*(1./(T) - 1/T25));
// Axis y1
cu=color("red");
plot2d(axeT,Rt,style=cu)
a = gca();
a.font_size = 3;  
xlabel("$T(" + char(176) + " C) = T-273.15$","FontSize",5)
ylabel("$Rt(T) = 10000.e^{\beta.(1/T - 1/(25+273.15))}$","FontSize",5,"Color", "red")
gca().children(1).children(1).thickness = 3;

//title("$Rt(T)$","FontSize", 5, "color","black")
xgrid(color("grey70")*[1 1])

Vt = R0./(R0+Rt);

// Axis y2
c=color("blue");
h2=newaxes();
h2.font_size = 3;
h2.font_color = c;
set(h2, "filled", "off", "foreground", c, "font_color", c);
plot2d(axeT,Vt,style=c)

h2.axes_visible(1)="off";
h2.y_location="right";
h2.children(1).children(1).thickness=3;
ylabel("$Vt(T)/V_{CC}$","FontSize",5,"color",c)
title("$Rt(T) \text{ et } Vt(T)/V_{CC}  \text{ et } \frac{1}{V_{CC}}.\frac{\partial Vt(T)}{\partial T}$","FontSize", 5, "color","black")
/*
waitClick();


//Vtprime = VCC*B*exp(B*(1./(T) - 1/T25))./((T.*(1+exp(B*(1./(T) - 1/T25))))^2);
Vtprime = R0*R25*B*exp(B*(1./(T) - 1/T25))./((T.*(R0+R25*exp(B*(1./(T) - 1/T25))))^2);

// Axis y3
c=color("darkgreen");
h3=newaxes();
h3.font_color=c;

plot2d(T-273.15,Vtprime,style=c)
h3.axes_visible(1)="off";
h3.filled="off";
h3.font_size = 3;
h3.y_location="middle";
h3.children(1).children(1).thickness=3;
ylabel("$\frac{1}{V_{CC}}.\frac{\partial Vt(T)}{\partial T}$","FontSize",5,"color",c, "position", [6 0.0105], "font_angle", 0)

function Vt = calcVt(T)
    T=T+273.15;
    Rt = R25*exp(B*((1/T) - (1/T25)));
    Vt = R25*VCC/(R25+Rt); 
endfunction

function waitClick()
    [%v0,%v1,%v2,%v3,%v4] = xclick();w = bool2s(%v0>64);
endfunction

waitClick();

// Animation
sca(a);
xstring(22, 54000, "$R_0=$");
gce.font_size = 6;
xstring(30.5, 54000, "$\Omega$");
gce.font_size = 6;
xstring(26, 54000, "10000");
t = get("hdl");
t.font_size = 6;

for R0 = 5000:PAS1:25000
    Vt = R0./(R0+Rt);
    Vtprime = R0*R25*B*exp(B*(1./(T) - 1/T25))./((T.*(R0+R25*exp(B*(1./(T) - 1/T25))))^2);
    
    h2.children(1).children(1).data = [T-273.15;Vt]';
    h3.children(1).children(1).data = [T-273.15;Vtprime]';
    //h3.ylabel("$\frac{1}{V_{CC}}.\frac{\partial Vt(T)}{\partial T}$","FontSize",4.5,"color",c, "position", [18 0.047])
    // Légende
    t.text = string(R0);
    sleep(3);
    if R0 == 10000 then
        waitClick();
    end
end

waitClick();

//*******************************************************************
//* Zoom sur la portion intéressante pour la sonde de réfrigérateur *
//*******************************************************************
clf;
R0=20000;
T=-2+273.15:0.1:12+273.15;


// 1/T = 1/T25 + 1/B * ln(Rt/R25)
// B*(1/T - 1/T25) = ln(Rt/R25)
// R25*exp(B*(1/T - 1/T25)) = Rt
Rt = R25*exp(B*(1./(T) - 1/T25));
// Axis y1
cu=color("red");
plot2d(T-273.15,Rt,style=cu)
a = gca();
a.font_size = 3;  
xlabel("$T(" + char(176) + " C) = T-273.15$","FontSize",5)
ylabel("$Rt(T) = 10000.e^{\beta.(1/T - 1/(25+273.15))}$","FontSize",5,"Color", "red")
gca().children(1).children(1).thickness = 3;

//title("$Rt(T)$","FontSize", 5, "color","black")
xgrid(color("grey70"))



Vt = R0./(R0+Rt);

// Axis y2
c=color("blue");
h2=newaxes();
h2.font_size = 3;
h2.font_color=c;

plot2d(T-273.15,Vt,style=c)
h2.axes_visible(1)="off";
h2.filled="off";
h2.y_location="right";
h2.children(1).children(1).thickness=3;
ylabel("$Vt(T)/V_{CC}$","FontSize",5,"color",c)
title("$Rt(T) \text{ , } Vt(T)/V_{CC} \text{ , } \frac{1}{V_{CC}}.\frac{\partial Vt(T)}{\partial T}$","FontSize", 5, "color","black")

//Vtprime = VCC*B*exp(B*(1./(T) - 1/T25))./((T.*(1+exp(B*(1./(T) - 1/T25))))^2);
Vtprime = R0*R25*B*exp(B*(1./(T) - 1/T25))./((T.*(R0+R25*exp(B*(1./(T) - 1/T25))))^2);

// Axis y3
c=color("darkgreen");
h3=newaxes();
h3.font_color=c;

plot2d(T-273.15,Vtprime,style=c)
h3.axes_visible(1)="off";
h3.filled="off";
h3.y_location="middle";
h3.children(1).children(1).thickness=3;
ylabel("$\frac{1}{V_{CC}}.\frac{\partial Vt(T)}{\partial T}$","FontSize",4.5,"color",c, "position", [18 0.047])


sca(a);
xstring(6, 36000, "$R_0=$");
gce.font_size = 6;
xstring(8.1, 36000, "$\Omega$");
gce.font_size = 6;
xstring(7, 36000, "10000");
t = get("hdl");
t.font_size = 6;

for R0 = 17000:PAS2:21000
    Vt = R0./(R0+Rt);
    Vtprime = R0*R25*B*exp(B*(1./(T) - 1/T25))./((T.*(R0+R25*exp(B*(1./(T) - 1/T25))))^2);
    

    h2.children(1).children(1).data = [T-273.15;Vt]';
    h3.children(1).children(1).data = [T-273.15;Vtprime]';
    //h3.ylabel("$\frac{1}{V_{CC}}.\frac{\partial Vt(T)}{\partial T}$","FontSize",4.5,"color",c, "position", [18 0.047])
    // Légende
    t.text = string(R0);
    waitClick();
end

// Coordonnées avec la souris
function souris_event(win, x, y, ibut)
  if ibut==-1000 then return,end
  [x,y]=xchange(x,y,'i2f')
  gcf().info_message = msprintf('Event code %d at mouse position is (%f,%f)',ibut,x,y);
endfunction


*/
sca(h2);
xstring(2, 0.5, "");
yt = get("hdl");
yt.font_size = 3;
//xstring(2, 0.4, "T=");
xt = get("hdl");
xt.font_size = 4;
while(1)
    xy = locate(1)
    yt.text = "T="+ string(xy(1)) + "      Vt/Vcc=" + string(xy(2));
    yt.data(1) = xy(1)-0.3;
    yt.data(2) = xy(2)+0.002; 
    //t.text = string(xy);
end