Update Content - 2025-01-20

content/zettels/temperature_sensors.md

@@ -245,46 +245,7 @@ Let's compare the temperature given by a Loopup table and the temperature given
 -   linear interpolation with one point every degree
 -   cubic interpolation with one point every 10 degrees
 
-The error is less than 0.1mK over the full range, validating the use of a lookup table to convert the resistance to temperature ([Figure 8](#figure--fig:temperature-sensor-lut-errors)).
-
-```matlab
-%% "Perfect" temperature and resistance
-R0 = 100; % [Ohm]
-A = 3.9083e-3; % [degC^-1]
-B = -5.775e-7; % [degC^-2]
-C = -4.183e-12; % [degC^-4]
-
-T1 = -200:0.1:0; % [degC]
-T2 = 0.1:0.1:850; % [degC]
-T_true = [T1,T2]; % [degC]
-R_true = [R0*(1 + A*T1 + B*T1.^2 + C*(T1-100).*T1.^3), R0*(1 + A*T2 + B*T2.^2)]; % [Ohm]
-
-%% Lookup table for Pt100 (3850 ppm/K) - Linear
-dT = 1;
-interp_method = 'linear';
-
-T1 = -200:dT:0; % [degC]
-T2 = dT:dT:850; % [degC]
-T_lut_linear = [T1,T2]; % [degC]
-R_lut_linear = [R0*(1 + A*T1 + B*T1.^2 + C*(T1-100).*T1.^3), R0*(1 + A*T2 + B*T2.^2)]; % [Ohm]
-
-T_meas_linear = interp1(R_lut_linear,T_lut_linear,R_true,interp_method); % interpolate the resistance using the LUT to find the corresponding temperature
-
-%% Lookup table for Pt100 (3850 ppm/K) - Makima
-dT = 10;
-interp_method = 'makima';
-
-T1 = -200:dT:0; % [degC]
-T2 = dT:dT:850; % [degC]
-T_lut_makima = [T1,T2]; % [degC]
-R_lut_makima = [R0*(1 + A*T1 + B*T1.^2 + C*(T1-100).*T1.^3), R0*(1 + A*T2 + B*T2.^2)]; % [Ohm]
-
-T_meas_makima = interp1(R_lut_makima,T_lut_makima,R_true,interp_method); % interpolate the resistance using the LUT to find the corresponding temperature
-```
-
-<a id="figure--fig:temperature-sensor-lut-errors"></a>
-
-{{< figure src="/ox-hugo/temperature_sensor_lut_errors.png" caption="<span class=\"figure-number\">Figure 8: </span>Interpolation errors in two cases when using a LUT for a Pt100" >}}
+The error is less than 0.1mK over the full range, validating the use of a lookup table to convert the resistance to temperature ([Figure 9](#figure--fig:temperature-sensor-lut-errors)).
 
 
 ### NTC thermistor {#ntc-thermistor}
@@ -327,7 +288,7 @@ T = -273.15+[T1,T2,T3,T4]; % [degC]
 
 <a id="figure--fig:temperature-sensor-ntc-curve"></a>
 
-{{< figure src="/ox-hugo/temperature_sensor_ntc_curve.png" caption="<span class=\"figure-number\">Figure 9: </span>Resistance as a function of the temperature for a given NTC" >}}
+{{< figure src="/ox-hugo/temperature_sensor_ntc_curve.png" caption="<span class=\"figure-number\">Figure 8: </span>Resistance as a function of the temperature for a given NTC" >}}
 
 To calculate the actual thermistor temperature as a function of the measured thermistor resistance, use the following equation:
 \\[ T = \frac{1}{a + b \ln(R\_t/R\_{25}) + c (Ln Rt/R25)^2 + d (Ln Rt/R25)^3) \\]
@@ -346,6 +307,108 @@ To calculate the actual thermistor temperature as a function of the measured the
 | 0.06831 to 0.01872 | 3.3368620E-03 | 2.4057263E-04 | -2.6687093E-06 | -4.0719355E-07 |
 
 
+### Approximation of formulas using lookup tables {#approximation-of-formulas-using-lookup-tables}
+
+First, let's compare the analytical formula with a LUT for a Pt100 ([Figure 9](#figure--fig:temperature-sensor-lut-errors)).
+The error (accuracy) is bellow 0.1mK for relatively small LUT.
+
+```matlab
+%% "Perfect" temperature and resistance
+R0 = 100; % [Ohm]
+A = 3.9083e-3; % [degC^-1]
+B = -5.775e-7; % [degC^-2]
+C = -4.183e-12; % [degC^-4]
+
+T1 = -200:0.1:0; % [degC]
+T2 = 0.1:0.1:850; % [degC]
+T_true = [T1,T2]; % [degC]
+R_true = [R0*(1 + A*T1 + B*T1.^2 + C*(T1-100).*T1.^3), R0*(1 + A*T2 + B*T2.^2)]; % [Ohm]
+
+%% Lookup table for Pt100 (3850 ppm/K) - Linear
+dT = 1;
+interp_method = 'linear';
+
+T1 = -200:dT:0; % [degC]
+T2 = dT:dT:850; % [degC]
+T_lut_linear = [T1,T2]; % [degC]
+R_lut_linear = [R0*(1 + A*T1 + B*T1.^2 + C*(T1-100).*T1.^3), R0*(1 + A*T2 + B*T2.^2)]; % [Ohm]
+
+T_meas_linear = interp1(R_lut_linear,T_lut_linear,R_true,interp_method); % interpolate the resistance using the LUT to find the corresponding temperature
+
+%% Lookup table for Pt100 (3850 ppm/K) - Makima
+dT = 10;
+interp_method = 'makima';
+
+T1 = -200:dT:0; % [degC]
+T2 = dT:dT:850; % [degC]
+T_lut_makima = [T1,T2]; % [degC]
+R_lut_makima = [R0*(1 + A*T1 + B*T1.^2 + C*(T1-100).*T1.^3), R0*(1 + A*T2 + B*T2.^2)]; % [Ohm]
+
+T_meas_makima = interp1(R_lut_makima,T_lut_makima,R_true,interp_method); % interpolate the resistance using the LUT to find the corresponding temperature
+```
+
+<a id="figure--fig:temperature-sensor-lut-errors"></a>
+
+{{< figure src="/ox-hugo/temperature_sensor_lut_errors.png" caption="<span class=\"figure-number\">Figure 9: </span>Interpolation errors in two cases when using a LUT for a Pt100" >}}
+
+NTC thermistors are more non-linear and therefore require finer LUT to have low accuracy errors.
+In order to have less than 0.1mK of accuracy, a LUT with linear interpolation requires approximately one point every 0.1 degree ([Figure 10](#figure--fig:temperature-sensor-lut-errors-ntc)).
+
+```matlab
+%% "Perfect" temperature and resistance of NTC (DC95F202VN)
+R0 = 2e3; % Resistance at 25deg
+dT_true = 0.01;
+
+T1 = 273.15+[-50:dT_true:0]; % [degK]
+T2 = 273.15+[0+dT_true:dT_true:50]; % [degK]
+T3 = 273.15+[50+dT_true:dT_true:100]; % [degK]
+T4 = 273.15+[100+dT_true:dT_true:150]; % [degK]
+
+R_true = R0*exp([[-1.4122478E+01 + 4.4136033E+03./T1 - 2.9034189E+04./T1.^2 - 9.3875035E+06./T1.^3]';
+                 [-1.4141963E+01 + 4.4307830E+03./T2 - 3.4078983E+04./T2.^2 - 8.8941929E+06./T2.^3]';
+                 [-1.4202172E+01 + 4.4975256E+03./T3 - 5.8421357E+04./T3.^2 - 5.9658796E+06./T3.^3]';
+                 [-1.6154078E+01 + 6.8483992E+03./T4 - 1.0004049E+06./T4.^2 + 1.1961431E+08./T4.^3]'])'; % [Ohm]
+
+T_true = -273.15+[T1,T2,T3,T4]; % [degC]
+
+%% Lookup table for NTC (DC95F202VN) - Linear
+dT = 0.1;
+interp_method = 'linear';
+
+T1 = 273.15+[-50:dT:0]; % [degK]
+T2 = 273.15+[0+dT:dT:50]; % [degK]
+T3 = 273.15+[50+dT:dT:100]; % [degK]
+T4 = 273.15+[100+dT:dT:150]; % [degK]
+T_lut_linear = -273.15+[T1,T2,T3,T4]; % [degC]
+R_lut_linear = R0*exp([[-1.4122478E+01 + 4.4136033E+03./T1 - 2.9034189E+04./T1.^2 - 9.3875035E+06./T1.^3]';
+                       [-1.4141963E+01 + 4.4307830E+03./T2 - 3.4078983E+04./T2.^2 - 8.8941929E+06./T2.^3]';
+                       [-1.4202172E+01 + 4.4975256E+03./T3 - 5.8421357E+04./T3.^2 - 5.9658796E+06./T3.^3]';
+                       [-1.6154078E+01 + 6.8483992E+03./T4 - 1.0004049E+06./T4.^2 + 1.1961431E+08./T4.^3]'])'; % [Ohm]
+
+T_meas_linear = interp1(R_lut_linear,T_lut_linear,R_true,interp_method); % interpolate the resistance using the LUT to find the corresponding temperature
+
+%% Lookup table for Pt100 (3850 ppm/K) - Makima
+dT = 1;
+interp_method = 'makima';
+
+T1 = 273.15+[-50:dT:0]; % [degK]
+T2 = 273.15+[0+dT:dT:50]; % [degK]
+T3 = 273.15+[50+dT:dT:100]; % [degK]
+T4 = 273.15+[100+dT:dT:150]; % [degK]
+T_lut_makima = -273.15+[T1,T2,T3,T4]; % [degC]
+R_lut_makima = R0*exp([[-1.4122478E+01 + 4.4136033E+03./T1 - 2.9034189E+04./T1.^2 - 9.3875035E+06./T1.^3]';
+                       [-1.4141963E+01 + 4.4307830E+03./T2 - 3.4078983E+04./T2.^2 - 8.8941929E+06./T2.^3]';
+                       [-1.4202172E+01 + 4.4975256E+03./T3 - 5.8421357E+04./T3.^2 - 5.9658796E+06./T3.^3]';
+                       [-1.6154078E+01 + 6.8483992E+03./T4 - 1.0004049E+06./T4.^2 + 1.1961431E+08./T4.^3]'])'; % [Ohm]
+
+T_meas_makima = interp1(R_lut_makima,T_lut_makima,R_true,interp_method); % interpolate the resistance using the LUT to find the corresponding temperature
+```
+
+<a id="figure--fig:temperature-sensor-lut-errors-ntc"></a>
+
+{{< figure src="/ox-hugo/temperature_sensor_lut_errors_ntc.png" caption="<span class=\"figure-number\">Figure 10: </span>Interpolation errors in two cases when using a LUT for a NTC" >}}
+
+
 ## Commercial Temperature Sensors {#commercial-temperature-sensors}
 
 
@@ -360,7 +423,7 @@ From (<a href="#citeproc_bib_item_2">Neto et al. 2022</a>), UHV compatible:
 > The part-though-hole (PTH) sensors were soldered to thin, 30 AWG, varnish insulated copper wires with small amounts of tin-lead (70/30) alloy.
 
 
-### Cryogenic temperatures {#cryogenic-temperatures}
+### Cryogenic temperatures (77K / -200degC) {#cryogenic-temperatures--77k-200degc}
 
 -   <https://shop.allectra.com/products/343-pt100-c2>
 -   <https://www.lakeshore.com/products/categories/overview/temperature-products/cryogenic-temperature-sensors/cernox>

content/zettels/wheatstone_bridge.md

@@ -0,0 +1,25 @@
++++
+title = "Wheatstone Bridge"
+author = ["Dehaeze Thomas"]
+draft = false
++++
+
+Tags
+:
+
+Wheatstone Bridge are used to measure an electrical resistance.
+
+They are used to read various sensors:
+
+-   [Strain Sensors]({{< relref "strain_sensors.md" >}})
+-   [Temperature Sensors]({{< relref "temperature_sensors.md" >}})
+
+<a id="figure--fig:wheatstone-bridge"></a>
+
+{{< figure src="/ox-hugo/wheatstone_bridge.jpg" caption="<span class=\"figure-number\">Figure 1: </span>Electrical schematic of a Wheatstone bridge" >}}
+
+
+## Bibliography {#bibliography}
+
+<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
+</div>